TSTP Solution File: ITP262^3 by cvc5---1.0.5
View Problem
- Process Solution
%------------------------------------------------------------------------------
% File : cvc5---1.0.5
% Problem : ITP262^3 : TPTP v8.1.2. Released v8.1.0.
% Transfm : none
% Format : tptp
% Command : do_cvc5 %s %d
% Computer : n013.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 03:28:01 EDT 2023
% Result : Timeout 299.91s 300.23s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 2.73/2.76 % Problem : ITP262^3 : TPTP v8.1.2. Released v8.1.0.
% 2.73/2.77 % Command : do_cvc5 %s %d
% 2.76/2.99 % Computer : n013.cluster.edu
% 2.76/2.99 % Model : x86_64 x86_64
% 2.76/2.99 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 2.76/2.99 % Memory : 8042.1875MB
% 2.76/2.99 % OS : Linux 3.10.0-693.el7.x86_64
% 2.76/2.99 % CPULimit : 300
% 2.76/2.99 % WCLimit : 300
% 2.76/2.99 % DateTime : Sun Aug 27 13:12:05 EDT 2023
% 2.76/2.99 % CPUTime :
% 5.41/5.58 %----Proving TH0
% 5.41/5.59 %------------------------------------------------------------------------------
% 5.41/5.59 % File : ITP262^3 : TPTP v8.1.2. Released v8.1.0.
% 5.41/5.59 % Domain : Interactive Theorem Proving
% 5.41/5.59 % Problem : Sledgehammer problem VEBT_DeleteCorrectness 00209_010241
% 5.41/5.59 % Version : [Des22] axioms.
% 5.41/5.59 % English :
% 5.41/5.59
% 5.41/5.59 % Refs : [BH+15] Blanchette et al. (2015), Mining the Archive of Formal
% 5.41/5.59 % : [Des22] Desharnais (2022), Email to Geoff Sutcliffe
% 5.41/5.59 % Source : [Des22]
% 5.41/5.59 % Names : 0073_VEBT_DeleteCorrectness_00209_010241 [Des22]
% 5.41/5.59
% 5.41/5.59 % Status : Theorem
% 5.41/5.59 % Rating : 0.77 v8.1.0
% 5.41/5.59 % Syntax : Number of formulae : 11165 (5808 unt; 916 typ; 0 def)
% 5.41/5.59 % Number of atoms : 28393 (12566 equ; 0 cnn)
% 5.41/5.59 % Maximal formula atoms : 71 ( 2 avg)
% 5.41/5.59 % Number of connectives : 116376 (2919 ~; 529 |;1869 &;100321 @)
% 5.41/5.59 % ( 0 <=>;10738 =>; 0 <=; 0 <~>)
% 5.41/5.59 % Maximal formula depth : 39 ( 6 avg)
% 5.41/5.59 % Number of types : 95 ( 94 usr)
% 5.41/5.59 % Number of type conns : 3561 (3561 >; 0 *; 0 +; 0 <<)
% 5.41/5.59 % Number of symbols : 825 ( 822 usr; 59 con; 0-8 aty)
% 5.41/5.59 % Number of variables : 25514 (1740 ^;23048 !; 726 ?;25514 :)
% 5.41/5.59 % SPC : TH0_THM_EQU_NAR
% 5.41/5.59
% 5.41/5.59 % Comments : This file was generated by Isabelle (most likely Sledgehammer)
% 5.41/5.59 % from the van Emde Boas Trees session in the Archive of Formal
% 5.41/5.59 % proofs -
% 5.41/5.59 % www.isa-afp.org/browser_info/current/AFP/Van_Emde_Boas_Trees
% 5.41/5.59 % 2022-02-18 07:49:00.137
% 5.41/5.59 %------------------------------------------------------------------------------
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Code____Numeral__Ointeger,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Int__Oint,type,
% 5.41/5.59 unique5024387138958732305ep_int: num > product_prod_int_int > product_prod_int_int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Divides_Ounique__euclidean__semiring__numeral__class_Odivmod__step_001t__Nat__Onat,type,
% 5.41/5.59 unique5026877609467782581ep_nat: num > product_prod_nat_nat > product_prod_nat_nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Complex__Ocomplex,type,
% 5.41/5.59 semiri5044797733671781792omplex: nat > complex ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Nat__Onat,type,
% 5.41/5.59 semiri1408675320244567234ct_nat: nat > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Factorial_Osemiring__char__0__class_Ofact_001t__Real__Oreal,type,
% 5.41/5.59 semiri2265585572941072030t_real: nat > real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Complex__Ocomplex,type,
% 5.41/5.59 invers8013647133539491842omplex: complex > complex ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Rat__Orat,type,
% 5.41/5.59 inverse_inverse_rat: rat > rat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fields_Oinverse__class_Oinverse_001t__Real__Oreal,type,
% 5.41/5.59 inverse_inverse_real: real > real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oat__bot_001t__Real__Oreal,type,
% 5.41/5.59 at_bot_real: filter_real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oat__top_001t__Nat__Onat,type,
% 5.41/5.59 at_top_nat: filter_nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oat__top_001t__Real__Oreal,type,
% 5.41/5.59 at_top_real: filter_real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oeventually_001t__Nat__Onat,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oeventually_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.59 eventu1038000079068216329at_nat: ( product_prod_nat_nat > $o ) > filter1242075044329608583at_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oeventually_001t__Real__Oreal,type,
% 5.41/5.59 eventually_real: ( real > $o ) > filter_real > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.59 filterlim_nat_nat: ( nat > nat ) > filter_nat > filter_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Ofilterlim_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.59 filterlim_nat_real: ( nat > real ) > filter_real > filter_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Ofilterlim_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.59 filterlim_real_real: ( real > real ) > filter_real > filter_real > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Ofiltermap_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.59 filtermap_real_real: ( real > real ) > filter_real > filter_real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
% 5.41/5.59 princi3496590319149328850omplex: set_Pr5085853215250843933omplex > filter6041513312241820739omplex ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oprincipal_001t__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J,type,
% 5.41/5.59 princi6114159922880469582l_real: set_Pr6218003697084177305l_real > filter2146258269922977983l_real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Filter_Oprod__filter_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.59 prod_filter_nat_nat: filter_nat > filter_nat > filter1242075044329608583at_nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ocard_001_Eo,type,
% 5.41/5.59 finite_card_o: set_o > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ocard_001t__Complex__Ocomplex,type,
% 5.41/5.59 finite_card_complex: set_complex > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ocard_001t__Int__Oint,type,
% 5.41/5.59 finite_card_int: set_int > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ocard_001t__Nat__Onat,type,
% 5.41/5.59 finite_card_nat: set_nat > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ocard_001t__Product____Type__Ounit,type,
% 5.41/5.59 finite410649719033368117t_unit: set_Product_unit > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ocard_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.59 finite_card_set_nat: set_set_nat > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ocard_001t__String__Ochar,type,
% 5.41/5.59 finite_card_char: set_char > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001_Eo,type,
% 5.41/5.59 finite_finite_o: set_o > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Complex__Ocomplex,type,
% 5.41/5.59 finite3207457112153483333omplex: set_complex > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Int__Oint,type,
% 5.41/5.59 finite_finite_int: set_int > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_I_Eo_J,type,
% 5.41/5.59 finite_finite_list_o: set_list_o > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.41/5.59 finite8712137658972009173omplex: set_list_complex > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Int__Oint_J,type,
% 5.41/5.59 finite3922522038869484883st_int: set_list_int > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.59 finite8100373058378681591st_nat: set_list_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Nat__Onat,type,
% 5.41/5.59 finite_finite_nat: set_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Num__Onum,type,
% 5.41/5.59 finite_finite_num: set_num > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Rat__Orat,type,
% 5.41/5.59 finite_finite_rat: set_rat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Real__Oreal,type,
% 5.41/5.59 finite_finite_real: set_real > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.41/5.59 finite6551019134538273531omplex: set_set_complex > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.59 finite6197958912794628473et_int: set_set_int > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.59 finite1152437895449049373et_nat: set_set_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Finite__Set_Ofinite_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.59 finite5795047828879050333T_VEBT: set_VEBT_VEBT > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Obij__betw_001t__Complex__Ocomplex_001t__Complex__Ocomplex,type,
% 5.41/5.59 bij_be1856998921033663316omplex: ( complex > complex ) > set_complex > set_complex > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.41/5.59 bij_betw_nat_complex: ( nat > complex ) > set_nat > set_complex > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Obij__betw_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.59 bij_betw_nat_nat: ( nat > nat ) > set_nat > set_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Ocomp_001_062_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.41/5.59 comp_C8797469213163452608nteger: ( ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_Mt__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_J_001t__Code____Numeral__Ointeger,type,
% 5.41/5.59 comp_C1593894019821074884nteger: ( code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ) > ( code_integer > code_integer ) > code_integer > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Ocomp_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.41/5.59 comp_C3531382070062128313er_num: ( code_integer > code_integer ) > ( num > code_integer ) > num > code_integer ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Ocomp_001t__Int__Oint_001t__Int__Oint_001t__Num__Onum,type,
% 5.41/5.59 comp_int_int_num: ( int > int ) > ( num > int ) > num > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Oid_001_Eo,type,
% 5.41/5.59 id_o: $o > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Oid_001t__Nat__Onat,type,
% 5.41/5.59 id_nat: nat > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J_001_062_It__Int__Oint_M_Eo_J,type,
% 5.41/5.59 map_fu434086159418415080_int_o: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > $o ) > int > $o ) > ( product_prod_nat_nat > product_prod_nat_nat > $o ) > int > int > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001_062_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.41/5.59 map_fu4960017516451851995nt_int: ( int > product_prod_nat_nat ) > ( ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ) > ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > int > int > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001_Eo_001_Eo,type,
% 5.41/5.59 map_fu4826362097070443709at_o_o: ( int > product_prod_nat_nat ) > ( $o > $o ) > ( product_prod_nat_nat > $o ) > int > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.59 map_fu2345160673673942751at_nat: ( int > product_prod_nat_nat ) > ( nat > nat ) > ( product_prod_nat_nat > nat ) > int > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Omap__fun_001t__Int__Oint_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_001t__Int__Oint,type,
% 5.41/5.59 map_fu3667384564859982768at_int: ( int > product_prod_nat_nat ) > ( product_prod_nat_nat > int ) > ( product_prod_nat_nat > product_prod_nat_nat ) > int > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Ostrict__mono__on_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.59 strict1292158309912662752at_nat: ( nat > nat ) > set_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Fun_Othe__inv__into_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.59 the_in5290026491893676941l_real: set_real > ( real > real ) > real > real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_OGcd__class_OGcd_001t__Int__Oint,type,
% 5.41/5.59 gcd_Gcd_int: set_int > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_OGcd__class_OGcd_001t__Nat__Onat,type,
% 5.41/5.59 gcd_Gcd_nat: set_nat > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_Obezw,type,
% 5.41/5.59 bezw: nat > nat > product_prod_int_int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_Obezw__rel,type,
% 5.41/5.59 bezw_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Code____Numeral__Ointeger,type,
% 5.41/5.59 gcd_gcd_Code_integer: code_integer > code_integer > code_integer ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Int__Oint,type,
% 5.41/5.59 gcd_gcd_int: int > int > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_Ogcd__class_Ogcd_001t__Nat__Onat,type,
% 5.41/5.59 gcd_gcd_nat: nat > nat > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_GCD_Ogcd__nat__rel,type,
% 5.41/5.59 gcd_nat_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Oabs__class_Oabs_001t__Code____Numeral__Ointeger,type,
% 5.41/5.59 abs_abs_Code_integer: code_integer > code_integer ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Oabs__class_Oabs_001t__Complex__Ocomplex,type,
% 5.41/5.59 abs_abs_complex: complex > complex ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Oabs__class_Oabs_001t__Int__Oint,type,
% 5.41/5.59 abs_abs_int: int > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Oabs__class_Oabs_001t__Rat__Orat,type,
% 5.41/5.59 abs_abs_rat: rat > rat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Oabs__class_Oabs_001t__Real__Oreal,type,
% 5.41/5.59 abs_abs_real: real > real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Complex__Ocomplex_M_Eo_J,type,
% 5.41/5.59 minus_8727706125548526216plex_o: ( complex > $o ) > ( complex > $o ) > complex > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Int__Oint_M_Eo_J,type,
% 5.41/5.59 minus_minus_int_o: ( int > $o ) > ( int > $o ) > int > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Nat__Onat_M_Eo_J,type,
% 5.41/5.59 minus_minus_nat_o: ( nat > $o ) > ( nat > $o ) > nat > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_M_Eo_J,type,
% 5.41/5.59 minus_711738161318947805_int_o: ( product_prod_int_int > $o ) > ( product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Real__Oreal_M_Eo_J,type,
% 5.41/5.59 minus_minus_real_o: ( real > $o ) > ( real > $o ) > real > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Code____Numeral__Ointeger,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Complex__Ocomplex,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Extended____Nat__Oenat,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Int__Oint,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Nat__Onat,type,
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% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Rat__Orat,type,
% 5.41/5.59 minus_minus_rat: rat > rat > rat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Real__Oreal,type,
% 5.41/5.59 minus_minus_real: real > real > real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.41/5.59 minus_811609699411566653omplex: set_complex > set_complex > set_complex ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Groups_Ominus__class_Ominus_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.41/5.59
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% 5.41/5.59 if_Pro3027730157355071871nt_int: $o > product_prod_int_int > product_prod_int_int > product_prod_int_int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.59 if_Pro6206227464963214023at_nat: $o > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_If_001t__Rat__Orat,type,
% 5.41/5.59 if_rat: $o > rat > rat > rat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_If_001t__Real__Oreal,type,
% 5.41/5.59 if_real: $o > real > real > real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_If_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.59 if_set_int: $o > set_int > set_int > set_int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_If_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.59 if_VEBT_VEBT: $o > vEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_OAbs__Integ,type,
% 5.41/5.59 abs_Integ: product_prod_nat_nat > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_ORep__Integ,type,
% 5.41/5.59 rep_Integ: int > product_prod_nat_nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oint__ge__less__than,type,
% 5.41/5.59 int_ge_less_than: int > set_Pr958786334691620121nt_int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oint__ge__less__than2,type,
% 5.41/5.59 int_ge_less_than2: int > set_Pr958786334691620121nt_int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Onat,type,
% 5.41/5.59 nat2: int > nat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oring__1__class_OInts_001t__Complex__Ocomplex,type,
% 5.41/5.59 ring_1_Ints_complex: set_complex ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oring__1__class_OInts_001t__Real__Oreal,type,
% 5.41/5.59 ring_1_Ints_real: set_real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Code____Numeral__Ointeger,type,
% 5.41/5.59 ring_18347121197199848620nteger: int > code_integer ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Complex__Ocomplex,type,
% 5.41/5.59 ring_17405671764205052669omplex: int > complex ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Int__Oint,type,
% 5.41/5.59 ring_1_of_int_int: int > int ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Rat__Orat,type,
% 5.41/5.59 ring_1_of_int_rat: int > rat ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Int_Oring__1__class_Oof__int_001t__Real__Oreal,type,
% 5.41/5.59 ring_1_of_int_real: int > real ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Lattices_Osemilattice__neutr__order_001t__Nat__Onat,type,
% 5.41/5.59 semila1623282765462674594er_nat: ( nat > nat > nat ) > nat > ( nat > nat > $o ) > ( nat > nat > $o ) > $o ).
% 5.41/5.59
% 5.41/5.59 thf(sy_c_Lattices_Osup__class_Osup_001t__Extended____Nat__Oenat,type,
% 5.41/5.60 sup_su3973961784419623482d_enat: extended_enat > extended_enat > extended_enat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Nat__Onat,type,
% 5.41/5.60 sup_sup_nat: nat > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Lattices_Osup__class_Osup_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 sup_sup_set_nat: set_nat > set_nat > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Int__Oint,type,
% 5.41/5.60 lattic8263393255366662781ax_int: set_int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Lattices__Big_Olinorder__class_OMax_001t__Nat__Onat,type,
% 5.41/5.60 lattic8265883725875713057ax_nat: set_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Limits_OBfun_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.60 bfun_nat_real: ( nat > real ) > filter_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Limits_Oat__infinity_001t__Real__Oreal,type,
% 5.41/5.60 at_infinity_real: filter_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oappend_001t__Int__Oint,type,
% 5.41/5.60 append_int: list_int > list_int > list_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oappend_001t__Nat__Onat,type,
% 5.41/5.60 append_nat: list_nat > list_nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Odistinct_001t__Int__Oint,type,
% 5.41/5.60 distinct_int: list_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Odistinct_001t__Nat__Onat,type,
% 5.41/5.60 distinct_nat: list_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olinorder__class_Osorted__list__of__set_001t__Nat__Onat,type,
% 5.41/5.60 linord2614967742042102400et_nat: set_nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_OCons_001t__Int__Oint,type,
% 5.41/5.60 cons_int: int > list_int > list_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_OCons_001t__Nat__Onat,type,
% 5.41/5.60 cons_nat: nat > list_nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_ONil_001t__Int__Oint,type,
% 5.41/5.60 nil_int: list_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_ONil_001t__Nat__Onat,type,
% 5.41/5.60 nil_nat: list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Omap_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.60 map_nat_nat: ( nat > nat ) > list_nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Oset_001_Eo,type,
% 5.41/5.60 set_o2: list_o > set_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Oset_001t__Complex__Ocomplex,type,
% 5.41/5.60 set_complex2: list_complex > set_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Oset_001t__Int__Oint,type,
% 5.41/5.60 set_int2: list_int > set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Oset_001t__Nat__Onat,type,
% 5.41/5.60 set_nat2: list_nat > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Oset_001t__Real__Oreal,type,
% 5.41/5.60 set_real2: list_real > set_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Oset_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 set_set_nat2: list_set_nat > set_set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Oset_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 set_VEBT_VEBT2: list_VEBT_VEBT > set_VEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist_Osize__list_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 size_list_VEBT_VEBT: ( vEBT_VEBT > nat ) > list_VEBT_VEBT > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist__update_001_Eo,type,
% 5.41/5.60 list_update_o: list_o > nat > $o > list_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist__update_001t__Complex__Ocomplex,type,
% 5.41/5.60 list_update_complex: list_complex > nat > complex > list_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist__update_001t__Int__Oint,type,
% 5.41/5.60 list_update_int: list_int > nat > int > list_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist__update_001t__Nat__Onat,type,
% 5.41/5.60 list_update_nat: list_nat > nat > nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist__update_001t__Real__Oreal,type,
% 5.41/5.60 list_update_real: list_real > nat > real > list_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist__update_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 list_update_set_nat: list_set_nat > nat > set_nat > list_set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Olist__update_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 list_u1324408373059187874T_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001_Eo,type,
% 5.41/5.60 nth_o: list_o > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Complex__Ocomplex,type,
% 5.41/5.60 nth_complex: list_complex > nat > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Int__Oint,type,
% 5.41/5.60 nth_int: list_int > nat > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Nat__Onat,type,
% 5.41/5.60 nth_nat: list_nat > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_M_Eo_J,type,
% 5.41/5.60 nth_Product_prod_o_o: list_P4002435161011370285od_o_o > nat > product_prod_o_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J,type,
% 5.41/5.60 nth_Pr1649062631805364268_o_int: list_P3795440434834930179_o_int > nat > product_prod_o_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J,type,
% 5.41/5.60 nth_Pr5826913651314560976_o_nat: list_P6285523579766656935_o_nat > nat > product_prod_o_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.60 nth_Pr6777367263587873994T_VEBT: list_P7495141550334521929T_VEBT > nat > produc2504756804600209347T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_M_Eo_J,type,
% 5.41/5.60 nth_Pr112076138515278198_nat_o: list_P7333126701944960589_nat_o > nat > product_prod_nat_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.60 nth_Pr744662078594809490T_VEBT: list_P5647936690300460905T_VEBT > nat > produc8025551001238799321T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J,type,
% 5.41/5.60 nth_Pr4606735188037164562VEBT_o: list_P3126845725202233233VEBT_o > nat > produc334124729049499915VEBT_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J,type,
% 5.41/5.60 nth_Pr6837108013167703752BT_int: list_P4547456442757143711BT_int > nat > produc4894624898956917775BT_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.41/5.60 nth_Pr1791586995822124652BT_nat: list_P7037539587688870467BT_nat > nat > produc9072475918466114483BT_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.60 nth_Pr4953567300277697838T_VEBT: list_P7413028617227757229T_VEBT > nat > produc8243902056947475879T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Real__Oreal,type,
% 5.41/5.60 nth_real: list_real > nat > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 nth_set_nat: list_set_nat > nat > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Onth_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 nth_VEBT_VEBT: list_VEBT_VEBT > nat > vEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001_Eo_001_Eo,type,
% 5.41/5.60 product_o_o: list_o > list_o > list_P4002435161011370285od_o_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001_Eo_001t__Int__Oint,type,
% 5.41/5.60 product_o_int: list_o > list_int > list_P3795440434834930179_o_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001_Eo_001t__Nat__Onat,type,
% 5.41/5.60 product_o_nat: list_o > list_nat > list_P6285523579766656935_o_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001_Eo_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 product_o_VEBT_VEBT: list_o > list_VEBT_VEBT > list_P7495141550334521929T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001t__Nat__Onat_001_Eo,type,
% 5.41/5.60 product_nat_o: list_nat > list_o > list_P7333126701944960589_nat_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 produc7156399406898700509T_VEBT: list_nat > list_VEBT_VEBT > list_P5647936690300460905T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.41/5.60 product_VEBT_VEBT_o: list_VEBT_VEBT > list_o > list_P3126845725202233233VEBT_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.41/5.60 produc7292646706713671643BT_int: list_VEBT_VEBT > list_int > list_P4547456442757143711BT_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.41/5.60 produc7295137177222721919BT_nat: list_VEBT_VEBT > list_nat > list_P7037539587688870467BT_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oproduct_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 produc4743750530478302277T_VEBT: list_VEBT_VEBT > list_VEBT_VEBT > list_P7413028617227757229T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oremdups_001t__Nat__Onat,type,
% 5.41/5.60 remdups_nat: list_nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oreplicate_001_Eo,type,
% 5.41/5.60 replicate_o: nat > $o > list_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oreplicate_001t__Complex__Ocomplex,type,
% 5.41/5.60 replicate_complex: nat > complex > list_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oreplicate_001t__Int__Oint,type,
% 5.41/5.60 replicate_int: nat > int > list_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oreplicate_001t__Nat__Onat,type,
% 5.41/5.60 replicate_nat: nat > nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oreplicate_001t__Real__Oreal,type,
% 5.41/5.60 replicate_real: nat > real > list_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oreplicate_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 replicate_set_nat: nat > set_nat > list_set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oreplicate_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 replicate_VEBT_VEBT: nat > vEBT_VEBT > list_VEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oupt,type,
% 5.41/5.60 upt: nat > nat > list_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oupto,type,
% 5.41/5.60 upto: int > int > list_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oupto__aux,type,
% 5.41/5.60 upto_aux: int > int > list_int > list_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_List_Oupto__rel,type,
% 5.41/5.60 upto_rel: product_prod_int_int > product_prod_int_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_OSuc,type,
% 5.41/5.60 suc: nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Ocompow_001_062_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.60 compow_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Onat_Ocase__nat_001_Eo,type,
% 5.41/5.60 case_nat_o: $o > ( nat > $o ) > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Onat_Ocase__nat_001t__Nat__Onat,type,
% 5.41/5.60 case_nat_nat: nat > ( nat > nat ) > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Onat_Ocase__nat_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.60 case_nat_option_num: option_num > ( nat > option_num ) > nat > option_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Onat_Opred,type,
% 5.41/5.60 pred: nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 semiri4939895301339042750nteger: nat > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Complex__Ocomplex,type,
% 5.41/5.60 semiri8010041392384452111omplex: nat > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Extended____Nat__Oenat,type,
% 5.41/5.60 semiri4216267220026989637d_enat: nat > extended_enat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Int__Oint,type,
% 5.41/5.60 semiri1314217659103216013at_int: nat > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Nat__Onat,type,
% 5.41/5.60 semiri1316708129612266289at_nat: nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Rat__Orat,type,
% 5.41/5.60 semiri681578069525770553at_rat: nat > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osemiring__1__class_Oof__nat_001t__Real__Oreal,type,
% 5.41/5.60 semiri5074537144036343181t_real: nat > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_I_Eo_J,type,
% 5.41/5.60 size_size_list_o: list_o > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.41/5.60 size_s3451745648224563538omplex: list_complex > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Int__Oint_J,type,
% 5.41/5.60 size_size_list_int: list_int > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.60 size_size_list_nat: list_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_M_Eo_J_J,type,
% 5.41/5.60 size_s1515746228057227161od_o_o: list_P4002435161011370285od_o_o > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Int__Oint_J_J,type,
% 5.41/5.60 size_s2953683556165314199_o_int: list_P3795440434834930179_o_int > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__Nat__Onat_J_J,type,
% 5.41/5.60 size_s5443766701097040955_o_nat: list_P6285523579766656935_o_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_I_Eo_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.41/5.60 size_s4313452262239582901T_VEBT: list_P7495141550334521929T_VEBT > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_M_Eo_J_J,type,
% 5.41/5.60 size_s6491369823275344609_nat_o: list_P7333126701944960589_nat_o > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__Nat__Onat_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.41/5.60 size_s4762443039079500285T_VEBT: list_P5647936690300460905T_VEBT > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_M_Eo_J_J,type,
% 5.41/5.60 size_s9168528473962070013VEBT_o: list_P3126845725202233233VEBT_o > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Int__Oint_J_J,type,
% 5.41/5.60 size_s3661962791536183091BT_int: list_P4547456442757143711BT_int > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J_J,type,
% 5.41/5.60 size_s6152045936467909847BT_nat: list_P7037539587688870467BT_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__VEBT____Definitions__OVEBT_J_J,type,
% 5.41/5.60 size_s7466405169056248089T_VEBT: list_P7413028617227757229T_VEBT > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Real__Oreal_J,type,
% 5.41/5.60 size_size_list_real: list_real > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.41/5.60 size_s3254054031482475050et_nat: list_set_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.60 size_s6755466524823107622T_VEBT: list_VEBT_VEBT > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Num__Onum,type,
% 5.41/5.60 size_size_num: num > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.41/5.60 size_size_option_nat: option_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.60 size_size_option_num: option_num > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.41/5.60 size_s170228958280169651at_nat: option4927543243414619207at_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__String__Ochar,type,
% 5.41/5.60 size_size_char: char > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat_Osize__class_Osize_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 size_size_VEBT_VEBT: vEBT_VEBT > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Olist__encode,type,
% 5.41/5.60 nat_list_encode: list_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Olist__encode__rel,type,
% 5.41/5.60 nat_list_encode_rel: list_nat > list_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Oprod__decode__aux,type,
% 5.41/5.60 nat_prod_decode_aux: nat > nat > product_prod_nat_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Oprod__decode__aux__rel,type,
% 5.41/5.60 nat_pr5047031295181774490ux_rel: product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Oprod__encode,type,
% 5.41/5.60 nat_prod_encode: product_prod_nat_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Oset__decode,type,
% 5.41/5.60 nat_set_decode: nat > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Oset__encode,type,
% 5.41/5.60 nat_set_encode: set_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Nat__Bijection_Otriangle,type,
% 5.41/5.60 nat_triangle: nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_NthRoot_Oroot,type,
% 5.41/5.60 root: nat > real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_NthRoot_Osqrt,type,
% 5.41/5.60 sqrt: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_OBitM,type,
% 5.41/5.60 bitM: num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oinc,type,
% 5.41/5.60 inc: num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 neg_nu8804712462038260780nteger: code_integer > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Complex__Ocomplex,type,
% 5.41/5.60 neg_nu7009210354673126013omplex: complex > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Int__Oint,type,
% 5.41/5.60 neg_numeral_dbl_int: int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Rat__Orat,type,
% 5.41/5.60 neg_numeral_dbl_rat: rat > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl_001t__Real__Oreal,type,
% 5.41/5.60 neg_numeral_dbl_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 neg_nu7757733837767384882nteger: code_integer > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Complex__Ocomplex,type,
% 5.41/5.60 neg_nu6511756317524482435omplex: complex > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Int__Oint,type,
% 5.41/5.60 neg_nu3811975205180677377ec_int: int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Rat__Orat,type,
% 5.41/5.60 neg_nu3179335615603231917ec_rat: rat > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__dec_001t__Real__Oreal,type,
% 5.41/5.60 neg_nu6075765906172075777c_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 neg_nu5831290666863070958nteger: code_integer > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Complex__Ocomplex,type,
% 5.41/5.60 neg_nu8557863876264182079omplex: complex > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Int__Oint,type,
% 5.41/5.60 neg_nu5851722552734809277nc_int: int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Rat__Orat,type,
% 5.41/5.60 neg_nu5219082963157363817nc_rat: rat > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Odbl__inc_001t__Real__Oreal,type,
% 5.41/5.60 neg_nu8295874005876285629c_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Oneg__numeral__class_Osub_001t__Int__Oint,type,
% 5.41/5.60 neg_numeral_sub_int: num > num > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onum_OBit0,type,
% 5.41/5.60 bit0: num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onum_OBit1,type,
% 5.41/5.60 bit1: num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onum_OOne,type,
% 5.41/5.60 one: num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onum_Ocase__num_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.60 case_num_option_num: option_num > ( num > option_num ) > ( num > option_num ) > num > option_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onum_Osize__num,type,
% 5.41/5.60 size_num: num > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onum__of__nat,type,
% 5.41/5.60 num_of_nat: nat > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 numera6620942414471956472nteger: num > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Complex__Ocomplex,type,
% 5.41/5.60 numera6690914467698888265omplex: num > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Extended____Nat__Oenat,type,
% 5.41/5.60 numera1916890842035813515d_enat: num > extended_enat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Int__Oint,type,
% 5.41/5.60 numeral_numeral_int: num > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Nat__Onat,type,
% 5.41/5.60 numeral_numeral_nat: num > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Rat__Orat,type,
% 5.41/5.60 numeral_numeral_rat: num > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Onumeral__class_Onumeral_001t__Real__Oreal,type,
% 5.41/5.60 numeral_numeral_real: num > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Opow,type,
% 5.41/5.60 pow: num > num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Opred__numeral,type,
% 5.41/5.60 pred_numeral: num > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Num_Osqr,type,
% 5.41/5.60 sqr: num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_ONone_001t__Nat__Onat,type,
% 5.41/5.60 none_nat: option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_ONone_001t__Num__Onum,type,
% 5.41/5.60 none_num: option_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_ONone_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.60 none_P5556105721700978146at_nat: option4927543243414619207at_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_OSome_001t__Nat__Onat,type,
% 5.41/5.60 some_nat: nat > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_OSome_001t__Num__Onum,type,
% 5.41/5.60 some_num: num > option_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_OSome_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.60 some_P7363390416028606310at_nat: product_prod_nat_nat > option4927543243414619207at_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Ocase__option_001_Eo_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.60 case_o184042715313410164at_nat: $o > ( product_prod_nat_nat > $o ) > option4927543243414619207at_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Ocase__option_001t__Int__Oint_001t__Num__Onum,type,
% 5.41/5.60 case_option_int_num: int > ( num > int ) > option_num > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Ocase__option_001t__Num__Onum_001t__Num__Onum,type,
% 5.41/5.60 case_option_num_num: num > ( num > num ) > option_num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Ocase__option_001t__Option__Ooption_It__Num__Onum_J_001t__Num__Onum,type,
% 5.41/5.60 case_o6005452278849405969um_num: option_num > ( num > option_num ) > option_num > option_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Osize__option_001t__Nat__Onat,type,
% 5.41/5.60 size_option_nat: ( nat > nat ) > option_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Osize__option_001t__Num__Onum,type,
% 5.41/5.60 size_option_num: ( num > nat ) > option_num > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Osize__option_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Othe_001t__Nat__Onat,type,
% 5.41/5.60 the_nat: option_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Othe_001t__Num__Onum,type,
% 5.41/5.60 the_num: option_num > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Option_Ooption_Othe_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Extended____Nat__Oenat,type,
% 5.41/5.60 bot_bo4199563552545308370d_enat: extended_enat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Nat__Onat,type,
% 5.41/5.60 bot_bot_nat: nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.41/5.60 bot_bot_set_complex: set_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Extended____Nat__Oenat_J,type,
% 5.41/5.60 bot_bo7653980558646680370d_enat: set_Extended_enat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.60 bot_bot_set_int: set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 bot_bot_set_nat: set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Num__Onum_J,type,
% 5.41/5.60 bot_bot_set_num: set_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Rat__Orat_J,type,
% 5.41/5.60 bot_bot_set_rat: set_rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.41/5.60 bot_bot_set_real: set_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 5.41/5.60 bot_bot_set_set_int: set_set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.41/5.60 bot_bot_set_set_nat: set_set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Obot__class_Obot_001t__Set__Oset_It__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.60 bot_bo8194388402131092736T_VEBT: set_VEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 ord_le6747313008572928689nteger: code_integer > code_integer > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Extended____Nat__Oenat,type,
% 5.41/5.60 ord_le72135733267957522d_enat: extended_enat > extended_enat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Int__Oint,type,
% 5.41/5.60 ord_less_int: int > int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Nat__Onat,type,
% 5.41/5.60 ord_less_nat: nat > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Num__Onum,type,
% 5.41/5.60 ord_less_num: num > num > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Rat__Orat,type,
% 5.41/5.60 ord_less_rat: rat > rat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Real__Oreal,type,
% 5.41/5.60 ord_less_real: real > real > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Code____Numeral__Ointeger_J,type,
% 5.41/5.60 ord_le1307284697595431911nteger: set_Code_integer > set_Code_integer > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.60 ord_less_set_int: set_int > set_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Rat__Orat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
% 5.41/5.60 ord_less_set_set_int: set_set_int > set_set_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.41/5.60 ord_less_set_set_nat: set_set_nat > set_set_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Complex__Ocomplex_M_Eo_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_062_It__Int__Oint_M_Eo_J_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Int__Oint_M_Eo_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Nat__Onat_M_Eo_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Real__Oreal_M_Eo_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001_062_It__Set__Oset_It__Nat__Onat_J_M_Eo_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Filter__Ofilter_It__Real__Oreal_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Num__Onum,type,
% 5.41/5.60 ord_less_eq_num: num > num > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Rat__Orat,type,
% 5.41/5.60 ord_less_eq_rat: rat > rat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Real__Oreal,type,
% 5.41/5.60 ord_less_eq_real: real > real > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_I_Eo_J,type,
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Num__Onum_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Real__Oreal_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Int__Oint_J_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Oless__eq_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Omax_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Omax_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Omax_001t__Num__Onum,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Omax_001t__Rat__Orat,type,
% 5.41/5.60 ord_max_rat: rat > rat > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Omax_001t__Real__Oreal,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oord__class_Omax_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.60 ord_max_set_int: set_int > set_int > set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oorder__class_OGreatest_001t__Nat__Onat,type,
% 5.41/5.60 order_Greatest_nat: ( nat > $o ) > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oorder__class_Oantimono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.60 order_9091379641038594480t_real: ( nat > real ) > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.60 order_mono_nat_nat: ( nat > nat ) > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Oorder__class_Omono_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.60 order_mono_nat_real: ( nat > real ) > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_I_Eo_J,type,
% 5.41/5.60 top_top_set_o: set_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Product____Type__Ounit_J,type,
% 5.41/5.60 top_to1996260823553986621t_unit: set_Product_unit ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.41/5.60 top_top_set_real: set_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Orderings_Otop__class_Otop_001t__Set__Oset_It__String__Ochar_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Power_Opower__class_Opower_001t__Code____Numeral__Ointeger,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Power_Opower__class_Opower_001t__Complex__Ocomplex,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Power_Opower__class_Opower_001t__Int__Oint,type,
% 5.41/5.60 power_power_int: int > nat > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Power_Opower__class_Opower_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Power_Opower__class_Opower_001t__Rat__Orat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Power_Opower__class_Opower_001t__Real__Oreal,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
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% 5.41/5.60 thf(sy_c_Product__Type_OPair_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001_062_It__Nat__Onat_M_062_It__Nat__Onat_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Nat__Onat_J_Mt__Option__Ooption_It__Nat__Onat_J_J,type,
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001_062_It__Num__Onum_M_062_It__Num__Onum_M_Eo_J_J_001t__Product____Type__Oprod_It__Option__Ooption_It__Num__Onum_J_Mt__Option__Ooption_It__Num__Onum_J_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001_Eo_001_Eo,type,
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% 5.41/5.60 thf(sy_c_Product__Type_OPair_001_Eo_001t__Nat__Onat,type,
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.60 product_Pair_int_int: int > int > product_prod_int_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001_Eo,type,
% 5.41/5.60 product_Pair_nat_o: nat > $o > product_prod_nat_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.60 product_Pair_nat_nat: nat > nat > product_prod_nat_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__Num__Onum,type,
% 5.41/5.60 product_Pair_nat_num: nat > num > product_prod_nat_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Nat__Onat_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 produc599794634098209291T_VEBT: nat > vEBT_VEBT > produc8025551001238799321T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Num__Onum_001t__Num__Onum,type,
% 5.41/5.60 product_Pair_num_num: num > num > product_prod_num_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Nat__Onat_J_001t__Option__Ooption_It__Nat__Onat_J,type,
% 5.41/5.60 produc5098337634421038937on_nat: option_nat > option_nat > produc4953844613479565601on_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Num__Onum_J_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.60 produc8585076106096196333on_num: option_num > option_num > produc3447558737645232053on_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J_001t__Option__Ooption_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.41/5.60 produc488173922507101015at_nat: option4927543243414619207at_nat > option4927543243414619207at_nat > produc6121120109295599847at_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001_Eo,type,
% 5.41/5.60 produc8721562602347293563VEBT_o: vEBT_VEBT > $o > produc334124729049499915VEBT_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Int__Oint,type,
% 5.41/5.60 produc736041933913180425BT_int: vEBT_VEBT > int > produc4894624898956917775BT_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__Nat__Onat,type,
% 5.41/5.60 produc738532404422230701BT_nat: vEBT_VEBT > nat > produc9072475918466114483BT_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_OPair_001t__VEBT____Definitions__OVEBT_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 produc537772716801021591T_VEBT: vEBT_VEBT > vEBT_VEBT > produc8243902056947475879T_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oapsnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 produc6499014454317279255nteger: ( code_integer > code_integer ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 5.41/5.60 produc127349428274296955eger_o: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc8763457246119570046nteger > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.41/5.60 produc2592262431452330817omplex: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex ) > produc8763457246119570046nteger > set_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.60 produc8604463032469472703et_int: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int ) > produc8763457246119570046nteger > set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 produc3558942015123893603et_nat: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat ) > produc8763457246119570046nteger > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Code____Numeral__Ointeger_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.41/5.60 produc815715089573277247t_real: ( ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real ) > produc8763457246119570046nteger > set_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 5.41/5.60 produc2558449545302689196_int_o: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc7773217078559923341nt_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Int__Oint_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.41/5.60 produc7959293469001253456omplex: ( ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex ) > produc7773217078559923341nt_int > set_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_001_Eo,type,
% 5.41/5.60 produc6253627499356882019eger_o: ( ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o ) > produc1908205239877642774nteger > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001_062_It__Product____Type__Oprod_It__Int__Oint_M_062_It__Product____Type__Ounit_Mt__Code____Evaluation__Oterm_J_J_Mt__Option__Ooption_It__Product____Type__Oprod_I_Eo_Mt__List__Olist_It__Code____Evaluation__Oterm_J_J_J_J_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_001_Eo,type,
% 5.41/5.60 produc1573362020775583542_int_o: ( ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o ) > produc2285326912895808259nt_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Int__Oint,type,
% 5.41/5.60 produc1553301316500091796er_int: ( code_integer > code_integer > int ) > produc8923325533196201883nteger > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Nat__Onat,type,
% 5.41/5.60 produc1555791787009142072er_nat: ( code_integer > code_integer > nat ) > produc8923325533196201883nteger > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Num__Onum,type,
% 5.41/5.60 produc7336495610019696514er_num: ( code_integer > code_integer > num ) > produc8923325533196201883nteger > num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J,type,
% 5.41/5.60 produc9125791028180074456eger_o: ( code_integer > code_integer > produc6271795597528267376eger_o ) > produc8923325533196201883nteger > produc6271795597528267376eger_o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J,type,
% 5.41/5.60 produc6916734918728496179nteger: ( code_integer > code_integer > produc8923325533196201883nteger ) > produc8923325533196201883nteger > produc8923325533196201883nteger ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Complex__Ocomplex_001t__Complex__Ocomplex_001_Eo,type,
% 5.41/5.60 produc6771430404735790350plex_o: ( complex > complex > $o ) > produc4411394909380815293omplex > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001_Eo,type,
% 5.41/5.60 produc4947309494688390418_int_o: ( int > int > $o ) > product_prod_int_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.60 produc8211389475949308722nt_int: ( int > int > int ) > product_prod_int_int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.41/5.60 produc4245557441103728435nt_int: ( int > int > product_prod_int_int ) > product_prod_int_int > product_prod_int_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Complex__Ocomplex_J,type,
% 5.41/5.60 produc8580519160106071146omplex: ( int > int > set_complex ) > product_prod_int_int > set_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.60 produc73460835934605544et_int: ( int > int > set_int ) > product_prod_int_int > set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 produc4251311855443802252et_nat: ( int > int > set_nat ) > product_prod_int_int > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Real__Oreal_J,type,
% 5.41/5.60 produc6452406959799940328t_real: ( int > int > set_real ) > product_prod_int_int > set_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Int__Oint_001t__Int__Oint_001t__Set__Oset_It__Set__Oset_It__Nat__Onat_J_J,type,
% 5.41/5.60 produc5233655623923918146et_nat: ( int > int > set_set_nat ) > product_prod_int_int > set_set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_M_Eo_J,type,
% 5.41/5.60 produc8739625826339149834_nat_o: ( nat > nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > product_prod_nat_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_062_It__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_Mt__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_J,type,
% 5.41/5.60 produc27273713700761075at_nat: ( nat > nat > product_prod_nat_nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001_Eo,type,
% 5.41/5.60 produc6081775807080527818_nat_o: ( nat > nat > $o ) > product_prod_nat_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Complex__Ocomplex,type,
% 5.41/5.60 produc1917071388513777916omplex: ( nat > nat > complex ) > product_prod_nat_nat > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Int__Oint,type,
% 5.41/5.60 produc6840382203811409530at_int: ( nat > nat > int ) > product_prod_nat_nat > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.60 produc6842872674320459806at_nat: ( nat > nat > nat ) > product_prod_nat_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.60 produc2626176000494625587at_nat: ( nat > nat > product_prod_nat_nat ) > product_prod_nat_nat > product_prod_nat_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Rat__Orat,type,
% 5.41/5.60 produc6207742614233964070at_rat: ( nat > nat > rat ) > product_prod_nat_nat > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.60 produc1703576794950452218t_real: ( nat > nat > real ) > product_prod_nat_nat > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Nat__Onat_001t__Num__Onum_001t__Option__Ooption_It__Num__Onum_J,type,
% 5.41/5.60 produc478579273971653890on_num: ( nat > num > option_num ) > product_prod_nat_num > option_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ocase__prod_001t__Real__Oreal_001t__Real__Oreal_001_Eo,type,
% 5.41/5.60 produc5414030515140494994real_o: ( real > real > $o ) > produc2422161461964618553l_real > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ofst_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.60 product_fst_int_int: product_prod_int_int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Ofst_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.60 product_fst_nat_nat: product_prod_nat_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Osnd_001t__Code____Numeral__Ointeger_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 produc6174133586879617921nteger: produc8923325533196201883nteger > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Osnd_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.60 product_snd_int_int: product_prod_int_int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Product__Type_Oprod_Osnd_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.60 product_snd_nat_nat: product_prod_nat_nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rat_OFract,type,
% 5.41/5.60 fract: int > int > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rat_OFrct,type,
% 5.41/5.60 frct: product_prod_int_int > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rat_Onormalize,type,
% 5.41/5.60 normalize: product_prod_int_int > product_prod_int_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rat_Oof__int,type,
% 5.41/5.60 of_int: int > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rat_Oquotient__of,type,
% 5.41/5.60 quotient_of: rat > product_prod_int_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_OReals_001t__Complex__Ocomplex,type,
% 5.41/5.60 real_V2521375963428798218omplex: set_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_Obounded__linear_001t__Real__Oreal_001t__Real__Oreal,type,
% 5.41/5.60 real_V5970128139526366754l_real: ( real > real ) > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Complex__Ocomplex,type,
% 5.41/5.60 real_V3694042436643373181omplex: complex > complex > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_Odist__class_Odist_001t__Real__Oreal,type,
% 5.41/5.60 real_V975177566351809787t_real: real > real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Complex__Ocomplex,type,
% 5.41/5.60 real_V1022390504157884413omplex: complex > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_Onorm__class_Onorm_001t__Real__Oreal,type,
% 5.41/5.60 real_V7735802525324610683m_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_Oof__real_001t__Complex__Ocomplex,type,
% 5.41/5.60 real_V4546457046886955230omplex: real > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Complex__Ocomplex,type,
% 5.41/5.60 real_V2046097035970521341omplex: real > complex > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Real__Vector__Spaces_OscaleR__class_OscaleR_001t__Real__Oreal,type,
% 5.41/5.60 real_V1485227260804924795R_real: real > real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odivide__class_Odivide_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 divide6298287555418463151nteger: code_integer > code_integer > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odivide__class_Odivide_001t__Complex__Ocomplex,type,
% 5.41/5.60 divide1717551699836669952omplex: complex > complex > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odivide__class_Odivide_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odivide__class_Odivide_001t__Nat__Onat,type,
% 5.41/5.60 divide_divide_nat: nat > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odivide__class_Odivide_001t__Rat__Orat,type,
% 5.41/5.60 divide_divide_rat: rat > rat > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odivide__class_Odivide_001t__Real__Oreal,type,
% 5.41/5.60 divide_divide_real: real > real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odvd__class_Odvd_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 dvd_dvd_Code_integer: code_integer > code_integer > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odvd__class_Odvd_001t__Complex__Ocomplex,type,
% 5.41/5.60 dvd_dvd_complex: complex > complex > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odvd__class_Odvd_001t__Int__Oint,type,
% 5.41/5.60 dvd_dvd_int: int > int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odvd__class_Odvd_001t__Nat__Onat,type,
% 5.41/5.60 dvd_dvd_nat: nat > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odvd__class_Odvd_001t__Rat__Orat,type,
% 5.41/5.60 dvd_dvd_rat: rat > rat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Odvd__class_Odvd_001t__Real__Oreal,type,
% 5.41/5.60 dvd_dvd_real: real > real > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Code____Numeral__Ointeger,type,
% 5.41/5.60 modulo364778990260209775nteger: code_integer > code_integer > code_integer ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Int__Oint,type,
% 5.41/5.60 modulo_modulo_int: int > int > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Omodulo__class_Omodulo_001t__Nat__Onat,type,
% 5.41/5.60 modulo_modulo_nat: nat > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Code____Numeral__Ointeger,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Complex__Ocomplex,type,
% 5.41/5.60 zero_n1201886186963655149omplex: $o > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Int__Oint,type,
% 5.41/5.60 zero_n2684676970156552555ol_int: $o > int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Rat__Orat,type,
% 5.41/5.60 zero_n2052037380579107095ol_rat: $o > rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Rings_Ozero__neq__one__class_Oof__bool_001t__Real__Oreal,type,
% 5.41/5.60 zero_n3304061248610475627l_real: $o > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Series_Osuminf_001t__Complex__Ocomplex,type,
% 5.41/5.60 suminf_complex: ( nat > complex ) > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Series_Osuminf_001t__Real__Oreal,type,
% 5.41/5.60 suminf_real: ( nat > real ) > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Series_Osummable_001t__Real__Oreal,type,
% 5.41/5.60 summable_real: ( nat > real ) > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Series_Osums_001t__Real__Oreal,type,
% 5.41/5.60 sums_real: ( nat > real ) > real > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Code____Numeral__Ointeger,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Complex__Ocomplex,type,
% 5.41/5.60 collect_complex: ( complex > $o ) > set_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__List__Olist_I_Eo_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__List__Olist_It__Complex__Ocomplex_J,type,
% 5.41/5.60 collect_list_complex: ( list_complex > $o ) > set_list_complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__List__Olist_It__Int__Oint_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__List__Olist_It__Nat__Onat_J,type,
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% 5.41/5.60
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Num__Onum,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Rat__Orat,type,
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Complex__Ocomplex_J,type,
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OCollect_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_OPow_001t__Nat__Onat,type,
% 5.41/5.60 pow_nat: set_nat > set_set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Int__Oint_001t__Int__Oint,type,
% 5.41/5.60 image_int_int: ( int > int ) > set_int > set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Nat__Onat,type,
% 5.41/5.60 image_nat_nat: ( nat > nat ) > set_nat > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Real__Oreal,type,
% 5.41/5.60 image_nat_real: ( nat > real ) > set_nat > set_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Nat__Onat_001t__String__Ochar,type,
% 5.41/5.60 image_nat_char: ( nat > char ) > set_nat > set_char ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Complex__Ocomplex_Mt__Complex__Ocomplex_J_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Filter__Ofilter_It__Product____Type__Oprod_It__Real__Oreal_Mt__Real__Oreal_J_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__Real__Oreal_001t__Real__Oreal,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oimage_001t__String__Ochar_001t__Nat__Onat,type,
% 5.41/5.60 image_char_nat: ( char > nat ) > set_char > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__Complex__Ocomplex,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__Int__Oint,type,
% 5.41/5.60 insert_int: int > set_int > set_int ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__Nat__Onat,type,
% 5.41/5.60 insert_nat: nat > set_nat > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__Num__Onum,type,
% 5.41/5.60 insert_num: num > set_num > set_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__Rat__Orat,type,
% 5.41/5.60 insert_rat: rat > set_rat > set_rat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__Real__Oreal,type,
% 5.41/5.60 insert_real: real > set_real > set_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set_Oinsert_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 insert_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > set_VEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Ofold__atLeastAtMost__nat_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Num__Onum,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Rat__Orat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Real__Oreal,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Int__Oint_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastAtMost_001t__Set__Oset_It__Nat__Onat_J,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeastLessThan_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatLeast_001t__Real__Oreal,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OatMost_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OgreaterThanAtMost_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Int__Oint,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OgreaterThanLessThan_001t__Real__Oreal,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OgreaterThan_001t__Real__Oreal,type,
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% 5.41/5.60
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% 5.41/5.60
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Num__Onum,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Rat__Orat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Set__Interval_Oord__class_OlessThan_001t__Real__Oreal,type,
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% 5.41/5.60
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% 5.41/5.60 thf(sy_c_String_Ochar_OChar,type,
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% 5.41/5.60 thf(sy_c_String_Ounique__euclidean__semiring__with__bit__operations__class_Ochar__of_001t__Nat__Onat,type,
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% 5.41/5.60
% 5.41/5.60 thf(sy_c_Topological__Spaces_Otopological__space__class_Onhds_001t__Real__Oreal,type,
% 5.41/5.60 topolo2815343760600316023s_real: real > filter_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Topological__Spaces_Ouniform__space__class_OCauchy_001t__Real__Oreal,type,
% 5.41/5.60 topolo4055970368930404560y_real: ( nat > real ) > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Complex__Ocomplex,type,
% 5.41/5.60 topolo896644834953643431omplex: filter6041513312241820739omplex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Topological__Spaces_Ouniformity__class_Ouniformity_001t__Real__Oreal,type,
% 5.41/5.60 topolo1511823702728130853y_real: filter2146258269922977983l_real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oarccos,type,
% 5.41/5.60 arccos: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oarcosh_001t__Real__Oreal,type,
% 5.41/5.60 arcosh_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oarcsin,type,
% 5.41/5.60 arcsin: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oarctan,type,
% 5.41/5.60 arctan: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oarsinh_001t__Real__Oreal,type,
% 5.41/5.60 arsinh_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oartanh_001t__Real__Oreal,type,
% 5.41/5.60 artanh_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Ocos_001t__Real__Oreal,type,
% 5.41/5.60 cos_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Ocos__coeff,type,
% 5.41/5.60 cos_coeff: nat > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Ocosh_001t__Real__Oreal,type,
% 5.41/5.60 cosh_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Ocot_001t__Real__Oreal,type,
% 5.41/5.60 cot_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oexp_001t__Complex__Ocomplex,type,
% 5.41/5.60 exp_complex: complex > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oexp_001t__Real__Oreal,type,
% 5.41/5.60 exp_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Oln__class_Oln_001t__Real__Oreal,type,
% 5.41/5.60 ln_ln_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Olog,type,
% 5.41/5.60 log: real > real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Opi,type,
% 5.41/5.60 pi: real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Opowr_001t__Real__Oreal,type,
% 5.41/5.60 powr_real: real > real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Osin_001t__Real__Oreal,type,
% 5.41/5.60 sin_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Osin__coeff,type,
% 5.41/5.60 sin_coeff: nat > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Osinh_001t__Real__Oreal,type,
% 5.41/5.60 sinh_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Otan_001t__Real__Oreal,type,
% 5.41/5.60 tan_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Otanh_001t__Complex__Ocomplex,type,
% 5.41/5.60 tanh_complex: complex > complex ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Transcendental_Otanh_001t__Real__Oreal,type,
% 5.41/5.60 tanh_real: real > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT_OLeaf,type,
% 5.41/5.60 vEBT_Leaf: $o > $o > vEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT_ONode,type,
% 5.41/5.60 vEBT_Node: option4927543243414619207at_nat > nat > list_VEBT_VEBT > vEBT_VEBT > vEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT_Osize__VEBT,type,
% 5.41/5.60 vEBT_size_VEBT: vEBT_VEBT > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oboth__member__options,type,
% 5.41/5.60 vEBT_V8194947554948674370ptions: vEBT_VEBT > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ohigh,type,
% 5.41/5.60 vEBT_VEBT_high: nat > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Oin__children,type,
% 5.41/5.60 vEBT_V5917875025757280293ildren: nat > list_VEBT_VEBT > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Olow,type,
% 5.41/5.60 vEBT_VEBT_low: nat > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima,type,
% 5.41/5.60 vEBT_VEBT_membermima: vEBT_VEBT > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Omembermima__rel,type,
% 5.41/5.60 vEBT_V4351362008482014158ma_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member,type,
% 5.41/5.60 vEBT_V5719532721284313246member: vEBT_VEBT > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Onaive__member__rel,type,
% 5.41/5.60 vEBT_V5765760719290551771er_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H,type,
% 5.41/5.60 vEBT_VEBT_valid: vEBT_VEBT > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_OVEBT__internal_Ovalid_H__rel,type,
% 5.41/5.60 vEBT_VEBT_valid_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_Oinvar__vebt,type,
% 5.41/5.60 vEBT_invar_vebt: vEBT_VEBT > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_Oset__vebt,type,
% 5.41/5.60 vEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_Ovebt__buildup,type,
% 5.41/5.60 vEBT_vebt_buildup: nat > vEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Definitions_Ovebt__buildup__rel,type,
% 5.41/5.60 vEBT_v4011308405150292612up_rel: nat > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Delete_Ovebt__delete,type,
% 5.41/5.60 vEBT_vebt_delete: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Delete_Ovebt__delete__rel,type,
% 5.41/5.60 vEBT_vebt_delete_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Insert_Ovebt__insert,type,
% 5.41/5.60 vEBT_vebt_insert: vEBT_VEBT > nat > vEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Insert_Ovebt__insert__rel,type,
% 5.41/5.60 vEBT_vebt_insert_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Member_OVEBT__internal_Obit__concat,type,
% 5.41/5.60 vEBT_VEBT_bit_concat: nat > nat > nat > nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull,type,
% 5.41/5.60 vEBT_VEBT_minNull: vEBT_VEBT > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Member_OVEBT__internal_OminNull__rel,type,
% 5.41/5.60 vEBT_V6963167321098673237ll_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Member_OVEBT__internal_Oset__vebt_H,type,
% 5.41/5.60 vEBT_VEBT_set_vebt: vEBT_VEBT > set_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Member_Ovebt__member,type,
% 5.41/5.60 vEBT_vebt_member: vEBT_VEBT > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Member_Ovebt__member__rel,type,
% 5.41/5.60 vEBT_vebt_member_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oadd,type,
% 5.41/5.60 vEBT_VEBT_add: option_nat > option_nat > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ogreater,type,
% 5.41/5.60 vEBT_VEBT_greater: option_nat > option_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Oless,type,
% 5.41/5.60 vEBT_VEBT_less: option_nat > option_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Olesseq,type,
% 5.41/5.60 vEBT_VEBT_lesseq: option_nat > option_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omax__in__set,type,
% 5.41/5.60 vEBT_VEBT_max_in_set: set_nat > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omin__in__set,type,
% 5.41/5.60 vEBT_VEBT_min_in_set: set_nat > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Omul,type,
% 5.41/5.60 vEBT_VEBT_mul: option_nat > option_nat > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Nat__Onat,type,
% 5.41/5.60 vEBT_V4262088993061758097ft_nat: ( nat > nat > nat ) > option_nat > option_nat > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Num__Onum,type,
% 5.41/5.60 vEBT_V819420779217536731ft_num: ( num > num > num ) > option_num > option_num > option_num ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Ooption__shift_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.60 vEBT_V1502963449132264192at_nat: ( product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat ) > option4927543243414619207at_nat > option4927543243414619207at_nat > option4927543243414619207at_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_OVEBT__internal_Opower,type,
% 5.41/5.60 vEBT_VEBT_power: option_nat > option_nat > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_Ovebt__maxt,type,
% 5.41/5.60 vEBT_vebt_maxt: vEBT_VEBT > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_Ovebt__maxt__rel,type,
% 5.41/5.60 vEBT_vebt_maxt_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_Ovebt__mint,type,
% 5.41/5.60 vEBT_vebt_mint: vEBT_VEBT > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__MinMax_Ovebt__mint__rel,type,
% 5.41/5.60 vEBT_vebt_mint_rel: vEBT_VEBT > vEBT_VEBT > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Pred_Ois__pred__in__set,type,
% 5.41/5.60 vEBT_is_pred_in_set: set_nat > nat > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Pred_Ovebt__pred,type,
% 5.41/5.60 vEBT_vebt_pred: vEBT_VEBT > nat > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Pred_Ovebt__pred__rel,type,
% 5.41/5.60 vEBT_vebt_pred_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Succ_Ois__succ__in__set,type,
% 5.41/5.60 vEBT_is_succ_in_set: set_nat > nat > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Succ_Ovebt__succ,type,
% 5.41/5.60 vEBT_vebt_succ: vEBT_VEBT > nat > option_nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_VEBT__Succ_Ovebt__succ__rel,type,
% 5.41/5.60 vEBT_vebt_succ_rel: produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Wellfounded_Oaccp_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.60 accp_list_nat: ( list_nat > list_nat > $o ) > list_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Wellfounded_Oaccp_001t__Nat__Onat,type,
% 5.41/5.60 accp_nat: ( nat > nat > $o ) > nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.41/5.60 accp_P1096762738010456898nt_int: ( product_prod_int_int > product_prod_int_int > $o ) > product_prod_int_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J,type,
% 5.41/5.60 accp_P4275260045618599050at_nat: ( product_prod_nat_nat > product_prod_nat_nat > $o ) > product_prod_nat_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__Num__Onum_Mt__Num__Onum_J,type,
% 5.41/5.60 accp_P3113834385874906142um_num: ( product_prod_num_num > product_prod_num_num > $o ) > product_prod_num_num > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Wellfounded_Oaccp_001t__Product____Type__Oprod_It__VEBT____Definitions__OVEBT_Mt__Nat__Onat_J,type,
% 5.41/5.60 accp_P2887432264394892906BT_nat: ( produc9072475918466114483BT_nat > produc9072475918466114483BT_nat > $o ) > produc9072475918466114483BT_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_Wellfounded_Oaccp_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 accp_VEBT_VEBT: ( vEBT_VEBT > vEBT_VEBT > $o ) > vEBT_VEBT > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_fChoice_001t__Real__Oreal,type,
% 5.41/5.60 fChoice_real: ( real > $o ) > real ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001_Eo,type,
% 5.41/5.60 member_o: $o > set_o > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Complex__Ocomplex,type,
% 5.41/5.60 member_complex: complex > set_complex > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Int__Oint,type,
% 5.41/5.60 member_int: int > set_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__List__Olist_I_Eo_J,type,
% 5.41/5.60 member_list_o: list_o > set_list_o > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__List__Olist_It__Int__Oint_J,type,
% 5.41/5.60 member_list_int: list_int > set_list_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__List__Olist_It__Nat__Onat_J,type,
% 5.41/5.60 member_list_nat: list_nat > set_list_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__List__Olist_It__VEBT____Definitions__OVEBT_J,type,
% 5.41/5.60 member2936631157270082147T_VEBT: list_VEBT_VEBT > set_list_VEBT_VEBT > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Nat__Onat,type,
% 5.41/5.60 member_nat: nat > set_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Num__Onum,type,
% 5.41/5.60 member_num: num > set_num > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J,type,
% 5.41/5.60 member5262025264175285858nt_int: product_prod_int_int > set_Pr958786334691620121nt_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Rat__Orat,type,
% 5.41/5.60 member_rat: rat > set_rat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Real__Oreal,type,
% 5.41/5.60 member_real: real > set_real > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Set__Oset_It__Int__Oint_J,type,
% 5.41/5.60 member_set_int: set_int > set_set_int > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__Set__Oset_It__Nat__Onat_J,type,
% 5.41/5.60 member_set_nat: set_nat > set_set_nat > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_c_member_001t__VEBT____Definitions__OVEBT,type,
% 5.41/5.60 member_VEBT_VEBT: vEBT_VEBT > set_VEBT_VEBT > $o ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_deg____,type,
% 5.41/5.60 deg: nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_m____,type,
% 5.41/5.60 m: nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_ma____,type,
% 5.41/5.60 ma: nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_maxs____,type,
% 5.41/5.60 maxs: nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_mi____,type,
% 5.41/5.60 mi: nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_na____,type,
% 5.41/5.60 na: nat ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_summary____,type,
% 5.41/5.60 summary: vEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_treeList____,type,
% 5.41/5.60 treeList: list_VEBT_VEBT ).
% 5.41/5.60
% 5.41/5.60 thf(sy_v_xa____,type,
% 5.41/5.60 xa: nat ).
% 5.41/5.60
% 5.41/5.60 % Relevant facts (10208)
% 5.41/5.60 thf(fact_0__C1_C,axiom,
% 5.41/5.60 vEBT_invar_vebt @ summary @ m ).
% 5.41/5.60
% 5.41/5.60 % "1"
% 5.41/5.60 thf(fact_1__092_060open_062both__member__options_Asummary_Amaxs_092_060close_062,axiom,
% 5.41/5.60 vEBT_V8194947554948674370ptions @ summary @ maxs ).
% 5.41/5.60
% 5.41/5.60 % \<open>both_member_options summary maxs\<close>
% 5.41/5.60 thf(fact_2__C8_C,axiom,
% 5.41/5.60 na = m ).
% 5.41/5.60
% 5.41/5.60 % "8"
% 5.41/5.60 thf(fact_3_bit__split__inv,axiom,
% 5.41/5.60 ! [X: nat,D: nat] :
% 5.41/5.60 ( ( vEBT_VEBT_bit_concat @ ( vEBT_VEBT_high @ X @ D ) @ ( vEBT_VEBT_low @ X @ D ) @ D )
% 5.41/5.60 = X ) ).
% 5.41/5.60
% 5.41/5.60 % bit_split_inv
% 5.41/5.60 thf(fact_4_dele__bmo__cont__corr,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.41/5.60 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.60 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ T @ X ) @ Y )
% 5.41/5.60 = ( ( X != Y )
% 5.41/5.60 & ( vEBT_V8194947554948674370ptions @ T @ Y ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % dele_bmo_cont_corr
% 5.41/5.60 thf(fact_5__092_060open_062invar__vebt_A_ItreeList_091high_Ax_An_A_058_061_Avebt__delete_A_ItreeList_A_B_Ahigh_Ax_An_J_A_Ilow_Ax_An_J_093_A_B_Amaxs_J_An_092_060close_062,axiom,
% 5.41/5.60 vEBT_invar_vebt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ na ).
% 5.41/5.60
% 5.41/5.60 % \<open>invar_vebt (treeList[high x n := vebt_delete (treeList ! high x n) (low x n)] ! maxs) n\<close>
% 5.41/5.60 thf(fact_6_xnotmi,axiom,
% 5.41/5.60 xa != mi ).
% 5.41/5.60
% 5.41/5.60 % xnotmi
% 5.41/5.60 thf(fact_7_hlist,axiom,
% 5.41/5.60 ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( vEBT_VEBT_high @ xa @ na ) )
% 5.41/5.60 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % hlist
% 5.41/5.60 thf(fact_8_nnvalid,axiom,
% 5.41/5.60 vEBT_invar_vebt @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) @ na ).
% 5.41/5.60
% 5.41/5.60 % nnvalid
% 5.41/5.60 thf(fact_9_ninNullc,axiom,
% 5.41/5.60 vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ).
% 5.41/5.60
% 5.41/5.60 % ninNullc
% 5.41/5.60 thf(fact_10_bb,axiom,
% 5.41/5.60 ( ( maxs
% 5.41/5.60 != ( vEBT_VEBT_high @ xa @ na ) )
% 5.41/5.60 & ( ord_less_nat @ maxs @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % bb
% 5.41/5.60 thf(fact_11_True,axiom,
% 5.41/5.60 xa = ma ).
% 5.41/5.60
% 5.41/5.60 % True
% 5.41/5.60 thf(fact_12_nothlist,axiom,
% 5.41/5.60 ! [I: nat] :
% 5.41/5.60 ( ( I
% 5.41/5.60 != ( vEBT_VEBT_high @ xa @ na ) )
% 5.41/5.60 => ( ( ord_less_nat @ I @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ I )
% 5.41/5.60 = ( nth_VEBT_VEBT @ treeList @ I ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nothlist
% 5.41/5.60 thf(fact_13__C4_C,axiom,
% 5.41/5.60 ! [I2: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.60 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ X2 ) )
% 5.41/5.60 = ( vEBT_V8194947554948674370ptions @ summary @ I2 ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % "4"
% 5.41/5.60 thf(fact_14_in__children__def,axiom,
% 5.41/5.60 ( vEBT_V5917875025757280293ildren
% 5.41/5.60 = ( ^ [N2: nat,TreeList: list_VEBT_VEBT,X3: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ ( vEBT_VEBT_high @ X3 @ N2 ) ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_children_def
% 5.41/5.60 thf(fact_15_newsummvalid,axiom,
% 5.41/5.60 vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ m ).
% 5.41/5.60
% 5.41/5.60 % newsummvalid
% 5.41/5.60 thf(fact_16__C4_OIH_C_I1_J,axiom,
% 5.41/5.60 ! [X4: vEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.41/5.60 => ( ( vEBT_invar_vebt @ X4 @ na )
% 5.41/5.60 & ! [Xa: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ X4 @ Xa ) @ na ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % "4.IH"(1)
% 5.41/5.60 thf(fact_17_list__update__id,axiom,
% 5.41/5.60 ! [Xs: list_nat,I: nat] :
% 5.41/5.60 ( ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ I ) )
% 5.41/5.60 = Xs ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_id
% 5.41/5.60 thf(fact_18_list__update__id,axiom,
% 5.41/5.60 ! [Xs: list_int,I: nat] :
% 5.41/5.60 ( ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ I ) )
% 5.41/5.60 = Xs ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_id
% 5.41/5.60 thf(fact_19_list__update__id,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,I: nat] :
% 5.41/5.60 ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ I ) )
% 5.41/5.60 = Xs ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_id
% 5.41/5.60 thf(fact_20_nth__list__update__neq,axiom,
% 5.41/5.60 ! [I: nat,J: nat,Xs: list_nat,X: nat] :
% 5.41/5.60 ( ( I != J )
% 5.41/5.60 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 5.41/5.60 = ( nth_nat @ Xs @ J ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update_neq
% 5.41/5.60 thf(fact_21_nth__list__update__neq,axiom,
% 5.41/5.60 ! [I: nat,J: nat,Xs: list_int,X: int] :
% 5.41/5.60 ( ( I != J )
% 5.41/5.60 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 5.41/5.60 = ( nth_int @ Xs @ J ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update_neq
% 5.41/5.60 thf(fact_22_nth__list__update__neq,axiom,
% 5.41/5.60 ! [I: nat,J: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.41/5.60 ( ( I != J )
% 5.41/5.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 5.41/5.60 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update_neq
% 5.41/5.60 thf(fact_23__092_060open_062treeList_A_B_Ahigh_Ax_An_A_092_060in_062_Aset_AtreeList_092_060close_062,axiom,
% 5.41/5.60 member_VEBT_VEBT @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( set_VEBT_VEBT2 @ treeList ) ).
% 5.41/5.60
% 5.41/5.60 % \<open>treeList ! high x n \<in> set treeList\<close>
% 5.41/5.60 thf(fact_24_allvalidinlist,axiom,
% 5.41/5.60 ! [X4: vEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) ) )
% 5.41/5.60 => ( vEBT_invar_vebt @ X4 @ na ) ) ).
% 5.41/5.60
% 5.41/5.60 % allvalidinlist
% 5.41/5.60 thf(fact_25__092_060open_062both__member__options_A_ItreeList_A_B_Ahigh_Ama_An_J_A_Ilow_Ama_An_J_092_060close_062,axiom,
% 5.41/5.60 vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ ma @ na ) ) @ ( vEBT_VEBT_low @ ma @ na ) ).
% 5.41/5.60
% 5.41/5.60 % \<open>both_member_options (treeList ! high ma n) (low ma n)\<close>
% 5.41/5.60 thf(fact_26__C111_C,axiom,
% 5.41/5.60 ! [I2: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.60 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ I2 ) @ X2 ) )
% 5.41/5.60 = ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) @ I2 ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % "111"
% 5.41/5.60 thf(fact_27__C4_OIH_C_I2_J,axiom,
% 5.41/5.60 ! [X: nat] : ( vEBT_invar_vebt @ ( vEBT_vebt_delete @ summary @ X ) @ m ) ).
% 5.41/5.60
% 5.41/5.60 % "4.IH"(2)
% 5.41/5.60 thf(fact_28_list__update__overwrite,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.41/5.60 ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I @ Y )
% 5.41/5.60 = ( list_u1324408373059187874T_VEBT @ Xs @ I @ Y ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_overwrite
% 5.41/5.60 thf(fact_29_not__min__Null__member,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT] :
% 5.41/5.60 ( ~ ( vEBT_VEBT_minNull @ T )
% 5.41/5.60 => ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ T @ X_1 ) ) ).
% 5.41/5.60
% 5.41/5.60 % not_min_Null_member
% 5.41/5.60 thf(fact_30__C5_C,axiom,
% 5.41/5.60 ( ( mi = ma )
% 5.41/5.60 => ! [X4: vEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.41/5.60 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % "5"
% 5.41/5.60 thf(fact_31__092_060open_062x_A_092_060noteq_062_Ami_A_092_060or_062_Ax_A_092_060noteq_062_Ama_092_060close_062,axiom,
% 5.41/5.60 ( ( xa != mi )
% 5.41/5.60 | ( xa != ma ) ) ).
% 5.41/5.60
% 5.41/5.60 % \<open>x \<noteq> mi \<or> x \<noteq> ma\<close>
% 5.41/5.60 thf(fact_32__C0_C,axiom,
% 5.41/5.60 ! [X4: vEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ treeList ) )
% 5.41/5.60 => ( vEBT_invar_vebt @ X4 @ na ) ) ).
% 5.41/5.60
% 5.41/5.60 % "0"
% 5.41/5.60 thf(fact_33_hlbound,axiom,
% 5.41/5.60 ( ( ord_less_nat @ ( vEBT_VEBT_high @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.60 & ( ord_less_nat @ ( vEBT_VEBT_low @ xa @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % hlbound
% 5.41/5.60 thf(fact_34__C4_Ohyps_C_I7_J,axiom,
% 5.41/5.60 ord_less_eq_nat @ mi @ ma ).
% 5.41/5.60
% 5.41/5.60 % "4.hyps"(7)
% 5.41/5.60 thf(fact_35__C4_Ohyps_C_I8_J,axiom,
% 5.41/5.60 ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ).
% 5.41/5.60
% 5.41/5.60 % "4.hyps"(8)
% 5.41/5.60 thf(fact_36__C2_C,axiom,
% 5.41/5.60 ( ( size_s6755466524823107622T_VEBT @ treeList )
% 5.41/5.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.41/5.60
% 5.41/5.60 % "2"
% 5.41/5.60 thf(fact_37__C7_C,axiom,
% 5.41/5.60 ( ( mi != ma )
% 5.41/5.60 => ! [I2: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.60 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.41/5.60 = I2 )
% 5.41/5.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.41/5.60 & ! [Y2: nat] :
% 5.41/5.60 ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 5.41/5.60 = I2 )
% 5.41/5.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 5.41/5.60 => ( ( ord_less_nat @ mi @ Y2 )
% 5.41/5.60 & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % "7"
% 5.41/5.60 thf(fact_38_list__update__swap,axiom,
% 5.41/5.60 ! [I: nat,I3: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT,X5: vEBT_VEBT] :
% 5.41/5.60 ( ( I != I3 )
% 5.41/5.60 => ( ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I3 @ X5 )
% 5.41/5.60 = ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I3 @ X5 ) @ I @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_swap
% 5.41/5.60 thf(fact_39_yhelper,axiom,
% 5.41/5.60 ! [Y: nat] :
% 5.41/5.60 ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ Y @ na ) ) @ ( vEBT_VEBT_low @ Y @ na ) )
% 5.41/5.60 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.60 => ( ( ord_less_nat @ mi @ Y )
% 5.41/5.60 & ( ord_less_eq_nat @ Y @ ma )
% 5.41/5.60 & ( ord_less_nat @ ( vEBT_VEBT_low @ Y @ na ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ na ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % yhelper
% 5.41/5.60 thf(fact_40__C7b_C,axiom,
% 5.41/5.60 ! [I2: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) )
% 5.41/5.60 => ( ( ( ( vEBT_VEBT_high @ ma @ na )
% 5.41/5.60 = I2 )
% 5.41/5.60 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ ma @ na ) ) )
% 5.41/5.60 & ! [Y2: nat] :
% 5.41/5.60 ( ( ( ( vEBT_VEBT_high @ Y2 @ na )
% 5.41/5.60 = I2 )
% 5.41/5.60 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ treeList @ I2 ) @ ( vEBT_VEBT_low @ Y2 @ na ) ) )
% 5.41/5.60 => ( ( ord_less_nat @ mi @ Y2 )
% 5.41/5.60 & ( ord_less_eq_nat @ Y2 @ ma ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % "7b"
% 5.41/5.60 thf(fact_41_valid__insert__both__member__options__pres,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.41/5.60 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.60 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.60 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.60 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.41/5.60 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ Y ) @ X ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % valid_insert_both_member_options_pres
% 5.41/5.60 thf(fact_42_valid__insert__both__member__options__add,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.60 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.60 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.60 => ( vEBT_V8194947554948674370ptions @ ( vEBT_vebt_insert @ T @ X ) @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % valid_insert_both_member_options_add
% 5.41/5.60 thf(fact_43_newlistlength,axiom,
% 5.41/5.60 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) )
% 5.41/5.60 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ m ) ) ).
% 5.41/5.60
% 5.41/5.60 % newlistlength
% 5.41/5.60 thf(fact_44__092_060open_062mi_A_092_060noteq_062_Ama_A_092_060and_062_Ax_A_060_A2_A_094_Adeg_092_060close_062,axiom,
% 5.41/5.60 ( ( mi != ma )
% 5.41/5.60 & ( ord_less_nat @ xa @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % \<open>mi \<noteq> ma \<and> x < 2 ^ deg\<close>
% 5.41/5.60 thf(fact_45_member__bound,axiom,
% 5.41/5.60 ! [Tree: vEBT_VEBT,X: nat,N: nat] :
% 5.41/5.60 ( ( vEBT_vebt_member @ Tree @ X )
% 5.41/5.60 => ( ( vEBT_invar_vebt @ Tree @ N )
% 5.41/5.60 => ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % member_bound
% 5.41/5.60 thf(fact_46_less__exp,axiom,
% 5.41/5.60 ! [N: nat] : ( ord_less_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % less_exp
% 5.41/5.60 thf(fact_47_semiring__norm_I85_J,axiom,
% 5.41/5.60 ! [M: num] :
% 5.41/5.60 ( ( bit0 @ M )
% 5.41/5.60 != one ) ).
% 5.41/5.60
% 5.41/5.60 % semiring_norm(85)
% 5.41/5.60 thf(fact_48_semiring__norm_I83_J,axiom,
% 5.41/5.60 ! [N: num] :
% 5.41/5.60 ( one
% 5.41/5.60 != ( bit0 @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % semiring_norm(83)
% 5.41/5.60 thf(fact_49_mem__Collect__eq,axiom,
% 5.41/5.60 ! [A: real,P: real > $o] :
% 5.41/5.60 ( ( member_real @ A @ ( collect_real @ P ) )
% 5.41/5.60 = ( P @ A ) ) ).
% 5.41/5.60
% 5.41/5.60 % mem_Collect_eq
% 5.41/5.60 thf(fact_50_mem__Collect__eq,axiom,
% 5.41/5.60 ! [A: product_prod_int_int,P: product_prod_int_int > $o] :
% 5.41/5.60 ( ( member5262025264175285858nt_int @ A @ ( collec213857154873943460nt_int @ P ) )
% 5.41/5.60 = ( P @ A ) ) ).
% 5.41/5.60
% 5.41/5.60 % mem_Collect_eq
% 5.41/5.60 thf(fact_51_mem__Collect__eq,axiom,
% 5.41/5.60 ! [A: complex,P: complex > $o] :
% 5.41/5.60 ( ( member_complex @ A @ ( collect_complex @ P ) )
% 5.41/5.60 = ( P @ A ) ) ).
% 5.41/5.60
% 5.41/5.60 % mem_Collect_eq
% 5.41/5.60 thf(fact_52_mem__Collect__eq,axiom,
% 5.41/5.60 ! [A: set_nat,P: set_nat > $o] :
% 5.41/5.60 ( ( member_set_nat @ A @ ( collect_set_nat @ P ) )
% 5.41/5.60 = ( P @ A ) ) ).
% 5.41/5.60
% 5.41/5.60 % mem_Collect_eq
% 5.41/5.60 thf(fact_53_mem__Collect__eq,axiom,
% 5.41/5.60 ! [A: nat,P: nat > $o] :
% 5.41/5.60 ( ( member_nat @ A @ ( collect_nat @ P ) )
% 5.41/5.60 = ( P @ A ) ) ).
% 5.41/5.60
% 5.41/5.60 % mem_Collect_eq
% 5.41/5.60 thf(fact_54_mem__Collect__eq,axiom,
% 5.41/5.60 ! [A: int,P: int > $o] :
% 5.41/5.60 ( ( member_int @ A @ ( collect_int @ P ) )
% 5.41/5.60 = ( P @ A ) ) ).
% 5.41/5.60
% 5.41/5.60 % mem_Collect_eq
% 5.41/5.60 thf(fact_55_Collect__mem__eq,axiom,
% 5.41/5.60 ! [A2: set_real] :
% 5.41/5.60 ( ( collect_real
% 5.41/5.60 @ ^ [X3: real] : ( member_real @ X3 @ A2 ) )
% 5.41/5.60 = A2 ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_mem_eq
% 5.41/5.60 thf(fact_56_Collect__mem__eq,axiom,
% 5.41/5.60 ! [A2: set_Pr958786334691620121nt_int] :
% 5.41/5.60 ( ( collec213857154873943460nt_int
% 5.41/5.60 @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A2 ) )
% 5.41/5.60 = A2 ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_mem_eq
% 5.41/5.60 thf(fact_57_Collect__mem__eq,axiom,
% 5.41/5.60 ! [A2: set_complex] :
% 5.41/5.60 ( ( collect_complex
% 5.41/5.60 @ ^ [X3: complex] : ( member_complex @ X3 @ A2 ) )
% 5.41/5.60 = A2 ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_mem_eq
% 5.41/5.60 thf(fact_58_Collect__mem__eq,axiom,
% 5.41/5.60 ! [A2: set_set_nat] :
% 5.41/5.60 ( ( collect_set_nat
% 5.41/5.60 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A2 ) )
% 5.41/5.60 = A2 ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_mem_eq
% 5.41/5.60 thf(fact_59_Collect__mem__eq,axiom,
% 5.41/5.60 ! [A2: set_nat] :
% 5.41/5.60 ( ( collect_nat
% 5.41/5.60 @ ^ [X3: nat] : ( member_nat @ X3 @ A2 ) )
% 5.41/5.60 = A2 ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_mem_eq
% 5.41/5.60 thf(fact_60_Collect__mem__eq,axiom,
% 5.41/5.60 ! [A2: set_int] :
% 5.41/5.60 ( ( collect_int
% 5.41/5.60 @ ^ [X3: int] : ( member_int @ X3 @ A2 ) )
% 5.41/5.60 = A2 ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_mem_eq
% 5.41/5.60 thf(fact_61_Collect__cong,axiom,
% 5.41/5.60 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.41/5.60 ( ! [X6: product_prod_int_int] :
% 5.41/5.60 ( ( P @ X6 )
% 5.41/5.60 = ( Q @ X6 ) )
% 5.41/5.60 => ( ( collec213857154873943460nt_int @ P )
% 5.41/5.60 = ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_cong
% 5.41/5.60 thf(fact_62_Collect__cong,axiom,
% 5.41/5.60 ! [P: complex > $o,Q: complex > $o] :
% 5.41/5.60 ( ! [X6: complex] :
% 5.41/5.60 ( ( P @ X6 )
% 5.41/5.60 = ( Q @ X6 ) )
% 5.41/5.60 => ( ( collect_complex @ P )
% 5.41/5.60 = ( collect_complex @ Q ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_cong
% 5.41/5.60 thf(fact_63_Collect__cong,axiom,
% 5.41/5.60 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.41/5.60 ( ! [X6: set_nat] :
% 5.41/5.60 ( ( P @ X6 )
% 5.41/5.60 = ( Q @ X6 ) )
% 5.41/5.60 => ( ( collect_set_nat @ P )
% 5.41/5.60 = ( collect_set_nat @ Q ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_cong
% 5.41/5.60 thf(fact_64_Collect__cong,axiom,
% 5.41/5.60 ! [P: nat > $o,Q: nat > $o] :
% 5.41/5.60 ( ! [X6: nat] :
% 5.41/5.60 ( ( P @ X6 )
% 5.41/5.60 = ( Q @ X6 ) )
% 5.41/5.60 => ( ( collect_nat @ P )
% 5.41/5.60 = ( collect_nat @ Q ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_cong
% 5.41/5.60 thf(fact_65_Collect__cong,axiom,
% 5.41/5.60 ! [P: int > $o,Q: int > $o] :
% 5.41/5.60 ( ! [X6: int] :
% 5.41/5.60 ( ( P @ X6 )
% 5.41/5.60 = ( Q @ X6 ) )
% 5.41/5.60 => ( ( collect_int @ P )
% 5.41/5.60 = ( collect_int @ Q ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Collect_cong
% 5.41/5.60 thf(fact_66_numeral__less__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.60 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_less_iff
% 5.41/5.60 thf(fact_67_numeral__less__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.60 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_less_iff
% 5.41/5.60 thf(fact_68_numeral__less__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.60 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_less_iff
% 5.41/5.60 thf(fact_69_numeral__less__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.60 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_less_iff
% 5.41/5.60 thf(fact_70_high__bound__aux,axiom,
% 5.41/5.60 ! [Ma: nat,N: nat,M: nat] :
% 5.41/5.60 ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.41/5.60 => ( ord_less_nat @ ( vEBT_VEBT_high @ Ma @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % high_bound_aux
% 5.41/5.60 thf(fact_71_min__Null__member,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,X: nat] :
% 5.41/5.60 ( ( vEBT_VEBT_minNull @ T )
% 5.41/5.60 => ~ ( vEBT_vebt_member @ T @ X ) ) ).
% 5.41/5.60
% 5.41/5.60 % min_Null_member
% 5.41/5.60 thf(fact_72__C3_C,axiom,
% 5.41/5.60 ( deg
% 5.41/5.60 = ( plus_plus_nat @ na @ m ) ) ).
% 5.41/5.60
% 5.41/5.60 % "3"
% 5.41/5.60 thf(fact_73_both__member__options__equiv__member,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.60 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.60 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.41/5.60 = ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % both_member_options_equiv_member
% 5.41/5.60 thf(fact_74_valid__member__both__member__options,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.60 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.60 => ( ( vEBT_V8194947554948674370ptions @ T @ X )
% 5.41/5.60 => ( vEBT_vebt_member @ T @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % valid_member_both_member_options
% 5.41/5.60 thf(fact_75_min__in__set__def,axiom,
% 5.41/5.60 ( vEBT_VEBT_min_in_set
% 5.41/5.60 = ( ^ [Xs2: set_nat,X3: nat] :
% 5.41/5.60 ( ( member_nat @ X3 @ Xs2 )
% 5.41/5.60 & ! [Y3: nat] :
% 5.41/5.60 ( ( member_nat @ Y3 @ Xs2 )
% 5.41/5.60 => ( ord_less_eq_nat @ X3 @ Y3 ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % min_in_set_def
% 5.41/5.60 thf(fact_76_max__in__set__def,axiom,
% 5.41/5.60 ( vEBT_VEBT_max_in_set
% 5.41/5.60 = ( ^ [Xs2: set_nat,X3: nat] :
% 5.41/5.60 ( ( member_nat @ X3 @ Xs2 )
% 5.41/5.60 & ! [Y3: nat] :
% 5.41/5.60 ( ( member_nat @ Y3 @ Xs2 )
% 5.41/5.60 => ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % max_in_set_def
% 5.41/5.60 thf(fact_77_inthall,axiom,
% 5.41/5.60 ! [Xs: list_complex,P: complex > $o,N: nat] :
% 5.41/5.60 ( ! [X6: complex] :
% 5.41/5.60 ( ( member_complex @ X6 @ ( set_complex2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_complex @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % inthall
% 5.41/5.60 thf(fact_78_inthall,axiom,
% 5.41/5.60 ! [Xs: list_real,P: real > $o,N: nat] :
% 5.41/5.60 ( ! [X6: real] :
% 5.41/5.60 ( ( member_real @ X6 @ ( set_real2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_real @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % inthall
% 5.41/5.60 thf(fact_79_inthall,axiom,
% 5.41/5.60 ! [Xs: list_set_nat,P: set_nat > $o,N: nat] :
% 5.41/5.60 ( ! [X6: set_nat] :
% 5.41/5.60 ( ( member_set_nat @ X6 @ ( set_set_nat2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_set_nat @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % inthall
% 5.41/5.60 thf(fact_80_inthall,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,N: nat] :
% 5.41/5.60 ( ! [X6: vEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % inthall
% 5.41/5.60 thf(fact_81_inthall,axiom,
% 5.41/5.60 ! [Xs: list_o,P: $o > $o,N: nat] :
% 5.41/5.60 ( ! [X6: $o] :
% 5.41/5.60 ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % inthall
% 5.41/5.60 thf(fact_82_inthall,axiom,
% 5.41/5.60 ! [Xs: list_nat,P: nat > $o,N: nat] :
% 5.41/5.60 ( ! [X6: nat] :
% 5.41/5.60 ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % inthall
% 5.41/5.60 thf(fact_83_inthall,axiom,
% 5.41/5.60 ! [Xs: list_int,P: int > $o,N: nat] :
% 5.41/5.60 ( ! [X6: int] :
% 5.41/5.60 ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % inthall
% 5.41/5.60 thf(fact_84_numeral__eq__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ( numera6690914467698888265omplex @ M )
% 5.41/5.60 = ( numera6690914467698888265omplex @ N ) )
% 5.41/5.60 = ( M = N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_eq_iff
% 5.41/5.60 thf(fact_85_numeral__eq__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ( numeral_numeral_real @ M )
% 5.41/5.60 = ( numeral_numeral_real @ N ) )
% 5.41/5.60 = ( M = N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_eq_iff
% 5.41/5.60 thf(fact_86_numeral__eq__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ( numeral_numeral_rat @ M )
% 5.41/5.60 = ( numeral_numeral_rat @ N ) )
% 5.41/5.60 = ( M = N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_eq_iff
% 5.41/5.60 thf(fact_87_numeral__eq__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ( numeral_numeral_nat @ M )
% 5.41/5.60 = ( numeral_numeral_nat @ N ) )
% 5.41/5.60 = ( M = N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_eq_iff
% 5.41/5.60 thf(fact_88_numeral__eq__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ( numeral_numeral_int @ M )
% 5.41/5.60 = ( numeral_numeral_int @ N ) )
% 5.41/5.60 = ( M = N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_eq_iff
% 5.41/5.60 thf(fact_89_semiring__norm_I87_J,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ( bit0 @ M )
% 5.41/5.60 = ( bit0 @ N ) )
% 5.41/5.60 = ( M = N ) ) ).
% 5.41/5.60
% 5.41/5.60 % semiring_norm(87)
% 5.41/5.60 thf(fact_90__C12_C,axiom,
% 5.41/5.60 ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ).
% 5.41/5.60
% 5.41/5.60 % "12"
% 5.41/5.60 thf(fact_91_inrg,axiom,
% 5.41/5.60 ( ( ord_less_eq_nat @ mi @ xa )
% 5.41/5.60 & ( ord_less_eq_nat @ xa @ ma ) ) ).
% 5.41/5.60
% 5.41/5.60 % inrg
% 5.41/5.60 thf(fact_92_numeral__le__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.60 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_le_iff
% 5.41/5.60 thf(fact_93_numeral__le__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.60 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_le_iff
% 5.41/5.60 thf(fact_94_numeral__le__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.60 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_le_iff
% 5.41/5.60 thf(fact_95_numeral__le__iff,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.60 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_le_iff
% 5.41/5.60 thf(fact_96_numeral__plus__numeral,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.60 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_plus_numeral
% 5.41/5.60 thf(fact_97_numeral__plus__numeral,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.60 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_plus_numeral
% 5.41/5.60 thf(fact_98_numeral__plus__numeral,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.60 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_plus_numeral
% 5.41/5.60 thf(fact_99_numeral__plus__numeral,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( plus_plus_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.60 = ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_plus_numeral
% 5.41/5.60 thf(fact_100_numeral__plus__numeral,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.60 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_plus_numeral
% 5.41/5.60 thf(fact_101_add__numeral__left,axiom,
% 5.41/5.60 ! [V: num,W: num,Z: complex] :
% 5.41/5.60 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.41/5.60 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.60
% 5.41/5.60 % add_numeral_left
% 5.41/5.60 thf(fact_102_add__numeral__left,axiom,
% 5.41/5.60 ! [V: num,W: num,Z: real] :
% 5.41/5.60 ( ( plus_plus_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.41/5.60 = ( plus_plus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.60
% 5.41/5.60 % add_numeral_left
% 5.41/5.60 thf(fact_103_add__numeral__left,axiom,
% 5.41/5.60 ! [V: num,W: num,Z: rat] :
% 5.41/5.60 ( ( plus_plus_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.41/5.60 = ( plus_plus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.60
% 5.41/5.60 % add_numeral_left
% 5.41/5.60 thf(fact_104_add__numeral__left,axiom,
% 5.41/5.60 ! [V: num,W: num,Z: nat] :
% 5.41/5.60 ( ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.41/5.60 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.60
% 5.41/5.60 % add_numeral_left
% 5.41/5.60 thf(fact_105_add__numeral__left,axiom,
% 5.41/5.60 ! [V: num,W: num,Z: int] :
% 5.41/5.60 ( ( plus_plus_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.41/5.60 = ( plus_plus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.60
% 5.41/5.60 % add_numeral_left
% 5.41/5.60 thf(fact_106_post__member__pre__member,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.41/5.60 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.60 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.60 => ( ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.60 => ( ( vEBT_vebt_member @ ( vEBT_vebt_insert @ T @ X ) @ Y )
% 5.41/5.60 => ( ( vEBT_vebt_member @ T @ Y )
% 5.41/5.60 | ( X = Y ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % post_member_pre_member
% 5.41/5.60 thf(fact_107_member__correct,axiom,
% 5.41/5.60 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.60 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.60 => ( ( vEBT_vebt_member @ T @ X )
% 5.41/5.60 = ( member_nat @ X @ ( vEBT_set_vebt @ T ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % member_correct
% 5.41/5.60 thf(fact_108_length__list__update,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 5.41/5.60 ( ( size_s6755466524823107622T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) )
% 5.41/5.60 = ( size_s6755466524823107622T_VEBT @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_list_update
% 5.41/5.60 thf(fact_109_length__list__update,axiom,
% 5.41/5.60 ! [Xs: list_o,I: nat,X: $o] :
% 5.41/5.60 ( ( size_size_list_o @ ( list_update_o @ Xs @ I @ X ) )
% 5.41/5.60 = ( size_size_list_o @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_list_update
% 5.41/5.60 thf(fact_110_length__list__update,axiom,
% 5.41/5.60 ! [Xs: list_nat,I: nat,X: nat] :
% 5.41/5.60 ( ( size_size_list_nat @ ( list_update_nat @ Xs @ I @ X ) )
% 5.41/5.60 = ( size_size_list_nat @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_list_update
% 5.41/5.60 thf(fact_111_length__list__update,axiom,
% 5.41/5.60 ! [Xs: list_int,I: nat,X: int] :
% 5.41/5.60 ( ( size_size_list_int @ ( list_update_int @ Xs @ I @ X ) )
% 5.41/5.60 = ( size_size_list_int @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_list_update
% 5.41/5.60 thf(fact_112_semiring__norm_I78_J,axiom,
% 5.41/5.60 ! [M: num,N: num] :
% 5.41/5.60 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.60 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % semiring_norm(78)
% 5.41/5.60 thf(fact_113_semiring__norm_I75_J,axiom,
% 5.41/5.60 ! [M: num] :
% 5.41/5.60 ~ ( ord_less_num @ M @ one ) ).
% 5.41/5.60
% 5.41/5.60 % semiring_norm(75)
% 5.41/5.60 thf(fact_114__C6_C,axiom,
% 5.41/5.60 ( ( ord_less_eq_nat @ mi @ ma )
% 5.41/5.60 & ( ord_less_nat @ ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ deg ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % "6"
% 5.41/5.60 thf(fact_115_list__update__beyond,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,I: nat,X: vEBT_VEBT] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ I )
% 5.41/5.60 => ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 5.41/5.60 = Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_beyond
% 5.41/5.60 thf(fact_116_list__update__beyond,axiom,
% 5.41/5.60 ! [Xs: list_o,I: nat,X: $o] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( size_size_list_o @ Xs ) @ I )
% 5.41/5.60 => ( ( list_update_o @ Xs @ I @ X )
% 5.41/5.60 = Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_beyond
% 5.41/5.60 thf(fact_117_list__update__beyond,axiom,
% 5.41/5.60 ! [Xs: list_nat,I: nat,X: nat] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( size_size_list_nat @ Xs ) @ I )
% 5.41/5.60 => ( ( list_update_nat @ Xs @ I @ X )
% 5.41/5.60 = Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_beyond
% 5.41/5.60 thf(fact_118_list__update__beyond,axiom,
% 5.41/5.60 ! [Xs: list_int,I: nat,X: int] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( size_size_list_int @ Xs ) @ I )
% 5.41/5.60 => ( ( list_update_int @ Xs @ I @ X )
% 5.41/5.60 = Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_beyond
% 5.41/5.60 thf(fact_119_semiring__norm_I76_J,axiom,
% 5.41/5.60 ! [N: num] : ( ord_less_num @ one @ ( bit0 @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % semiring_norm(76)
% 5.41/5.60 thf(fact_120_nth__list__update__eq,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ I )
% 5.41/5.60 = X ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update_eq
% 5.41/5.60 thf(fact_121_nth__list__update__eq,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_o,X: $o] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ I )
% 5.41/5.60 = X ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update_eq
% 5.41/5.60 thf(fact_122_nth__list__update__eq,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_nat,X: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ I )
% 5.41/5.60 = X ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update_eq
% 5.41/5.60 thf(fact_123_nth__list__update__eq,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_int,X: int] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ I )
% 5.41/5.60 = X ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update_eq
% 5.41/5.60 thf(fact_124_set__swap,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_VEBT_VEBT,J: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( ( ord_less_nat @ J @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ ( nth_VEBT_VEBT @ Xs @ J ) ) @ J @ ( nth_VEBT_VEBT @ Xs @ I ) ) )
% 5.41/5.60 = ( set_VEBT_VEBT2 @ Xs ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_swap
% 5.41/5.60 thf(fact_125_set__swap,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_o,J: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( ( ord_less_nat @ J @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( ( set_o2 @ ( list_update_o @ ( list_update_o @ Xs @ I @ ( nth_o @ Xs @ J ) ) @ J @ ( nth_o @ Xs @ I ) ) )
% 5.41/5.60 = ( set_o2 @ Xs ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_swap
% 5.41/5.60 thf(fact_126_set__swap,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_nat,J: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( ( ord_less_nat @ J @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( ( set_nat2 @ ( list_update_nat @ ( list_update_nat @ Xs @ I @ ( nth_nat @ Xs @ J ) ) @ J @ ( nth_nat @ Xs @ I ) ) )
% 5.41/5.60 = ( set_nat2 @ Xs ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_swap
% 5.41/5.60 thf(fact_127_set__swap,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_int,J: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( ( ord_less_nat @ J @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( ( set_int2 @ ( list_update_int @ ( list_update_int @ Xs @ I @ ( nth_int @ Xs @ J ) ) @ J @ ( nth_int @ Xs @ I ) ) )
% 5.41/5.60 = ( set_int2 @ Xs ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_swap
% 5.41/5.60 thf(fact_128_Ex__list__of__length,axiom,
% 5.41/5.60 ! [N: nat] :
% 5.41/5.60 ? [Xs3: list_VEBT_VEBT] :
% 5.41/5.60 ( ( size_s6755466524823107622T_VEBT @ Xs3 )
% 5.41/5.60 = N ) ).
% 5.41/5.60
% 5.41/5.60 % Ex_list_of_length
% 5.41/5.60 thf(fact_129_Ex__list__of__length,axiom,
% 5.41/5.60 ! [N: nat] :
% 5.41/5.60 ? [Xs3: list_o] :
% 5.41/5.60 ( ( size_size_list_o @ Xs3 )
% 5.41/5.60 = N ) ).
% 5.41/5.60
% 5.41/5.60 % Ex_list_of_length
% 5.41/5.60 thf(fact_130_Ex__list__of__length,axiom,
% 5.41/5.60 ! [N: nat] :
% 5.41/5.60 ? [Xs3: list_nat] :
% 5.41/5.60 ( ( size_size_list_nat @ Xs3 )
% 5.41/5.60 = N ) ).
% 5.41/5.60
% 5.41/5.60 % Ex_list_of_length
% 5.41/5.60 thf(fact_131_Ex__list__of__length,axiom,
% 5.41/5.60 ! [N: nat] :
% 5.41/5.60 ? [Xs3: list_int] :
% 5.41/5.60 ( ( size_size_list_int @ Xs3 )
% 5.41/5.60 = N ) ).
% 5.41/5.60
% 5.41/5.60 % Ex_list_of_length
% 5.41/5.60 thf(fact_132_neq__if__length__neq,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.41/5.60 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.41/5.60 != ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.41/5.60 => ( Xs != Ys ) ) ).
% 5.41/5.60
% 5.41/5.60 % neq_if_length_neq
% 5.41/5.60 thf(fact_133_neq__if__length__neq,axiom,
% 5.41/5.60 ! [Xs: list_o,Ys: list_o] :
% 5.41/5.60 ( ( ( size_size_list_o @ Xs )
% 5.41/5.60 != ( size_size_list_o @ Ys ) )
% 5.41/5.60 => ( Xs != Ys ) ) ).
% 5.41/5.60
% 5.41/5.60 % neq_if_length_neq
% 5.41/5.60 thf(fact_134_neq__if__length__neq,axiom,
% 5.41/5.60 ! [Xs: list_nat,Ys: list_nat] :
% 5.41/5.60 ( ( ( size_size_list_nat @ Xs )
% 5.41/5.60 != ( size_size_list_nat @ Ys ) )
% 5.41/5.60 => ( Xs != Ys ) ) ).
% 5.41/5.60
% 5.41/5.60 % neq_if_length_neq
% 5.41/5.60 thf(fact_135_neq__if__length__neq,axiom,
% 5.41/5.60 ! [Xs: list_int,Ys: list_int] :
% 5.41/5.60 ( ( ( size_size_list_int @ Xs )
% 5.41/5.60 != ( size_size_list_int @ Ys ) )
% 5.41/5.60 => ( Xs != Ys ) ) ).
% 5.41/5.60
% 5.41/5.60 % neq_if_length_neq
% 5.41/5.60 thf(fact_136_is__num__normalize_I1_J,axiom,
% 5.41/5.60 ! [A: real,B: real,C: real] :
% 5.41/5.60 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.41/5.60 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % is_num_normalize(1)
% 5.41/5.60 thf(fact_137_is__num__normalize_I1_J,axiom,
% 5.41/5.60 ! [A: rat,B: rat,C: rat] :
% 5.41/5.60 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.41/5.60 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % is_num_normalize(1)
% 5.41/5.60 thf(fact_138_is__num__normalize_I1_J,axiom,
% 5.41/5.60 ! [A: int,B: int,C: int] :
% 5.41/5.60 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.60 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % is_num_normalize(1)
% 5.41/5.60 thf(fact_139_length__induct,axiom,
% 5.41/5.60 ! [P: list_VEBT_VEBT > $o,Xs: list_VEBT_VEBT] :
% 5.41/5.60 ( ! [Xs3: list_VEBT_VEBT] :
% 5.41/5.60 ( ! [Ys2: list_VEBT_VEBT] :
% 5.41/5.60 ( ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ Ys2 ) @ ( size_s6755466524823107622T_VEBT @ Xs3 ) )
% 5.41/5.60 => ( P @ Ys2 ) )
% 5.41/5.60 => ( P @ Xs3 ) )
% 5.41/5.60 => ( P @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_induct
% 5.41/5.60 thf(fact_140_length__induct,axiom,
% 5.41/5.60 ! [P: list_o > $o,Xs: list_o] :
% 5.41/5.60 ( ! [Xs3: list_o] :
% 5.41/5.60 ( ! [Ys2: list_o] :
% 5.41/5.60 ( ( ord_less_nat @ ( size_size_list_o @ Ys2 ) @ ( size_size_list_o @ Xs3 ) )
% 5.41/5.60 => ( P @ Ys2 ) )
% 5.41/5.60 => ( P @ Xs3 ) )
% 5.41/5.60 => ( P @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_induct
% 5.41/5.60 thf(fact_141_length__induct,axiom,
% 5.41/5.60 ! [P: list_nat > $o,Xs: list_nat] :
% 5.41/5.60 ( ! [Xs3: list_nat] :
% 5.41/5.60 ( ! [Ys2: list_nat] :
% 5.41/5.60 ( ( ord_less_nat @ ( size_size_list_nat @ Ys2 ) @ ( size_size_list_nat @ Xs3 ) )
% 5.41/5.60 => ( P @ Ys2 ) )
% 5.41/5.60 => ( P @ Xs3 ) )
% 5.41/5.60 => ( P @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_induct
% 5.41/5.60 thf(fact_142_length__induct,axiom,
% 5.41/5.60 ! [P: list_int > $o,Xs: list_int] :
% 5.41/5.60 ( ! [Xs3: list_int] :
% 5.41/5.60 ( ! [Ys2: list_int] :
% 5.41/5.60 ( ( ord_less_nat @ ( size_size_list_int @ Ys2 ) @ ( size_size_list_int @ Xs3 ) )
% 5.41/5.60 => ( P @ Ys2 ) )
% 5.41/5.60 => ( P @ Xs3 ) )
% 5.41/5.60 => ( P @ Xs ) ) ).
% 5.41/5.60
% 5.41/5.60 % length_induct
% 5.41/5.60 thf(fact_143_numeral__Bit0,axiom,
% 5.41/5.60 ! [N: num] :
% 5.41/5.60 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.41/5.60 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_Bit0
% 5.41/5.60 thf(fact_144_numeral__Bit0,axiom,
% 5.41/5.60 ! [N: num] :
% 5.41/5.60 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.41/5.60 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_Bit0
% 5.41/5.60 thf(fact_145_numeral__Bit0,axiom,
% 5.41/5.60 ! [N: num] :
% 5.41/5.60 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.41/5.60 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_Bit0
% 5.41/5.60 thf(fact_146_numeral__Bit0,axiom,
% 5.41/5.60 ! [N: num] :
% 5.41/5.60 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.41/5.60 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_Bit0
% 5.41/5.60 thf(fact_147_numeral__Bit0,axiom,
% 5.41/5.60 ! [N: num] :
% 5.41/5.60 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.41/5.60 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % numeral_Bit0
% 5.41/5.60 thf(fact_148_nth__equalityI,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.41/5.60 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.41/5.60 = ( size_s6755466524823107622T_VEBT @ Ys ) )
% 5.41/5.60 => ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( ( nth_VEBT_VEBT @ Xs @ I4 )
% 5.41/5.60 = ( nth_VEBT_VEBT @ Ys @ I4 ) ) )
% 5.41/5.60 => ( Xs = Ys ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_equalityI
% 5.41/5.60 thf(fact_149_nth__equalityI,axiom,
% 5.41/5.60 ! [Xs: list_o,Ys: list_o] :
% 5.41/5.60 ( ( ( size_size_list_o @ Xs )
% 5.41/5.60 = ( size_size_list_o @ Ys ) )
% 5.41/5.60 => ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( ( nth_o @ Xs @ I4 )
% 5.41/5.60 = ( nth_o @ Ys @ I4 ) ) )
% 5.41/5.60 => ( Xs = Ys ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_equalityI
% 5.41/5.60 thf(fact_150_nth__equalityI,axiom,
% 5.41/5.60 ! [Xs: list_nat,Ys: list_nat] :
% 5.41/5.60 ( ( ( size_size_list_nat @ Xs )
% 5.41/5.60 = ( size_size_list_nat @ Ys ) )
% 5.41/5.60 => ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( ( nth_nat @ Xs @ I4 )
% 5.41/5.60 = ( nth_nat @ Ys @ I4 ) ) )
% 5.41/5.60 => ( Xs = Ys ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_equalityI
% 5.41/5.60 thf(fact_151_nth__equalityI,axiom,
% 5.41/5.60 ! [Xs: list_int,Ys: list_int] :
% 5.41/5.60 ( ( ( size_size_list_int @ Xs )
% 5.41/5.60 = ( size_size_list_int @ Ys ) )
% 5.41/5.60 => ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( ( nth_int @ Xs @ I4 )
% 5.41/5.60 = ( nth_int @ Ys @ I4 ) ) )
% 5.41/5.60 => ( Xs = Ys ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_equalityI
% 5.41/5.60 thf(fact_152_Skolem__list__nth,axiom,
% 5.41/5.60 ! [K: nat,P: nat > vEBT_VEBT > $o] :
% 5.41/5.60 ( ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ? [X2: vEBT_VEBT] : ( P @ I5 @ X2 ) ) )
% 5.41/5.60 = ( ? [Xs2: list_VEBT_VEBT] :
% 5.41/5.60 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.41/5.60 = K )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ( P @ I5 @ ( nth_VEBT_VEBT @ Xs2 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Skolem_list_nth
% 5.41/5.60 thf(fact_153_Skolem__list__nth,axiom,
% 5.41/5.60 ! [K: nat,P: nat > $o > $o] :
% 5.41/5.60 ( ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ? [X2: $o] : ( P @ I5 @ X2 ) ) )
% 5.41/5.60 = ( ? [Xs2: list_o] :
% 5.41/5.60 ( ( ( size_size_list_o @ Xs2 )
% 5.41/5.60 = K )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ( P @ I5 @ ( nth_o @ Xs2 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Skolem_list_nth
% 5.41/5.60 thf(fact_154_Skolem__list__nth,axiom,
% 5.41/5.60 ! [K: nat,P: nat > nat > $o] :
% 5.41/5.60 ( ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ? [X2: nat] : ( P @ I5 @ X2 ) ) )
% 5.41/5.60 = ( ? [Xs2: list_nat] :
% 5.41/5.60 ( ( ( size_size_list_nat @ Xs2 )
% 5.41/5.60 = K )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ( P @ I5 @ ( nth_nat @ Xs2 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Skolem_list_nth
% 5.41/5.60 thf(fact_155_Skolem__list__nth,axiom,
% 5.41/5.60 ! [K: nat,P: nat > int > $o] :
% 5.41/5.60 ( ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ? [X2: int] : ( P @ I5 @ X2 ) ) )
% 5.41/5.60 = ( ? [Xs2: list_int] :
% 5.41/5.60 ( ( ( size_size_list_int @ Xs2 )
% 5.41/5.60 = K )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ K )
% 5.41/5.60 => ( P @ I5 @ ( nth_int @ Xs2 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % Skolem_list_nth
% 5.41/5.60 thf(fact_156_list__eq__iff__nth__eq,axiom,
% 5.41/5.60 ( ( ^ [Y4: list_VEBT_VEBT,Z2: list_VEBT_VEBT] : ( Y4 = Z2 ) )
% 5.41/5.60 = ( ^ [Xs2: list_VEBT_VEBT,Ys3: list_VEBT_VEBT] :
% 5.41/5.60 ( ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.41/5.60 = ( size_s6755466524823107622T_VEBT @ Ys3 ) )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs2 ) )
% 5.41/5.60 => ( ( nth_VEBT_VEBT @ Xs2 @ I5 )
% 5.41/5.60 = ( nth_VEBT_VEBT @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_eq_iff_nth_eq
% 5.41/5.60 thf(fact_157_list__eq__iff__nth__eq,axiom,
% 5.41/5.60 ( ( ^ [Y4: list_o,Z2: list_o] : ( Y4 = Z2 ) )
% 5.41/5.60 = ( ^ [Xs2: list_o,Ys3: list_o] :
% 5.41/5.60 ( ( ( size_size_list_o @ Xs2 )
% 5.41/5.60 = ( size_size_list_o @ Ys3 ) )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs2 ) )
% 5.41/5.60 => ( ( nth_o @ Xs2 @ I5 )
% 5.41/5.60 = ( nth_o @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_eq_iff_nth_eq
% 5.41/5.60 thf(fact_158_list__eq__iff__nth__eq,axiom,
% 5.41/5.60 ( ( ^ [Y4: list_nat,Z2: list_nat] : ( Y4 = Z2 ) )
% 5.41/5.60 = ( ^ [Xs2: list_nat,Ys3: list_nat] :
% 5.41/5.60 ( ( ( size_size_list_nat @ Xs2 )
% 5.41/5.60 = ( size_size_list_nat @ Ys3 ) )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs2 ) )
% 5.41/5.60 => ( ( nth_nat @ Xs2 @ I5 )
% 5.41/5.60 = ( nth_nat @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_eq_iff_nth_eq
% 5.41/5.60 thf(fact_159_list__eq__iff__nth__eq,axiom,
% 5.41/5.60 ( ( ^ [Y4: list_int,Z2: list_int] : ( Y4 = Z2 ) )
% 5.41/5.60 = ( ^ [Xs2: list_int,Ys3: list_int] :
% 5.41/5.60 ( ( ( size_size_list_int @ Xs2 )
% 5.41/5.60 = ( size_size_list_int @ Ys3 ) )
% 5.41/5.60 & ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs2 ) )
% 5.41/5.60 => ( ( nth_int @ Xs2 @ I5 )
% 5.41/5.60 = ( nth_int @ Ys3 @ I5 ) ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_eq_iff_nth_eq
% 5.41/5.60 thf(fact_160_power2__nat__le__imp__le,axiom,
% 5.41/5.60 ! [M: nat,N: nat] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ N )
% 5.41/5.60 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % power2_nat_le_imp_le
% 5.41/5.60 thf(fact_161_power2__nat__le__eq__le,axiom,
% 5.41/5.60 ! [M: nat,N: nat] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( power_power_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.60 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.60
% 5.41/5.60 % power2_nat_le_eq_le
% 5.41/5.60 thf(fact_162_self__le__ge2__pow,axiom,
% 5.41/5.60 ! [K: nat,M: nat] :
% 5.41/5.60 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.60 => ( ord_less_eq_nat @ M @ ( power_power_nat @ K @ M ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % self_le_ge2_pow
% 5.41/5.60 thf(fact_163_all__set__conv__all__nth,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.41/5.60 ( ( ! [X3: vEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.60 => ( P @ X3 ) ) )
% 5.41/5.60 = ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_VEBT_VEBT @ Xs @ I5 ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_set_conv_all_nth
% 5.41/5.60 thf(fact_164_all__set__conv__all__nth,axiom,
% 5.41/5.60 ! [Xs: list_o,P: $o > $o] :
% 5.41/5.60 ( ( ! [X3: $o] :
% 5.41/5.60 ( ( member_o @ X3 @ ( set_o2 @ Xs ) )
% 5.41/5.60 => ( P @ X3 ) ) )
% 5.41/5.60 = ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_o @ Xs @ I5 ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_set_conv_all_nth
% 5.41/5.60 thf(fact_165_all__set__conv__all__nth,axiom,
% 5.41/5.60 ! [Xs: list_nat,P: nat > $o] :
% 5.41/5.60 ( ( ! [X3: nat] :
% 5.41/5.60 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.41/5.60 => ( P @ X3 ) ) )
% 5.41/5.60 = ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_nat @ Xs @ I5 ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_set_conv_all_nth
% 5.41/5.60 thf(fact_166_all__set__conv__all__nth,axiom,
% 5.41/5.60 ! [Xs: list_int,P: int > $o] :
% 5.41/5.60 ( ( ! [X3: int] :
% 5.41/5.60 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.41/5.60 => ( P @ X3 ) ) )
% 5.41/5.60 = ( ! [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_int @ Xs @ I5 ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_set_conv_all_nth
% 5.41/5.60 thf(fact_167_all__nth__imp__all__set,axiom,
% 5.41/5.60 ! [Xs: list_complex,P: complex > $o,X: complex] :
% 5.41/5.60 ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_complex @ Xs @ I4 ) ) )
% 5.41/5.60 => ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.41/5.60 => ( P @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_nth_imp_all_set
% 5.41/5.60 thf(fact_168_all__nth__imp__all__set,axiom,
% 5.41/5.60 ! [Xs: list_real,P: real > $o,X: real] :
% 5.41/5.60 ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_size_list_real @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_real @ Xs @ I4 ) ) )
% 5.41/5.60 => ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.41/5.60 => ( P @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_nth_imp_all_set
% 5.41/5.60 thf(fact_169_all__nth__imp__all__set,axiom,
% 5.41/5.60 ! [Xs: list_set_nat,P: set_nat > $o,X: set_nat] :
% 5.41/5.60 ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_set_nat @ Xs @ I4 ) ) )
% 5.41/5.60 => ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.41/5.60 => ( P @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_nth_imp_all_set
% 5.41/5.60 thf(fact_170_all__nth__imp__all__set,axiom,
% 5.41/5.60 ! [Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.41/5.60 ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_VEBT_VEBT @ Xs @ I4 ) ) )
% 5.41/5.60 => ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.60 => ( P @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_nth_imp_all_set
% 5.41/5.60 thf(fact_171_all__nth__imp__all__set,axiom,
% 5.41/5.60 ! [Xs: list_o,P: $o > $o,X: $o] :
% 5.41/5.60 ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_o @ Xs @ I4 ) ) )
% 5.41/5.60 => ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.41/5.60 => ( P @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_nth_imp_all_set
% 5.41/5.60 thf(fact_172_all__nth__imp__all__set,axiom,
% 5.41/5.60 ! [Xs: list_nat,P: nat > $o,X: nat] :
% 5.41/5.60 ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_nat @ Xs @ I4 ) ) )
% 5.41/5.60 => ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.41/5.60 => ( P @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_nth_imp_all_set
% 5.41/5.60 thf(fact_173_all__nth__imp__all__set,axiom,
% 5.41/5.60 ! [Xs: list_int,P: int > $o,X: int] :
% 5.41/5.60 ( ! [I4: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I4 @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( P @ ( nth_int @ Xs @ I4 ) ) )
% 5.41/5.60 => ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.41/5.60 => ( P @ X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % all_nth_imp_all_set
% 5.41/5.60 thf(fact_174_in__set__conv__nth,axiom,
% 5.41/5.60 ! [X: complex,Xs: list_complex] :
% 5.41/5.60 ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.41/5.60 = ( ? [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.41/5.60 & ( ( nth_complex @ Xs @ I5 )
% 5.41/5.60 = X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_set_conv_nth
% 5.41/5.60 thf(fact_175_in__set__conv__nth,axiom,
% 5.41/5.60 ! [X: real,Xs: list_real] :
% 5.41/5.60 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.41/5.60 = ( ? [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_real @ Xs ) )
% 5.41/5.60 & ( ( nth_real @ Xs @ I5 )
% 5.41/5.60 = X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_set_conv_nth
% 5.41/5.60 thf(fact_176_in__set__conv__nth,axiom,
% 5.41/5.60 ! [X: set_nat,Xs: list_set_nat] :
% 5.41/5.60 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.41/5.60 = ( ? [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.41/5.60 & ( ( nth_set_nat @ Xs @ I5 )
% 5.41/5.60 = X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_set_conv_nth
% 5.41/5.60 thf(fact_177_in__set__conv__nth,axiom,
% 5.41/5.60 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.60 = ( ? [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 & ( ( nth_VEBT_VEBT @ Xs @ I5 )
% 5.41/5.60 = X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_set_conv_nth
% 5.41/5.60 thf(fact_178_in__set__conv__nth,axiom,
% 5.41/5.60 ! [X: $o,Xs: list_o] :
% 5.41/5.60 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.41/5.60 = ( ? [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 & ( ( nth_o @ Xs @ I5 )
% 5.41/5.60 = X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_set_conv_nth
% 5.41/5.60 thf(fact_179_in__set__conv__nth,axiom,
% 5.41/5.60 ! [X: nat,Xs: list_nat] :
% 5.41/5.60 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.41/5.60 = ( ? [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 & ( ( nth_nat @ Xs @ I5 )
% 5.41/5.60 = X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_set_conv_nth
% 5.41/5.60 thf(fact_180_in__set__conv__nth,axiom,
% 5.41/5.60 ! [X: int,Xs: list_int] :
% 5.41/5.60 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.41/5.60 = ( ? [I5: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I5 @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 & ( ( nth_int @ Xs @ I5 )
% 5.41/5.60 = X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % in_set_conv_nth
% 5.41/5.60 thf(fact_181_list__ball__nth,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_VEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( ! [X6: vEBT_VEBT] :
% 5.41/5.60 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( P @ ( nth_VEBT_VEBT @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_ball_nth
% 5.41/5.60 thf(fact_182_list__ball__nth,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_o,P: $o > $o] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( ! [X6: $o] :
% 5.41/5.60 ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( P @ ( nth_o @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_ball_nth
% 5.41/5.60 thf(fact_183_list__ball__nth,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_nat,P: nat > $o] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( ! [X6: nat] :
% 5.41/5.60 ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( P @ ( nth_nat @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_ball_nth
% 5.41/5.60 thf(fact_184_list__ball__nth,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_int,P: int > $o] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( ! [X6: int] :
% 5.41/5.60 ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 5.41/5.60 => ( P @ X6 ) )
% 5.41/5.60 => ( P @ ( nth_int @ Xs @ N ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_ball_nth
% 5.41/5.60 thf(fact_185_nth__mem,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_complex] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.41/5.60 => ( member_complex @ ( nth_complex @ Xs @ N ) @ ( set_complex2 @ Xs ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_mem
% 5.41/5.60 thf(fact_186_nth__mem,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_real] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.41/5.60 => ( member_real @ ( nth_real @ Xs @ N ) @ ( set_real2 @ Xs ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_mem
% 5.41/5.60 thf(fact_187_nth__mem,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_set_nat] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.41/5.60 => ( member_set_nat @ ( nth_set_nat @ Xs @ N ) @ ( set_set_nat2 @ Xs ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_mem
% 5.41/5.60 thf(fact_188_nth__mem,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_VEBT_VEBT] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( member_VEBT_VEBT @ ( nth_VEBT_VEBT @ Xs @ N ) @ ( set_VEBT_VEBT2 @ Xs ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_mem
% 5.41/5.60 thf(fact_189_nth__mem,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_o] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( member_o @ ( nth_o @ Xs @ N ) @ ( set_o2 @ Xs ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_mem
% 5.41/5.60 thf(fact_190_nth__mem,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_nat] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( member_nat @ ( nth_nat @ Xs @ N ) @ ( set_nat2 @ Xs ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_mem
% 5.41/5.60 thf(fact_191_nth__mem,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_int] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( member_int @ ( nth_int @ Xs @ N ) @ ( set_int2 @ Xs ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_mem
% 5.41/5.60 thf(fact_192_set__update__memI,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_complex,X: complex] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_s3451745648224563538omplex @ Xs ) )
% 5.41/5.60 => ( member_complex @ X @ ( set_complex2 @ ( list_update_complex @ Xs @ N @ X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_update_memI
% 5.41/5.60 thf(fact_193_set__update__memI,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_real,X: real] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_real @ Xs ) )
% 5.41/5.60 => ( member_real @ X @ ( set_real2 @ ( list_update_real @ Xs @ N @ X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_update_memI
% 5.41/5.60 thf(fact_194_set__update__memI,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_set_nat,X: set_nat] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_s3254054031482475050et_nat @ Xs ) )
% 5.41/5.60 => ( member_set_nat @ X @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ N @ X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_update_memI
% 5.41/5.60 thf(fact_195_set__update__memI,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ N @ X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_update_memI
% 5.41/5.60 thf(fact_196_set__update__memI,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_o,X: $o] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( member_o @ X @ ( set_o2 @ ( list_update_o @ Xs @ N @ X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_update_memI
% 5.41/5.60 thf(fact_197_set__update__memI,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_nat,X: nat] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( member_nat @ X @ ( set_nat2 @ ( list_update_nat @ Xs @ N @ X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_update_memI
% 5.41/5.60 thf(fact_198_set__update__memI,axiom,
% 5.41/5.60 ! [N: nat,Xs: list_int,X: int] :
% 5.41/5.60 ( ( ord_less_nat @ N @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( member_int @ X @ ( set_int2 @ ( list_update_int @ Xs @ N @ X ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % set_update_memI
% 5.41/5.60 thf(fact_199_nth__list__update,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_VEBT_VEBT,J: nat,X: vEBT_VEBT] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( ( ( I = J )
% 5.41/5.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 5.41/5.60 = X ) )
% 5.41/5.60 & ( ( I != J )
% 5.41/5.60 => ( ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) @ J )
% 5.41/5.60 = ( nth_VEBT_VEBT @ Xs @ J ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update
% 5.41/5.60 thf(fact_200_nth__list__update,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_o,X: $o,J: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( ( nth_o @ ( list_update_o @ Xs @ I @ X ) @ J )
% 5.41/5.60 = ( ( ( I = J )
% 5.41/5.60 => X )
% 5.41/5.60 & ( ( I != J )
% 5.41/5.60 => ( nth_o @ Xs @ J ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update
% 5.41/5.60 thf(fact_201_nth__list__update,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_nat,J: nat,X: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.41/5.60 => ( ( ( I = J )
% 5.41/5.60 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 5.41/5.60 = X ) )
% 5.41/5.60 & ( ( I != J )
% 5.41/5.60 => ( ( nth_nat @ ( list_update_nat @ Xs @ I @ X ) @ J )
% 5.41/5.60 = ( nth_nat @ Xs @ J ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update
% 5.41/5.60 thf(fact_202_nth__list__update,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_int,J: nat,X: int] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.41/5.60 => ( ( ( I = J )
% 5.41/5.60 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 5.41/5.60 = X ) )
% 5.41/5.60 & ( ( I != J )
% 5.41/5.60 => ( ( nth_int @ ( list_update_int @ Xs @ I @ X ) @ J )
% 5.41/5.60 = ( nth_int @ Xs @ J ) ) ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % nth_list_update
% 5.41/5.60 thf(fact_203_list__update__same__conv,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_s6755466524823107622T_VEBT @ Xs ) )
% 5.41/5.60 => ( ( ( list_u1324408373059187874T_VEBT @ Xs @ I @ X )
% 5.41/5.60 = Xs )
% 5.41/5.60 = ( ( nth_VEBT_VEBT @ Xs @ I )
% 5.41/5.60 = X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_same_conv
% 5.41/5.60 thf(fact_204_list__update__same__conv,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_o,X: $o] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_o @ Xs ) )
% 5.41/5.60 => ( ( ( list_update_o @ Xs @ I @ X )
% 5.41/5.60 = Xs )
% 5.41/5.60 = ( ( nth_o @ Xs @ I )
% 5.41/5.60 = X ) ) ) ).
% 5.41/5.60
% 5.41/5.60 % list_update_same_conv
% 5.41/5.60 thf(fact_205_list__update__same__conv,axiom,
% 5.41/5.60 ! [I: nat,Xs: list_nat,X: nat] :
% 5.41/5.60 ( ( ord_less_nat @ I @ ( size_size_list_nat @ Xs ) )
% 5.41/5.61 => ( ( ( list_update_nat @ Xs @ I @ X )
% 5.41/5.61 = Xs )
% 5.41/5.61 = ( ( nth_nat @ Xs @ I )
% 5.41/5.61 = X ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % list_update_same_conv
% 5.41/5.61 thf(fact_206_list__update__same__conv,axiom,
% 5.41/5.61 ! [I: nat,Xs: list_int,X: int] :
% 5.41/5.61 ( ( ord_less_nat @ I @ ( size_size_list_int @ Xs ) )
% 5.41/5.61 => ( ( ( list_update_int @ Xs @ I @ X )
% 5.41/5.61 = Xs )
% 5.41/5.61 = ( ( nth_int @ Xs @ I )
% 5.41/5.61 = X ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % list_update_same_conv
% 5.41/5.61 thf(fact_207_set__n__deg__not__0,axiom,
% 5.41/5.61 ! [TreeList2: list_VEBT_VEBT,N: nat,M: nat] :
% 5.41/5.61 ( ! [X6: vEBT_VEBT] :
% 5.41/5.61 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.61 => ( vEBT_invar_vebt @ X6 @ N ) )
% 5.41/5.61 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.41/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.61 => ( ord_less_eq_nat @ one_one_nat @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % set_n_deg_not_0
% 5.41/5.61 thf(fact_208_bit__concat__def,axiom,
% 5.41/5.61 ( vEBT_VEBT_bit_concat
% 5.41/5.61 = ( ^ [H: nat,L: nat,D2: nat] : ( plus_plus_nat @ ( times_times_nat @ H @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ D2 ) ) @ L ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % bit_concat_def
% 5.41/5.61 thf(fact_209_low__inv,axiom,
% 5.41/5.61 ! [X: nat,N: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.61 => ( ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.41/5.61 = X ) ) ).
% 5.41/5.61
% 5.41/5.61 % low_inv
% 5.41/5.61 thf(fact_210_high__inv,axiom,
% 5.41/5.61 ! [X: nat,N: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.61 => ( ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ X ) @ N )
% 5.41/5.61 = Y ) ) ).
% 5.41/5.61
% 5.41/5.61 % high_inv
% 5.41/5.61 thf(fact_211__C9_C,axiom,
% 5.41/5.61 ( ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = na ) ).
% 5.41/5.61
% 5.41/5.61 % "9"
% 5.41/5.61 thf(fact_212_nat__add__left__cancel__le,axiom,
% 5.41/5.61 ! [K: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.41/5.61 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_add_left_cancel_le
% 5.41/5.61 thf(fact_213_nat__add__left__cancel__less,axiom,
% 5.41/5.61 ! [K: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.41/5.61 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_add_left_cancel_less
% 5.41/5.61 thf(fact_214_enat__ord__number_I2_J,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( ord_le72135733267957522d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.41/5.61 = ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % enat_ord_number(2)
% 5.41/5.61 thf(fact_215_add__less__cancel__right,axiom,
% 5.41/5.61 ! [A: real,C: real,B: real] :
% 5.41/5.61 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.41/5.61 = ( ord_less_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_right
% 5.41/5.61 thf(fact_216_add__less__cancel__right,axiom,
% 5.41/5.61 ! [A: rat,C: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.61 = ( ord_less_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_right
% 5.41/5.61 thf(fact_217_add__less__cancel__right,axiom,
% 5.41/5.61 ! [A: nat,C: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.61 = ( ord_less_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_right
% 5.41/5.61 thf(fact_218_add__less__cancel__right,axiom,
% 5.41/5.61 ! [A: int,C: int,B: int] :
% 5.41/5.61 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.41/5.61 = ( ord_less_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_right
% 5.41/5.61 thf(fact_219_add__less__cancel__left,axiom,
% 5.41/5.61 ! [C: real,A: real,B: real] :
% 5.41/5.61 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.41/5.61 = ( ord_less_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_left
% 5.41/5.61 thf(fact_220_add__less__cancel__left,axiom,
% 5.41/5.61 ! [C: rat,A: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.41/5.61 = ( ord_less_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_left
% 5.41/5.61 thf(fact_221_add__less__cancel__left,axiom,
% 5.41/5.61 ! [C: nat,A: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.41/5.61 = ( ord_less_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_left
% 5.41/5.61 thf(fact_222_add__less__cancel__left,axiom,
% 5.41/5.61 ! [C: int,A: int,B: int] :
% 5.41/5.61 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.41/5.61 = ( ord_less_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_cancel_left
% 5.41/5.61 thf(fact_223_add__le__cancel__right,axiom,
% 5.41/5.61 ! [A: real,C: real,B: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.41/5.61 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_right
% 5.41/5.61 thf(fact_224_add__le__cancel__right,axiom,
% 5.41/5.61 ! [A: rat,C: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.61 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_right
% 5.41/5.61 thf(fact_225_add__le__cancel__right,axiom,
% 5.41/5.61 ! [A: nat,C: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.61 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_right
% 5.41/5.61 thf(fact_226_add__le__cancel__right,axiom,
% 5.41/5.61 ! [A: int,C: int,B: int] :
% 5.41/5.61 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.41/5.61 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_right
% 5.41/5.61 thf(fact_227_add__le__cancel__left,axiom,
% 5.41/5.61 ! [C: real,A: real,B: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.41/5.61 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_left
% 5.41/5.61 thf(fact_228_add__le__cancel__left,axiom,
% 5.41/5.61 ! [C: rat,A: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.41/5.61 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_left
% 5.41/5.61 thf(fact_229_add__le__cancel__left,axiom,
% 5.41/5.61 ! [C: nat,A: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.41/5.61 = ( ord_less_eq_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_left
% 5.41/5.61 thf(fact_230_add__le__cancel__left,axiom,
% 5.41/5.61 ! [C: int,A: int,B: int] :
% 5.41/5.61 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.41/5.61 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_cancel_left
% 5.41/5.61 thf(fact_231__C11_C,axiom,
% 5.41/5.61 ord_less_eq_nat @ one_one_nat @ na ).
% 5.41/5.61
% 5.41/5.61 % "11"
% 5.41/5.61 thf(fact_232_add__left__cancel,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( ( plus_plus_real @ A @ B )
% 5.41/5.61 = ( plus_plus_real @ A @ C ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_cancel
% 5.41/5.61 thf(fact_233_add__left__cancel,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( ( plus_plus_rat @ A @ B )
% 5.41/5.61 = ( plus_plus_rat @ A @ C ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_cancel
% 5.41/5.61 thf(fact_234_add__left__cancel,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( ( plus_plus_nat @ A @ B )
% 5.41/5.61 = ( plus_plus_nat @ A @ C ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_cancel
% 5.41/5.61 thf(fact_235_add__left__cancel,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( ( plus_plus_int @ A @ B )
% 5.41/5.61 = ( plus_plus_int @ A @ C ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_cancel
% 5.41/5.61 thf(fact_236_add__right__cancel,axiom,
% 5.41/5.61 ! [B: real,A: real,C: real] :
% 5.41/5.61 ( ( ( plus_plus_real @ B @ A )
% 5.41/5.61 = ( plus_plus_real @ C @ A ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_cancel
% 5.41/5.61 thf(fact_237_add__right__cancel,axiom,
% 5.41/5.61 ! [B: rat,A: rat,C: rat] :
% 5.41/5.61 ( ( ( plus_plus_rat @ B @ A )
% 5.41/5.61 = ( plus_plus_rat @ C @ A ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_cancel
% 5.41/5.61 thf(fact_238_add__right__cancel,axiom,
% 5.41/5.61 ! [B: nat,A: nat,C: nat] :
% 5.41/5.61 ( ( ( plus_plus_nat @ B @ A )
% 5.41/5.61 = ( plus_plus_nat @ C @ A ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_cancel
% 5.41/5.61 thf(fact_239_add__right__cancel,axiom,
% 5.41/5.61 ! [B: int,A: int,C: int] :
% 5.41/5.61 ( ( ( plus_plus_int @ B @ A )
% 5.41/5.61 = ( plus_plus_int @ C @ A ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_cancel
% 5.41/5.61 thf(fact_240_pow__sum,axiom,
% 5.41/5.61 ! [A: nat,B: nat] :
% 5.41/5.61 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.61 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % pow_sum
% 5.41/5.61 thf(fact_241_high__def,axiom,
% 5.41/5.61 ( vEBT_VEBT_high
% 5.41/5.61 = ( ^ [X3: nat,N2: nat] : ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % high_def
% 5.41/5.61 thf(fact_242_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.61 ! [V: num,W: num,Z: complex] :
% 5.41/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Z ) )
% 5.41/5.61 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_left_semiring_numeral
% 5.41/5.61 thf(fact_243_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.61 ! [V: num,W: num,Z: real] :
% 5.41/5.61 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Z ) )
% 5.41/5.61 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_left_semiring_numeral
% 5.41/5.61 thf(fact_244_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.61 ! [V: num,W: num,Z: rat] :
% 5.41/5.61 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Z ) )
% 5.41/5.61 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_left_semiring_numeral
% 5.41/5.61 thf(fact_245_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.61 ! [V: num,W: num,Z: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( times_times_nat @ ( numeral_numeral_nat @ W ) @ Z ) )
% 5.41/5.61 = ( times_times_nat @ ( numeral_numeral_nat @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_left_semiring_numeral
% 5.41/5.61 thf(fact_246_mult__numeral__left__semiring__numeral,axiom,
% 5.41/5.61 ! [V: num,W: num,Z: int] :
% 5.41/5.61 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Z ) )
% 5.41/5.61 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_left_semiring_numeral
% 5.41/5.61 thf(fact_247_numeral__times__numeral,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.61 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_times_numeral
% 5.41/5.61 thf(fact_248_numeral__times__numeral,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.61 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_times_numeral
% 5.41/5.61 thf(fact_249_numeral__times__numeral,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.61 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_times_numeral
% 5.41/5.61 thf(fact_250_numeral__times__numeral,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.61 = ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_times_numeral
% 5.41/5.61 thf(fact_251_numeral__times__numeral,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.61 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_times_numeral
% 5.41/5.61 thf(fact_252_mult_Oright__neutral,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( times_times_complex @ A @ one_one_complex )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.right_neutral
% 5.41/5.61 thf(fact_253_mult_Oright__neutral,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( times_times_real @ A @ one_one_real )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.right_neutral
% 5.41/5.61 thf(fact_254_mult_Oright__neutral,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( times_times_rat @ A @ one_one_rat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.right_neutral
% 5.41/5.61 thf(fact_255_mult_Oright__neutral,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( times_times_nat @ A @ one_one_nat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.right_neutral
% 5.41/5.61 thf(fact_256_mult_Oright__neutral,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( times_times_int @ A @ one_one_int )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.right_neutral
% 5.41/5.61 thf(fact_257_mult__1,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( times_times_complex @ one_one_complex @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_1
% 5.41/5.61 thf(fact_258_mult__1,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( times_times_real @ one_one_real @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_1
% 5.41/5.61 thf(fact_259_mult__1,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( times_times_rat @ one_one_rat @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_1
% 5.41/5.61 thf(fact_260_mult__1,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( times_times_nat @ one_one_nat @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_1
% 5.41/5.61 thf(fact_261_mult__1,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( times_times_int @ one_one_int @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_1
% 5.41/5.61 thf(fact_262_power__one,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ( ( power_power_rat @ one_one_rat @ N )
% 5.41/5.61 = one_one_rat ) ).
% 5.41/5.61
% 5.41/5.61 % power_one
% 5.41/5.61 thf(fact_263_power__one,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ( ( power_power_nat @ one_one_nat @ N )
% 5.41/5.61 = one_one_nat ) ).
% 5.41/5.61
% 5.41/5.61 % power_one
% 5.41/5.61 thf(fact_264_power__one,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ( ( power_power_real @ one_one_real @ N )
% 5.41/5.61 = one_one_real ) ).
% 5.41/5.61
% 5.41/5.61 % power_one
% 5.41/5.61 thf(fact_265_power__one,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ( ( power_power_int @ one_one_int @ N )
% 5.41/5.61 = one_one_int ) ).
% 5.41/5.61
% 5.41/5.61 % power_one
% 5.41/5.61 thf(fact_266_power__one,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ( ( power_power_complex @ one_one_complex @ N )
% 5.41/5.61 = one_one_complex ) ).
% 5.41/5.61
% 5.41/5.61 % power_one
% 5.41/5.61 thf(fact_267_power__one__right,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( power_power_nat @ A @ one_one_nat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % power_one_right
% 5.41/5.61 thf(fact_268_power__one__right,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( power_power_real @ A @ one_one_nat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % power_one_right
% 5.41/5.61 thf(fact_269_power__one__right,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( power_power_int @ A @ one_one_nat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % power_one_right
% 5.41/5.61 thf(fact_270_power__one__right,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( power_power_complex @ A @ one_one_nat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % power_one_right
% 5.41/5.61 thf(fact_271_nat__1__eq__mult__iff,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( one_one_nat
% 5.41/5.61 = ( times_times_nat @ M @ N ) )
% 5.41/5.61 = ( ( M = one_one_nat )
% 5.41/5.61 & ( N = one_one_nat ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_1_eq_mult_iff
% 5.41/5.61 thf(fact_272_nat__mult__eq__1__iff,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( ( times_times_nat @ M @ N )
% 5.41/5.61 = one_one_nat )
% 5.41/5.61 = ( ( M = one_one_nat )
% 5.41/5.61 & ( N = one_one_nat ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_mult_eq_1_iff
% 5.41/5.61 thf(fact_273_semiring__norm_I6_J,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.61 = ( bit0 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % semiring_norm(6)
% 5.41/5.61 thf(fact_274_semiring__norm_I71_J,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.61 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % semiring_norm(71)
% 5.41/5.61 thf(fact_275_semiring__norm_I68_J,axiom,
% 5.41/5.61 ! [N: num] : ( ord_less_eq_num @ one @ N ) ).
% 5.41/5.61
% 5.41/5.61 % semiring_norm(68)
% 5.41/5.61 thf(fact_276_distrib__right__numeral,axiom,
% 5.41/5.61 ! [A: complex,B: complex,V: num] :
% 5.41/5.61 ( ( times_times_complex @ ( plus_plus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.41/5.61 = ( plus_plus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_right_numeral
% 5.41/5.61 thf(fact_277_distrib__right__numeral,axiom,
% 5.41/5.61 ! [A: real,B: real,V: num] :
% 5.41/5.61 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.61 = ( plus_plus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_right_numeral
% 5.41/5.61 thf(fact_278_distrib__right__numeral,axiom,
% 5.41/5.61 ! [A: rat,B: rat,V: num] :
% 5.41/5.61 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.61 = ( plus_plus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_right_numeral
% 5.41/5.61 thf(fact_279_distrib__right__numeral,axiom,
% 5.41/5.61 ! [A: nat,B: nat,V: num] :
% 5.41/5.61 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.61 = ( plus_plus_nat @ ( times_times_nat @ A @ ( numeral_numeral_nat @ V ) ) @ ( times_times_nat @ B @ ( numeral_numeral_nat @ V ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_right_numeral
% 5.41/5.61 thf(fact_280_distrib__right__numeral,axiom,
% 5.41/5.61 ! [A: int,B: int,V: num] :
% 5.41/5.61 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.61 = ( plus_plus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_right_numeral
% 5.41/5.61 thf(fact_281_distrib__left__numeral,axiom,
% 5.41/5.61 ! [V: num,B: complex,C: complex] :
% 5.41/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( plus_plus_complex @ B @ C ) )
% 5.41/5.61 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_left_numeral
% 5.41/5.61 thf(fact_282_distrib__left__numeral,axiom,
% 5.41/5.61 ! [V: num,B: real,C: real] :
% 5.41/5.61 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( plus_plus_real @ B @ C ) )
% 5.41/5.61 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_left_numeral
% 5.41/5.61 thf(fact_283_distrib__left__numeral,axiom,
% 5.41/5.61 ! [V: num,B: rat,C: rat] :
% 5.41/5.61 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.61 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_left_numeral
% 5.41/5.61 thf(fact_284_distrib__left__numeral,axiom,
% 5.41/5.61 ! [V: num,B: nat,C: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ V ) @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ B ) @ ( times_times_nat @ ( numeral_numeral_nat @ V ) @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_left_numeral
% 5.41/5.61 thf(fact_285_distrib__left__numeral,axiom,
% 5.41/5.61 ! [V: num,B: int,C: int] :
% 5.41/5.61 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( plus_plus_int @ B @ C ) )
% 5.41/5.61 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % distrib_left_numeral
% 5.41/5.61 thf(fact_286_numeral__eq__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ( numera6690914467698888265omplex @ N )
% 5.41/5.61 = one_one_complex )
% 5.41/5.61 = ( N = one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_eq_one_iff
% 5.41/5.61 thf(fact_287_numeral__eq__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ( numeral_numeral_real @ N )
% 5.41/5.61 = one_one_real )
% 5.41/5.61 = ( N = one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_eq_one_iff
% 5.41/5.61 thf(fact_288_numeral__eq__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ( numeral_numeral_rat @ N )
% 5.41/5.61 = one_one_rat )
% 5.41/5.61 = ( N = one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_eq_one_iff
% 5.41/5.61 thf(fact_289_numeral__eq__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ( numeral_numeral_nat @ N )
% 5.41/5.61 = one_one_nat )
% 5.41/5.61 = ( N = one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_eq_one_iff
% 5.41/5.61 thf(fact_290_numeral__eq__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ( numeral_numeral_int @ N )
% 5.41/5.61 = one_one_int )
% 5.41/5.61 = ( N = one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_eq_one_iff
% 5.41/5.61 thf(fact_291_one__eq__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( one_one_complex
% 5.41/5.61 = ( numera6690914467698888265omplex @ N ) )
% 5.41/5.61 = ( one = N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_eq_numeral_iff
% 5.41/5.61 thf(fact_292_one__eq__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( one_one_real
% 5.41/5.61 = ( numeral_numeral_real @ N ) )
% 5.41/5.61 = ( one = N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_eq_numeral_iff
% 5.41/5.61 thf(fact_293_one__eq__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( one_one_rat
% 5.41/5.61 = ( numeral_numeral_rat @ N ) )
% 5.41/5.61 = ( one = N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_eq_numeral_iff
% 5.41/5.61 thf(fact_294_one__eq__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( one_one_nat
% 5.41/5.61 = ( numeral_numeral_nat @ N ) )
% 5.41/5.61 = ( one = N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_eq_numeral_iff
% 5.41/5.61 thf(fact_295_one__eq__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( one_one_int
% 5.41/5.61 = ( numeral_numeral_int @ N ) )
% 5.41/5.61 = ( one = N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_eq_numeral_iff
% 5.41/5.61 thf(fact_296_power__inject__exp,axiom,
% 5.41/5.61 ! [A: real,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.61 => ( ( ( power_power_real @ A @ M )
% 5.41/5.61 = ( power_power_real @ A @ N ) )
% 5.41/5.61 = ( M = N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_inject_exp
% 5.41/5.61 thf(fact_297_power__inject__exp,axiom,
% 5.41/5.61 ! [A: rat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ( ( power_power_rat @ A @ M )
% 5.41/5.61 = ( power_power_rat @ A @ N ) )
% 5.41/5.61 = ( M = N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_inject_exp
% 5.41/5.61 thf(fact_298_power__inject__exp,axiom,
% 5.41/5.61 ! [A: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ( ( power_power_nat @ A @ M )
% 5.41/5.61 = ( power_power_nat @ A @ N ) )
% 5.41/5.61 = ( M = N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_inject_exp
% 5.41/5.61 thf(fact_299_power__inject__exp,axiom,
% 5.41/5.61 ! [A: int,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.61 => ( ( ( power_power_int @ A @ M )
% 5.41/5.61 = ( power_power_int @ A @ N ) )
% 5.41/5.61 = ( M = N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_inject_exp
% 5.41/5.61 thf(fact_300_semiring__norm_I2_J,axiom,
% 5.41/5.61 ( ( plus_plus_num @ one @ one )
% 5.41/5.61 = ( bit0 @ one ) ) ).
% 5.41/5.61
% 5.41/5.61 % semiring_norm(2)
% 5.41/5.61 thf(fact_301_semiring__norm_I69_J,axiom,
% 5.41/5.61 ! [M: num] :
% 5.41/5.61 ~ ( ord_less_eq_num @ ( bit0 @ M ) @ one ) ).
% 5.41/5.61
% 5.41/5.61 % semiring_norm(69)
% 5.41/5.61 thf(fact_302_enat__ord__number_I1_J,axiom,
% 5.41/5.61 ! [M: num,N: num] :
% 5.41/5.61 ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ M ) @ ( numera1916890842035813515d_enat @ N ) )
% 5.41/5.61 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % enat_ord_number(1)
% 5.41/5.61 thf(fact_303_le__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [A: real,B: real,W: num] :
% 5.41/5.61 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.61 = ( ord_less_eq_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_divide_eq_numeral1(1)
% 5.41/5.61 thf(fact_304_le__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [A: rat,B: rat,W: num] :
% 5.41/5.61 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.61 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_divide_eq_numeral1(1)
% 5.41/5.61 thf(fact_305_divide__le__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [B: real,W: num,A: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.41/5.61 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % divide_le_eq_numeral1(1)
% 5.41/5.61 thf(fact_306_divide__le__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [B: rat,W: num,A: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.41/5.61 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % divide_le_eq_numeral1(1)
% 5.41/5.61 thf(fact_307_divide__less__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [B: real,W: num,A: real] :
% 5.41/5.61 ( ( ord_less_real @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) @ A )
% 5.41/5.61 = ( ord_less_real @ B @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % divide_less_eq_numeral1(1)
% 5.41/5.61 thf(fact_308_divide__less__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [B: rat,W: num,A: rat] :
% 5.41/5.61 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) @ A )
% 5.41/5.61 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % divide_less_eq_numeral1(1)
% 5.41/5.61 thf(fact_309_less__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [A: real,B: real,W: num] :
% 5.41/5.61 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.61 = ( ord_less_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_divide_eq_numeral1(1)
% 5.41/5.61 thf(fact_310_less__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.61 ! [A: rat,B: rat,W: num] :
% 5.41/5.61 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.61 = ( ord_less_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_divide_eq_numeral1(1)
% 5.41/5.61 thf(fact_311_power__strict__increasing__iff,axiom,
% 5.41/5.61 ! [B: real,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.61 => ( ( ord_less_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.41/5.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing_iff
% 5.41/5.61 thf(fact_312_power__strict__increasing__iff,axiom,
% 5.41/5.61 ! [B: rat,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ B )
% 5.41/5.61 => ( ( ord_less_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.41/5.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing_iff
% 5.41/5.61 thf(fact_313_power__strict__increasing__iff,axiom,
% 5.41/5.61 ! [B: nat,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ B )
% 5.41/5.61 => ( ( ord_less_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.41/5.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing_iff
% 5.41/5.61 thf(fact_314_power__strict__increasing__iff,axiom,
% 5.41/5.61 ! [B: int,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ B )
% 5.41/5.61 => ( ( ord_less_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.41/5.61 = ( ord_less_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing_iff
% 5.41/5.61 thf(fact_315_power__add__numeral,axiom,
% 5.41/5.61 ! [A: complex,M: num,N: num] :
% 5.41/5.61 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.61 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral
% 5.41/5.61 thf(fact_316_power__add__numeral,axiom,
% 5.41/5.61 ! [A: real,M: num,N: num] :
% 5.41/5.61 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.61 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral
% 5.41/5.61 thf(fact_317_power__add__numeral,axiom,
% 5.41/5.61 ! [A: rat,M: num,N: num] :
% 5.41/5.61 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.61 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral
% 5.41/5.61 thf(fact_318_power__add__numeral,axiom,
% 5.41/5.61 ! [A: nat,M: num,N: num] :
% 5.41/5.61 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.61 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral
% 5.41/5.61 thf(fact_319_power__add__numeral,axiom,
% 5.41/5.61 ! [A: int,M: num,N: num] :
% 5.41/5.61 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) )
% 5.41/5.61 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral
% 5.41/5.61 thf(fact_320_power__add__numeral2,axiom,
% 5.41/5.61 ! [A: complex,M: num,N: num,B: complex] :
% 5.41/5.61 ( ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.41/5.61 = ( times_times_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral2
% 5.41/5.61 thf(fact_321_power__add__numeral2,axiom,
% 5.41/5.61 ! [A: real,M: num,N: num,B: real] :
% 5.41/5.61 ( ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.41/5.61 = ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral2
% 5.41/5.61 thf(fact_322_power__add__numeral2,axiom,
% 5.41/5.61 ! [A: rat,M: num,N: num,B: rat] :
% 5.41/5.61 ( ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.41/5.61 = ( times_times_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral2
% 5.41/5.61 thf(fact_323_power__add__numeral2,axiom,
% 5.41/5.61 ! [A: nat,M: num,N: num,B: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.41/5.61 = ( times_times_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral2
% 5.41/5.61 thf(fact_324_power__add__numeral2,axiom,
% 5.41/5.61 ! [A: int,M: num,N: num,B: int] :
% 5.41/5.61 ( ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ N ) ) @ B ) )
% 5.41/5.61 = ( times_times_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( plus_plus_num @ M @ N ) ) ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add_numeral2
% 5.41/5.61 thf(fact_325_one__add__one,axiom,
% 5.41/5.61 ( ( plus_plus_complex @ one_one_complex @ one_one_complex )
% 5.41/5.61 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_add_one
% 5.41/5.61 thf(fact_326_one__add__one,axiom,
% 5.41/5.61 ( ( plus_plus_real @ one_one_real @ one_one_real )
% 5.41/5.61 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_add_one
% 5.41/5.61 thf(fact_327_one__add__one,axiom,
% 5.41/5.61 ( ( plus_plus_rat @ one_one_rat @ one_one_rat )
% 5.41/5.61 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_add_one
% 5.41/5.61 thf(fact_328_one__add__one,axiom,
% 5.41/5.61 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.41/5.61 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_add_one
% 5.41/5.61 thf(fact_329_one__add__one,axiom,
% 5.41/5.61 ( ( plus_plus_int @ one_one_int @ one_one_int )
% 5.41/5.61 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_add_one
% 5.41/5.61 thf(fact_330_power__increasing__iff,axiom,
% 5.41/5.61 ! [B: real,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.61 => ( ( ord_less_eq_real @ ( power_power_real @ B @ X ) @ ( power_power_real @ B @ Y ) )
% 5.41/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing_iff
% 5.41/5.61 thf(fact_331_power__increasing__iff,axiom,
% 5.41/5.61 ! [B: rat,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ B )
% 5.41/5.61 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ X ) @ ( power_power_rat @ B @ Y ) )
% 5.41/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing_iff
% 5.41/5.61 thf(fact_332_power__increasing__iff,axiom,
% 5.41/5.61 ! [B: nat,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ B )
% 5.41/5.61 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ X ) @ ( power_power_nat @ B @ Y ) )
% 5.41/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing_iff
% 5.41/5.61 thf(fact_333_power__increasing__iff,axiom,
% 5.41/5.61 ! [B: int,X: nat,Y: nat] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ B )
% 5.41/5.61 => ( ( ord_less_eq_int @ ( power_power_int @ B @ X ) @ ( power_power_int @ B @ Y ) )
% 5.41/5.61 = ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing_iff
% 5.41/5.61 thf(fact_334_numeral__plus__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ one_one_complex )
% 5.41/5.61 = ( numera6690914467698888265omplex @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_plus_one
% 5.41/5.61 thf(fact_335_numeral__plus__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.41/5.61 = ( numeral_numeral_real @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_plus_one
% 5.41/5.61 thf(fact_336_numeral__plus__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.41/5.61 = ( numeral_numeral_rat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_plus_one
% 5.41/5.61 thf(fact_337_numeral__plus__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.41/5.61 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_plus_one
% 5.41/5.61 thf(fact_338_numeral__plus__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.41/5.61 = ( numeral_numeral_int @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_plus_one
% 5.41/5.61 thf(fact_339_one__plus__numeral,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.61 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral
% 5.41/5.61 thf(fact_340_one__plus__numeral,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.41/5.61 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral
% 5.41/5.61 thf(fact_341_one__plus__numeral,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.41/5.61 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral
% 5.41/5.61 thf(fact_342_one__plus__numeral,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.41/5.61 = ( numeral_numeral_nat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral
% 5.41/5.61 thf(fact_343_one__plus__numeral,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.41/5.61 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral
% 5.41/5.61 thf(fact_344_numeral__le__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ one_one_real )
% 5.41/5.61 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_le_one_iff
% 5.41/5.61 thf(fact_345_numeral__le__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat )
% 5.41/5.61 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_le_one_iff
% 5.41/5.61 thf(fact_346_numeral__le__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat )
% 5.41/5.61 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_le_one_iff
% 5.41/5.61 thf(fact_347_numeral__le__one__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ one_one_int )
% 5.41/5.61 = ( ord_less_eq_num @ N @ one ) ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_le_one_iff
% 5.41/5.61 thf(fact_348_one__less__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ ( numeral_numeral_real @ N ) )
% 5.41/5.61 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_less_numeral_iff
% 5.41/5.61 thf(fact_349_one__less__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) )
% 5.41/5.61 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_less_numeral_iff
% 5.41/5.61 thf(fact_350_one__less__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) )
% 5.41/5.61 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_less_numeral_iff
% 5.41/5.61 thf(fact_351_one__less__numeral__iff,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ ( numeral_numeral_int @ N ) )
% 5.41/5.61 = ( ord_less_num @ one @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_less_numeral_iff
% 5.41/5.61 thf(fact_352_enat__less__induct,axiom,
% 5.41/5.61 ! [P: extended_enat > $o,N: extended_enat] :
% 5.41/5.61 ( ! [N3: extended_enat] :
% 5.41/5.61 ( ! [M2: extended_enat] :
% 5.41/5.61 ( ( ord_le72135733267957522d_enat @ M2 @ N3 )
% 5.41/5.61 => ( P @ M2 ) )
% 5.41/5.61 => ( P @ N3 ) )
% 5.41/5.61 => ( P @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % enat_less_induct
% 5.41/5.61 thf(fact_353_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.61 thf(fact_354_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.61 thf(fact_355_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.61 thf(fact_356_ab__semigroup__mult__class_Omult__ac_I1_J,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_mult_class.mult_ac(1)
% 5.41/5.61 thf(fact_357_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( times_times_complex @ one_one_complex @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % comm_monoid_mult_class.mult_1
% 5.41/5.61 thf(fact_358_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( times_times_real @ one_one_real @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % comm_monoid_mult_class.mult_1
% 5.41/5.61 thf(fact_359_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( times_times_rat @ one_one_rat @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % comm_monoid_mult_class.mult_1
% 5.41/5.61 thf(fact_360_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( times_times_nat @ one_one_nat @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % comm_monoid_mult_class.mult_1
% 5.41/5.61 thf(fact_361_comm__monoid__mult__class_Omult__1,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( times_times_int @ one_one_int @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % comm_monoid_mult_class.mult_1
% 5.41/5.61 thf(fact_362_mult_Oassoc,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( times_times_real @ ( times_times_real @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.assoc
% 5.41/5.61 thf(fact_363_mult_Oassoc,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( times_times_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.assoc
% 5.41/5.61 thf(fact_364_mult_Oassoc,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.assoc
% 5.41/5.61 thf(fact_365_mult_Oassoc,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( times_times_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.61 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.assoc
% 5.41/5.61 thf(fact_366_mult_Ocommute,axiom,
% 5.41/5.61 ( times_times_real
% 5.41/5.61 = ( ^ [A3: real,B2: real] : ( times_times_real @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.commute
% 5.41/5.61 thf(fact_367_mult_Ocommute,axiom,
% 5.41/5.61 ( times_times_rat
% 5.41/5.61 = ( ^ [A3: rat,B2: rat] : ( times_times_rat @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.commute
% 5.41/5.61 thf(fact_368_mult_Ocommute,axiom,
% 5.41/5.61 ( times_times_nat
% 5.41/5.61 = ( ^ [A3: nat,B2: nat] : ( times_times_nat @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.commute
% 5.41/5.61 thf(fact_369_mult_Ocommute,axiom,
% 5.41/5.61 ( times_times_int
% 5.41/5.61 = ( ^ [A3: int,B2: int] : ( times_times_int @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.commute
% 5.41/5.61 thf(fact_370_mult_Ocomm__neutral,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( times_times_complex @ A @ one_one_complex )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.comm_neutral
% 5.41/5.61 thf(fact_371_mult_Ocomm__neutral,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( times_times_real @ A @ one_one_real )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.comm_neutral
% 5.41/5.61 thf(fact_372_mult_Ocomm__neutral,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( times_times_rat @ A @ one_one_rat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.comm_neutral
% 5.41/5.61 thf(fact_373_mult_Ocomm__neutral,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( times_times_nat @ A @ one_one_nat )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.comm_neutral
% 5.41/5.61 thf(fact_374_mult_Ocomm__neutral,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( times_times_int @ A @ one_one_int )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult.comm_neutral
% 5.41/5.61 thf(fact_375_mult_Oleft__commute,axiom,
% 5.41/5.61 ! [B: real,A: real,C: real] :
% 5.41/5.61 ( ( times_times_real @ B @ ( times_times_real @ A @ C ) )
% 5.41/5.61 = ( times_times_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.left_commute
% 5.41/5.61 thf(fact_376_mult_Oleft__commute,axiom,
% 5.41/5.61 ! [B: rat,A: rat,C: rat] :
% 5.41/5.61 ( ( times_times_rat @ B @ ( times_times_rat @ A @ C ) )
% 5.41/5.61 = ( times_times_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.left_commute
% 5.41/5.61 thf(fact_377_mult_Oleft__commute,axiom,
% 5.41/5.61 ! [B: nat,A: nat,C: nat] :
% 5.41/5.61 ( ( times_times_nat @ B @ ( times_times_nat @ A @ C ) )
% 5.41/5.61 = ( times_times_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.left_commute
% 5.41/5.61 thf(fact_378_mult_Oleft__commute,axiom,
% 5.41/5.61 ! [B: int,A: int,C: int] :
% 5.41/5.61 ( ( times_times_int @ B @ ( times_times_int @ A @ C ) )
% 5.41/5.61 = ( times_times_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult.left_commute
% 5.41/5.61 thf(fact_379_nat__mult__1,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ( ( times_times_nat @ one_one_nat @ N )
% 5.41/5.61 = N ) ).
% 5.41/5.61
% 5.41/5.61 % nat_mult_1
% 5.41/5.61 thf(fact_380_one__reorient,axiom,
% 5.41/5.61 ! [X: complex] :
% 5.41/5.61 ( ( one_one_complex = X )
% 5.41/5.61 = ( X = one_one_complex ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_reorient
% 5.41/5.61 thf(fact_381_one__reorient,axiom,
% 5.41/5.61 ! [X: real] :
% 5.41/5.61 ( ( one_one_real = X )
% 5.41/5.61 = ( X = one_one_real ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_reorient
% 5.41/5.61 thf(fact_382_one__reorient,axiom,
% 5.41/5.61 ! [X: rat] :
% 5.41/5.61 ( ( one_one_rat = X )
% 5.41/5.61 = ( X = one_one_rat ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_reorient
% 5.41/5.61 thf(fact_383_one__reorient,axiom,
% 5.41/5.61 ! [X: nat] :
% 5.41/5.61 ( ( one_one_nat = X )
% 5.41/5.61 = ( X = one_one_nat ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_reorient
% 5.41/5.61 thf(fact_384_one__reorient,axiom,
% 5.41/5.61 ! [X: int] :
% 5.41/5.61 ( ( one_one_int = X )
% 5.41/5.61 = ( X = one_one_int ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_reorient
% 5.41/5.61 thf(fact_385_nat__mult__1__right,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ( ( times_times_nat @ N @ one_one_nat )
% 5.41/5.61 = N ) ).
% 5.41/5.61
% 5.41/5.61 % nat_mult_1_right
% 5.41/5.61 thf(fact_386_power__one__over,axiom,
% 5.41/5.61 ! [A: complex,N: nat] :
% 5.41/5.61 ( ( power_power_complex @ ( divide1717551699836669952omplex @ one_one_complex @ A ) @ N )
% 5.41/5.61 = ( divide1717551699836669952omplex @ one_one_complex @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_one_over
% 5.41/5.61 thf(fact_387_power__one__over,axiom,
% 5.41/5.61 ! [A: real,N: nat] :
% 5.41/5.61 ( ( power_power_real @ ( divide_divide_real @ one_one_real @ A ) @ N )
% 5.41/5.61 = ( divide_divide_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_one_over
% 5.41/5.61 thf(fact_388_power__one__over,axiom,
% 5.41/5.61 ! [A: rat,N: nat] :
% 5.41/5.61 ( ( power_power_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ N )
% 5.41/5.61 = ( divide_divide_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_one_over
% 5.41/5.61 thf(fact_389_left__right__inverse__power,axiom,
% 5.41/5.61 ! [X: complex,Y: complex,N: nat] :
% 5.41/5.61 ( ( ( times_times_complex @ X @ Y )
% 5.41/5.61 = one_one_complex )
% 5.41/5.61 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 5.41/5.61 = one_one_complex ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_right_inverse_power
% 5.41/5.61 thf(fact_390_left__right__inverse__power,axiom,
% 5.41/5.61 ! [X: real,Y: real,N: nat] :
% 5.41/5.61 ( ( ( times_times_real @ X @ Y )
% 5.41/5.61 = one_one_real )
% 5.41/5.61 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 5.41/5.61 = one_one_real ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_right_inverse_power
% 5.41/5.61 thf(fact_391_left__right__inverse__power,axiom,
% 5.41/5.61 ! [X: rat,Y: rat,N: nat] :
% 5.41/5.61 ( ( ( times_times_rat @ X @ Y )
% 5.41/5.61 = one_one_rat )
% 5.41/5.61 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 5.41/5.61 = one_one_rat ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_right_inverse_power
% 5.41/5.61 thf(fact_392_left__right__inverse__power,axiom,
% 5.41/5.61 ! [X: nat,Y: nat,N: nat] :
% 5.41/5.61 ( ( ( times_times_nat @ X @ Y )
% 5.41/5.61 = one_one_nat )
% 5.41/5.61 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) )
% 5.41/5.61 = one_one_nat ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_right_inverse_power
% 5.41/5.61 thf(fact_393_left__right__inverse__power,axiom,
% 5.41/5.61 ! [X: int,Y: int,N: nat] :
% 5.41/5.61 ( ( ( times_times_int @ X @ Y )
% 5.41/5.61 = one_one_int )
% 5.41/5.61 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 5.41/5.61 = one_one_int ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_right_inverse_power
% 5.41/5.61 thf(fact_394_le__cube,axiom,
% 5.41/5.61 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ ( times_times_nat @ M @ M ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_cube
% 5.41/5.61 thf(fact_395_le__square,axiom,
% 5.41/5.61 ! [M: nat] : ( ord_less_eq_nat @ M @ ( times_times_nat @ M @ M ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_square
% 5.41/5.61 thf(fact_396_mult__le__mono,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.41/5.61 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ L2 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_le_mono
% 5.41/5.61 thf(fact_397_mult__le__mono1,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ord_less_eq_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_le_mono1
% 5.41/5.61 thf(fact_398_mult__le__mono2,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ord_less_eq_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_le_mono2
% 5.41/5.61 thf(fact_399_add__mult__distrib,axiom,
% 5.41/5.61 ! [M: nat,N: nat,K: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( plus_plus_nat @ M @ N ) @ K )
% 5.41/5.61 = ( plus_plus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mult_distrib
% 5.41/5.61 thf(fact_400_add__mult__distrib2,axiom,
% 5.41/5.61 ! [K: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( times_times_nat @ K @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.61 = ( plus_plus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mult_distrib2
% 5.41/5.61 thf(fact_401_power__gt1__lemma,axiom,
% 5.41/5.61 ! [A: real,N: nat] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.61 => ( ord_less_real @ one_one_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_gt1_lemma
% 5.41/5.61 thf(fact_402_power__gt1__lemma,axiom,
% 5.41/5.61 ! [A: rat,N: nat] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_gt1_lemma
% 5.41/5.61 thf(fact_403_power__gt1__lemma,axiom,
% 5.41/5.61 ! [A: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_gt1_lemma
% 5.41/5.61 thf(fact_404_power__gt1__lemma,axiom,
% 5.41/5.61 ! [A: int,N: nat] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.61 => ( ord_less_int @ one_one_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_gt1_lemma
% 5.41/5.61 thf(fact_405_power__less__power__Suc,axiom,
% 5.41/5.61 ! [A: real,N: nat] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.61 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_power_Suc
% 5.41/5.61 thf(fact_406_power__less__power__Suc,axiom,
% 5.41/5.61 ! [A: rat,N: nat] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_power_Suc
% 5.41/5.61 thf(fact_407_power__less__power__Suc,axiom,
% 5.41/5.61 ! [A: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_power_Suc
% 5.41/5.61 thf(fact_408_power__less__power__Suc,axiom,
% 5.41/5.61 ! [A: int,N: nat] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.61 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_power_Suc
% 5.41/5.61 thf(fact_409_power__divide,axiom,
% 5.41/5.61 ! [A: complex,B: complex,N: nat] :
% 5.41/5.61 ( ( power_power_complex @ ( divide1717551699836669952omplex @ A @ B ) @ N )
% 5.41/5.61 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_divide
% 5.41/5.61 thf(fact_410_power__divide,axiom,
% 5.41/5.61 ! [A: real,B: real,N: nat] :
% 5.41/5.61 ( ( power_power_real @ ( divide_divide_real @ A @ B ) @ N )
% 5.41/5.61 = ( divide_divide_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_divide
% 5.41/5.61 thf(fact_411_power__divide,axiom,
% 5.41/5.61 ! [A: rat,B: rat,N: nat] :
% 5.41/5.61 ( ( power_power_rat @ ( divide_divide_rat @ A @ B ) @ N )
% 5.41/5.61 = ( divide_divide_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_divide
% 5.41/5.61 thf(fact_412_add__One__commute,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ( ( plus_plus_num @ one @ N )
% 5.41/5.61 = ( plus_plus_num @ N @ one ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_One_commute
% 5.41/5.61 thf(fact_413_le__num__One__iff,axiom,
% 5.41/5.61 ! [X: num] :
% 5.41/5.61 ( ( ord_less_eq_num @ X @ one )
% 5.41/5.61 = ( X = one ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_num_One_iff
% 5.41/5.61 thf(fact_414_power__commutes,axiom,
% 5.41/5.61 ! [A: complex,N: nat] :
% 5.41/5.61 ( ( times_times_complex @ ( power_power_complex @ A @ N ) @ A )
% 5.41/5.61 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commutes
% 5.41/5.61 thf(fact_415_power__commutes,axiom,
% 5.41/5.61 ! [A: real,N: nat] :
% 5.41/5.61 ( ( times_times_real @ ( power_power_real @ A @ N ) @ A )
% 5.41/5.61 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commutes
% 5.41/5.61 thf(fact_416_power__commutes,axiom,
% 5.41/5.61 ! [A: rat,N: nat] :
% 5.41/5.61 ( ( times_times_rat @ ( power_power_rat @ A @ N ) @ A )
% 5.41/5.61 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commutes
% 5.41/5.61 thf(fact_417_power__commutes,axiom,
% 5.41/5.61 ! [A: nat,N: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( power_power_nat @ A @ N ) @ A )
% 5.41/5.61 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commutes
% 5.41/5.61 thf(fact_418_power__commutes,axiom,
% 5.41/5.61 ! [A: int,N: nat] :
% 5.41/5.61 ( ( times_times_int @ ( power_power_int @ A @ N ) @ A )
% 5.41/5.61 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commutes
% 5.41/5.61 thf(fact_419_power__mult__distrib,axiom,
% 5.41/5.61 ! [A: complex,B: complex,N: nat] :
% 5.41/5.61 ( ( power_power_complex @ ( times_times_complex @ A @ B ) @ N )
% 5.41/5.61 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ ( power_power_complex @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult_distrib
% 5.41/5.61 thf(fact_420_power__mult__distrib,axiom,
% 5.41/5.61 ! [A: real,B: real,N: nat] :
% 5.41/5.61 ( ( power_power_real @ ( times_times_real @ A @ B ) @ N )
% 5.41/5.61 = ( times_times_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult_distrib
% 5.41/5.61 thf(fact_421_power__mult__distrib,axiom,
% 5.41/5.61 ! [A: rat,B: rat,N: nat] :
% 5.41/5.61 ( ( power_power_rat @ ( times_times_rat @ A @ B ) @ N )
% 5.41/5.61 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult_distrib
% 5.41/5.61 thf(fact_422_power__mult__distrib,axiom,
% 5.41/5.61 ! [A: nat,B: nat,N: nat] :
% 5.41/5.61 ( ( power_power_nat @ ( times_times_nat @ A @ B ) @ N )
% 5.41/5.61 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult_distrib
% 5.41/5.61 thf(fact_423_power__mult__distrib,axiom,
% 5.41/5.61 ! [A: int,B: int,N: nat] :
% 5.41/5.61 ( ( power_power_int @ ( times_times_int @ A @ B ) @ N )
% 5.41/5.61 = ( times_times_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult_distrib
% 5.41/5.61 thf(fact_424_power__commuting__commutes,axiom,
% 5.41/5.61 ! [X: complex,Y: complex,N: nat] :
% 5.41/5.61 ( ( ( times_times_complex @ X @ Y )
% 5.41/5.61 = ( times_times_complex @ Y @ X ) )
% 5.41/5.61 => ( ( times_times_complex @ ( power_power_complex @ X @ N ) @ Y )
% 5.41/5.61 = ( times_times_complex @ Y @ ( power_power_complex @ X @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commuting_commutes
% 5.41/5.61 thf(fact_425_power__commuting__commutes,axiom,
% 5.41/5.61 ! [X: real,Y: real,N: nat] :
% 5.41/5.61 ( ( ( times_times_real @ X @ Y )
% 5.41/5.61 = ( times_times_real @ Y @ X ) )
% 5.41/5.61 => ( ( times_times_real @ ( power_power_real @ X @ N ) @ Y )
% 5.41/5.61 = ( times_times_real @ Y @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commuting_commutes
% 5.41/5.61 thf(fact_426_power__commuting__commutes,axiom,
% 5.41/5.61 ! [X: rat,Y: rat,N: nat] :
% 5.41/5.61 ( ( ( times_times_rat @ X @ Y )
% 5.41/5.61 = ( times_times_rat @ Y @ X ) )
% 5.41/5.61 => ( ( times_times_rat @ ( power_power_rat @ X @ N ) @ Y )
% 5.41/5.61 = ( times_times_rat @ Y @ ( power_power_rat @ X @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commuting_commutes
% 5.41/5.61 thf(fact_427_power__commuting__commutes,axiom,
% 5.41/5.61 ! [X: nat,Y: nat,N: nat] :
% 5.41/5.61 ( ( ( times_times_nat @ X @ Y )
% 5.41/5.61 = ( times_times_nat @ Y @ X ) )
% 5.41/5.61 => ( ( times_times_nat @ ( power_power_nat @ X @ N ) @ Y )
% 5.41/5.61 = ( times_times_nat @ Y @ ( power_power_nat @ X @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commuting_commutes
% 5.41/5.61 thf(fact_428_power__commuting__commutes,axiom,
% 5.41/5.61 ! [X: int,Y: int,N: nat] :
% 5.41/5.61 ( ( ( times_times_int @ X @ Y )
% 5.41/5.61 = ( times_times_int @ Y @ X ) )
% 5.41/5.61 => ( ( times_times_int @ ( power_power_int @ X @ N ) @ Y )
% 5.41/5.61 = ( times_times_int @ Y @ ( power_power_int @ X @ N ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_commuting_commutes
% 5.41/5.61 thf(fact_429_power__mult,axiom,
% 5.41/5.61 ! [A: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_nat @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.61 = ( power_power_nat @ ( power_power_nat @ A @ M ) @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult
% 5.41/5.61 thf(fact_430_power__mult,axiom,
% 5.41/5.61 ! [A: real,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_real @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.61 = ( power_power_real @ ( power_power_real @ A @ M ) @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult
% 5.41/5.61 thf(fact_431_power__mult,axiom,
% 5.41/5.61 ! [A: int,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_int @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.61 = ( power_power_int @ ( power_power_int @ A @ M ) @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult
% 5.41/5.61 thf(fact_432_power__mult,axiom,
% 5.41/5.61 ! [A: complex,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_complex @ A @ ( times_times_nat @ M @ N ) )
% 5.41/5.61 = ( power_power_complex @ ( power_power_complex @ A @ M ) @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_mult
% 5.41/5.61 thf(fact_433_le__numeral__extra_I4_J,axiom,
% 5.41/5.61 ord_less_eq_real @ one_one_real @ one_one_real ).
% 5.41/5.61
% 5.41/5.61 % le_numeral_extra(4)
% 5.41/5.61 thf(fact_434_le__numeral__extra_I4_J,axiom,
% 5.41/5.61 ord_less_eq_rat @ one_one_rat @ one_one_rat ).
% 5.41/5.61
% 5.41/5.61 % le_numeral_extra(4)
% 5.41/5.61 thf(fact_435_le__numeral__extra_I4_J,axiom,
% 5.41/5.61 ord_less_eq_nat @ one_one_nat @ one_one_nat ).
% 5.41/5.61
% 5.41/5.61 % le_numeral_extra(4)
% 5.41/5.61 thf(fact_436_le__numeral__extra_I4_J,axiom,
% 5.41/5.61 ord_less_eq_int @ one_one_int @ one_one_int ).
% 5.41/5.61
% 5.41/5.61 % le_numeral_extra(4)
% 5.41/5.61 thf(fact_437_less__numeral__extra_I4_J,axiom,
% 5.41/5.61 ~ ( ord_less_real @ one_one_real @ one_one_real ) ).
% 5.41/5.61
% 5.41/5.61 % less_numeral_extra(4)
% 5.41/5.61 thf(fact_438_less__numeral__extra_I4_J,axiom,
% 5.41/5.61 ~ ( ord_less_rat @ one_one_rat @ one_one_rat ) ).
% 5.41/5.61
% 5.41/5.61 % less_numeral_extra(4)
% 5.41/5.61 thf(fact_439_less__numeral__extra_I4_J,axiom,
% 5.41/5.61 ~ ( ord_less_nat @ one_one_nat @ one_one_nat ) ).
% 5.41/5.61
% 5.41/5.61 % less_numeral_extra(4)
% 5.41/5.61 thf(fact_440_less__numeral__extra_I4_J,axiom,
% 5.41/5.61 ~ ( ord_less_int @ one_one_int @ one_one_int ) ).
% 5.41/5.61
% 5.41/5.61 % less_numeral_extra(4)
% 5.41/5.61 thf(fact_441_left__add__mult__distrib,axiom,
% 5.41/5.61 ! [I: nat,U: nat,J: nat,K: nat] :
% 5.41/5.61 ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ K ) )
% 5.41/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ I @ J ) @ U ) @ K ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_add_mult_distrib
% 5.41/5.61 thf(fact_442_subset__code_I1_J,axiom,
% 5.41/5.61 ! [Xs: list_complex,B3: set_complex] :
% 5.41/5.61 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ B3 )
% 5.41/5.61 = ( ! [X3: complex] :
% 5.41/5.61 ( ( member_complex @ X3 @ ( set_complex2 @ Xs ) )
% 5.41/5.61 => ( member_complex @ X3 @ B3 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % subset_code(1)
% 5.41/5.61 thf(fact_443_subset__code_I1_J,axiom,
% 5.41/5.61 ! [Xs: list_real,B3: set_real] :
% 5.41/5.61 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ B3 )
% 5.41/5.61 = ( ! [X3: real] :
% 5.41/5.61 ( ( member_real @ X3 @ ( set_real2 @ Xs ) )
% 5.41/5.61 => ( member_real @ X3 @ B3 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % subset_code(1)
% 5.41/5.61 thf(fact_444_subset__code_I1_J,axiom,
% 5.41/5.61 ! [Xs: list_set_nat,B3: set_set_nat] :
% 5.41/5.61 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ B3 )
% 5.41/5.61 = ( ! [X3: set_nat] :
% 5.41/5.61 ( ( member_set_nat @ X3 @ ( set_set_nat2 @ Xs ) )
% 5.41/5.61 => ( member_set_nat @ X3 @ B3 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % subset_code(1)
% 5.41/5.61 thf(fact_445_subset__code_I1_J,axiom,
% 5.41/5.61 ! [Xs: list_VEBT_VEBT,B3: set_VEBT_VEBT] :
% 5.41/5.61 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ B3 )
% 5.41/5.61 = ( ! [X3: vEBT_VEBT] :
% 5.41/5.61 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.61 => ( member_VEBT_VEBT @ X3 @ B3 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % subset_code(1)
% 5.41/5.61 thf(fact_446_subset__code_I1_J,axiom,
% 5.41/5.61 ! [Xs: list_nat,B3: set_nat] :
% 5.41/5.61 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ B3 )
% 5.41/5.61 = ( ! [X3: nat] :
% 5.41/5.61 ( ( member_nat @ X3 @ ( set_nat2 @ Xs ) )
% 5.41/5.61 => ( member_nat @ X3 @ B3 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % subset_code(1)
% 5.41/5.61 thf(fact_447_subset__code_I1_J,axiom,
% 5.41/5.61 ! [Xs: list_int,B3: set_int] :
% 5.41/5.61 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ B3 )
% 5.41/5.61 = ( ! [X3: int] :
% 5.41/5.61 ( ( member_int @ X3 @ ( set_int2 @ Xs ) )
% 5.41/5.61 => ( member_int @ X3 @ B3 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % subset_code(1)
% 5.41/5.61 thf(fact_448_divide__numeral__1,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % divide_numeral_1
% 5.41/5.61 thf(fact_449_divide__numeral__1,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( divide_divide_real @ A @ ( numeral_numeral_real @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % divide_numeral_1
% 5.41/5.61 thf(fact_450_divide__numeral__1,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( divide_divide_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % divide_numeral_1
% 5.41/5.61 thf(fact_451_mult__numeral__1,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ one ) @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1
% 5.41/5.61 thf(fact_452_mult__numeral__1,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( times_times_real @ ( numeral_numeral_real @ one ) @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1
% 5.41/5.61 thf(fact_453_mult__numeral__1,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( times_times_rat @ ( numeral_numeral_rat @ one ) @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1
% 5.41/5.61 thf(fact_454_mult__numeral__1,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ one ) @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1
% 5.41/5.61 thf(fact_455_mult__numeral__1,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( times_times_int @ ( numeral_numeral_int @ one ) @ A )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1
% 5.41/5.61 thf(fact_456_mult__numeral__1__right,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1_right
% 5.41/5.61 thf(fact_457_mult__numeral__1__right,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( times_times_real @ A @ ( numeral_numeral_real @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1_right
% 5.41/5.61 thf(fact_458_mult__numeral__1__right,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( times_times_rat @ A @ ( numeral_numeral_rat @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1_right
% 5.41/5.61 thf(fact_459_mult__numeral__1__right,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( times_times_nat @ A @ ( numeral_numeral_nat @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1_right
% 5.41/5.61 thf(fact_460_mult__numeral__1__right,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( times_times_int @ A @ ( numeral_numeral_int @ one ) )
% 5.41/5.61 = A ) ).
% 5.41/5.61
% 5.41/5.61 % mult_numeral_1_right
% 5.41/5.61 thf(fact_461_power__add,axiom,
% 5.41/5.61 ! [A: complex,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_complex @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.61 = ( times_times_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add
% 5.41/5.61 thf(fact_462_power__add,axiom,
% 5.41/5.61 ! [A: real,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_real @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.61 = ( times_times_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add
% 5.41/5.61 thf(fact_463_power__add,axiom,
% 5.41/5.61 ! [A: rat,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_rat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.61 = ( times_times_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add
% 5.41/5.61 thf(fact_464_power__add,axiom,
% 5.41/5.61 ! [A: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_nat @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.61 = ( times_times_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add
% 5.41/5.61 thf(fact_465_power__add,axiom,
% 5.41/5.61 ! [A: int,M: nat,N: nat] :
% 5.41/5.61 ( ( power_power_int @ A @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.61 = ( times_times_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_add
% 5.41/5.61 thf(fact_466_one__le__numeral,axiom,
% 5.41/5.61 ! [N: num] : ( ord_less_eq_real @ one_one_real @ ( numeral_numeral_real @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_numeral
% 5.41/5.61 thf(fact_467_one__le__numeral,axiom,
% 5.41/5.61 ! [N: num] : ( ord_less_eq_rat @ one_one_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_numeral
% 5.41/5.61 thf(fact_468_one__le__numeral,axiom,
% 5.41/5.61 ! [N: num] : ( ord_less_eq_nat @ one_one_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_numeral
% 5.41/5.61 thf(fact_469_one__le__numeral,axiom,
% 5.41/5.61 ! [N: num] : ( ord_less_eq_int @ one_one_int @ ( numeral_numeral_int @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_numeral
% 5.41/5.61 thf(fact_470_not__numeral__less__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ one_one_real ) ).
% 5.41/5.61
% 5.41/5.61 % not_numeral_less_one
% 5.41/5.61 thf(fact_471_not__numeral__less__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ one_one_rat ) ).
% 5.41/5.61
% 5.41/5.61 % not_numeral_less_one
% 5.41/5.61 thf(fact_472_not__numeral__less__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ one_one_nat ) ).
% 5.41/5.61
% 5.41/5.61 % not_numeral_less_one
% 5.41/5.61 thf(fact_473_not__numeral__less__one,axiom,
% 5.41/5.61 ! [N: num] :
% 5.41/5.61 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ).
% 5.41/5.61
% 5.41/5.61 % not_numeral_less_one
% 5.41/5.61 thf(fact_474_one__plus__numeral__commute,axiom,
% 5.41/5.61 ! [X: num] :
% 5.41/5.61 ( ( plus_plus_complex @ one_one_complex @ ( numera6690914467698888265omplex @ X ) )
% 5.41/5.61 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral_commute
% 5.41/5.61 thf(fact_475_one__plus__numeral__commute,axiom,
% 5.41/5.61 ! [X: num] :
% 5.41/5.61 ( ( plus_plus_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.41/5.61 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral_commute
% 5.41/5.61 thf(fact_476_one__plus__numeral__commute,axiom,
% 5.41/5.61 ! [X: num] :
% 5.41/5.61 ( ( plus_plus_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.41/5.61 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral_commute
% 5.41/5.61 thf(fact_477_one__plus__numeral__commute,axiom,
% 5.41/5.61 ! [X: num] :
% 5.41/5.61 ( ( plus_plus_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.41/5.61 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral_commute
% 5.41/5.61 thf(fact_478_one__plus__numeral__commute,axiom,
% 5.41/5.61 ! [X: num] :
% 5.41/5.61 ( ( plus_plus_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.41/5.61 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_plus_numeral_commute
% 5.41/5.61 thf(fact_479_numeral__One,axiom,
% 5.41/5.61 ( ( numera6690914467698888265omplex @ one )
% 5.41/5.61 = one_one_complex ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_One
% 5.41/5.61 thf(fact_480_numeral__One,axiom,
% 5.41/5.61 ( ( numeral_numeral_real @ one )
% 5.41/5.61 = one_one_real ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_One
% 5.41/5.61 thf(fact_481_numeral__One,axiom,
% 5.41/5.61 ( ( numeral_numeral_rat @ one )
% 5.41/5.61 = one_one_rat ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_One
% 5.41/5.61 thf(fact_482_numeral__One,axiom,
% 5.41/5.61 ( ( numeral_numeral_nat @ one )
% 5.41/5.61 = one_one_nat ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_One
% 5.41/5.61 thf(fact_483_numeral__One,axiom,
% 5.41/5.61 ( ( numeral_numeral_int @ one )
% 5.41/5.61 = one_one_int ) ).
% 5.41/5.61
% 5.41/5.61 % numeral_One
% 5.41/5.61 thf(fact_484_one__le__power,axiom,
% 5.41/5.61 ! [A: real,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.41/5.61 => ( ord_less_eq_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_power
% 5.41/5.61 thf(fact_485_one__le__power,axiom,
% 5.41/5.61 ! [A: rat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ord_less_eq_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_power
% 5.41/5.61 thf(fact_486_one__le__power,axiom,
% 5.41/5.61 ! [A: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ord_less_eq_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_power
% 5.41/5.61 thf(fact_487_one__le__power,axiom,
% 5.41/5.61 ! [A: int,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.41/5.61 => ( ord_less_eq_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % one_le_power
% 5.41/5.61 thf(fact_488_numerals_I1_J,axiom,
% 5.41/5.61 ( ( numeral_numeral_nat @ one )
% 5.41/5.61 = one_one_nat ) ).
% 5.41/5.61
% 5.41/5.61 % numerals(1)
% 5.41/5.61 thf(fact_489_set__update__subsetI,axiom,
% 5.41/5.61 ! [Xs: list_complex,A2: set_complex,X: complex,I: nat] :
% 5.41/5.61 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs ) @ A2 )
% 5.41/5.61 => ( ( member_complex @ X @ A2 )
% 5.41/5.61 => ( ord_le211207098394363844omplex @ ( set_complex2 @ ( list_update_complex @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % set_update_subsetI
% 5.41/5.61 thf(fact_490_set__update__subsetI,axiom,
% 5.41/5.61 ! [Xs: list_real,A2: set_real,X: real,I: nat] :
% 5.41/5.61 ( ( ord_less_eq_set_real @ ( set_real2 @ Xs ) @ A2 )
% 5.41/5.61 => ( ( member_real @ X @ A2 )
% 5.41/5.61 => ( ord_less_eq_set_real @ ( set_real2 @ ( list_update_real @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % set_update_subsetI
% 5.41/5.61 thf(fact_491_set__update__subsetI,axiom,
% 5.41/5.61 ! [Xs: list_set_nat,A2: set_set_nat,X: set_nat,I: nat] :
% 5.41/5.61 ( ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ Xs ) @ A2 )
% 5.41/5.61 => ( ( member_set_nat @ X @ A2 )
% 5.41/5.61 => ( ord_le6893508408891458716et_nat @ ( set_set_nat2 @ ( list_update_set_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % set_update_subsetI
% 5.41/5.61 thf(fact_492_set__update__subsetI,axiom,
% 5.41/5.61 ! [Xs: list_nat,A2: set_nat,X: nat,I: nat] :
% 5.41/5.61 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs ) @ A2 )
% 5.41/5.61 => ( ( member_nat @ X @ A2 )
% 5.41/5.61 => ( ord_less_eq_set_nat @ ( set_nat2 @ ( list_update_nat @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % set_update_subsetI
% 5.41/5.61 thf(fact_493_set__update__subsetI,axiom,
% 5.41/5.61 ! [Xs: list_VEBT_VEBT,A2: set_VEBT_VEBT,X: vEBT_VEBT,I: nat] :
% 5.41/5.61 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) @ A2 )
% 5.41/5.61 => ( ( member_VEBT_VEBT @ X @ A2 )
% 5.41/5.61 => ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ ( list_u1324408373059187874T_VEBT @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % set_update_subsetI
% 5.41/5.61 thf(fact_494_set__update__subsetI,axiom,
% 5.41/5.61 ! [Xs: list_int,A2: set_int,X: int,I: nat] :
% 5.41/5.61 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs ) @ A2 )
% 5.41/5.61 => ( ( member_int @ X @ A2 )
% 5.41/5.61 => ( ord_less_eq_set_int @ ( set_int2 @ ( list_update_int @ Xs @ I @ X ) ) @ A2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % set_update_subsetI
% 5.41/5.61 thf(fact_495_power__less__imp__less__exp,axiom,
% 5.41/5.61 ! [A: real,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.61 => ( ( ord_less_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.41/5.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_imp_less_exp
% 5.41/5.61 thf(fact_496_power__less__imp__less__exp,axiom,
% 5.41/5.61 ! [A: rat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ( ord_less_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.41/5.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_imp_less_exp
% 5.41/5.61 thf(fact_497_power__less__imp__less__exp,axiom,
% 5.41/5.61 ! [A: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ( ord_less_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_imp_less_exp
% 5.41/5.61 thf(fact_498_power__less__imp__less__exp,axiom,
% 5.41/5.61 ! [A: int,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.61 => ( ( ord_less_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.41/5.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_less_imp_less_exp
% 5.41/5.61 thf(fact_499_power__strict__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: real] :
% 5.41/5.61 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.61 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing
% 5.41/5.61 thf(fact_500_power__strict__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: rat] :
% 5.41/5.61 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing
% 5.41/5.61 thf(fact_501_power__strict__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: nat] :
% 5.41/5.61 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing
% 5.41/5.61 thf(fact_502_power__strict__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: int] :
% 5.41/5.61 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.61 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_strict_increasing
% 5.41/5.61 thf(fact_503_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.61 thf(fact_504_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.61 thf(fact_505_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.61 thf(fact_506_ab__semigroup__add__class_Oadd__ac_I1_J,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % ab_semigroup_add_class.add_ac(1)
% 5.41/5.61 thf(fact_507_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.61 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ( plus_plus_real @ I @ K )
% 5.41/5.61 = ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(4)
% 5.41/5.61 thf(fact_508_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.61 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ( plus_plus_rat @ I @ K )
% 5.41/5.61 = ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(4)
% 5.41/5.61 thf(fact_509_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ( plus_plus_nat @ I @ K )
% 5.41/5.61 = ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(4)
% 5.41/5.61 thf(fact_510_add__mono__thms__linordered__semiring_I4_J,axiom,
% 5.41/5.61 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ( plus_plus_int @ I @ K )
% 5.41/5.61 = ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(4)
% 5.41/5.61 thf(fact_511_group__cancel_Oadd1,axiom,
% 5.41/5.61 ! [A2: real,K: real,A: real,B: real] :
% 5.41/5.61 ( ( A2
% 5.41/5.61 = ( plus_plus_real @ K @ A ) )
% 5.41/5.61 => ( ( plus_plus_real @ A2 @ B )
% 5.41/5.61 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add1
% 5.41/5.61 thf(fact_512_group__cancel_Oadd1,axiom,
% 5.41/5.61 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.41/5.61 ( ( A2
% 5.41/5.61 = ( plus_plus_rat @ K @ A ) )
% 5.41/5.61 => ( ( plus_plus_rat @ A2 @ B )
% 5.41/5.61 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add1
% 5.41/5.61 thf(fact_513_group__cancel_Oadd1,axiom,
% 5.41/5.61 ! [A2: nat,K: nat,A: nat,B: nat] :
% 5.41/5.61 ( ( A2
% 5.41/5.61 = ( plus_plus_nat @ K @ A ) )
% 5.41/5.61 => ( ( plus_plus_nat @ A2 @ B )
% 5.41/5.61 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add1
% 5.41/5.61 thf(fact_514_group__cancel_Oadd1,axiom,
% 5.41/5.61 ! [A2: int,K: int,A: int,B: int] :
% 5.41/5.61 ( ( A2
% 5.41/5.61 = ( plus_plus_int @ K @ A ) )
% 5.41/5.61 => ( ( plus_plus_int @ A2 @ B )
% 5.41/5.61 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add1
% 5.41/5.61 thf(fact_515_group__cancel_Oadd2,axiom,
% 5.41/5.61 ! [B3: real,K: real,B: real,A: real] :
% 5.41/5.61 ( ( B3
% 5.41/5.61 = ( plus_plus_real @ K @ B ) )
% 5.41/5.61 => ( ( plus_plus_real @ A @ B3 )
% 5.41/5.61 = ( plus_plus_real @ K @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add2
% 5.41/5.61 thf(fact_516_group__cancel_Oadd2,axiom,
% 5.41/5.61 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.41/5.61 ( ( B3
% 5.41/5.61 = ( plus_plus_rat @ K @ B ) )
% 5.41/5.61 => ( ( plus_plus_rat @ A @ B3 )
% 5.41/5.61 = ( plus_plus_rat @ K @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add2
% 5.41/5.61 thf(fact_517_group__cancel_Oadd2,axiom,
% 5.41/5.61 ! [B3: nat,K: nat,B: nat,A: nat] :
% 5.41/5.61 ( ( B3
% 5.41/5.61 = ( plus_plus_nat @ K @ B ) )
% 5.41/5.61 => ( ( plus_plus_nat @ A @ B3 )
% 5.41/5.61 = ( plus_plus_nat @ K @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add2
% 5.41/5.61 thf(fact_518_group__cancel_Oadd2,axiom,
% 5.41/5.61 ! [B3: int,K: int,B: int,A: int] :
% 5.41/5.61 ( ( B3
% 5.41/5.61 = ( plus_plus_int @ K @ B ) )
% 5.41/5.61 => ( ( plus_plus_int @ A @ B3 )
% 5.41/5.61 = ( plus_plus_int @ K @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % group_cancel.add2
% 5.41/5.61 thf(fact_519_add_Oassoc,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( plus_plus_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.assoc
% 5.41/5.61 thf(fact_520_add_Oassoc,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( plus_plus_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.assoc
% 5.41/5.61 thf(fact_521_add_Oassoc,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( plus_plus_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.assoc
% 5.41/5.61 thf(fact_522_add_Oassoc,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( plus_plus_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.61 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.assoc
% 5.41/5.61 thf(fact_523_add_Oleft__cancel,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( ( plus_plus_real @ A @ B )
% 5.41/5.61 = ( plus_plus_real @ A @ C ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.left_cancel
% 5.41/5.61 thf(fact_524_add_Oleft__cancel,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( ( plus_plus_rat @ A @ B )
% 5.41/5.61 = ( plus_plus_rat @ A @ C ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.left_cancel
% 5.41/5.61 thf(fact_525_add_Oleft__cancel,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( ( plus_plus_int @ A @ B )
% 5.41/5.61 = ( plus_plus_int @ A @ C ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.left_cancel
% 5.41/5.61 thf(fact_526_add_Oright__cancel,axiom,
% 5.41/5.61 ! [B: real,A: real,C: real] :
% 5.41/5.61 ( ( ( plus_plus_real @ B @ A )
% 5.41/5.61 = ( plus_plus_real @ C @ A ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.right_cancel
% 5.41/5.61 thf(fact_527_add_Oright__cancel,axiom,
% 5.41/5.61 ! [B: rat,A: rat,C: rat] :
% 5.41/5.61 ( ( ( plus_plus_rat @ B @ A )
% 5.41/5.61 = ( plus_plus_rat @ C @ A ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.right_cancel
% 5.41/5.61 thf(fact_528_add_Oright__cancel,axiom,
% 5.41/5.61 ! [B: int,A: int,C: int] :
% 5.41/5.61 ( ( ( plus_plus_int @ B @ A )
% 5.41/5.61 = ( plus_plus_int @ C @ A ) )
% 5.41/5.61 = ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.right_cancel
% 5.41/5.61 thf(fact_529_add_Ocommute,axiom,
% 5.41/5.61 ( plus_plus_real
% 5.41/5.61 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.commute
% 5.41/5.61 thf(fact_530_add_Ocommute,axiom,
% 5.41/5.61 ( plus_plus_rat
% 5.41/5.61 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.commute
% 5.41/5.61 thf(fact_531_add_Ocommute,axiom,
% 5.41/5.61 ( plus_plus_nat
% 5.41/5.61 = ( ^ [A3: nat,B2: nat] : ( plus_plus_nat @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.commute
% 5.41/5.61 thf(fact_532_add_Ocommute,axiom,
% 5.41/5.61 ( plus_plus_int
% 5.41/5.61 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ B2 @ A3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.commute
% 5.41/5.61 thf(fact_533_add_Oleft__commute,axiom,
% 5.41/5.61 ! [B: real,A: real,C: real] :
% 5.41/5.61 ( ( plus_plus_real @ B @ ( plus_plus_real @ A @ C ) )
% 5.41/5.61 = ( plus_plus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.left_commute
% 5.41/5.61 thf(fact_534_add_Oleft__commute,axiom,
% 5.41/5.61 ! [B: rat,A: rat,C: rat] :
% 5.41/5.61 ( ( plus_plus_rat @ B @ ( plus_plus_rat @ A @ C ) )
% 5.41/5.61 = ( plus_plus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.left_commute
% 5.41/5.61 thf(fact_535_add_Oleft__commute,axiom,
% 5.41/5.61 ! [B: nat,A: nat,C: nat] :
% 5.41/5.61 ( ( plus_plus_nat @ B @ ( plus_plus_nat @ A @ C ) )
% 5.41/5.61 = ( plus_plus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.left_commute
% 5.41/5.61 thf(fact_536_add_Oleft__commute,axiom,
% 5.41/5.61 ! [B: int,A: int,C: int] :
% 5.41/5.61 ( ( plus_plus_int @ B @ ( plus_plus_int @ A @ C ) )
% 5.41/5.61 = ( plus_plus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add.left_commute
% 5.41/5.61 thf(fact_537_add__left__imp__eq,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( ( plus_plus_real @ A @ B )
% 5.41/5.61 = ( plus_plus_real @ A @ C ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_imp_eq
% 5.41/5.61 thf(fact_538_add__left__imp__eq,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( ( plus_plus_rat @ A @ B )
% 5.41/5.61 = ( plus_plus_rat @ A @ C ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_imp_eq
% 5.41/5.61 thf(fact_539_add__left__imp__eq,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( ( plus_plus_nat @ A @ B )
% 5.41/5.61 = ( plus_plus_nat @ A @ C ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_imp_eq
% 5.41/5.61 thf(fact_540_add__left__imp__eq,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( ( plus_plus_int @ A @ B )
% 5.41/5.61 = ( plus_plus_int @ A @ C ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_imp_eq
% 5.41/5.61 thf(fact_541_add__right__imp__eq,axiom,
% 5.41/5.61 ! [B: real,A: real,C: real] :
% 5.41/5.61 ( ( ( plus_plus_real @ B @ A )
% 5.41/5.61 = ( plus_plus_real @ C @ A ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_imp_eq
% 5.41/5.61 thf(fact_542_add__right__imp__eq,axiom,
% 5.41/5.61 ! [B: rat,A: rat,C: rat] :
% 5.41/5.61 ( ( ( plus_plus_rat @ B @ A )
% 5.41/5.61 = ( plus_plus_rat @ C @ A ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_imp_eq
% 5.41/5.61 thf(fact_543_add__right__imp__eq,axiom,
% 5.41/5.61 ! [B: nat,A: nat,C: nat] :
% 5.41/5.61 ( ( ( plus_plus_nat @ B @ A )
% 5.41/5.61 = ( plus_plus_nat @ C @ A ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_imp_eq
% 5.41/5.61 thf(fact_544_add__right__imp__eq,axiom,
% 5.41/5.61 ! [B: int,A: int,C: int] :
% 5.41/5.61 ( ( ( plus_plus_int @ B @ A )
% 5.41/5.61 = ( plus_plus_int @ C @ A ) )
% 5.41/5.61 => ( B = C ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_imp_eq
% 5.41/5.61 thf(fact_545_power__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: real] :
% 5.41/5.61 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_eq_real @ one_one_real @ A )
% 5.41/5.61 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing
% 5.41/5.61 thf(fact_546_power__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: rat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing
% 5.41/5.61 thf(fact_547_power__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing
% 5.41/5.61 thf(fact_548_power__increasing,axiom,
% 5.41/5.61 ! [N: nat,N4: nat,A: int] :
% 5.41/5.61 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.61 => ( ( ord_less_eq_int @ one_one_int @ A )
% 5.41/5.61 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ A @ N4 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_increasing
% 5.41/5.61 thf(fact_549_nat__neq__iff,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( M != N )
% 5.41/5.61 = ( ( ord_less_nat @ M @ N )
% 5.41/5.61 | ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_neq_iff
% 5.41/5.61 thf(fact_550_less__not__refl,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ~ ( ord_less_nat @ N @ N ) ).
% 5.41/5.61
% 5.41/5.61 % less_not_refl
% 5.41/5.61 thf(fact_551_less__not__refl2,axiom,
% 5.41/5.61 ! [N: nat,M: nat] :
% 5.41/5.61 ( ( ord_less_nat @ N @ M )
% 5.41/5.61 => ( M != N ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_not_refl2
% 5.41/5.61 thf(fact_552_less__not__refl3,axiom,
% 5.41/5.61 ! [S: nat,T: nat] :
% 5.41/5.61 ( ( ord_less_nat @ S @ T )
% 5.41/5.61 => ( S != T ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_not_refl3
% 5.41/5.61 thf(fact_553_less__irrefl__nat,axiom,
% 5.41/5.61 ! [N: nat] :
% 5.41/5.61 ~ ( ord_less_nat @ N @ N ) ).
% 5.41/5.61
% 5.41/5.61 % less_irrefl_nat
% 5.41/5.61 thf(fact_554_nat__less__induct,axiom,
% 5.41/5.61 ! [P: nat > $o,N: nat] :
% 5.41/5.61 ( ! [N3: nat] :
% 5.41/5.61 ( ! [M2: nat] :
% 5.41/5.61 ( ( ord_less_nat @ M2 @ N3 )
% 5.41/5.61 => ( P @ M2 ) )
% 5.41/5.61 => ( P @ N3 ) )
% 5.41/5.61 => ( P @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_less_induct
% 5.41/5.61 thf(fact_555_infinite__descent,axiom,
% 5.41/5.61 ! [P: nat > $o,N: nat] :
% 5.41/5.61 ( ! [N3: nat] :
% 5.41/5.61 ( ~ ( P @ N3 )
% 5.41/5.61 => ? [M2: nat] :
% 5.41/5.61 ( ( ord_less_nat @ M2 @ N3 )
% 5.41/5.61 & ~ ( P @ M2 ) ) )
% 5.41/5.61 => ( P @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % infinite_descent
% 5.41/5.61 thf(fact_556_linorder__neqE__nat,axiom,
% 5.41/5.61 ! [X: nat,Y: nat] :
% 5.41/5.61 ( ( X != Y )
% 5.41/5.61 => ( ~ ( ord_less_nat @ X @ Y )
% 5.41/5.61 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % linorder_neqE_nat
% 5.41/5.61 thf(fact_557_le__refl,axiom,
% 5.41/5.61 ! [N: nat] : ( ord_less_eq_nat @ N @ N ) ).
% 5.41/5.61
% 5.41/5.61 % le_refl
% 5.41/5.61 thf(fact_558_le__trans,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ( ord_less_eq_nat @ J @ K )
% 5.41/5.61 => ( ord_less_eq_nat @ I @ K ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_trans
% 5.41/5.61 thf(fact_559_eq__imp__le,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( M = N )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % eq_imp_le
% 5.41/5.61 thf(fact_560_le__antisym,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.61 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.61 => ( M = N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_antisym
% 5.41/5.61 thf(fact_561_nat__le__linear,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.61 | ( ord_less_eq_nat @ N @ M ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_le_linear
% 5.41/5.61 thf(fact_562_Nat_Oex__has__greatest__nat,axiom,
% 5.41/5.61 ! [P: nat > $o,K: nat,B: nat] :
% 5.41/5.61 ( ( P @ K )
% 5.41/5.61 => ( ! [Y5: nat] :
% 5.41/5.61 ( ( P @ Y5 )
% 5.41/5.61 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.41/5.61 => ? [X6: nat] :
% 5.41/5.61 ( ( P @ X6 )
% 5.41/5.61 & ! [Y2: nat] :
% 5.41/5.61 ( ( P @ Y2 )
% 5.41/5.61 => ( ord_less_eq_nat @ Y2 @ X6 ) ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % Nat.ex_has_greatest_nat
% 5.41/5.61 thf(fact_563_size__neq__size__imp__neq,axiom,
% 5.41/5.61 ! [X: list_VEBT_VEBT,Y: list_VEBT_VEBT] :
% 5.41/5.61 ( ( ( size_s6755466524823107622T_VEBT @ X )
% 5.41/5.61 != ( size_s6755466524823107622T_VEBT @ Y ) )
% 5.41/5.61 => ( X != Y ) ) ).
% 5.41/5.61
% 5.41/5.61 % size_neq_size_imp_neq
% 5.41/5.61 thf(fact_564_size__neq__size__imp__neq,axiom,
% 5.41/5.61 ! [X: list_o,Y: list_o] :
% 5.41/5.61 ( ( ( size_size_list_o @ X )
% 5.41/5.61 != ( size_size_list_o @ Y ) )
% 5.41/5.61 => ( X != Y ) ) ).
% 5.41/5.61
% 5.41/5.61 % size_neq_size_imp_neq
% 5.41/5.61 thf(fact_565_size__neq__size__imp__neq,axiom,
% 5.41/5.61 ! [X: list_nat,Y: list_nat] :
% 5.41/5.61 ( ( ( size_size_list_nat @ X )
% 5.41/5.61 != ( size_size_list_nat @ Y ) )
% 5.41/5.61 => ( X != Y ) ) ).
% 5.41/5.61
% 5.41/5.61 % size_neq_size_imp_neq
% 5.41/5.61 thf(fact_566_size__neq__size__imp__neq,axiom,
% 5.41/5.61 ! [X: list_int,Y: list_int] :
% 5.41/5.61 ( ( ( size_size_list_int @ X )
% 5.41/5.61 != ( size_size_list_int @ Y ) )
% 5.41/5.61 => ( X != Y ) ) ).
% 5.41/5.61
% 5.41/5.61 % size_neq_size_imp_neq
% 5.41/5.61 thf(fact_567_size__neq__size__imp__neq,axiom,
% 5.41/5.61 ! [X: num,Y: num] :
% 5.41/5.61 ( ( ( size_size_num @ X )
% 5.41/5.61 != ( size_size_num @ Y ) )
% 5.41/5.61 => ( X != Y ) ) ).
% 5.41/5.61
% 5.41/5.61 % size_neq_size_imp_neq
% 5.41/5.61 thf(fact_568_mult__2,axiom,
% 5.41/5.61 ! [Z: complex] :
% 5.41/5.61 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z )
% 5.41/5.61 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2
% 5.41/5.61 thf(fact_569_mult__2,axiom,
% 5.41/5.61 ! [Z: real] :
% 5.41/5.61 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z )
% 5.41/5.61 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2
% 5.41/5.61 thf(fact_570_mult__2,axiom,
% 5.41/5.61 ! [Z: rat] :
% 5.41/5.61 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ Z )
% 5.41/5.61 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2
% 5.41/5.61 thf(fact_571_mult__2,axiom,
% 5.41/5.61 ! [Z: nat] :
% 5.41/5.61 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Z )
% 5.41/5.61 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2
% 5.41/5.61 thf(fact_572_mult__2,axiom,
% 5.41/5.61 ! [Z: int] :
% 5.41/5.61 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Z )
% 5.41/5.61 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2
% 5.41/5.61 thf(fact_573_mult__2__right,axiom,
% 5.41/5.61 ! [Z: complex] :
% 5.41/5.61 ( ( times_times_complex @ Z @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_complex @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2_right
% 5.41/5.61 thf(fact_574_mult__2__right,axiom,
% 5.41/5.61 ! [Z: real] :
% 5.41/5.61 ( ( times_times_real @ Z @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_real @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2_right
% 5.41/5.61 thf(fact_575_mult__2__right,axiom,
% 5.41/5.61 ! [Z: rat] :
% 5.41/5.61 ( ( times_times_rat @ Z @ ( numeral_numeral_rat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_rat @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2_right
% 5.41/5.61 thf(fact_576_mult__2__right,axiom,
% 5.41/5.61 ! [Z: nat] :
% 5.41/5.61 ( ( times_times_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_nat @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2_right
% 5.41/5.61 thf(fact_577_mult__2__right,axiom,
% 5.41/5.61 ! [Z: int] :
% 5.41/5.61 ( ( times_times_int @ Z @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_int @ Z @ Z ) ) ).
% 5.41/5.61
% 5.41/5.61 % mult_2_right
% 5.41/5.61 thf(fact_578_left__add__twice,axiom,
% 5.41/5.61 ! [A: complex,B: complex] :
% 5.41/5.61 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ A @ B ) )
% 5.41/5.61 = ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_add_twice
% 5.41/5.61 thf(fact_579_left__add__twice,axiom,
% 5.41/5.61 ! [A: real,B: real] :
% 5.41/5.61 ( ( plus_plus_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.41/5.61 = ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_add_twice
% 5.41/5.61 thf(fact_580_left__add__twice,axiom,
% 5.41/5.61 ! [A: rat,B: rat] :
% 5.41/5.61 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.61 = ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_add_twice
% 5.41/5.61 thf(fact_581_left__add__twice,axiom,
% 5.41/5.61 ! [A: nat,B: nat] :
% 5.41/5.61 ( ( plus_plus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.61 = ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_add_twice
% 5.41/5.61 thf(fact_582_left__add__twice,axiom,
% 5.41/5.61 ! [A: int,B: int] :
% 5.41/5.61 ( ( plus_plus_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.41/5.61 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % left_add_twice
% 5.41/5.61 thf(fact_583_power4__eq__xxxx,axiom,
% 5.41/5.61 ! [X: complex] :
% 5.41/5.61 ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.61 = ( times_times_complex @ ( times_times_complex @ ( times_times_complex @ X @ X ) @ X ) @ X ) ) ).
% 5.41/5.61
% 5.41/5.61 % power4_eq_xxxx
% 5.41/5.61 thf(fact_584_power4__eq__xxxx,axiom,
% 5.41/5.61 ! [X: real] :
% 5.41/5.61 ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.61 = ( times_times_real @ ( times_times_real @ ( times_times_real @ X @ X ) @ X ) @ X ) ) ).
% 5.41/5.61
% 5.41/5.61 % power4_eq_xxxx
% 5.41/5.61 thf(fact_585_power4__eq__xxxx,axiom,
% 5.41/5.61 ! [X: rat] :
% 5.41/5.61 ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.61 = ( times_times_rat @ ( times_times_rat @ ( times_times_rat @ X @ X ) @ X ) @ X ) ) ).
% 5.41/5.61
% 5.41/5.61 % power4_eq_xxxx
% 5.41/5.61 thf(fact_586_power4__eq__xxxx,axiom,
% 5.41/5.61 ! [X: nat] :
% 5.41/5.61 ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.61 = ( times_times_nat @ ( times_times_nat @ ( times_times_nat @ X @ X ) @ X ) @ X ) ) ).
% 5.41/5.61
% 5.41/5.61 % power4_eq_xxxx
% 5.41/5.61 thf(fact_587_power4__eq__xxxx,axiom,
% 5.41/5.61 ! [X: int] :
% 5.41/5.61 ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.61 = ( times_times_int @ ( times_times_int @ ( times_times_int @ X @ X ) @ X ) @ X ) ) ).
% 5.41/5.61
% 5.41/5.61 % power4_eq_xxxx
% 5.41/5.61 thf(fact_588_power2__eq__square,axiom,
% 5.41/5.61 ! [A: complex] :
% 5.41/5.61 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( times_times_complex @ A @ A ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_eq_square
% 5.41/5.61 thf(fact_589_power2__eq__square,axiom,
% 5.41/5.61 ! [A: real] :
% 5.41/5.61 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( times_times_real @ A @ A ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_eq_square
% 5.41/5.61 thf(fact_590_power2__eq__square,axiom,
% 5.41/5.61 ! [A: rat] :
% 5.41/5.61 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( times_times_rat @ A @ A ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_eq_square
% 5.41/5.61 thf(fact_591_power2__eq__square,axiom,
% 5.41/5.61 ! [A: nat] :
% 5.41/5.61 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( times_times_nat @ A @ A ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_eq_square
% 5.41/5.61 thf(fact_592_power2__eq__square,axiom,
% 5.41/5.61 ! [A: int] :
% 5.41/5.61 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( times_times_int @ A @ A ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_eq_square
% 5.41/5.61 thf(fact_593_power__even__eq,axiom,
% 5.41/5.61 ! [A: nat,N: nat] :
% 5.41/5.61 ( ( power_power_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.61 = ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_even_eq
% 5.41/5.61 thf(fact_594_power__even__eq,axiom,
% 5.41/5.61 ! [A: real,N: nat] :
% 5.41/5.61 ( ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.61 = ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_even_eq
% 5.41/5.61 thf(fact_595_power__even__eq,axiom,
% 5.41/5.61 ! [A: int,N: nat] :
% 5.41/5.61 ( ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.61 = ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_even_eq
% 5.41/5.61 thf(fact_596_power__even__eq,axiom,
% 5.41/5.61 ! [A: complex,N: nat] :
% 5.41/5.61 ( ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.61 = ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_even_eq
% 5.41/5.61 thf(fact_597_power__le__imp__le__exp,axiom,
% 5.41/5.61 ! [A: real,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.61 => ( ( ord_less_eq_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_le_imp_le_exp
% 5.41/5.61 thf(fact_598_power__le__imp__le__exp,axiom,
% 5.41/5.61 ! [A: rat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.61 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_le_imp_le_exp
% 5.41/5.61 thf(fact_599_power__le__imp__le__exp,axiom,
% 5.41/5.61 ! [A: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.61 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_le_imp_le_exp
% 5.41/5.61 thf(fact_600_power__le__imp__le__exp,axiom,
% 5.41/5.61 ! [A: int,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.61 => ( ( ord_less_eq_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power_le_imp_le_exp
% 5.41/5.61 thf(fact_601_one__power2,axiom,
% 5.41/5.61 ( ( power_power_rat @ one_one_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = one_one_rat ) ).
% 5.41/5.61
% 5.41/5.61 % one_power2
% 5.41/5.61 thf(fact_602_one__power2,axiom,
% 5.41/5.61 ( ( power_power_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = one_one_nat ) ).
% 5.41/5.61
% 5.41/5.61 % one_power2
% 5.41/5.61 thf(fact_603_one__power2,axiom,
% 5.41/5.61 ( ( power_power_real @ one_one_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = one_one_real ) ).
% 5.41/5.61
% 5.41/5.61 % one_power2
% 5.41/5.61 thf(fact_604_one__power2,axiom,
% 5.41/5.61 ( ( power_power_int @ one_one_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = one_one_int ) ).
% 5.41/5.61
% 5.41/5.61 % one_power2
% 5.41/5.61 thf(fact_605_one__power2,axiom,
% 5.41/5.61 ( ( power_power_complex @ one_one_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = one_one_complex ) ).
% 5.41/5.61
% 5.41/5.61 % one_power2
% 5.41/5.61 thf(fact_606_nat__1__add__1,axiom,
% 5.41/5.61 ( ( plus_plus_nat @ one_one_nat @ one_one_nat )
% 5.41/5.61 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_1_add_1
% 5.41/5.61 thf(fact_607_power2__sum,axiom,
% 5.41/5.61 ! [X: complex,Y: complex] :
% 5.41/5.61 ( ( power_power_complex @ ( plus_plus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_sum
% 5.41/5.61 thf(fact_608_power2__sum,axiom,
% 5.41/5.61 ! [X: real,Y: real] :
% 5.41/5.61 ( ( power_power_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_sum
% 5.41/5.61 thf(fact_609_power2__sum,axiom,
% 5.41/5.61 ! [X: rat,Y: rat] :
% 5.41/5.61 ( ( power_power_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_sum
% 5.41/5.61 thf(fact_610_power2__sum,axiom,
% 5.41/5.61 ! [X: nat,Y: nat] :
% 5.41/5.61 ( ( power_power_nat @ ( plus_plus_nat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_nat @ ( plus_plus_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_sum
% 5.41/5.61 thf(fact_611_power2__sum,axiom,
% 5.41/5.61 ! [X: int,Y: int] :
% 5.41/5.61 ( ( power_power_int @ ( plus_plus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.61 = ( plus_plus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % power2_sum
% 5.41/5.61 thf(fact_612_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.61 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.61 ( ( ( ord_less_eq_real @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(3)
% 5.41/5.61 thf(fact_613_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.61 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.61 ( ( ( ord_less_eq_rat @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(3)
% 5.41/5.61 thf(fact_614_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(3)
% 5.41/5.61 thf(fact_615_add__mono__thms__linordered__semiring_I3_J,axiom,
% 5.41/5.61 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.61 ( ( ( ord_less_eq_int @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(3)
% 5.41/5.61 thf(fact_616_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.61 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_eq_real @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(2)
% 5.41/5.61 thf(fact_617_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.61 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(2)
% 5.41/5.61 thf(fact_618_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(2)
% 5.41/5.61 thf(fact_619_add__mono__thms__linordered__semiring_I2_J,axiom,
% 5.41/5.61 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_eq_int @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(2)
% 5.41/5.61 thf(fact_620_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.61 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.61 ( ( ( ord_less_eq_real @ I @ J )
% 5.41/5.61 & ( ord_less_eq_real @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(1)
% 5.41/5.61 thf(fact_621_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.61 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.61 ( ( ( ord_less_eq_rat @ I @ J )
% 5.41/5.61 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(1)
% 5.41/5.61 thf(fact_622_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(1)
% 5.41/5.61 thf(fact_623_add__mono__thms__linordered__semiring_I1_J,axiom,
% 5.41/5.61 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.61 ( ( ( ord_less_eq_int @ I @ J )
% 5.41/5.61 & ( ord_less_eq_int @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_semiring(1)
% 5.41/5.61 thf(fact_624_add__mono,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.61 => ( ( ord_less_eq_real @ C @ D )
% 5.41/5.61 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono
% 5.41/5.61 thf(fact_625_add__mono,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.61 => ( ( ord_less_eq_rat @ C @ D )
% 5.41/5.61 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono
% 5.41/5.61 thf(fact_626_add__mono,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.61 => ( ( ord_less_eq_nat @ C @ D )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono
% 5.41/5.61 thf(fact_627_add__mono,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.61 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.61 => ( ( ord_less_eq_int @ C @ D )
% 5.41/5.61 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono
% 5.41/5.61 thf(fact_628_add__left__mono,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.61 => ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_mono
% 5.41/5.61 thf(fact_629_add__left__mono,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.61 => ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_mono
% 5.41/5.61 thf(fact_630_add__left__mono,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_mono
% 5.41/5.61 thf(fact_631_add__left__mono,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.61 => ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_left_mono
% 5.41/5.61 thf(fact_632_less__eqE,axiom,
% 5.41/5.61 ! [A: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.61 => ~ ! [C2: nat] :
% 5.41/5.61 ( B
% 5.41/5.61 != ( plus_plus_nat @ A @ C2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_eqE
% 5.41/5.61 thf(fact_633_add__right__mono,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.61 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_mono
% 5.41/5.61 thf(fact_634_add__right__mono,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.61 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_mono
% 5.41/5.61 thf(fact_635_add__right__mono,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_mono
% 5.41/5.61 thf(fact_636_add__right__mono,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.61 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_right_mono
% 5.41/5.61 thf(fact_637_le__iff__add,axiom,
% 5.41/5.61 ( ord_less_eq_nat
% 5.41/5.61 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.61 ? [C3: nat] :
% 5.41/5.61 ( B2
% 5.41/5.61 = ( plus_plus_nat @ A3 @ C3 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_iff_add
% 5.41/5.61 thf(fact_638_add__le__imp__le__left,axiom,
% 5.41/5.61 ! [C: real,A: real,B: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.41/5.61 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_left
% 5.41/5.61 thf(fact_639_add__le__imp__le__left,axiom,
% 5.41/5.61 ! [C: rat,A: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.41/5.61 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_left
% 5.41/5.61 thf(fact_640_add__le__imp__le__left,axiom,
% 5.41/5.61 ! [C: nat,A: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.41/5.61 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_left
% 5.41/5.61 thf(fact_641_add__le__imp__le__left,axiom,
% 5.41/5.61 ! [C: int,A: int,B: int] :
% 5.41/5.61 ( ( ord_less_eq_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.41/5.61 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_left
% 5.41/5.61 thf(fact_642_add__le__imp__le__right,axiom,
% 5.41/5.61 ! [A: real,C: real,B: real] :
% 5.41/5.61 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.41/5.61 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_right
% 5.41/5.61 thf(fact_643_add__le__imp__le__right,axiom,
% 5.41/5.61 ! [A: rat,C: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.61 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_right
% 5.41/5.61 thf(fact_644_add__le__imp__le__right,axiom,
% 5.41/5.61 ! [A: nat,C: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.61 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_right
% 5.41/5.61 thf(fact_645_add__le__imp__le__right,axiom,
% 5.41/5.61 ! [A: int,C: int,B: int] :
% 5.41/5.61 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.41/5.61 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_imp_le_right
% 5.41/5.61 thf(fact_646_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.61 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.61 ( ( ( ord_less_real @ I @ J )
% 5.41/5.61 & ( ord_less_real @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(5)
% 5.41/5.61 thf(fact_647_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.61 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.61 ( ( ( ord_less_rat @ I @ J )
% 5.41/5.61 & ( ord_less_rat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(5)
% 5.41/5.61 thf(fact_648_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ( ord_less_nat @ I @ J )
% 5.41/5.61 & ( ord_less_nat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(5)
% 5.41/5.61 thf(fact_649_add__mono__thms__linordered__field_I5_J,axiom,
% 5.41/5.61 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.61 ( ( ( ord_less_int @ I @ J )
% 5.41/5.61 & ( ord_less_int @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(5)
% 5.41/5.61 thf(fact_650_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.61 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_real @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(2)
% 5.41/5.61 thf(fact_651_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.61 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_rat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(2)
% 5.41/5.61 thf(fact_652_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_nat @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(2)
% 5.41/5.61 thf(fact_653_add__mono__thms__linordered__field_I2_J,axiom,
% 5.41/5.61 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.61 ( ( ( I = J )
% 5.41/5.61 & ( ord_less_int @ K @ L2 ) )
% 5.41/5.61 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(2)
% 5.41/5.61 thf(fact_654_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.61 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.61 ( ( ( ord_less_real @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(1)
% 5.41/5.61 thf(fact_655_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.61 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.61 ( ( ( ord_less_rat @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(1)
% 5.41/5.61 thf(fact_656_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ( ord_less_nat @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(1)
% 5.41/5.61 thf(fact_657_add__mono__thms__linordered__field_I1_J,axiom,
% 5.41/5.61 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.61 ( ( ( ord_less_int @ I @ J )
% 5.41/5.61 & ( K = L2 ) )
% 5.41/5.61 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_mono_thms_linordered_field(1)
% 5.41/5.61 thf(fact_658_add__strict__mono,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.61 ( ( ord_less_real @ A @ B )
% 5.41/5.61 => ( ( ord_less_real @ C @ D )
% 5.41/5.61 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_mono
% 5.41/5.61 thf(fact_659_add__strict__mono,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.61 ( ( ord_less_rat @ A @ B )
% 5.41/5.61 => ( ( ord_less_rat @ C @ D )
% 5.41/5.61 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_mono
% 5.41/5.61 thf(fact_660_add__strict__mono,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.61 ( ( ord_less_nat @ A @ B )
% 5.41/5.61 => ( ( ord_less_nat @ C @ D )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_mono
% 5.41/5.61 thf(fact_661_add__strict__mono,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.61 ( ( ord_less_int @ A @ B )
% 5.41/5.61 => ( ( ord_less_int @ C @ D )
% 5.41/5.61 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_mono
% 5.41/5.61 thf(fact_662_add__strict__left__mono,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( ord_less_real @ A @ B )
% 5.41/5.61 => ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_left_mono
% 5.41/5.61 thf(fact_663_add__strict__left__mono,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( ord_less_rat @ A @ B )
% 5.41/5.61 => ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_left_mono
% 5.41/5.61 thf(fact_664_add__strict__left__mono,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( ord_less_nat @ A @ B )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_left_mono
% 5.41/5.61 thf(fact_665_add__strict__left__mono,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( ord_less_int @ A @ B )
% 5.41/5.61 => ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_left_mono
% 5.41/5.61 thf(fact_666_add__strict__right__mono,axiom,
% 5.41/5.61 ! [A: real,B: real,C: real] :
% 5.41/5.61 ( ( ord_less_real @ A @ B )
% 5.41/5.61 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_right_mono
% 5.41/5.61 thf(fact_667_add__strict__right__mono,axiom,
% 5.41/5.61 ! [A: rat,B: rat,C: rat] :
% 5.41/5.61 ( ( ord_less_rat @ A @ B )
% 5.41/5.61 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_right_mono
% 5.41/5.61 thf(fact_668_add__strict__right__mono,axiom,
% 5.41/5.61 ! [A: nat,B: nat,C: nat] :
% 5.41/5.61 ( ( ord_less_nat @ A @ B )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_right_mono
% 5.41/5.61 thf(fact_669_add__strict__right__mono,axiom,
% 5.41/5.61 ! [A: int,B: int,C: int] :
% 5.41/5.61 ( ( ord_less_int @ A @ B )
% 5.41/5.61 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_strict_right_mono
% 5.41/5.61 thf(fact_670_add__less__imp__less__left,axiom,
% 5.41/5.61 ! [C: real,A: real,B: real] :
% 5.41/5.61 ( ( ord_less_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.41/5.61 => ( ord_less_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_left
% 5.41/5.61 thf(fact_671_add__less__imp__less__left,axiom,
% 5.41/5.61 ! [C: rat,A: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.41/5.61 => ( ord_less_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_left
% 5.41/5.61 thf(fact_672_add__less__imp__less__left,axiom,
% 5.41/5.61 ! [C: nat,A: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.41/5.61 => ( ord_less_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_left
% 5.41/5.61 thf(fact_673_add__less__imp__less__left,axiom,
% 5.41/5.61 ! [C: int,A: int,B: int] :
% 5.41/5.61 ( ( ord_less_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.41/5.61 => ( ord_less_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_left
% 5.41/5.61 thf(fact_674_add__less__imp__less__right,axiom,
% 5.41/5.61 ! [A: real,C: real,B: real] :
% 5.41/5.61 ( ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.41/5.61 => ( ord_less_real @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_right
% 5.41/5.61 thf(fact_675_add__less__imp__less__right,axiom,
% 5.41/5.61 ! [A: rat,C: rat,B: rat] :
% 5.41/5.61 ( ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.61 => ( ord_less_rat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_right
% 5.41/5.61 thf(fact_676_add__less__imp__less__right,axiom,
% 5.41/5.61 ! [A: nat,C: nat,B: nat] :
% 5.41/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.61 => ( ord_less_nat @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_right
% 5.41/5.61 thf(fact_677_add__less__imp__less__right,axiom,
% 5.41/5.61 ! [A: int,C: int,B: int] :
% 5.41/5.61 ( ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.41/5.61 => ( ord_less_int @ A @ B ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_imp_less_right
% 5.41/5.61 thf(fact_678_nat__less__le,axiom,
% 5.41/5.61 ( ord_less_nat
% 5.41/5.61 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.41/5.61 & ( M3 != N2 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % nat_less_le
% 5.41/5.61 thf(fact_679_less__imp__le__nat,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ M @ N )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_imp_le_nat
% 5.41/5.61 thf(fact_680_le__eq__less__or__eq,axiom,
% 5.41/5.61 ( ord_less_eq_nat
% 5.41/5.61 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.61 ( ( ord_less_nat @ M3 @ N2 )
% 5.41/5.61 | ( M3 = N2 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_eq_less_or_eq
% 5.41/5.61 thf(fact_681_less__or__eq__imp__le,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( ( ord_less_nat @ M @ N )
% 5.41/5.61 | ( M = N ) )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_or_eq_imp_le
% 5.41/5.61 thf(fact_682_le__neq__implies__less,axiom,
% 5.41/5.61 ! [M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.61 => ( ( M != N )
% 5.41/5.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_neq_implies_less
% 5.41/5.61 thf(fact_683_less__mono__imp__le__mono,axiom,
% 5.41/5.61 ! [F: nat > nat,I: nat,J: nat] :
% 5.41/5.61 ( ! [I4: nat,J2: nat] :
% 5.41/5.61 ( ( ord_less_nat @ I4 @ J2 )
% 5.41/5.61 => ( ord_less_nat @ ( F @ I4 ) @ ( F @ J2 ) ) )
% 5.41/5.61 => ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ord_less_eq_nat @ ( F @ I ) @ ( F @ J ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_mono_imp_le_mono
% 5.41/5.61 thf(fact_684_add__lessD1,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat] :
% 5.41/5.61 ( ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.41/5.61 => ( ord_less_nat @ I @ K ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_lessD1
% 5.41/5.61 thf(fact_685_add__less__mono,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ord_less_nat @ I @ J )
% 5.41/5.61 => ( ( ord_less_nat @ K @ L2 )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_mono
% 5.41/5.61 thf(fact_686_not__add__less1,axiom,
% 5.41/5.61 ! [I: nat,J: nat] :
% 5.41/5.61 ~ ( ord_less_nat @ ( plus_plus_nat @ I @ J ) @ I ) ).
% 5.41/5.61
% 5.41/5.61 % not_add_less1
% 5.41/5.61 thf(fact_687_not__add__less2,axiom,
% 5.41/5.61 ! [J: nat,I: nat] :
% 5.41/5.61 ~ ( ord_less_nat @ ( plus_plus_nat @ J @ I ) @ I ) ).
% 5.41/5.61
% 5.41/5.61 % not_add_less2
% 5.41/5.61 thf(fact_688_add__less__mono1,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat] :
% 5.41/5.61 ( ( ord_less_nat @ I @ J )
% 5.41/5.61 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_less_mono1
% 5.41/5.61 thf(fact_689_trans__less__add1,axiom,
% 5.41/5.61 ! [I: nat,J: nat,M: nat] :
% 5.41/5.61 ( ( ord_less_nat @ I @ J )
% 5.41/5.61 => ( ord_less_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % trans_less_add1
% 5.41/5.61 thf(fact_690_trans__less__add2,axiom,
% 5.41/5.61 ! [I: nat,J: nat,M: nat] :
% 5.41/5.61 ( ( ord_less_nat @ I @ J )
% 5.41/5.61 => ( ord_less_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % trans_less_add2
% 5.41/5.61 thf(fact_691_less__add__eq__less,axiom,
% 5.41/5.61 ! [K: nat,L2: nat,M: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_nat @ K @ L2 )
% 5.41/5.61 => ( ( ( plus_plus_nat @ M @ L2 )
% 5.41/5.61 = ( plus_plus_nat @ K @ N ) )
% 5.41/5.61 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % less_add_eq_less
% 5.41/5.61 thf(fact_692_add__leE,axiom,
% 5.41/5.61 ! [M: nat,K: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.41/5.61 => ~ ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.61 => ~ ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_leE
% 5.41/5.61 thf(fact_693_le__add1,axiom,
% 5.41/5.61 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ N @ M ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_add1
% 5.41/5.61 thf(fact_694_le__add2,axiom,
% 5.41/5.61 ! [N: nat,M: nat] : ( ord_less_eq_nat @ N @ ( plus_plus_nat @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_add2
% 5.41/5.61 thf(fact_695_add__leD1,axiom,
% 5.41/5.61 ! [M: nat,K: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.41/5.61 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_leD1
% 5.41/5.61 thf(fact_696_add__leD2,axiom,
% 5.41/5.61 ! [M: nat,K: nat,N: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ ( plus_plus_nat @ M @ K ) @ N )
% 5.41/5.61 => ( ord_less_eq_nat @ K @ N ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_leD2
% 5.41/5.61 thf(fact_697_le__Suc__ex,axiom,
% 5.41/5.61 ! [K: nat,L2: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ K @ L2 )
% 5.41/5.61 => ? [N3: nat] :
% 5.41/5.61 ( L2
% 5.41/5.61 = ( plus_plus_nat @ K @ N3 ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % le_Suc_ex
% 5.41/5.61 thf(fact_698_add__le__mono,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ( ord_less_eq_nat @ K @ L2 )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_mono
% 5.41/5.61 thf(fact_699_add__le__mono1,axiom,
% 5.41/5.61 ! [I: nat,J: nat,K: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % add_le_mono1
% 5.41/5.61 thf(fact_700_trans__le__add1,axiom,
% 5.41/5.61 ! [I: nat,J: nat,M: nat] :
% 5.41/5.61 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.61 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ J @ M ) ) ) ).
% 5.41/5.61
% 5.41/5.61 % trans_le_add1
% 5.41/5.62 thf(fact_701_trans__le__add2,axiom,
% 5.41/5.62 ! [I: nat,J: nat,M: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.62 => ( ord_less_eq_nat @ I @ ( plus_plus_nat @ M @ J ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % trans_le_add2
% 5.41/5.62 thf(fact_702_nat__le__iff__add,axiom,
% 5.41/5.62 ( ord_less_eq_nat
% 5.41/5.62 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.62 ? [K2: nat] :
% 5.41/5.62 ( N2
% 5.41/5.62 = ( plus_plus_nat @ M3 @ K2 ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nat_le_iff_add
% 5.41/5.62 thf(fact_703_ex__power__ivl1,axiom,
% 5.41/5.62 ! [B: nat,K: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.41/5.62 => ( ( ord_less_eq_nat @ one_one_nat @ K )
% 5.41/5.62 => ? [N3: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.41/5.62 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ex_power_ivl1
% 5.41/5.62 thf(fact_704_ex__power__ivl2,axiom,
% 5.41/5.62 ! [B: nat,K: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.41/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.62 => ? [N3: nat] :
% 5.41/5.62 ( ( ord_less_nat @ ( power_power_nat @ B @ N3 ) @ K )
% 5.41/5.62 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N3 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ex_power_ivl2
% 5.41/5.62 thf(fact_705_add__less__le__mono,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.62 ( ( ord_less_real @ A @ B )
% 5.41/5.62 => ( ( ord_less_eq_real @ C @ D )
% 5.41/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_le_mono
% 5.41/5.62 thf(fact_706_add__less__le__mono,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.62 ( ( ord_less_rat @ A @ B )
% 5.41/5.62 => ( ( ord_less_eq_rat @ C @ D )
% 5.41/5.62 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_le_mono
% 5.41/5.62 thf(fact_707_add__less__le__mono,axiom,
% 5.41/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.62 ( ( ord_less_nat @ A @ B )
% 5.41/5.62 => ( ( ord_less_eq_nat @ C @ D )
% 5.41/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_le_mono
% 5.41/5.62 thf(fact_708_add__less__le__mono,axiom,
% 5.41/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.62 ( ( ord_less_int @ A @ B )
% 5.41/5.62 => ( ( ord_less_eq_int @ C @ D )
% 5.41/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_le_mono
% 5.41/5.62 thf(fact_709_add__le__less__mono,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.62 => ( ( ord_less_real @ C @ D )
% 5.41/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_less_mono
% 5.41/5.62 thf(fact_710_add__le__less__mono,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.62 => ( ( ord_less_rat @ C @ D )
% 5.41/5.62 => ( ord_less_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_less_mono
% 5.41/5.62 thf(fact_711_add__le__less__mono,axiom,
% 5.41/5.62 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.62 => ( ( ord_less_nat @ C @ D )
% 5.41/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_less_mono
% 5.41/5.62 thf(fact_712_add__le__less__mono,axiom,
% 5.41/5.62 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.62 => ( ( ord_less_int @ C @ D )
% 5.41/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_less_mono
% 5.41/5.62 thf(fact_713_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.62 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.62 ( ( ( ord_less_real @ I @ J )
% 5.41/5.62 & ( ord_less_eq_real @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(3)
% 5.41/5.62 thf(fact_714_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.62 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.62 ( ( ( ord_less_rat @ I @ J )
% 5.41/5.62 & ( ord_less_eq_rat @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(3)
% 5.41/5.62 thf(fact_715_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.62 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.62 ( ( ( ord_less_nat @ I @ J )
% 5.41/5.62 & ( ord_less_eq_nat @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(3)
% 5.41/5.62 thf(fact_716_add__mono__thms__linordered__field_I3_J,axiom,
% 5.41/5.62 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.62 ( ( ( ord_less_int @ I @ J )
% 5.41/5.62 & ( ord_less_eq_int @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(3)
% 5.41/5.62 thf(fact_717_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.62 ! [I: real,J: real,K: real,L2: real] :
% 5.41/5.62 ( ( ( ord_less_eq_real @ I @ J )
% 5.41/5.62 & ( ord_less_real @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_real @ ( plus_plus_real @ I @ K ) @ ( plus_plus_real @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(4)
% 5.41/5.62 thf(fact_718_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.62 ! [I: rat,J: rat,K: rat,L2: rat] :
% 5.41/5.62 ( ( ( ord_less_eq_rat @ I @ J )
% 5.41/5.62 & ( ord_less_rat @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_rat @ ( plus_plus_rat @ I @ K ) @ ( plus_plus_rat @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(4)
% 5.41/5.62 thf(fact_719_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.62 ! [I: nat,J: nat,K: nat,L2: nat] :
% 5.41/5.62 ( ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.62 & ( ord_less_nat @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ ( plus_plus_nat @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(4)
% 5.41/5.62 thf(fact_720_add__mono__thms__linordered__field_I4_J,axiom,
% 5.41/5.62 ! [I: int,J: int,K: int,L2: int] :
% 5.41/5.62 ( ( ( ord_less_eq_int @ I @ J )
% 5.41/5.62 & ( ord_less_int @ K @ L2 ) )
% 5.41/5.62 => ( ord_less_int @ ( plus_plus_int @ I @ K ) @ ( plus_plus_int @ J @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono_thms_linordered_field(4)
% 5.41/5.62 thf(fact_721_mono__nat__linear__lb,axiom,
% 5.41/5.62 ! [F: nat > nat,M: nat,K: nat] :
% 5.41/5.62 ( ! [M4: nat,N3: nat] :
% 5.41/5.62 ( ( ord_less_nat @ M4 @ N3 )
% 5.41/5.62 => ( ord_less_nat @ ( F @ M4 ) @ ( F @ N3 ) ) )
% 5.41/5.62 => ( ord_less_eq_nat @ ( plus_plus_nat @ ( F @ M ) @ K ) @ ( F @ ( plus_plus_nat @ M @ K ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mono_nat_linear_lb
% 5.41/5.62 thf(fact_722_set__vebt__set__vebt_H__valid,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,N: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.62 => ( ( vEBT_set_vebt @ T )
% 5.41/5.62 = ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % set_vebt_set_vebt'_valid
% 5.41/5.62 thf(fact_723_add__self__div__2,axiom,
% 5.41/5.62 ! [M: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.62 = M ) ).
% 5.41/5.62
% 5.41/5.62 % add_self_div_2
% 5.41/5.62 thf(fact_724_both__member__options__ding,axiom,
% 5.41/5.62 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.41/5.62 => ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.41/5.62 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.62 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % both_member_options_ding
% 5.41/5.62 thf(fact_725_sum__squares__bound,axiom,
% 5.41/5.62 ! [X: real,Y: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % sum_squares_bound
% 5.41/5.62 thf(fact_726_sum__squares__bound,axiom,
% 5.41/5.62 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % sum_squares_bound
% 5.41/5.62 thf(fact_727_div__exp__eq,axiom,
% 5.41/5.62 ! [A: nat,M: nat,N: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.62 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_exp_eq
% 5.41/5.62 thf(fact_728_div__exp__eq,axiom,
% 5.41/5.62 ! [A: int,M: nat,N: nat] :
% 5.41/5.62 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.62 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_exp_eq
% 5.41/5.62 thf(fact_729_field__less__half__sum,axiom,
% 5.41/5.62 ! [X: real,Y: real] :
% 5.41/5.62 ( ( ord_less_real @ X @ Y )
% 5.41/5.62 => ( ord_less_real @ X @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % field_less_half_sum
% 5.41/5.62 thf(fact_730_field__less__half__sum,axiom,
% 5.41/5.62 ! [X: rat,Y: rat] :
% 5.41/5.62 ( ( ord_less_rat @ X @ Y )
% 5.41/5.62 => ( ord_less_rat @ X @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % field_less_half_sum
% 5.41/5.62 thf(fact_731_div__by__1,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ A @ one_one_complex )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_1
% 5.41/5.62 thf(fact_732_div__by__1,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( divide_divide_real @ A @ one_one_real )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_1
% 5.41/5.62 thf(fact_733_div__by__1,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ A @ one_one_rat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_1
% 5.41/5.62 thf(fact_734_div__by__1,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_1
% 5.41/5.62 thf(fact_735_div__by__1,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( divide_divide_int @ A @ one_one_int )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_1
% 5.41/5.62 thf(fact_736_bits__div__by__1,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ A @ one_one_nat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % bits_div_by_1
% 5.41/5.62 thf(fact_737_bits__div__by__1,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( divide_divide_int @ A @ one_one_int )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % bits_div_by_1
% 5.41/5.62 thf(fact_738_times__divide__eq__left,axiom,
% 5.41/5.62 ! [B: complex,C: complex,A: complex] :
% 5.41/5.62 ( ( times_times_complex @ ( divide1717551699836669952omplex @ B @ C ) @ A )
% 5.41/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ B @ A ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_eq_left
% 5.41/5.62 thf(fact_739_times__divide__eq__left,axiom,
% 5.41/5.62 ! [B: real,C: real,A: real] :
% 5.41/5.62 ( ( times_times_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.41/5.62 = ( divide_divide_real @ ( times_times_real @ B @ A ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_eq_left
% 5.41/5.62 thf(fact_740_times__divide__eq__left,axiom,
% 5.41/5.62 ! [B: rat,C: rat,A: rat] :
% 5.41/5.62 ( ( times_times_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.41/5.62 = ( divide_divide_rat @ ( times_times_rat @ B @ A ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_eq_left
% 5.41/5.62 thf(fact_741_divide__divide__eq__left,axiom,
% 5.41/5.62 ! [A: complex,B: complex,C: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_left
% 5.41/5.62 thf(fact_742_divide__divide__eq__left,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.41/5.62 = ( divide_divide_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_left
% 5.41/5.62 thf(fact_743_divide__divide__eq__left,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.41/5.62 = ( divide_divide_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_left
% 5.41/5.62 thf(fact_744_divide__divide__eq__right,axiom,
% 5.41/5.62 ! [A: complex,B: complex,C: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_right
% 5.41/5.62 thf(fact_745_divide__divide__eq__right,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( divide_divide_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.62 = ( divide_divide_real @ ( times_times_real @ A @ C ) @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_right
% 5.41/5.62 thf(fact_746_divide__divide__eq__right,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.62 = ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_right
% 5.41/5.62 thf(fact_747_times__divide__eq__right,axiom,
% 5.41/5.62 ! [A: complex,B: complex,C: complex] :
% 5.41/5.62 ( ( times_times_complex @ A @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_eq_right
% 5.41/5.62 thf(fact_748_times__divide__eq__right,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( times_times_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.62 = ( divide_divide_real @ ( times_times_real @ A @ B ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_eq_right
% 5.41/5.62 thf(fact_749_times__divide__eq__right,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( times_times_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.62 = ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_eq_right
% 5.41/5.62 thf(fact_750_deg__deg__n,axiom,
% 5.41/5.62 ! [Info: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ ( vEBT_Node @ Info @ Deg @ TreeList2 @ Summary ) @ N )
% 5.41/5.62 => ( Deg = N ) ) ).
% 5.41/5.62
% 5.41/5.62 % deg_deg_n
% 5.41/5.62 thf(fact_751_semiring__norm_I13_J,axiom,
% 5.41/5.62 ! [M: num,N: num] :
% 5.41/5.62 ( ( times_times_num @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.62 = ( bit0 @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % semiring_norm(13)
% 5.41/5.62 thf(fact_752_semiring__norm_I11_J,axiom,
% 5.41/5.62 ! [M: num] :
% 5.41/5.62 ( ( times_times_num @ M @ one )
% 5.41/5.62 = M ) ).
% 5.41/5.62
% 5.41/5.62 % semiring_norm(11)
% 5.41/5.62 thf(fact_753_semiring__norm_I12_J,axiom,
% 5.41/5.62 ! [N: num] :
% 5.41/5.62 ( ( times_times_num @ one @ N )
% 5.41/5.62 = N ) ).
% 5.41/5.62
% 5.41/5.62 % semiring_norm(12)
% 5.41/5.62 thf(fact_754_num__double,axiom,
% 5.41/5.62 ! [N: num] :
% 5.41/5.62 ( ( times_times_num @ ( bit0 @ one ) @ N )
% 5.41/5.62 = ( bit0 @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % num_double
% 5.41/5.62 thf(fact_755_power__mult__numeral,axiom,
% 5.41/5.62 ! [A: nat,M: num,N: num] :
% 5.41/5.62 ( ( power_power_nat @ ( power_power_nat @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.62 = ( power_power_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_mult_numeral
% 5.41/5.62 thf(fact_756_power__mult__numeral,axiom,
% 5.41/5.62 ! [A: real,M: num,N: num] :
% 5.41/5.62 ( ( power_power_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.62 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_mult_numeral
% 5.41/5.62 thf(fact_757_power__mult__numeral,axiom,
% 5.41/5.62 ! [A: int,M: num,N: num] :
% 5.41/5.62 ( ( power_power_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.62 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_mult_numeral
% 5.41/5.62 thf(fact_758_power__mult__numeral,axiom,
% 5.41/5.62 ! [A: complex,M: num,N: num] :
% 5.41/5.62 ( ( power_power_complex @ ( power_power_complex @ A @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.62 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_mult_numeral
% 5.41/5.62 thf(fact_759_succ__member,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.41/5.62 ( ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.41/5.62 = ( ( vEBT_vebt_member @ T @ Y )
% 5.41/5.62 & ( ord_less_nat @ X @ Y )
% 5.41/5.62 & ! [Z3: nat] :
% 5.41/5.62 ( ( ( vEBT_vebt_member @ T @ Z3 )
% 5.41/5.62 & ( ord_less_nat @ X @ Z3 ) )
% 5.41/5.62 => ( ord_less_eq_nat @ Y @ Z3 ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % succ_member
% 5.41/5.62 thf(fact_760_pred__member,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,X: nat,Y: nat] :
% 5.41/5.62 ( ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Y )
% 5.41/5.62 = ( ( vEBT_vebt_member @ T @ Y )
% 5.41/5.62 & ( ord_less_nat @ Y @ X )
% 5.41/5.62 & ! [Z3: nat] :
% 5.41/5.62 ( ( ( vEBT_vebt_member @ T @ Z3 )
% 5.41/5.62 & ( ord_less_nat @ Z3 @ X ) )
% 5.41/5.62 => ( ord_less_eq_nat @ Z3 @ Y ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % pred_member
% 5.41/5.62 thf(fact_761_two__realpow__ge__one,axiom,
% 5.41/5.62 ! [N: nat] : ( ord_less_eq_real @ one_one_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % two_realpow_ge_one
% 5.41/5.62 thf(fact_762_four__x__squared,axiom,
% 5.41/5.62 ! [X: real] :
% 5.41/5.62 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.62 = ( power_power_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % four_x_squared
% 5.41/5.62 thf(fact_763_L2__set__mult__ineq__lemma,axiom,
% 5.41/5.62 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( times_times_real @ A @ C ) ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % L2_set_mult_ineq_lemma
% 5.41/5.62 thf(fact_764_div__mult2__numeral__eq,axiom,
% 5.41/5.62 ! [A: nat,K: num,L2: num] :
% 5.41/5.62 ( ( divide_divide_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.62 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult2_numeral_eq
% 5.41/5.62 thf(fact_765_div__mult2__numeral__eq,axiom,
% 5.41/5.62 ! [A: int,K: num,L2: num] :
% 5.41/5.62 ( ( divide_divide_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ L2 ) )
% 5.41/5.62 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( times_times_num @ K @ L2 ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult2_numeral_eq
% 5.41/5.62 thf(fact_766_linorder__neqE__linordered__idom,axiom,
% 5.41/5.62 ! [X: real,Y: real] :
% 5.41/5.62 ( ( X != Y )
% 5.41/5.62 => ( ~ ( ord_less_real @ X @ Y )
% 5.41/5.62 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % linorder_neqE_linordered_idom
% 5.41/5.62 thf(fact_767_linorder__neqE__linordered__idom,axiom,
% 5.41/5.62 ! [X: rat,Y: rat] :
% 5.41/5.62 ( ( X != Y )
% 5.41/5.62 => ( ~ ( ord_less_rat @ X @ Y )
% 5.41/5.62 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % linorder_neqE_linordered_idom
% 5.41/5.62 thf(fact_768_linorder__neqE__linordered__idom,axiom,
% 5.41/5.62 ! [X: int,Y: int] :
% 5.41/5.62 ( ( X != Y )
% 5.41/5.62 => ( ~ ( ord_less_int @ X @ Y )
% 5.41/5.62 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % linorder_neqE_linordered_idom
% 5.41/5.62 thf(fact_769_linordered__field__no__ub,axiom,
% 5.41/5.62 ! [X4: real] :
% 5.41/5.62 ? [X_1: real] : ( ord_less_real @ X4 @ X_1 ) ).
% 5.41/5.62
% 5.41/5.62 % linordered_field_no_ub
% 5.41/5.62 thf(fact_770_linordered__field__no__ub,axiom,
% 5.41/5.62 ! [X4: rat] :
% 5.41/5.62 ? [X_1: rat] : ( ord_less_rat @ X4 @ X_1 ) ).
% 5.41/5.62
% 5.41/5.62 % linordered_field_no_ub
% 5.41/5.62 thf(fact_771_linordered__field__no__lb,axiom,
% 5.41/5.62 ! [X4: real] :
% 5.41/5.62 ? [Y5: real] : ( ord_less_real @ Y5 @ X4 ) ).
% 5.41/5.62
% 5.41/5.62 % linordered_field_no_lb
% 5.41/5.62 thf(fact_772_linordered__field__no__lb,axiom,
% 5.41/5.62 ! [X4: rat] :
% 5.41/5.62 ? [Y5: rat] : ( ord_less_rat @ Y5 @ X4 ) ).
% 5.41/5.62
% 5.41/5.62 % linordered_field_no_lb
% 5.41/5.62 thf(fact_773_combine__common__factor,axiom,
% 5.41/5.62 ! [A: real,E: real,B: real,C: real] :
% 5.41/5.62 ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ C ) )
% 5.41/5.62 = ( plus_plus_real @ ( times_times_real @ ( plus_plus_real @ A @ B ) @ E ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % combine_common_factor
% 5.41/5.62 thf(fact_774_combine__common__factor,axiom,
% 5.41/5.62 ! [A: rat,E: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ C ) )
% 5.41/5.62 = ( plus_plus_rat @ ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ E ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % combine_common_factor
% 5.41/5.62 thf(fact_775_combine__common__factor,axiom,
% 5.41/5.62 ! [A: nat,E: nat,B: nat,C: nat] :
% 5.41/5.62 ( ( plus_plus_nat @ ( times_times_nat @ A @ E ) @ ( plus_plus_nat @ ( times_times_nat @ B @ E ) @ C ) )
% 5.41/5.62 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ E ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % combine_common_factor
% 5.41/5.62 thf(fact_776_combine__common__factor,axiom,
% 5.41/5.62 ! [A: int,E: int,B: int,C: int] :
% 5.41/5.62 ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ C ) )
% 5.41/5.62 = ( plus_plus_int @ ( times_times_int @ ( plus_plus_int @ A @ B ) @ E ) @ C ) ) ).
% 5.41/5.62
% 5.41/5.62 % combine_common_factor
% 5.41/5.62 thf(fact_777_distrib__right,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_right
% 5.41/5.62 thf(fact_778_distrib__right,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_right
% 5.41/5.62 thf(fact_779_distrib__right,axiom,
% 5.41/5.62 ! [A: nat,B: nat,C: nat] :
% 5.41/5.62 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_right
% 5.41/5.62 thf(fact_780_distrib__right,axiom,
% 5.41/5.62 ! [A: int,B: int,C: int] :
% 5.41/5.62 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_right
% 5.41/5.62 thf(fact_781_distrib__left,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.41/5.62 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_left
% 5.41/5.62 thf(fact_782_distrib__left,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.62 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_left
% 5.41/5.62 thf(fact_783_distrib__left,axiom,
% 5.41/5.62 ! [A: nat,B: nat,C: nat] :
% 5.41/5.62 ( ( times_times_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.62 = ( plus_plus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_left
% 5.41/5.62 thf(fact_784_distrib__left,axiom,
% 5.41/5.62 ! [A: int,B: int,C: int] :
% 5.41/5.62 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.41/5.62 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % distrib_left
% 5.41/5.62 thf(fact_785_comm__semiring__class_Odistrib,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % comm_semiring_class.distrib
% 5.41/5.62 thf(fact_786_comm__semiring__class_Odistrib,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % comm_semiring_class.distrib
% 5.41/5.62 thf(fact_787_comm__semiring__class_Odistrib,axiom,
% 5.41/5.62 ! [A: nat,B: nat,C: nat] :
% 5.41/5.62 ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % comm_semiring_class.distrib
% 5.41/5.62 thf(fact_788_comm__semiring__class_Odistrib,axiom,
% 5.41/5.62 ! [A: int,B: int,C: int] :
% 5.41/5.62 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % comm_semiring_class.distrib
% 5.41/5.62 thf(fact_789_ring__class_Oring__distribs_I1_J,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( times_times_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.41/5.62 = ( plus_plus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ring_class.ring_distribs(1)
% 5.41/5.62 thf(fact_790_ring__class_Oring__distribs_I1_J,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( times_times_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.62 = ( plus_plus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ring_class.ring_distribs(1)
% 5.41/5.62 thf(fact_791_ring__class_Oring__distribs_I1_J,axiom,
% 5.41/5.62 ! [A: int,B: int,C: int] :
% 5.41/5.62 ( ( times_times_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.41/5.62 = ( plus_plus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ring_class.ring_distribs(1)
% 5.41/5.62 thf(fact_792_ring__class_Oring__distribs_I2_J,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( times_times_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ring_class.ring_distribs(2)
% 5.41/5.62 thf(fact_793_ring__class_Oring__distribs_I2_J,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( times_times_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ring_class.ring_distribs(2)
% 5.41/5.62 thf(fact_794_ring__class_Oring__distribs_I2_J,axiom,
% 5.41/5.62 ! [A: int,B: int,C: int] :
% 5.41/5.62 ( ( times_times_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % ring_class.ring_distribs(2)
% 5.41/5.62 thf(fact_795_divide__divide__eq__left_H,axiom,
% 5.41/5.62 ! [A: complex,B: complex,C: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ A @ B ) @ C )
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ ( times_times_complex @ C @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_left'
% 5.41/5.62 thf(fact_796_divide__divide__eq__left_H,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( divide_divide_real @ ( divide_divide_real @ A @ B ) @ C )
% 5.41/5.62 = ( divide_divide_real @ A @ ( times_times_real @ C @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_left'
% 5.41/5.62 thf(fact_797_divide__divide__eq__left_H,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ ( divide_divide_rat @ A @ B ) @ C )
% 5.41/5.62 = ( divide_divide_rat @ A @ ( times_times_rat @ C @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_eq_left'
% 5.41/5.62 thf(fact_798_divide__divide__times__eq,axiom,
% 5.41/5.62 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ W ) @ ( times_times_complex @ Y @ Z ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_times_eq
% 5.41/5.62 thf(fact_799_divide__divide__times__eq,axiom,
% 5.41/5.62 ! [X: real,Y: real,Z: real,W: real] :
% 5.41/5.62 ( ( divide_divide_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.41/5.62 = ( divide_divide_real @ ( times_times_real @ X @ W ) @ ( times_times_real @ Y @ Z ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_times_eq
% 5.41/5.62 thf(fact_800_divide__divide__times__eq,axiom,
% 5.41/5.62 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.41/5.62 = ( divide_divide_rat @ ( times_times_rat @ X @ W ) @ ( times_times_rat @ Y @ Z ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_divide_times_eq
% 5.41/5.62 thf(fact_801_times__divide__times__eq,axiom,
% 5.41/5.62 ! [X: complex,Y: complex,Z: complex,W: complex] :
% 5.41/5.62 ( ( times_times_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ Z @ W ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ Y @ W ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_times_eq
% 5.41/5.62 thf(fact_802_times__divide__times__eq,axiom,
% 5.41/5.62 ! [X: real,Y: real,Z: real,W: real] :
% 5.41/5.62 ( ( times_times_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ Z @ W ) )
% 5.41/5.62 = ( divide_divide_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ W ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_times_eq
% 5.41/5.62 thf(fact_803_times__divide__times__eq,axiom,
% 5.41/5.62 ! [X: rat,Y: rat,Z: rat,W: rat] :
% 5.41/5.62 ( ( times_times_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ Z @ W ) )
% 5.41/5.62 = ( divide_divide_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ W ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % times_divide_times_eq
% 5.41/5.62 thf(fact_804_add__divide__distrib,axiom,
% 5.41/5.62 ! [A: complex,B: complex,C: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_divide_distrib
% 5.41/5.62 thf(fact_805_add__divide__distrib,axiom,
% 5.41/5.62 ! [A: real,B: real,C: real] :
% 5.41/5.62 ( ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_divide_distrib
% 5.41/5.62 thf(fact_806_add__divide__distrib,axiom,
% 5.41/5.62 ! [A: rat,B: rat,C: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ C )
% 5.41/5.62 = ( plus_plus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_divide_distrib
% 5.41/5.62 thf(fact_807_div__le__dividend,axiom,
% 5.41/5.62 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ M ) ).
% 5.41/5.62
% 5.41/5.62 % div_le_dividend
% 5.41/5.62 thf(fact_808_div__le__mono,axiom,
% 5.41/5.62 ! [M: nat,N: nat,K: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.62 => ( ord_less_eq_nat @ ( divide_divide_nat @ M @ K ) @ ( divide_divide_nat @ N @ K ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_le_mono
% 5.41/5.62 thf(fact_809_div__mult2__eq,axiom,
% 5.41/5.62 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.41/5.62 = ( divide_divide_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult2_eq
% 5.41/5.62 thf(fact_810_less__1__mult,axiom,
% 5.41/5.62 ! [M: real,N: real] :
% 5.41/5.62 ( ( ord_less_real @ one_one_real @ M )
% 5.41/5.62 => ( ( ord_less_real @ one_one_real @ N )
% 5.41/5.62 => ( ord_less_real @ one_one_real @ ( times_times_real @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_1_mult
% 5.41/5.62 thf(fact_811_less__1__mult,axiom,
% 5.41/5.62 ! [M: rat,N: rat] :
% 5.41/5.62 ( ( ord_less_rat @ one_one_rat @ M )
% 5.41/5.62 => ( ( ord_less_rat @ one_one_rat @ N )
% 5.41/5.62 => ( ord_less_rat @ one_one_rat @ ( times_times_rat @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_1_mult
% 5.41/5.62 thf(fact_812_less__1__mult,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ one_one_nat @ M )
% 5.41/5.62 => ( ( ord_less_nat @ one_one_nat @ N )
% 5.41/5.62 => ( ord_less_nat @ one_one_nat @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_1_mult
% 5.41/5.62 thf(fact_813_less__1__mult,axiom,
% 5.41/5.62 ! [M: int,N: int] :
% 5.41/5.62 ( ( ord_less_int @ one_one_int @ M )
% 5.41/5.62 => ( ( ord_less_int @ one_one_int @ N )
% 5.41/5.62 => ( ord_less_int @ one_one_int @ ( times_times_int @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_1_mult
% 5.41/5.62 thf(fact_814_less__add__one,axiom,
% 5.41/5.62 ! [A: real] : ( ord_less_real @ A @ ( plus_plus_real @ A @ one_one_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_one
% 5.41/5.62 thf(fact_815_less__add__one,axiom,
% 5.41/5.62 ! [A: rat] : ( ord_less_rat @ A @ ( plus_plus_rat @ A @ one_one_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_one
% 5.41/5.62 thf(fact_816_less__add__one,axiom,
% 5.41/5.62 ! [A: nat] : ( ord_less_nat @ A @ ( plus_plus_nat @ A @ one_one_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_one
% 5.41/5.62 thf(fact_817_less__add__one,axiom,
% 5.41/5.62 ! [A: int] : ( ord_less_int @ A @ ( plus_plus_int @ A @ one_one_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_one
% 5.41/5.62 thf(fact_818_add__mono1,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_real @ A @ B )
% 5.41/5.62 => ( ord_less_real @ ( plus_plus_real @ A @ one_one_real ) @ ( plus_plus_real @ B @ one_one_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono1
% 5.41/5.62 thf(fact_819_add__mono1,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_rat @ A @ B )
% 5.41/5.62 => ( ord_less_rat @ ( plus_plus_rat @ A @ one_one_rat ) @ ( plus_plus_rat @ B @ one_one_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono1
% 5.41/5.62 thf(fact_820_add__mono1,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ord_less_nat @ A @ B )
% 5.41/5.62 => ( ord_less_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( plus_plus_nat @ B @ one_one_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono1
% 5.41/5.62 thf(fact_821_add__mono1,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_int @ A @ B )
% 5.41/5.62 => ( ord_less_int @ ( plus_plus_int @ A @ one_one_int ) @ ( plus_plus_int @ B @ one_one_int ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_mono1
% 5.41/5.62 thf(fact_822_less__mult__imp__div__less,axiom,
% 5.41/5.62 ! [M: nat,I: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ M @ ( times_times_nat @ I @ N ) )
% 5.41/5.62 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ I ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_mult_imp_div_less
% 5.41/5.62 thf(fact_823_div__times__less__eq__dividend,axiom,
% 5.41/5.62 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) @ M ) ).
% 5.41/5.62
% 5.41/5.62 % div_times_less_eq_dividend
% 5.41/5.62 thf(fact_824_times__div__less__eq__dividend,axiom,
% 5.41/5.62 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) @ M ) ).
% 5.41/5.62
% 5.41/5.62 % times_div_less_eq_dividend
% 5.41/5.62 thf(fact_825_gt__half__sum,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_real @ A @ B )
% 5.41/5.62 => ( ord_less_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % gt_half_sum
% 5.41/5.62 thf(fact_826_gt__half__sum,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_rat @ A @ B )
% 5.41/5.62 => ( ord_less_rat @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % gt_half_sum
% 5.41/5.62 thf(fact_827_less__half__sum,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_real @ A @ B )
% 5.41/5.62 => ( ord_less_real @ A @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ one_one_real @ one_one_real ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_half_sum
% 5.41/5.62 thf(fact_828_less__half__sum,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_rat @ A @ B )
% 5.41/5.62 => ( ord_less_rat @ A @ ( divide_divide_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_half_sum
% 5.41/5.62 thf(fact_829_numeral__Bit0__div__2,axiom,
% 5.41/5.62 ! [N: num] :
% 5.41/5.62 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.62 = ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % numeral_Bit0_div_2
% 5.41/5.62 thf(fact_830_numeral__Bit0__div__2,axiom,
% 5.41/5.62 ! [N: num] :
% 5.41/5.62 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.62 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % numeral_Bit0_div_2
% 5.41/5.62 thf(fact_831_field__sum__of__halves,axiom,
% 5.41/5.62 ! [X: real] :
% 5.41/5.62 ( ( plus_plus_real @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.62 = X ) ).
% 5.41/5.62
% 5.41/5.62 % field_sum_of_halves
% 5.41/5.62 thf(fact_832_field__sum__of__halves,axiom,
% 5.41/5.62 ! [X: rat] :
% 5.41/5.62 ( ( plus_plus_rat @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) @ ( divide_divide_rat @ X @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.41/5.62 = X ) ).
% 5.41/5.62
% 5.41/5.62 % field_sum_of_halves
% 5.41/5.62 thf(fact_833_power__minus__is__div,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.62 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ A @ B ) )
% 5.41/5.62 = ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_minus_is_div
% 5.41/5.62 thf(fact_834_discrete,axiom,
% 5.41/5.62 ( ord_less_nat
% 5.41/5.62 = ( ^ [A3: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ A3 @ one_one_nat ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % discrete
% 5.41/5.62 thf(fact_835_discrete,axiom,
% 5.41/5.62 ( ord_less_int
% 5.41/5.62 = ( ^ [A3: int] : ( ord_less_eq_int @ ( plus_plus_int @ A3 @ one_one_int ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % discrete
% 5.41/5.62 thf(fact_836_low__def,axiom,
% 5.41/5.62 ( vEBT_VEBT_low
% 5.41/5.62 = ( ^ [X3: nat,N2: nat] : ( modulo_modulo_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % low_def
% 5.41/5.62 thf(fact_837__092_060open_062Some_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_Ax_An_J_J_092_060close_062,axiom,
% 5.41/5.62 ( ( some_nat @ maxs )
% 5.41/5.62 = ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % \<open>Some maxs = vebt_maxt (vebt_delete summary (high x n))\<close>
% 5.41/5.62 thf(fact_838_dbl__simps_I3_J,axiom,
% 5.41/5.62 ( ( neg_nu7009210354673126013omplex @ one_one_complex )
% 5.41/5.62 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(3)
% 5.41/5.62 thf(fact_839_dbl__simps_I3_J,axiom,
% 5.41/5.62 ( ( neg_numeral_dbl_real @ one_one_real )
% 5.41/5.62 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(3)
% 5.41/5.62 thf(fact_840_dbl__simps_I3_J,axiom,
% 5.41/5.62 ( ( neg_numeral_dbl_rat @ one_one_rat )
% 5.41/5.62 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(3)
% 5.41/5.62 thf(fact_841_dbl__simps_I3_J,axiom,
% 5.41/5.62 ( ( neg_numeral_dbl_int @ one_one_int )
% 5.41/5.62 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(3)
% 5.41/5.62 thf(fact_842_power__numeral,axiom,
% 5.41/5.62 ! [K: num,L2: num] :
% 5.41/5.62 ( ( power_power_complex @ ( numera6690914467698888265omplex @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.62 = ( numera6690914467698888265omplex @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_numeral
% 5.41/5.62 thf(fact_843_power__numeral,axiom,
% 5.41/5.62 ! [K: num,L2: num] :
% 5.41/5.62 ( ( power_power_real @ ( numeral_numeral_real @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.62 = ( numeral_numeral_real @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_numeral
% 5.41/5.62 thf(fact_844_power__numeral,axiom,
% 5.41/5.62 ! [K: num,L2: num] :
% 5.41/5.62 ( ( power_power_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.62 = ( numeral_numeral_rat @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_numeral
% 5.41/5.62 thf(fact_845_power__numeral,axiom,
% 5.41/5.62 ! [K: num,L2: num] :
% 5.41/5.62 ( ( power_power_nat @ ( numeral_numeral_nat @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.62 = ( numeral_numeral_nat @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_numeral
% 5.41/5.62 thf(fact_846_power__numeral,axiom,
% 5.41/5.62 ! [K: num,L2: num] :
% 5.41/5.62 ( ( power_power_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_nat @ L2 ) )
% 5.41/5.62 = ( numeral_numeral_int @ ( pow @ K @ L2 ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_numeral
% 5.41/5.62 thf(fact_847_both__member__options__from__chilf__to__complete__tree,axiom,
% 5.41/5.62 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.41/5.62 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.62 => ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.41/5.62 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.62 => ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % both_member_options_from_chilf_to_complete_tree
% 5.41/5.62 thf(fact_848_arith__geo__mean,axiom,
% 5.41/5.62 ! [U: real,X: real,Y: real] :
% 5.41/5.62 ( ( ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.62 = ( times_times_real @ X @ Y ) )
% 5.41/5.62 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.62 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.62 => ( ord_less_eq_real @ U @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % arith_geo_mean
% 5.41/5.62 thf(fact_849_arith__geo__mean,axiom,
% 5.41/5.62 ! [U: rat,X: rat,Y: rat] :
% 5.41/5.62 ( ( ( power_power_rat @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.62 = ( times_times_rat @ X @ Y ) )
% 5.41/5.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.62 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.62 => ( ord_less_eq_rat @ U @ ( divide_divide_rat @ ( plus_plus_rat @ X @ Y ) @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % arith_geo_mean
% 5.41/5.62 thf(fact_850_False,axiom,
% 5.41/5.62 ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 5.41/5.62 != none_nat ) ).
% 5.41/5.62
% 5.41/5.62 % False
% 5.41/5.62 thf(fact_851_valid__tree__deg__neq__0,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT] :
% 5.41/5.62 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % valid_tree_deg_neq_0
% 5.41/5.62 thf(fact_852_valid__0__not,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT] :
% 5.41/5.62 ~ ( vEBT_invar_vebt @ T @ zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % valid_0_not
% 5.41/5.62 thf(fact_853_deg__not__0,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,N: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.62 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % deg_not_0
% 5.41/5.62 thf(fact_854_maxbmo,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,X: nat] :
% 5.41/5.62 ( ( ( vEBT_vebt_maxt @ T )
% 5.41/5.62 = ( some_nat @ X ) )
% 5.41/5.62 => ( vEBT_V8194947554948674370ptions @ T @ X ) ) ).
% 5.41/5.62
% 5.41/5.62 % maxbmo
% 5.41/5.62 thf(fact_855_power__shift,axiom,
% 5.41/5.62 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.62 ( ( ( power_power_nat @ X @ Y )
% 5.41/5.62 = Z )
% 5.41/5.62 = ( ( vEBT_VEBT_power @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.41/5.62 = ( some_nat @ Z ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % power_shift
% 5.41/5.62 thf(fact_856_maxt__member,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.62 => ( ( ( vEBT_vebt_maxt @ T )
% 5.41/5.62 = ( some_nat @ Maxi ) )
% 5.41/5.62 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % maxt_member
% 5.41/5.62 thf(fact_857_zdiv__numeral__Bit0,axiom,
% 5.41/5.62 ! [V: num,W: num] :
% 5.41/5.62 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.41/5.62 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % zdiv_numeral_Bit0
% 5.41/5.62 thf(fact_858_bot__nat__0_Onot__eq__extremum,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( A != zero_zero_nat )
% 5.41/5.62 = ( ord_less_nat @ zero_zero_nat @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % bot_nat_0.not_eq_extremum
% 5.41/5.62 thf(fact_859_neq0__conv,axiom,
% 5.41/5.62 ! [N: nat] :
% 5.41/5.62 ( ( N != zero_zero_nat )
% 5.41/5.62 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % neq0_conv
% 5.41/5.62 thf(fact_860_less__nat__zero__code,axiom,
% 5.41/5.62 ! [N: nat] :
% 5.41/5.62 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % less_nat_zero_code
% 5.41/5.62 thf(fact_861_bot__nat__0_Oextremum,axiom,
% 5.41/5.62 ! [A: nat] : ( ord_less_eq_nat @ zero_zero_nat @ A ) ).
% 5.41/5.62
% 5.41/5.62 % bot_nat_0.extremum
% 5.41/5.62 thf(fact_862_le0,axiom,
% 5.41/5.62 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.41/5.62
% 5.41/5.62 % le0
% 5.41/5.62 thf(fact_863_add__is__0,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ( plus_plus_nat @ M @ N )
% 5.41/5.62 = zero_zero_nat )
% 5.41/5.62 = ( ( M = zero_zero_nat )
% 5.41/5.62 & ( N = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_is_0
% 5.41/5.62 thf(fact_864_Nat_Oadd__0__right,axiom,
% 5.41/5.62 ! [M: nat] :
% 5.41/5.62 ( ( plus_plus_nat @ M @ zero_zero_nat )
% 5.41/5.62 = M ) ).
% 5.41/5.62
% 5.41/5.62 % Nat.add_0_right
% 5.41/5.62 thf(fact_865_mod__mod__trivial,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.41/5.62 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_mod_trivial
% 5.41/5.62 thf(fact_866_mod__mod__trivial,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.41/5.62 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_mod_trivial
% 5.41/5.62 thf(fact_867_mod__mod__trivial,axiom,
% 5.41/5.62 ! [A: code_integer,B: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.41/5.62 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_mod_trivial
% 5.41/5.62 thf(fact_868_diff__self__eq__0,axiom,
% 5.41/5.62 ! [M: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ M @ M )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % diff_self_eq_0
% 5.41/5.62 thf(fact_869_diff__0__eq__0,axiom,
% 5.41/5.62 ! [N: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ zero_zero_nat @ N )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % diff_0_eq_0
% 5.41/5.62 thf(fact_870_mult__is__0,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ( times_times_nat @ M @ N )
% 5.41/5.62 = zero_zero_nat )
% 5.41/5.62 = ( ( M = zero_zero_nat )
% 5.41/5.62 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_is_0
% 5.41/5.62 thf(fact_871_mult__0__right,axiom,
% 5.41/5.62 ! [M: nat] :
% 5.41/5.62 ( ( times_times_nat @ M @ zero_zero_nat )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % mult_0_right
% 5.41/5.62 thf(fact_872_mult__cancel1,axiom,
% 5.41/5.62 ! [K: nat,M: nat,N: nat] :
% 5.41/5.62 ( ( ( times_times_nat @ K @ M )
% 5.41/5.62 = ( times_times_nat @ K @ N ) )
% 5.41/5.62 = ( ( M = N )
% 5.41/5.62 | ( K = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel1
% 5.41/5.62 thf(fact_873_mult__cancel2,axiom,
% 5.41/5.62 ! [M: nat,K: nat,N: nat] :
% 5.41/5.62 ( ( ( times_times_nat @ M @ K )
% 5.41/5.62 = ( times_times_nat @ N @ K ) )
% 5.41/5.62 = ( ( M = N )
% 5.41/5.62 | ( K = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel2
% 5.41/5.62 thf(fact_874_not__real__square__gt__zero,axiom,
% 5.41/5.62 ! [X: real] :
% 5.41/5.62 ( ( ~ ( ord_less_real @ zero_zero_real @ ( times_times_real @ X @ X ) ) )
% 5.41/5.62 = ( X = zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % not_real_square_gt_zero
% 5.41/5.62 thf(fact_875_real__divide__square__eq,axiom,
% 5.41/5.62 ! [R: real,A: real] :
% 5.41/5.62 ( ( divide_divide_real @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ R ) )
% 5.41/5.62 = ( divide_divide_real @ A @ R ) ) ).
% 5.41/5.62
% 5.41/5.62 % real_divide_square_eq
% 5.41/5.62 thf(fact_876_i0__less,axiom,
% 5.41/5.62 ! [N: extended_enat] :
% 5.41/5.62 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.41/5.62 = ( N != zero_z5237406670263579293d_enat ) ) ).
% 5.41/5.62
% 5.41/5.62 % i0_less
% 5.41/5.62 thf(fact_877_maxt__corr__help,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,N: nat,Maxi: nat,X: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.62 => ( ( ( vEBT_vebt_maxt @ T )
% 5.41/5.62 = ( some_nat @ Maxi ) )
% 5.41/5.62 => ( ( vEBT_vebt_member @ T @ X )
% 5.41/5.62 => ( ord_less_eq_nat @ X @ Maxi ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % maxt_corr_help
% 5.41/5.62 thf(fact_878_maxt__corr,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.62 => ( ( ( vEBT_vebt_maxt @ T )
% 5.41/5.62 = ( some_nat @ X ) )
% 5.41/5.62 => ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % maxt_corr
% 5.41/5.62 thf(fact_879_maxt__sound,axiom,
% 5.41/5.62 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.62 => ( ( vEBT_VEBT_max_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.41/5.62 => ( ( vEBT_vebt_maxt @ T )
% 5.41/5.62 = ( some_nat @ X ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % maxt_sound
% 5.41/5.62 thf(fact_880_mi__eq__ma__no__ch,axiom,
% 5.41/5.62 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.41/5.62 => ( ( Mi = Ma )
% 5.41/5.62 => ( ! [X4: vEBT_VEBT] :
% 5.41/5.62 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.62 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) )
% 5.41/5.62 & ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_12 ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mi_eq_ma_no_ch
% 5.41/5.62 thf(fact_881_le__zero__eq,axiom,
% 5.41/5.62 ! [N: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.41/5.62 = ( N = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_zero_eq
% 5.41/5.62 thf(fact_882_not__gr__zero,axiom,
% 5.41/5.62 ! [N: nat] :
% 5.41/5.62 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.41/5.62 = ( N = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % not_gr_zero
% 5.41/5.62 thf(fact_883_mult__zero__left,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( times_times_complex @ zero_zero_complex @ A )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_left
% 5.41/5.62 thf(fact_884_mult__zero__left,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( times_times_real @ zero_zero_real @ A )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_left
% 5.41/5.62 thf(fact_885_mult__zero__left,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( times_times_rat @ zero_zero_rat @ A )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_left
% 5.41/5.62 thf(fact_886_mult__zero__left,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( times_times_nat @ zero_zero_nat @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_left
% 5.41/5.62 thf(fact_887_mult__zero__left,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( times_times_int @ zero_zero_int @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_left
% 5.41/5.62 thf(fact_888_mult__zero__right,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( times_times_complex @ A @ zero_zero_complex )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_right
% 5.41/5.62 thf(fact_889_mult__zero__right,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( times_times_real @ A @ zero_zero_real )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_right
% 5.41/5.62 thf(fact_890_mult__zero__right,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( times_times_rat @ A @ zero_zero_rat )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_right
% 5.41/5.62 thf(fact_891_mult__zero__right,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( times_times_nat @ A @ zero_zero_nat )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_right
% 5.41/5.62 thf(fact_892_mult__zero__right,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( times_times_int @ A @ zero_zero_int )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % mult_zero_right
% 5.41/5.62 thf(fact_893_mult__eq__0__iff,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( ( times_times_complex @ A @ B )
% 5.41/5.62 = zero_zero_complex )
% 5.41/5.62 = ( ( A = zero_zero_complex )
% 5.41/5.62 | ( B = zero_zero_complex ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_eq_0_iff
% 5.41/5.62 thf(fact_894_mult__eq__0__iff,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ( times_times_real @ A @ B )
% 5.41/5.62 = zero_zero_real )
% 5.41/5.62 = ( ( A = zero_zero_real )
% 5.41/5.62 | ( B = zero_zero_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_eq_0_iff
% 5.41/5.62 thf(fact_895_mult__eq__0__iff,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ( times_times_rat @ A @ B )
% 5.41/5.62 = zero_zero_rat )
% 5.41/5.62 = ( ( A = zero_zero_rat )
% 5.41/5.62 | ( B = zero_zero_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_eq_0_iff
% 5.41/5.62 thf(fact_896_mult__eq__0__iff,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ( times_times_nat @ A @ B )
% 5.41/5.62 = zero_zero_nat )
% 5.41/5.62 = ( ( A = zero_zero_nat )
% 5.41/5.62 | ( B = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_eq_0_iff
% 5.41/5.62 thf(fact_897_mult__eq__0__iff,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ( times_times_int @ A @ B )
% 5.41/5.62 = zero_zero_int )
% 5.41/5.62 = ( ( A = zero_zero_int )
% 5.41/5.62 | ( B = zero_zero_int ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_eq_0_iff
% 5.41/5.62 thf(fact_898_mult__cancel__left,axiom,
% 5.41/5.62 ! [C: complex,A: complex,B: complex] :
% 5.41/5.62 ( ( ( times_times_complex @ C @ A )
% 5.41/5.62 = ( times_times_complex @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left
% 5.41/5.62 thf(fact_899_mult__cancel__left,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( ( times_times_real @ C @ A )
% 5.41/5.62 = ( times_times_real @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left
% 5.41/5.62 thf(fact_900_mult__cancel__left,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( ( times_times_rat @ C @ A )
% 5.41/5.62 = ( times_times_rat @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left
% 5.41/5.62 thf(fact_901_mult__cancel__left,axiom,
% 5.41/5.62 ! [C: nat,A: nat,B: nat] :
% 5.41/5.62 ( ( ( times_times_nat @ C @ A )
% 5.41/5.62 = ( times_times_nat @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_nat )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left
% 5.41/5.62 thf(fact_902_mult__cancel__left,axiom,
% 5.41/5.62 ! [C: int,A: int,B: int] :
% 5.41/5.62 ( ( ( times_times_int @ C @ A )
% 5.41/5.62 = ( times_times_int @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_int )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left
% 5.41/5.62 thf(fact_903_mult__cancel__right,axiom,
% 5.41/5.62 ! [A: complex,C: complex,B: complex] :
% 5.41/5.62 ( ( ( times_times_complex @ A @ C )
% 5.41/5.62 = ( times_times_complex @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right
% 5.41/5.62 thf(fact_904_mult__cancel__right,axiom,
% 5.41/5.62 ! [A: real,C: real,B: real] :
% 5.41/5.62 ( ( ( times_times_real @ A @ C )
% 5.41/5.62 = ( times_times_real @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right
% 5.41/5.62 thf(fact_905_mult__cancel__right,axiom,
% 5.41/5.62 ! [A: rat,C: rat,B: rat] :
% 5.41/5.62 ( ( ( times_times_rat @ A @ C )
% 5.41/5.62 = ( times_times_rat @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right
% 5.41/5.62 thf(fact_906_mult__cancel__right,axiom,
% 5.41/5.62 ! [A: nat,C: nat,B: nat] :
% 5.41/5.62 ( ( ( times_times_nat @ A @ C )
% 5.41/5.62 = ( times_times_nat @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_nat )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right
% 5.41/5.62 thf(fact_907_mult__cancel__right,axiom,
% 5.41/5.62 ! [A: int,C: int,B: int] :
% 5.41/5.62 ( ( ( times_times_int @ A @ C )
% 5.41/5.62 = ( times_times_int @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_int )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right
% 5.41/5.62 thf(fact_908_add_Oright__neutral,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add.right_neutral
% 5.41/5.62 thf(fact_909_add_Oright__neutral,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add.right_neutral
% 5.41/5.62 thf(fact_910_add_Oright__neutral,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add.right_neutral
% 5.41/5.62 thf(fact_911_add_Oright__neutral,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add.right_neutral
% 5.41/5.62 thf(fact_912_add_Oright__neutral,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add.right_neutral
% 5.41/5.62 thf(fact_913_double__zero__sym,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( zero_zero_real
% 5.41/5.62 = ( plus_plus_real @ A @ A ) )
% 5.41/5.62 = ( A = zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_zero_sym
% 5.41/5.62 thf(fact_914_double__zero__sym,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( zero_zero_rat
% 5.41/5.62 = ( plus_plus_rat @ A @ A ) )
% 5.41/5.62 = ( A = zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_zero_sym
% 5.41/5.62 thf(fact_915_double__zero__sym,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( zero_zero_int
% 5.41/5.62 = ( plus_plus_int @ A @ A ) )
% 5.41/5.62 = ( A = zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_zero_sym
% 5.41/5.62 thf(fact_916_add__cancel__left__left,axiom,
% 5.41/5.62 ! [B: complex,A: complex] :
% 5.41/5.62 ( ( ( plus_plus_complex @ B @ A )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_complex ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_left
% 5.41/5.62 thf(fact_917_add__cancel__left__left,axiom,
% 5.41/5.62 ! [B: real,A: real] :
% 5.41/5.62 ( ( ( plus_plus_real @ B @ A )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_left
% 5.41/5.62 thf(fact_918_add__cancel__left__left,axiom,
% 5.41/5.62 ! [B: rat,A: rat] :
% 5.41/5.62 ( ( ( plus_plus_rat @ B @ A )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_left
% 5.41/5.62 thf(fact_919_add__cancel__left__left,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( ( plus_plus_nat @ B @ A )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_left
% 5.41/5.62 thf(fact_920_add__cancel__left__left,axiom,
% 5.41/5.62 ! [B: int,A: int] :
% 5.41/5.62 ( ( ( plus_plus_int @ B @ A )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_left
% 5.41/5.62 thf(fact_921_add__cancel__left__right,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( ( plus_plus_complex @ A @ B )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_complex ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_right
% 5.41/5.62 thf(fact_922_add__cancel__left__right,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ( plus_plus_real @ A @ B )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_right
% 5.41/5.62 thf(fact_923_add__cancel__left__right,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ( plus_plus_rat @ A @ B )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_right
% 5.41/5.62 thf(fact_924_add__cancel__left__right,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ( plus_plus_nat @ A @ B )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_right
% 5.41/5.62 thf(fact_925_add__cancel__left__right,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ( plus_plus_int @ A @ B )
% 5.41/5.62 = A )
% 5.41/5.62 = ( B = zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_left_right
% 5.41/5.62 thf(fact_926_add__cancel__right__left,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_complex @ B @ A ) )
% 5.41/5.62 = ( B = zero_zero_complex ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_left
% 5.41/5.62 thf(fact_927_add__cancel__right__left,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_real @ B @ A ) )
% 5.41/5.62 = ( B = zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_left
% 5.41/5.62 thf(fact_928_add__cancel__right__left,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_rat @ B @ A ) )
% 5.41/5.62 = ( B = zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_left
% 5.41/5.62 thf(fact_929_add__cancel__right__left,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_nat @ B @ A ) )
% 5.41/5.62 = ( B = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_left
% 5.41/5.62 thf(fact_930_add__cancel__right__left,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_int @ B @ A ) )
% 5.41/5.62 = ( B = zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_left
% 5.41/5.62 thf(fact_931_add__cancel__right__right,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_complex @ A @ B ) )
% 5.41/5.62 = ( B = zero_zero_complex ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_right
% 5.41/5.62 thf(fact_932_add__cancel__right__right,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_real @ A @ B ) )
% 5.41/5.62 = ( B = zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_right
% 5.41/5.62 thf(fact_933_add__cancel__right__right,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_rat @ A @ B ) )
% 5.41/5.62 = ( B = zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_right
% 5.41/5.62 thf(fact_934_add__cancel__right__right,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_nat @ A @ B ) )
% 5.41/5.62 = ( B = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_right
% 5.41/5.62 thf(fact_935_add__cancel__right__right,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( A
% 5.41/5.62 = ( plus_plus_int @ A @ B ) )
% 5.41/5.62 = ( B = zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_cancel_right_right
% 5.41/5.62 thf(fact_936_add__eq__0__iff__both__eq__0,axiom,
% 5.41/5.62 ! [X: nat,Y: nat] :
% 5.41/5.62 ( ( ( plus_plus_nat @ X @ Y )
% 5.41/5.62 = zero_zero_nat )
% 5.41/5.62 = ( ( X = zero_zero_nat )
% 5.41/5.62 & ( Y = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_eq_0_iff_both_eq_0
% 5.41/5.62 thf(fact_937_zero__eq__add__iff__both__eq__0,axiom,
% 5.41/5.62 ! [X: nat,Y: nat] :
% 5.41/5.62 ( ( zero_zero_nat
% 5.41/5.62 = ( plus_plus_nat @ X @ Y ) )
% 5.41/5.62 = ( ( X = zero_zero_nat )
% 5.41/5.62 & ( Y = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_eq_add_iff_both_eq_0
% 5.41/5.62 thf(fact_938_add__0,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_0
% 5.41/5.62 thf(fact_939_add__0,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_0
% 5.41/5.62 thf(fact_940_add__0,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_0
% 5.41/5.62 thf(fact_941_add__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_0
% 5.41/5.62 thf(fact_942_add__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_0
% 5.41/5.62 thf(fact_943_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( minus_minus_complex @ A @ A )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.62 thf(fact_944_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( minus_minus_real @ A @ A )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.62 thf(fact_945_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ A @ A )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.62 thf(fact_946_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ A @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.62 thf(fact_947_cancel__comm__monoid__add__class_Odiff__cancel,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( minus_minus_int @ A @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % cancel_comm_monoid_add_class.diff_cancel
% 5.41/5.62 thf(fact_948_diff__zero,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_zero
% 5.41/5.62 thf(fact_949_diff__zero,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_zero
% 5.41/5.62 thf(fact_950_diff__zero,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_zero
% 5.41/5.62 thf(fact_951_diff__zero,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ A @ zero_zero_nat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_zero
% 5.41/5.62 thf(fact_952_diff__zero,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_zero
% 5.41/5.62 thf(fact_953_zero__diff,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ zero_zero_nat @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % zero_diff
% 5.41/5.62 thf(fact_954_diff__0__right,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( minus_minus_complex @ A @ zero_zero_complex )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_0_right
% 5.41/5.62 thf(fact_955_diff__0__right,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( minus_minus_real @ A @ zero_zero_real )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_0_right
% 5.41/5.62 thf(fact_956_diff__0__right,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ A @ zero_zero_rat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_0_right
% 5.41/5.62 thf(fact_957_diff__0__right,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( minus_minus_int @ A @ zero_zero_int )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_0_right
% 5.41/5.62 thf(fact_958_diff__self,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( minus_minus_complex @ A @ A )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % diff_self
% 5.41/5.62 thf(fact_959_diff__self,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( minus_minus_real @ A @ A )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % diff_self
% 5.41/5.62 thf(fact_960_diff__self,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ A @ A )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % diff_self
% 5.41/5.62 thf(fact_961_diff__self,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( minus_minus_int @ A @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % diff_self
% 5.41/5.62 thf(fact_962_div__0,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ zero_zero_complex @ A )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % div_0
% 5.41/5.62 thf(fact_963_div__0,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( divide_divide_real @ zero_zero_real @ A )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % div_0
% 5.41/5.62 thf(fact_964_div__0,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ zero_zero_rat @ A )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % div_0
% 5.41/5.62 thf(fact_965_div__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % div_0
% 5.41/5.62 thf(fact_966_div__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % div_0
% 5.41/5.62 thf(fact_967_divide__eq__0__iff,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.41/5.62 = zero_zero_complex )
% 5.41/5.62 = ( ( A = zero_zero_complex )
% 5.41/5.62 | ( B = zero_zero_complex ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_eq_0_iff
% 5.41/5.62 thf(fact_968_divide__eq__0__iff,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ( divide_divide_real @ A @ B )
% 5.41/5.62 = zero_zero_real )
% 5.41/5.62 = ( ( A = zero_zero_real )
% 5.41/5.62 | ( B = zero_zero_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_eq_0_iff
% 5.41/5.62 thf(fact_969_divide__eq__0__iff,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ( divide_divide_rat @ A @ B )
% 5.41/5.62 = zero_zero_rat )
% 5.41/5.62 = ( ( A = zero_zero_rat )
% 5.41/5.62 | ( B = zero_zero_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_eq_0_iff
% 5.41/5.62 thf(fact_970_div__by__0,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_0
% 5.41/5.62 thf(fact_971_div__by__0,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_0
% 5.41/5.62 thf(fact_972_div__by__0,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_0
% 5.41/5.62 thf(fact_973_div__by__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_0
% 5.41/5.62 thf(fact_974_div__by__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % div_by_0
% 5.41/5.62 thf(fact_975_divide__cancel__left,axiom,
% 5.41/5.62 ! [C: complex,A: complex,B: complex] :
% 5.41/5.62 ( ( ( divide1717551699836669952omplex @ C @ A )
% 5.41/5.62 = ( divide1717551699836669952omplex @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_cancel_left
% 5.41/5.62 thf(fact_976_divide__cancel__left,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( ( divide_divide_real @ C @ A )
% 5.41/5.62 = ( divide_divide_real @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_cancel_left
% 5.41/5.62 thf(fact_977_divide__cancel__left,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( ( divide_divide_rat @ C @ A )
% 5.41/5.62 = ( divide_divide_rat @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_cancel_left
% 5.41/5.62 thf(fact_978_divide__cancel__right,axiom,
% 5.41/5.62 ! [A: complex,C: complex,B: complex] :
% 5.41/5.62 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.41/5.62 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_cancel_right
% 5.41/5.62 thf(fact_979_divide__cancel__right,axiom,
% 5.41/5.62 ! [A: real,C: real,B: real] :
% 5.41/5.62 ( ( ( divide_divide_real @ A @ C )
% 5.41/5.62 = ( divide_divide_real @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_cancel_right
% 5.41/5.62 thf(fact_980_divide__cancel__right,axiom,
% 5.41/5.62 ! [A: rat,C: rat,B: rat] :
% 5.41/5.62 ( ( ( divide_divide_rat @ A @ C )
% 5.41/5.62 = ( divide_divide_rat @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_cancel_right
% 5.41/5.62 thf(fact_981_bits__div__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ zero_zero_nat @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % bits_div_0
% 5.41/5.62 thf(fact_982_bits__div__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( divide_divide_int @ zero_zero_int @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % bits_div_0
% 5.41/5.62 thf(fact_983_bits__div__by__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( divide_divide_nat @ A @ zero_zero_nat )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % bits_div_by_0
% 5.41/5.62 thf(fact_984_bits__div__by__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( divide_divide_int @ A @ zero_zero_int )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % bits_div_by_0
% 5.41/5.62 thf(fact_985_division__ring__divide__zero,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( divide1717551699836669952omplex @ A @ zero_zero_complex )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % division_ring_divide_zero
% 5.41/5.62 thf(fact_986_division__ring__divide__zero,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( divide_divide_real @ A @ zero_zero_real )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % division_ring_divide_zero
% 5.41/5.62 thf(fact_987_division__ring__divide__zero,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( divide_divide_rat @ A @ zero_zero_rat )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % division_ring_divide_zero
% 5.41/5.62 thf(fact_988_half__nonnegative__int__iff,axiom,
% 5.41/5.62 ! [K: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.41/5.62 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.62
% 5.41/5.62 % half_nonnegative_int_iff
% 5.41/5.62 thf(fact_989_half__negative__int__iff,axiom,
% 5.41/5.62 ! [K: int] :
% 5.41/5.62 ( ( ord_less_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.41/5.62 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % half_negative_int_iff
% 5.41/5.62 thf(fact_990_add__diff__cancel,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel
% 5.41/5.62 thf(fact_991_add__diff__cancel,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel
% 5.41/5.62 thf(fact_992_add__diff__cancel,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel
% 5.41/5.62 thf(fact_993_diff__add__cancel,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_add_cancel
% 5.41/5.62 thf(fact_994_diff__add__cancel,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_add_cancel
% 5.41/5.62 thf(fact_995_diff__add__cancel,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % diff_add_cancel
% 5.41/5.62 thf(fact_996_add__diff__cancel__left,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( minus_minus_real @ ( plus_plus_real @ C @ A ) @ ( plus_plus_real @ C @ B ) )
% 5.41/5.62 = ( minus_minus_real @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left
% 5.41/5.62 thf(fact_997_add__diff__cancel__left,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ ( plus_plus_rat @ C @ A ) @ ( plus_plus_rat @ C @ B ) )
% 5.41/5.62 = ( minus_minus_rat @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left
% 5.41/5.62 thf(fact_998_add__diff__cancel__left,axiom,
% 5.41/5.62 ! [C: nat,A: nat,B: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ ( plus_plus_nat @ C @ B ) )
% 5.41/5.62 = ( minus_minus_nat @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left
% 5.41/5.62 thf(fact_999_add__diff__cancel__left,axiom,
% 5.41/5.62 ! [C: int,A: int,B: int] :
% 5.41/5.62 ( ( minus_minus_int @ ( plus_plus_int @ C @ A ) @ ( plus_plus_int @ C @ B ) )
% 5.41/5.62 = ( minus_minus_int @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left
% 5.41/5.62 thf(fact_1000_add__diff__cancel__left_H,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ A )
% 5.41/5.62 = B ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left'
% 5.41/5.62 thf(fact_1001_add__diff__cancel__left_H,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ A )
% 5.41/5.62 = B ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left'
% 5.41/5.62 thf(fact_1002_add__diff__cancel__left_H,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ A )
% 5.41/5.62 = B ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left'
% 5.41/5.62 thf(fact_1003_add__diff__cancel__left_H,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ A )
% 5.41/5.62 = B ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_left'
% 5.41/5.62 thf(fact_1004_add__diff__cancel__right,axiom,
% 5.41/5.62 ! [A: real,C: real,B: real] :
% 5.41/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ C ) )
% 5.41/5.62 = ( minus_minus_real @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right
% 5.41/5.62 thf(fact_1005_add__diff__cancel__right,axiom,
% 5.41/5.62 ! [A: rat,C: rat,B: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.62 = ( minus_minus_rat @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right
% 5.41/5.62 thf(fact_1006_add__diff__cancel__right,axiom,
% 5.41/5.62 ! [A: nat,C: nat,B: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ C ) @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.62 = ( minus_minus_nat @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right
% 5.41/5.62 thf(fact_1007_add__diff__cancel__right,axiom,
% 5.41/5.62 ! [A: int,C: int,B: int] :
% 5.41/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ C ) )
% 5.41/5.62 = ( minus_minus_int @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right
% 5.41/5.62 thf(fact_1008_add__diff__cancel__right_H,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right'
% 5.41/5.62 thf(fact_1009_add__diff__cancel__right_H,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right'
% 5.41/5.62 thf(fact_1010_add__diff__cancel__right_H,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right'
% 5.41/5.62 thf(fact_1011_add__diff__cancel__right_H,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % add_diff_cancel_right'
% 5.41/5.62 thf(fact_1012_bits__mod__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % bits_mod_0
% 5.41/5.62 thf(fact_1013_bits__mod__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % bits_mod_0
% 5.41/5.62 thf(fact_1014_bits__mod__0,axiom,
% 5.41/5.62 ! [A: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.62 = zero_z3403309356797280102nteger ) ).
% 5.41/5.62
% 5.41/5.62 % bits_mod_0
% 5.41/5.62 thf(fact_1015_mod__self,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( modulo_modulo_nat @ A @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % mod_self
% 5.41/5.62 thf(fact_1016_mod__self,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ A @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % mod_self
% 5.41/5.62 thf(fact_1017_mod__self,axiom,
% 5.41/5.62 ! [A: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ A @ A )
% 5.41/5.62 = zero_z3403309356797280102nteger ) ).
% 5.41/5.62
% 5.41/5.62 % mod_self
% 5.41/5.62 thf(fact_1018_mod__by__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( modulo_modulo_nat @ A @ zero_zero_nat )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % mod_by_0
% 5.41/5.62 thf(fact_1019_mod__by__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ A @ zero_zero_int )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % mod_by_0
% 5.41/5.62 thf(fact_1020_mod__by__0,axiom,
% 5.41/5.62 ! [A: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ A @ zero_z3403309356797280102nteger )
% 5.41/5.62 = A ) ).
% 5.41/5.62
% 5.41/5.62 % mod_by_0
% 5.41/5.62 thf(fact_1021_mod__0,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( modulo_modulo_nat @ zero_zero_nat @ A )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % mod_0
% 5.41/5.62 thf(fact_1022_mod__0,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ zero_zero_int @ A )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % mod_0
% 5.41/5.62 thf(fact_1023_mod__0,axiom,
% 5.41/5.62 ! [A: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.62 = zero_z3403309356797280102nteger ) ).
% 5.41/5.62
% 5.41/5.62 % mod_0
% 5.41/5.62 thf(fact_1024_insert__simp__mima,axiom,
% 5.41/5.62 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.62 ( ( ( X = Mi )
% 5.41/5.62 | ( X = Ma ) )
% 5.41/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.62 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % insert_simp_mima
% 5.41/5.62 thf(fact_1025_mod__add__self1,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( modulo_modulo_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.41/5.62 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_add_self1
% 5.41/5.62 thf(fact_1026_mod__add__self1,axiom,
% 5.41/5.62 ! [B: int,A: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.41/5.62 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_add_self1
% 5.41/5.62 thf(fact_1027_mod__add__self1,axiom,
% 5.41/5.62 ! [B: code_integer,A: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ B @ A ) @ B )
% 5.41/5.62 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_add_self1
% 5.41/5.62 thf(fact_1028_mod__add__self2,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.41/5.62 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_add_self2
% 5.41/5.62 thf(fact_1029_mod__add__self2,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.41/5.62 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_add_self2
% 5.41/5.62 thf(fact_1030_mod__add__self2,axiom,
% 5.41/5.62 ! [A: code_integer,B: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ B )
% 5.41/5.62 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_add_self2
% 5.41/5.62 thf(fact_1031_minus__mod__self2,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.41/5.62 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % minus_mod_self2
% 5.41/5.62 thf(fact_1032_minus__mod__self2,axiom,
% 5.41/5.62 ! [A: code_integer,B: code_integer] :
% 5.41/5.62 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ B )
% 5.41/5.62 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % minus_mod_self2
% 5.41/5.62 thf(fact_1033_add__gr__0,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.62 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.62 | ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_gr_0
% 5.41/5.62 thf(fact_1034_zero__less__diff,axiom,
% 5.41/5.62 ! [N: nat,M: nat] :
% 5.41/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( minus_minus_nat @ N @ M ) )
% 5.41/5.62 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_less_diff
% 5.41/5.62 thf(fact_1035_mult__less__cancel2,axiom,
% 5.41/5.62 ! [M: nat,K: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.41/5.62 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.62 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_less_cancel2
% 5.41/5.62 thf(fact_1036_nat__0__less__mult__iff,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ M @ N ) )
% 5.41/5.62 = ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.62 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nat_0_less_mult_iff
% 5.41/5.62 thf(fact_1037_nat__mult__less__cancel__disj,axiom,
% 5.41/5.62 ! [K: nat,M: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.62 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.62 & ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nat_mult_less_cancel_disj
% 5.41/5.62 thf(fact_1038_div__less,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ M @ N )
% 5.41/5.62 => ( ( divide_divide_nat @ M @ N )
% 5.41/5.62 = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_less
% 5.41/5.62 thf(fact_1039_diff__is__0__eq_H,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.62 => ( ( minus_minus_nat @ M @ N )
% 5.41/5.62 = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_is_0_eq'
% 5.41/5.62 thf(fact_1040_diff__is__0__eq,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ( minus_minus_nat @ M @ N )
% 5.41/5.62 = zero_zero_nat )
% 5.41/5.62 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_is_0_eq
% 5.41/5.62 thf(fact_1041_diff__diff__cancel,axiom,
% 5.41/5.62 ! [I: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ I @ N )
% 5.41/5.62 => ( ( minus_minus_nat @ N @ ( minus_minus_nat @ N @ I ) )
% 5.41/5.62 = I ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_diff_cancel
% 5.41/5.62 thf(fact_1042_less__one,axiom,
% 5.41/5.62 ! [N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ N @ one_one_nat )
% 5.41/5.62 = ( N = zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_one
% 5.41/5.62 thf(fact_1043_diff__diff__left,axiom,
% 5.41/5.62 ! [I: nat,J: nat,K: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.41/5.62 = ( minus_minus_nat @ I @ ( plus_plus_nat @ J @ K ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_diff_left
% 5.41/5.62 thf(fact_1044_nat__zero__less__power__iff,axiom,
% 5.41/5.62 ! [X: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ X @ N ) )
% 5.41/5.62 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.41/5.62 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nat_zero_less_power_iff
% 5.41/5.62 thf(fact_1045_nat__mult__div__cancel__disj,axiom,
% 5.41/5.62 ! [K: nat,M: nat,N: nat] :
% 5.41/5.62 ( ( ( K = zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.62 = zero_zero_nat ) )
% 5.41/5.62 & ( ( K != zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.62 = ( divide_divide_nat @ M @ N ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nat_mult_div_cancel_disj
% 5.41/5.62 thf(fact_1046_mod__less,axiom,
% 5.41/5.62 ! [M: nat,N: nat] :
% 5.41/5.62 ( ( ord_less_nat @ M @ N )
% 5.41/5.62 => ( ( modulo_modulo_nat @ M @ N )
% 5.41/5.62 = M ) ) ).
% 5.41/5.62
% 5.41/5.62 % mod_less
% 5.41/5.62 thf(fact_1047_delt__out__of__range,axiom,
% 5.41/5.62 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.62 ( ( ( ord_less_nat @ X @ Mi )
% 5.41/5.62 | ( ord_less_nat @ Ma @ X ) )
% 5.41/5.62 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.62 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.62 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % delt_out_of_range
% 5.41/5.62 thf(fact_1048_dbl__simps_I2_J,axiom,
% 5.41/5.62 ( ( neg_nu7009210354673126013omplex @ zero_zero_complex )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(2)
% 5.41/5.62 thf(fact_1049_dbl__simps_I2_J,axiom,
% 5.41/5.62 ( ( neg_numeral_dbl_real @ zero_zero_real )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(2)
% 5.41/5.62 thf(fact_1050_dbl__simps_I2_J,axiom,
% 5.41/5.62 ( ( neg_numeral_dbl_rat @ zero_zero_rat )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(2)
% 5.41/5.62 thf(fact_1051_dbl__simps_I2_J,axiom,
% 5.41/5.62 ( ( neg_numeral_dbl_int @ zero_zero_int )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % dbl_simps(2)
% 5.41/5.62 thf(fact_1052__092_060open_062_092_060And_062thesis_O_A_I_092_060And_062maxs_O_ASome_Amaxs_A_061_Avebt__maxt_A_Ivebt__delete_Asummary_A_Ihigh_Ax_An_J_J_A_092_060Longrightarrow_062_Athesis_J_A_092_060Longrightarrow_062_Athesis_092_060close_062,axiom,
% 5.41/5.62 ~ ! [Maxs: nat] :
% 5.41/5.62 ( ( some_nat @ Maxs )
% 5.41/5.62 != ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % \<open>\<And>thesis. (\<And>maxs. Some maxs = vebt_maxt (vebt_delete summary (high x n)) \<Longrightarrow> thesis) \<Longrightarrow> thesis\<close>
% 5.41/5.62 thf(fact_1053_mi__ma__2__deg,axiom,
% 5.41/5.62 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.41/5.62 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.41/5.62 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.41/5.62 & ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mi_ma_2_deg
% 5.41/5.62 thf(fact_1054_add__le__same__cancel1,axiom,
% 5.41/5.62 ! [B: real,A: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel1
% 5.41/5.62 thf(fact_1055_add__le__same__cancel1,axiom,
% 5.41/5.62 ! [B: rat,A: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel1
% 5.41/5.62 thf(fact_1056_add__le__same__cancel1,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel1
% 5.41/5.62 thf(fact_1057_add__le__same__cancel1,axiom,
% 5.41/5.62 ! [B: int,A: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel1
% 5.41/5.62 thf(fact_1058_add__le__same__cancel2,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel2
% 5.41/5.62 thf(fact_1059_add__le__same__cancel2,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel2
% 5.41/5.62 thf(fact_1060_add__le__same__cancel2,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_eq_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel2
% 5.41/5.62 thf(fact_1061_add__le__same__cancel2,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_le_same_cancel2
% 5.41/5.62 thf(fact_1062_le__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.41/5.62 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel1
% 5.41/5.62 thf(fact_1063_le__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.62 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel1
% 5.41/5.62 thf(fact_1064_le__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.62 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel1
% 5.41/5.62 thf(fact_1065_le__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.41/5.62 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel1
% 5.41/5.62 thf(fact_1066_le__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.41/5.62 = ( ord_less_eq_real @ zero_zero_real @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel2
% 5.41/5.62 thf(fact_1067_le__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.41/5.62 = ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel2
% 5.41/5.62 thf(fact_1068_le__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.41/5.62 = ( ord_less_eq_nat @ zero_zero_nat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel2
% 5.41/5.62 thf(fact_1069_le__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.41/5.62 = ( ord_less_eq_int @ zero_zero_int @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_same_cancel2
% 5.41/5.62 thf(fact_1070_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.41/5.62 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_add_le_zero_iff_single_add_le_zero
% 5.41/5.62 thf(fact_1071_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.41/5.62 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_add_le_zero_iff_single_add_le_zero
% 5.41/5.62 thf(fact_1072_double__add__le__zero__iff__single__add__le__zero,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.41/5.62 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_add_le_zero_iff_single_add_le_zero
% 5.41/5.62 thf(fact_1073_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.41/5.62 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_le_double_add_iff_zero_le_single_add
% 5.41/5.62 thf(fact_1074_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.41/5.62 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_le_double_add_iff_zero_le_single_add
% 5.41/5.62 thf(fact_1075_zero__le__double__add__iff__zero__le__single__add,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.41/5.62 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_le_double_add_iff_zero_le_single_add
% 5.41/5.62 thf(fact_1076_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ A ) )
% 5.41/5.62 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_less_double_add_iff_zero_less_single_add
% 5.41/5.62 thf(fact_1077_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ A ) )
% 5.41/5.62 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_less_double_add_iff_zero_less_single_add
% 5.41/5.62 thf(fact_1078_zero__less__double__add__iff__zero__less__single__add,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ A ) )
% 5.41/5.62 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % zero_less_double_add_iff_zero_less_single_add
% 5.41/5.62 thf(fact_1079_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( ord_less_real @ ( plus_plus_real @ A @ A ) @ zero_zero_real )
% 5.41/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_add_less_zero_iff_single_add_less_zero
% 5.41/5.62 thf(fact_1080_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( ord_less_rat @ ( plus_plus_rat @ A @ A ) @ zero_zero_rat )
% 5.41/5.62 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_add_less_zero_iff_single_add_less_zero
% 5.41/5.62 thf(fact_1081_double__add__less__zero__iff__single__add__less__zero,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( ord_less_int @ ( plus_plus_int @ A @ A ) @ zero_zero_int )
% 5.41/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % double_add_less_zero_iff_single_add_less_zero
% 5.41/5.62 thf(fact_1082_less__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.41/5.62 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel2
% 5.41/5.62 thf(fact_1083_less__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.41/5.62 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel2
% 5.41/5.62 thf(fact_1084_less__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ord_less_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.41/5.62 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel2
% 5.41/5.62 thf(fact_1085_less__add__same__cancel2,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.41/5.62 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel2
% 5.41/5.62 thf(fact_1086_less__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.41/5.62 = ( ord_less_real @ zero_zero_real @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel1
% 5.41/5.62 thf(fact_1087_less__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.62 = ( ord_less_rat @ zero_zero_rat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel1
% 5.41/5.62 thf(fact_1088_less__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ord_less_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.62 = ( ord_less_nat @ zero_zero_nat @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel1
% 5.41/5.62 thf(fact_1089_less__add__same__cancel1,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.41/5.62 = ( ord_less_int @ zero_zero_int @ B ) ) ).
% 5.41/5.62
% 5.41/5.62 % less_add_same_cancel1
% 5.41/5.62 thf(fact_1090_add__less__same__cancel2,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_real @ ( plus_plus_real @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel2
% 5.41/5.62 thf(fact_1091_add__less__same__cancel2,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel2
% 5.41/5.62 thf(fact_1092_add__less__same__cancel2,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel2
% 5.41/5.62 thf(fact_1093_add__less__same__cancel2,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.41/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel2
% 5.41/5.62 thf(fact_1094_add__less__same__cancel1,axiom,
% 5.41/5.62 ! [B: real,A: real] :
% 5.41/5.62 ( ( ord_less_real @ ( plus_plus_real @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel1
% 5.41/5.62 thf(fact_1095_add__less__same__cancel1,axiom,
% 5.41/5.62 ! [B: rat,A: rat] :
% 5.41/5.62 ( ( ord_less_rat @ ( plus_plus_rat @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel1
% 5.41/5.62 thf(fact_1096_add__less__same__cancel1,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( ord_less_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_nat @ A @ zero_zero_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel1
% 5.41/5.62 thf(fact_1097_add__less__same__cancel1,axiom,
% 5.41/5.62 ! [B: int,A: int] :
% 5.41/5.62 ( ( ord_less_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.41/5.62 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % add_less_same_cancel1
% 5.41/5.62 thf(fact_1098_diff__ge__0__iff__ge,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.41/5.62 = ( ord_less_eq_real @ B @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_ge_0_iff_ge
% 5.41/5.62 thf(fact_1099_diff__ge__0__iff__ge,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.41/5.62 = ( ord_less_eq_rat @ B @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_ge_0_iff_ge
% 5.41/5.62 thf(fact_1100_diff__ge__0__iff__ge,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.41/5.62 = ( ord_less_eq_int @ B @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_ge_0_iff_ge
% 5.41/5.62 thf(fact_1101_diff__gt__0__iff__gt,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ord_less_real @ zero_zero_real @ ( minus_minus_real @ A @ B ) )
% 5.41/5.62 = ( ord_less_real @ B @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_gt_0_iff_gt
% 5.41/5.62 thf(fact_1102_diff__gt__0__iff__gt,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ord_less_rat @ zero_zero_rat @ ( minus_minus_rat @ A @ B ) )
% 5.41/5.62 = ( ord_less_rat @ B @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_gt_0_iff_gt
% 5.41/5.62 thf(fact_1103_diff__gt__0__iff__gt,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( ord_less_int @ zero_zero_int @ ( minus_minus_int @ A @ B ) )
% 5.41/5.62 = ( ord_less_int @ B @ A ) ) ).
% 5.41/5.62
% 5.41/5.62 % diff_gt_0_iff_gt
% 5.41/5.62 thf(fact_1104_sum__squares__eq__zero__iff,axiom,
% 5.41/5.62 ! [X: real,Y: real] :
% 5.41/5.62 ( ( ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.41/5.62 = zero_zero_real )
% 5.41/5.62 = ( ( X = zero_zero_real )
% 5.41/5.62 & ( Y = zero_zero_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % sum_squares_eq_zero_iff
% 5.41/5.62 thf(fact_1105_sum__squares__eq__zero__iff,axiom,
% 5.41/5.62 ! [X: rat,Y: rat] :
% 5.41/5.62 ( ( ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.41/5.62 = zero_zero_rat )
% 5.41/5.62 = ( ( X = zero_zero_rat )
% 5.41/5.62 & ( Y = zero_zero_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % sum_squares_eq_zero_iff
% 5.41/5.62 thf(fact_1106_sum__squares__eq__zero__iff,axiom,
% 5.41/5.62 ! [X: int,Y: int] :
% 5.41/5.62 ( ( ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.41/5.62 = zero_zero_int )
% 5.41/5.62 = ( ( X = zero_zero_int )
% 5.41/5.62 & ( Y = zero_zero_int ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % sum_squares_eq_zero_iff
% 5.41/5.62 thf(fact_1107_mult__cancel__left1,axiom,
% 5.41/5.62 ! [C: complex,B: complex] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_complex @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( B = one_one_complex ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left1
% 5.41/5.62 thf(fact_1108_mult__cancel__left1,axiom,
% 5.41/5.62 ! [C: real,B: real] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_real @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( B = one_one_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left1
% 5.41/5.62 thf(fact_1109_mult__cancel__left1,axiom,
% 5.41/5.62 ! [C: rat,B: rat] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_rat @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( B = one_one_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left1
% 5.41/5.62 thf(fact_1110_mult__cancel__left1,axiom,
% 5.41/5.62 ! [C: int,B: int] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_int @ C @ B ) )
% 5.41/5.62 = ( ( C = zero_zero_int )
% 5.41/5.62 | ( B = one_one_int ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left1
% 5.41/5.62 thf(fact_1111_mult__cancel__left2,axiom,
% 5.41/5.62 ! [C: complex,A: complex] :
% 5.41/5.62 ( ( ( times_times_complex @ C @ A )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( A = one_one_complex ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left2
% 5.41/5.62 thf(fact_1112_mult__cancel__left2,axiom,
% 5.41/5.62 ! [C: real,A: real] :
% 5.41/5.62 ( ( ( times_times_real @ C @ A )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( A = one_one_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left2
% 5.41/5.62 thf(fact_1113_mult__cancel__left2,axiom,
% 5.41/5.62 ! [C: rat,A: rat] :
% 5.41/5.62 ( ( ( times_times_rat @ C @ A )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( A = one_one_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left2
% 5.41/5.62 thf(fact_1114_mult__cancel__left2,axiom,
% 5.41/5.62 ! [C: int,A: int] :
% 5.41/5.62 ( ( ( times_times_int @ C @ A )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_int )
% 5.41/5.62 | ( A = one_one_int ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_left2
% 5.41/5.62 thf(fact_1115_mult__cancel__right1,axiom,
% 5.41/5.62 ! [C: complex,B: complex] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_complex @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( B = one_one_complex ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right1
% 5.41/5.62 thf(fact_1116_mult__cancel__right1,axiom,
% 5.41/5.62 ! [C: real,B: real] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_real @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( B = one_one_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right1
% 5.41/5.62 thf(fact_1117_mult__cancel__right1,axiom,
% 5.41/5.62 ! [C: rat,B: rat] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_rat @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( B = one_one_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right1
% 5.41/5.62 thf(fact_1118_mult__cancel__right1,axiom,
% 5.41/5.62 ! [C: int,B: int] :
% 5.41/5.62 ( ( C
% 5.41/5.62 = ( times_times_int @ B @ C ) )
% 5.41/5.62 = ( ( C = zero_zero_int )
% 5.41/5.62 | ( B = one_one_int ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right1
% 5.41/5.62 thf(fact_1119_mult__cancel__right2,axiom,
% 5.41/5.62 ! [A: complex,C: complex] :
% 5.41/5.62 ( ( ( times_times_complex @ A @ C )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_complex )
% 5.41/5.62 | ( A = one_one_complex ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right2
% 5.41/5.62 thf(fact_1120_mult__cancel__right2,axiom,
% 5.41/5.62 ! [A: real,C: real] :
% 5.41/5.62 ( ( ( times_times_real @ A @ C )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_real )
% 5.41/5.62 | ( A = one_one_real ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right2
% 5.41/5.62 thf(fact_1121_mult__cancel__right2,axiom,
% 5.41/5.62 ! [A: rat,C: rat] :
% 5.41/5.62 ( ( ( times_times_rat @ A @ C )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_rat )
% 5.41/5.62 | ( A = one_one_rat ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right2
% 5.41/5.62 thf(fact_1122_mult__cancel__right2,axiom,
% 5.41/5.62 ! [A: int,C: int] :
% 5.41/5.62 ( ( ( times_times_int @ A @ C )
% 5.41/5.62 = C )
% 5.41/5.62 = ( ( C = zero_zero_int )
% 5.41/5.62 | ( A = one_one_int ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_cancel_right2
% 5.41/5.62 thf(fact_1123_mult__divide__mult__cancel__left__if,axiom,
% 5.41/5.62 ! [C: complex,A: complex,B: complex] :
% 5.41/5.62 ( ( ( C = zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.41/5.62 = zero_zero_complex ) )
% 5.41/5.62 & ( ( C != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_divide_mult_cancel_left_if
% 5.41/5.62 thf(fact_1124_mult__divide__mult__cancel__left__if,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( ( C = zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.62 = zero_zero_real ) )
% 5.41/5.62 & ( ( C != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.62 = ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_divide_mult_cancel_left_if
% 5.41/5.62 thf(fact_1125_mult__divide__mult__cancel__left__if,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( ( C = zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.62 = zero_zero_rat ) )
% 5.41/5.62 & ( ( C != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.62 = ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % mult_divide_mult_cancel_left_if
% 5.41/5.62 thf(fact_1126_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.41/5.62 ! [C: complex,A: complex,B: complex] :
% 5.41/5.62 ( ( C != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_left
% 5.41/5.62 thf(fact_1127_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( C != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_left
% 5.41/5.62 thf(fact_1128_nonzero__mult__divide__mult__cancel__left,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( C != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.62 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_left
% 5.41/5.62 thf(fact_1129_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( A != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ A )
% 5.41/5.62 = B ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_left
% 5.41/5.62 thf(fact_1130_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( A != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ A )
% 5.41/5.62 = B ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_left
% 5.41/5.62 thf(fact_1131_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( A != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ A )
% 5.41/5.62 = B ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_left
% 5.41/5.62 thf(fact_1132_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( A != zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ A )
% 5.41/5.62 = B ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_left
% 5.41/5.62 thf(fact_1133_nonzero__mult__div__cancel__left,axiom,
% 5.41/5.62 ! [A: int,B: int] :
% 5.41/5.62 ( ( A != zero_zero_int )
% 5.41/5.62 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ A )
% 5.41/5.62 = B ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_left
% 5.41/5.62 thf(fact_1134_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.41/5.62 ! [C: complex,A: complex,B: complex] :
% 5.41/5.62 ( ( C != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ B @ C ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_left2
% 5.41/5.62 thf(fact_1135_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( C != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ B @ C ) )
% 5.41/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_left2
% 5.41/5.62 thf(fact_1136_nonzero__mult__divide__mult__cancel__left2,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( C != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.62 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_left2
% 5.41/5.62 thf(fact_1137_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.41/5.62 ! [C: complex,A: complex,B: complex] :
% 5.41/5.62 ( ( C != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_right
% 5.41/5.62 thf(fact_1138_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( C != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.41/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_right
% 5.41/5.62 thf(fact_1139_nonzero__mult__divide__mult__cancel__right,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( C != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.62 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_right
% 5.41/5.62 thf(fact_1140_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.62 ! [B: complex,A: complex] :
% 5.41/5.62 ( ( B != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_right
% 5.41/5.62 thf(fact_1141_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.62 ! [B: real,A: real] :
% 5.41/5.62 ( ( B != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_right
% 5.41/5.62 thf(fact_1142_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.62 ! [B: rat,A: rat] :
% 5.41/5.62 ( ( B != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_right
% 5.41/5.62 thf(fact_1143_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( B != zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_right
% 5.41/5.62 thf(fact_1144_nonzero__mult__div__cancel__right,axiom,
% 5.41/5.62 ! [B: int,A: int] :
% 5.41/5.62 ( ( B != zero_zero_int )
% 5.41/5.62 => ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_div_cancel_right
% 5.41/5.62 thf(fact_1145_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.41/5.62 ! [C: complex,A: complex,B: complex] :
% 5.41/5.62 ( ( C != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ C @ B ) )
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_right2
% 5.41/5.62 thf(fact_1146_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.41/5.62 ! [C: real,A: real,B: real] :
% 5.41/5.62 ( ( C != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ C @ B ) )
% 5.41/5.62 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_right2
% 5.41/5.62 thf(fact_1147_nonzero__mult__divide__mult__cancel__right2,axiom,
% 5.41/5.62 ! [C: rat,A: rat,B: rat] :
% 5.41/5.62 ( ( C != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.62 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % nonzero_mult_divide_mult_cancel_right2
% 5.41/5.62 thf(fact_1148_div__mult__mult1,axiom,
% 5.41/5.62 ! [C: nat,A: nat,B: nat] :
% 5.41/5.62 ( ( C != zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.41/5.62 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult_mult1
% 5.41/5.62 thf(fact_1149_div__mult__mult1,axiom,
% 5.41/5.62 ! [C: int,A: int,B: int] :
% 5.41/5.62 ( ( C != zero_zero_int )
% 5.41/5.62 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.62 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult_mult1
% 5.41/5.62 thf(fact_1150_div__mult__mult2,axiom,
% 5.41/5.62 ! [C: nat,A: nat,B: nat] :
% 5.41/5.62 ( ( C != zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.41/5.62 = ( divide_divide_nat @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult_mult2
% 5.41/5.62 thf(fact_1151_div__mult__mult2,axiom,
% 5.41/5.62 ! [C: int,A: int,B: int] :
% 5.41/5.62 ( ( C != zero_zero_int )
% 5.41/5.62 => ( ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.62 = ( divide_divide_int @ A @ B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult_mult2
% 5.41/5.62 thf(fact_1152_div__mult__mult1__if,axiom,
% 5.41/5.62 ! [C: nat,A: nat,B: nat] :
% 5.41/5.62 ( ( ( C = zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.41/5.62 = zero_zero_nat ) )
% 5.41/5.62 & ( ( C != zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.41/5.62 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult_mult1_if
% 5.41/5.62 thf(fact_1153_div__mult__mult1__if,axiom,
% 5.41/5.62 ! [C: int,A: int,B: int] :
% 5.41/5.62 ( ( ( C = zero_zero_int )
% 5.41/5.62 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.62 = zero_zero_int ) )
% 5.41/5.62 & ( ( C != zero_zero_int )
% 5.41/5.62 => ( ( divide_divide_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.62 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_mult_mult1_if
% 5.41/5.62 thf(fact_1154_le__add__diff__inverse,axiom,
% 5.41/5.62 ! [B: real,A: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ B @ A )
% 5.41/5.62 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse
% 5.41/5.62 thf(fact_1155_le__add__diff__inverse,axiom,
% 5.41/5.62 ! [B: rat,A: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.62 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse
% 5.41/5.62 thf(fact_1156_le__add__diff__inverse,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.62 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse
% 5.41/5.62 thf(fact_1157_le__add__diff__inverse,axiom,
% 5.41/5.62 ! [B: int,A: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.62 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse
% 5.41/5.62 thf(fact_1158_le__add__diff__inverse2,axiom,
% 5.41/5.62 ! [B: real,A: real] :
% 5.41/5.62 ( ( ord_less_eq_real @ B @ A )
% 5.41/5.62 => ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse2
% 5.41/5.62 thf(fact_1159_le__add__diff__inverse2,axiom,
% 5.41/5.62 ! [B: rat,A: rat] :
% 5.41/5.62 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.62 => ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse2
% 5.41/5.62 thf(fact_1160_le__add__diff__inverse2,axiom,
% 5.41/5.62 ! [B: nat,A: nat] :
% 5.41/5.62 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.62 => ( ( plus_plus_nat @ ( minus_minus_nat @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse2
% 5.41/5.62 thf(fact_1161_le__add__diff__inverse2,axiom,
% 5.41/5.62 ! [B: int,A: int] :
% 5.41/5.62 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.62 => ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ B )
% 5.41/5.62 = A ) ) ).
% 5.41/5.62
% 5.41/5.62 % le_add_diff_inverse2
% 5.41/5.62 thf(fact_1162_diff__add__zero,axiom,
% 5.41/5.62 ! [A: nat,B: nat] :
% 5.41/5.62 ( ( minus_minus_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.62 = zero_zero_nat ) ).
% 5.41/5.62
% 5.41/5.62 % diff_add_zero
% 5.41/5.62 thf(fact_1163_diff__numeral__special_I9_J,axiom,
% 5.41/5.62 ( ( minus_minus_complex @ one_one_complex @ one_one_complex )
% 5.41/5.62 = zero_zero_complex ) ).
% 5.41/5.62
% 5.41/5.62 % diff_numeral_special(9)
% 5.41/5.62 thf(fact_1164_diff__numeral__special_I9_J,axiom,
% 5.41/5.62 ( ( minus_minus_real @ one_one_real @ one_one_real )
% 5.41/5.62 = zero_zero_real ) ).
% 5.41/5.62
% 5.41/5.62 % diff_numeral_special(9)
% 5.41/5.62 thf(fact_1165_diff__numeral__special_I9_J,axiom,
% 5.41/5.62 ( ( minus_minus_rat @ one_one_rat @ one_one_rat )
% 5.41/5.62 = zero_zero_rat ) ).
% 5.41/5.62
% 5.41/5.62 % diff_numeral_special(9)
% 5.41/5.62 thf(fact_1166_diff__numeral__special_I9_J,axiom,
% 5.41/5.62 ( ( minus_minus_int @ one_one_int @ one_one_int )
% 5.41/5.62 = zero_zero_int ) ).
% 5.41/5.62
% 5.41/5.62 % diff_numeral_special(9)
% 5.41/5.62 thf(fact_1167_divide__eq__1__iff,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.41/5.62 = one_one_complex )
% 5.41/5.62 = ( ( B != zero_zero_complex )
% 5.41/5.62 & ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_eq_1_iff
% 5.41/5.62 thf(fact_1168_divide__eq__1__iff,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( ( divide_divide_real @ A @ B )
% 5.41/5.62 = one_one_real )
% 5.41/5.62 = ( ( B != zero_zero_real )
% 5.41/5.62 & ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_eq_1_iff
% 5.41/5.62 thf(fact_1169_divide__eq__1__iff,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( ( divide_divide_rat @ A @ B )
% 5.41/5.62 = one_one_rat )
% 5.41/5.62 = ( ( B != zero_zero_rat )
% 5.41/5.62 & ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_eq_1_iff
% 5.41/5.62 thf(fact_1170_div__self,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( A != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.62 = one_one_complex ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_self
% 5.41/5.62 thf(fact_1171_div__self,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( A != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ A @ A )
% 5.41/5.62 = one_one_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_self
% 5.41/5.62 thf(fact_1172_div__self,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.62 ( ( A != zero_zero_rat )
% 5.41/5.62 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.62 = one_one_rat ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_self
% 5.41/5.62 thf(fact_1173_div__self,axiom,
% 5.41/5.62 ! [A: nat] :
% 5.41/5.62 ( ( A != zero_zero_nat )
% 5.41/5.62 => ( ( divide_divide_nat @ A @ A )
% 5.41/5.62 = one_one_nat ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_self
% 5.41/5.62 thf(fact_1174_div__self,axiom,
% 5.41/5.62 ! [A: int] :
% 5.41/5.62 ( ( A != zero_zero_int )
% 5.41/5.62 => ( ( divide_divide_int @ A @ A )
% 5.41/5.62 = one_one_int ) ) ).
% 5.41/5.62
% 5.41/5.62 % div_self
% 5.41/5.62 thf(fact_1175_one__eq__divide__iff,axiom,
% 5.41/5.62 ! [A: complex,B: complex] :
% 5.41/5.62 ( ( one_one_complex
% 5.41/5.62 = ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.62 = ( ( B != zero_zero_complex )
% 5.41/5.62 & ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % one_eq_divide_iff
% 5.41/5.62 thf(fact_1176_one__eq__divide__iff,axiom,
% 5.41/5.62 ! [A: real,B: real] :
% 5.41/5.62 ( ( one_one_real
% 5.41/5.62 = ( divide_divide_real @ A @ B ) )
% 5.41/5.62 = ( ( B != zero_zero_real )
% 5.41/5.62 & ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % one_eq_divide_iff
% 5.41/5.62 thf(fact_1177_one__eq__divide__iff,axiom,
% 5.41/5.62 ! [A: rat,B: rat] :
% 5.41/5.62 ( ( one_one_rat
% 5.41/5.62 = ( divide_divide_rat @ A @ B ) )
% 5.41/5.62 = ( ( B != zero_zero_rat )
% 5.41/5.62 & ( A = B ) ) ) ).
% 5.41/5.62
% 5.41/5.62 % one_eq_divide_iff
% 5.41/5.62 thf(fact_1178_divide__self,axiom,
% 5.41/5.62 ! [A: complex] :
% 5.41/5.62 ( ( A != zero_zero_complex )
% 5.41/5.62 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.62 = one_one_complex ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_self
% 5.41/5.62 thf(fact_1179_divide__self,axiom,
% 5.41/5.62 ! [A: real] :
% 5.41/5.62 ( ( A != zero_zero_real )
% 5.41/5.62 => ( ( divide_divide_real @ A @ A )
% 5.41/5.62 = one_one_real ) ) ).
% 5.41/5.62
% 5.41/5.62 % divide_self
% 5.41/5.62 thf(fact_1180_divide__self,axiom,
% 5.41/5.62 ! [A: rat] :
% 5.41/5.63 ( ( A != zero_zero_rat )
% 5.41/5.63 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.63 = one_one_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_self
% 5.41/5.63 thf(fact_1181_divide__self__if,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( ( A = zero_zero_complex )
% 5.41/5.63 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.63 = zero_zero_complex ) )
% 5.41/5.63 & ( ( A != zero_zero_complex )
% 5.41/5.63 => ( ( divide1717551699836669952omplex @ A @ A )
% 5.41/5.63 = one_one_complex ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_self_if
% 5.41/5.63 thf(fact_1182_divide__self__if,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ( A = zero_zero_real )
% 5.41/5.63 => ( ( divide_divide_real @ A @ A )
% 5.41/5.63 = zero_zero_real ) )
% 5.41/5.63 & ( ( A != zero_zero_real )
% 5.41/5.63 => ( ( divide_divide_real @ A @ A )
% 5.41/5.63 = one_one_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_self_if
% 5.41/5.63 thf(fact_1183_divide__self__if,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ( A = zero_zero_rat )
% 5.41/5.63 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.63 = zero_zero_rat ) )
% 5.41/5.63 & ( ( A != zero_zero_rat )
% 5.41/5.63 => ( ( divide_divide_rat @ A @ A )
% 5.41/5.63 = one_one_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_self_if
% 5.41/5.63 thf(fact_1184_divide__eq__eq__1,axiom,
% 5.41/5.63 ! [B: real,A: real] :
% 5.41/5.63 ( ( ( divide_divide_real @ B @ A )
% 5.41/5.63 = one_one_real )
% 5.41/5.63 = ( ( A != zero_zero_real )
% 5.41/5.63 & ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_eq_eq_1
% 5.41/5.63 thf(fact_1185_divide__eq__eq__1,axiom,
% 5.41/5.63 ! [B: rat,A: rat] :
% 5.41/5.63 ( ( ( divide_divide_rat @ B @ A )
% 5.41/5.63 = one_one_rat )
% 5.41/5.63 = ( ( A != zero_zero_rat )
% 5.41/5.63 & ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_eq_eq_1
% 5.41/5.63 thf(fact_1186_eq__divide__eq__1,axiom,
% 5.41/5.63 ! [B: real,A: real] :
% 5.41/5.63 ( ( one_one_real
% 5.41/5.63 = ( divide_divide_real @ B @ A ) )
% 5.41/5.63 = ( ( A != zero_zero_real )
% 5.41/5.63 & ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_divide_eq_1
% 5.41/5.63 thf(fact_1187_eq__divide__eq__1,axiom,
% 5.41/5.63 ! [B: rat,A: rat] :
% 5.41/5.63 ( ( one_one_rat
% 5.41/5.63 = ( divide_divide_rat @ B @ A ) )
% 5.41/5.63 = ( ( A != zero_zero_rat )
% 5.41/5.63 & ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_divide_eq_1
% 5.41/5.63 thf(fact_1188_one__divide__eq__0__iff,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ( divide_divide_real @ one_one_real @ A )
% 5.41/5.63 = zero_zero_real )
% 5.41/5.63 = ( A = zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_divide_eq_0_iff
% 5.41/5.63 thf(fact_1189_one__divide__eq__0__iff,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ( divide_divide_rat @ one_one_rat @ A )
% 5.41/5.63 = zero_zero_rat )
% 5.41/5.63 = ( A = zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % one_divide_eq_0_iff
% 5.41/5.63 thf(fact_1190_zero__eq__1__divide__iff,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( zero_zero_real
% 5.41/5.63 = ( divide_divide_real @ one_one_real @ A ) )
% 5.41/5.63 = ( A = zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_eq_1_divide_iff
% 5.41/5.63 thf(fact_1191_zero__eq__1__divide__iff,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( zero_zero_rat
% 5.41/5.63 = ( divide_divide_rat @ one_one_rat @ A ) )
% 5.41/5.63 = ( A = zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_eq_1_divide_iff
% 5.41/5.63 thf(fact_1192_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B: complex,C: complex] :
% 5.41/5.63 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( minus_minus_complex @ B @ C ) )
% 5.41/5.63 = ( minus_minus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ B ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_1193_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B: real,C: real] :
% 5.41/5.63 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( minus_minus_real @ B @ C ) )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ V ) @ B ) @ ( times_times_real @ ( numeral_numeral_real @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_1194_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B: rat,C: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( minus_minus_rat @ B @ C ) )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ B ) @ ( times_times_rat @ ( numeral_numeral_rat @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_1195_right__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [V: num,B: int,C: int] :
% 5.41/5.63 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( minus_minus_int @ B @ C ) )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ V ) @ B ) @ ( times_times_int @ ( numeral_numeral_int @ V ) @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib_numeral
% 5.41/5.63 thf(fact_1196_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: complex,B: complex,V: num] :
% 5.41/5.63 ( ( times_times_complex @ ( minus_minus_complex @ A @ B ) @ ( numera6690914467698888265omplex @ V ) )
% 5.41/5.63 = ( minus_minus_complex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ B @ ( numera6690914467698888265omplex @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_1197_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: real,B: real,V: num] :
% 5.41/5.63 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ A @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ B @ ( numeral_numeral_real @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_1198_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: rat,B: rat,V: num] :
% 5.41/5.63 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ B @ ( numeral_numeral_rat @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_1199_left__diff__distrib__numeral,axiom,
% 5.41/5.63 ! [A: int,B: int,V: num] :
% 5.41/5.63 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ A @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ B @ ( numeral_numeral_int @ V ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib_numeral
% 5.41/5.63 thf(fact_1200_power__zero__numeral,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ K ) )
% 5.41/5.63 = zero_zero_rat ) ).
% 5.41/5.63
% 5.41/5.63 % power_zero_numeral
% 5.41/5.63 thf(fact_1201_power__zero__numeral,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ K ) )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % power_zero_numeral
% 5.41/5.63 thf(fact_1202_power__zero__numeral,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ K ) )
% 5.41/5.63 = zero_zero_real ) ).
% 5.41/5.63
% 5.41/5.63 % power_zero_numeral
% 5.41/5.63 thf(fact_1203_power__zero__numeral,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ K ) )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % power_zero_numeral
% 5.41/5.63 thf(fact_1204_power__zero__numeral,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ K ) )
% 5.41/5.63 = zero_zero_complex ) ).
% 5.41/5.63
% 5.41/5.63 % power_zero_numeral
% 5.41/5.63 thf(fact_1205_power__eq__0__iff,axiom,
% 5.41/5.63 ! [A: rat,N: nat] :
% 5.41/5.63 ( ( ( power_power_rat @ A @ N )
% 5.41/5.63 = zero_zero_rat )
% 5.41/5.63 = ( ( A = zero_zero_rat )
% 5.41/5.63 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_eq_0_iff
% 5.41/5.63 thf(fact_1206_power__eq__0__iff,axiom,
% 5.41/5.63 ! [A: nat,N: nat] :
% 5.41/5.63 ( ( ( power_power_nat @ A @ N )
% 5.41/5.63 = zero_zero_nat )
% 5.41/5.63 = ( ( A = zero_zero_nat )
% 5.41/5.63 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_eq_0_iff
% 5.41/5.63 thf(fact_1207_power__eq__0__iff,axiom,
% 5.41/5.63 ! [A: real,N: nat] :
% 5.41/5.63 ( ( ( power_power_real @ A @ N )
% 5.41/5.63 = zero_zero_real )
% 5.41/5.63 = ( ( A = zero_zero_real )
% 5.41/5.63 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_eq_0_iff
% 5.41/5.63 thf(fact_1208_power__eq__0__iff,axiom,
% 5.41/5.63 ! [A: int,N: nat] :
% 5.41/5.63 ( ( ( power_power_int @ A @ N )
% 5.41/5.63 = zero_zero_int )
% 5.41/5.63 = ( ( A = zero_zero_int )
% 5.41/5.63 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_eq_0_iff
% 5.41/5.63 thf(fact_1209_power__eq__0__iff,axiom,
% 5.41/5.63 ! [A: complex,N: nat] :
% 5.41/5.63 ( ( ( power_power_complex @ A @ N )
% 5.41/5.63 = zero_zero_complex )
% 5.41/5.63 = ( ( A = zero_zero_complex )
% 5.41/5.63 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_eq_0_iff
% 5.41/5.63 thf(fact_1210_mod__mult__self2__is__0,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ B )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self2_is_0
% 5.41/5.63 thf(fact_1211_mod__mult__self2__is__0,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ B )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self2_is_0
% 5.41/5.63 thf(fact_1212_mod__mult__self2__is__0,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ B )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self2_is_0
% 5.41/5.63 thf(fact_1213_mod__mult__self1__is__0,axiom,
% 5.41/5.63 ! [B: nat,A: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ B @ A ) @ B )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self1_is_0
% 5.41/5.63 thf(fact_1214_mod__mult__self1__is__0,axiom,
% 5.41/5.63 ! [B: int,A: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( times_times_int @ B @ A ) @ B )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self1_is_0
% 5.41/5.63 thf(fact_1215_mod__mult__self1__is__0,axiom,
% 5.41/5.63 ! [B: code_integer,A: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ B @ A ) @ B )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self1_is_0
% 5.41/5.63 thf(fact_1216_bits__mod__by__1,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % bits_mod_by_1
% 5.41/5.63 thf(fact_1217_bits__mod__by__1,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % bits_mod_by_1
% 5.41/5.63 thf(fact_1218_bits__mod__by__1,axiom,
% 5.41/5.63 ! [A: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ).
% 5.41/5.63
% 5.41/5.63 % bits_mod_by_1
% 5.41/5.63 thf(fact_1219_mod__by__1,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ A @ one_one_nat )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % mod_by_1
% 5.41/5.63 thf(fact_1220_mod__by__1,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ A @ one_one_int )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % mod_by_1
% 5.41/5.63 thf(fact_1221_mod__by__1,axiom,
% 5.41/5.63 ! [A: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ A @ one_one_Code_integer )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ).
% 5.41/5.63
% 5.41/5.63 % mod_by_1
% 5.41/5.63 thf(fact_1222_mod__div__trivial,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % mod_div_trivial
% 5.41/5.63 thf(fact_1223_mod__div__trivial,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % mod_div_trivial
% 5.41/5.63 thf(fact_1224_mod__div__trivial,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ).
% 5.41/5.63
% 5.41/5.63 % mod_div_trivial
% 5.41/5.63 thf(fact_1225_bits__mod__div__trivial,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( divide_divide_nat @ ( modulo_modulo_nat @ A @ B ) @ B )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % bits_mod_div_trivial
% 5.41/5.63 thf(fact_1226_bits__mod__div__trivial,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( divide_divide_int @ ( modulo_modulo_int @ A @ B ) @ B )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % bits_mod_div_trivial
% 5.41/5.63 thf(fact_1227_bits__mod__div__trivial,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ).
% 5.41/5.63
% 5.41/5.63 % bits_mod_div_trivial
% 5.41/5.63 thf(fact_1228_mod__mult__self4,axiom,
% 5.41/5.63 ! [B: nat,C: nat,A: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.41/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self4
% 5.41/5.63 thf(fact_1229_mod__mult__self4,axiom,
% 5.41/5.63 ! [B: int,C: int,A: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.41/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self4
% 5.41/5.63 thf(fact_1230_mod__mult__self4,axiom,
% 5.41/5.63 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ C ) @ A ) @ B )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self4
% 5.41/5.63 thf(fact_1231_mod__mult__self3,axiom,
% 5.41/5.63 ! [C: nat,B: nat,A: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.41/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self3
% 5.41/5.63 thf(fact_1232_mod__mult__self3,axiom,
% 5.41/5.63 ! [C: int,B: int,A: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.41/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self3
% 5.41/5.63 thf(fact_1233_mod__mult__self3,axiom,
% 5.41/5.63 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ B ) @ A ) @ B )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self3
% 5.41/5.63 thf(fact_1234_mod__mult__self2,axiom,
% 5.41/5.63 ! [A: nat,B: nat,C: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.41/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self2
% 5.41/5.63 thf(fact_1235_mod__mult__self2,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.41/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self2
% 5.41/5.63 thf(fact_1236_mod__mult__self2,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) ) @ B )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self2
% 5.41/5.63 thf(fact_1237_mod__mult__self1,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.41/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self1
% 5.41/5.63 thf(fact_1238_mod__mult__self1,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.41/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self1
% 5.41/5.63 thf(fact_1239_mod__mult__self1,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ B ) ) @ B )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_self1
% 5.41/5.63 thf(fact_1240_mult__le__cancel2,axiom,
% 5.41/5.63 ! [M: nat,K: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) )
% 5.41/5.63 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_le_cancel2
% 5.41/5.63 thf(fact_1241_nat__mult__le__cancel__disj,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.63 = ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.63 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_mult_le_cancel_disj
% 5.41/5.63 thf(fact_1242_Nat_Oadd__diff__assoc,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.add_diff_assoc
% 5.41/5.63 thf(fact_1243_Nat_Oadd__diff__assoc2,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.41/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.add_diff_assoc2
% 5.41/5.63 thf(fact_1244_Nat_Odiff__diff__right,axiom,
% 5.41/5.63 ! [K: nat,J: nat,I: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.63 => ( ( minus_minus_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.63 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.diff_diff_right
% 5.41/5.63 thf(fact_1245_div__mult__self__is__m,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( divide_divide_nat @ ( times_times_nat @ M @ N ) @ N )
% 5.41/5.63 = M ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self_is_m
% 5.41/5.63 thf(fact_1246_div__mult__self1__is__m,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( divide_divide_nat @ ( times_times_nat @ N @ M ) @ N )
% 5.41/5.63 = M ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self1_is_m
% 5.41/5.63 thf(fact_1247_dbl__simps_I5_J,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.41/5.63 = ( numera6690914467698888265omplex @ ( bit0 @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % dbl_simps(5)
% 5.41/5.63 thf(fact_1248_dbl__simps_I5_J,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) )
% 5.41/5.63 = ( numeral_numeral_real @ ( bit0 @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % dbl_simps(5)
% 5.41/5.63 thf(fact_1249_dbl__simps_I5_J,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) )
% 5.41/5.63 = ( numeral_numeral_rat @ ( bit0 @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % dbl_simps(5)
% 5.41/5.63 thf(fact_1250_dbl__simps_I5_J,axiom,
% 5.41/5.63 ! [K: num] :
% 5.41/5.63 ( ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) )
% 5.41/5.63 = ( numeral_numeral_int @ ( bit0 @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % dbl_simps(5)
% 5.41/5.63 thf(fact_1251_both__member__options__from__complete__tree__to__child,axiom,
% 5.41/5.63 ! [Deg: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ one_one_nat @ Deg )
% 5.41/5.63 => ( ( vEBT_V8194947554948674370ptions @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.63 => ( ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.63 | ( X = Mi )
% 5.41/5.63 | ( X = Ma ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % both_member_options_from_complete_tree_to_child
% 5.41/5.63 thf(fact_1252__C10_C,axiom,
% 5.41/5.63 vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ deg ).
% 5.41/5.63
% 5.41/5.63 % "10"
% 5.41/5.63 thf(fact_1253_member__inv,axiom,
% 5.41/5.63 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.41/5.63 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.63 & ( ( X = Mi )
% 5.41/5.63 | ( X = Ma )
% 5.41/5.63 | ( ( ord_less_nat @ X @ Ma )
% 5.41/5.63 & ( ord_less_nat @ Mi @ X )
% 5.41/5.63 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.63 & ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % member_inv
% 5.41/5.63 thf(fact_1254_zero__le__divide__1__iff,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.41/5.63 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_le_divide_1_iff
% 5.41/5.63 thf(fact_1255_zero__le__divide__1__iff,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.41/5.63 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_le_divide_1_iff
% 5.41/5.63 thf(fact_1256_divide__le__0__1__iff,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.41/5.63 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_0_1_iff
% 5.41/5.63 thf(fact_1257_divide__le__0__1__iff,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.41/5.63 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_0_1_iff
% 5.41/5.63 thf(fact_1258_divide__less__0__1__iff,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ord_less_real @ ( divide_divide_real @ one_one_real @ A ) @ zero_zero_real )
% 5.41/5.63 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_0_1_iff
% 5.41/5.63 thf(fact_1259_divide__less__0__1__iff,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ A ) @ zero_zero_rat )
% 5.41/5.63 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_0_1_iff
% 5.41/5.63 thf(fact_1260_divide__less__eq__1__neg,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.63 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.41/5.63 = ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_eq_1_neg
% 5.41/5.63 thf(fact_1261_divide__less__eq__1__neg,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.63 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.41/5.63 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_eq_1_neg
% 5.41/5.63 thf(fact_1262_divide__less__eq__1__pos,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.63 => ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.41/5.63 = ( ord_less_real @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_eq_1_pos
% 5.41/5.63 thf(fact_1263_divide__less__eq__1__pos,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.63 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.41/5.63 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_less_eq_1_pos
% 5.41/5.63 thf(fact_1264_less__divide__eq__1__neg,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.63 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.41/5.63 = ( ord_less_real @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_divide_eq_1_neg
% 5.41/5.63 thf(fact_1265_less__divide__eq__1__neg,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.63 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.41/5.63 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_divide_eq_1_neg
% 5.41/5.63 thf(fact_1266_less__divide__eq__1__pos,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.63 => ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.41/5.63 = ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_divide_eq_1_pos
% 5.41/5.63 thf(fact_1267_less__divide__eq__1__pos,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.63 => ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.41/5.63 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_divide_eq_1_pos
% 5.41/5.63 thf(fact_1268_zero__less__divide__1__iff,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ one_one_real @ A ) )
% 5.41/5.63 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_less_divide_1_iff
% 5.41/5.63 thf(fact_1269_zero__less__divide__1__iff,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ one_one_rat @ A ) )
% 5.41/5.63 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_less_divide_1_iff
% 5.41/5.63 thf(fact_1270_divide__eq__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [B: complex,W: num,A: complex] :
% 5.41/5.63 ( ( ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.63 = A )
% 5.41/5.63 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.63 != zero_zero_complex )
% 5.41/5.63 => ( B
% 5.41/5.63 = ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.41/5.63 & ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.63 = zero_zero_complex )
% 5.41/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_eq_eq_numeral1(1)
% 5.41/5.63 thf(fact_1271_divide__eq__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [B: real,W: num,A: real] :
% 5.41/5.63 ( ( ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) )
% 5.41/5.63 = A )
% 5.41/5.63 = ( ( ( ( numeral_numeral_real @ W )
% 5.41/5.63 != zero_zero_real )
% 5.41/5.63 => ( B
% 5.41/5.63 = ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) ) )
% 5.41/5.63 & ( ( ( numeral_numeral_real @ W )
% 5.41/5.63 = zero_zero_real )
% 5.41/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_eq_eq_numeral1(1)
% 5.41/5.63 thf(fact_1272_divide__eq__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [B: rat,W: num,A: rat] :
% 5.41/5.63 ( ( ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) )
% 5.41/5.63 = A )
% 5.41/5.63 = ( ( ( ( numeral_numeral_rat @ W )
% 5.41/5.63 != zero_zero_rat )
% 5.41/5.63 => ( B
% 5.41/5.63 = ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) ) ) )
% 5.41/5.63 & ( ( ( numeral_numeral_rat @ W )
% 5.41/5.63 = zero_zero_rat )
% 5.41/5.63 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_eq_eq_numeral1(1)
% 5.41/5.63 thf(fact_1273_eq__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [A: complex,B: complex,W: num] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( divide1717551699836669952omplex @ B @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.63 = ( ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.63 != zero_zero_complex )
% 5.41/5.63 => ( ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.63 = B ) )
% 5.41/5.63 & ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.63 = zero_zero_complex )
% 5.41/5.63 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_divide_eq_numeral1(1)
% 5.41/5.63 thf(fact_1274_eq__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [A: real,B: real,W: num] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( divide_divide_real @ B @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.63 = ( ( ( ( numeral_numeral_real @ W )
% 5.41/5.63 != zero_zero_real )
% 5.41/5.63 => ( ( times_times_real @ A @ ( numeral_numeral_real @ W ) )
% 5.41/5.63 = B ) )
% 5.41/5.63 & ( ( ( numeral_numeral_real @ W )
% 5.41/5.63 = zero_zero_real )
% 5.41/5.63 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_divide_eq_numeral1(1)
% 5.41/5.63 thf(fact_1275_eq__divide__eq__numeral1_I1_J,axiom,
% 5.41/5.63 ! [A: rat,B: rat,W: num] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( divide_divide_rat @ B @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.63 = ( ( ( ( numeral_numeral_rat @ W )
% 5.41/5.63 != zero_zero_rat )
% 5.41/5.63 => ( ( times_times_rat @ A @ ( numeral_numeral_rat @ W ) )
% 5.41/5.63 = B ) )
% 5.41/5.63 & ( ( ( numeral_numeral_rat @ W )
% 5.41/5.63 = zero_zero_rat )
% 5.41/5.63 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_divide_eq_numeral1(1)
% 5.41/5.63 thf(fact_1276_div__mult__self4,axiom,
% 5.41/5.63 ! [B: nat,C: nat,A: nat] :
% 5.41/5.63 ( ( B != zero_zero_nat )
% 5.41/5.63 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ C ) @ A ) @ B )
% 5.41/5.63 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self4
% 5.41/5.63 thf(fact_1277_div__mult__self4,axiom,
% 5.41/5.63 ! [B: int,C: int,A: int] :
% 5.41/5.63 ( ( B != zero_zero_int )
% 5.41/5.63 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ B @ C ) @ A ) @ B )
% 5.41/5.63 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self4
% 5.41/5.63 thf(fact_1278_div__mult__self3,axiom,
% 5.41/5.63 ! [B: nat,C: nat,A: nat] :
% 5.41/5.63 ( ( B != zero_zero_nat )
% 5.41/5.63 => ( ( divide_divide_nat @ ( plus_plus_nat @ ( times_times_nat @ C @ B ) @ A ) @ B )
% 5.41/5.63 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self3
% 5.41/5.63 thf(fact_1279_div__mult__self3,axiom,
% 5.41/5.63 ! [B: int,C: int,A: int] :
% 5.41/5.63 ( ( B != zero_zero_int )
% 5.41/5.63 => ( ( divide_divide_int @ ( plus_plus_int @ ( times_times_int @ C @ B ) @ A ) @ B )
% 5.41/5.63 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self3
% 5.41/5.63 thf(fact_1280_div__mult__self2,axiom,
% 5.41/5.63 ! [B: nat,A: nat,C: nat] :
% 5.41/5.63 ( ( B != zero_zero_nat )
% 5.41/5.63 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ B @ C ) ) @ B )
% 5.41/5.63 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self2
% 5.41/5.63 thf(fact_1281_div__mult__self2,axiom,
% 5.41/5.63 ! [B: int,A: int,C: int] :
% 5.41/5.63 ( ( B != zero_zero_int )
% 5.41/5.63 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ B @ C ) ) @ B )
% 5.41/5.63 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self2
% 5.41/5.63 thf(fact_1282_div__mult__self1,axiom,
% 5.41/5.63 ! [B: nat,A: nat,C: nat] :
% 5.41/5.63 ( ( B != zero_zero_nat )
% 5.41/5.63 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ ( times_times_nat @ C @ B ) ) @ B )
% 5.41/5.63 = ( plus_plus_nat @ C @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self1
% 5.41/5.63 thf(fact_1283_div__mult__self1,axiom,
% 5.41/5.63 ! [B: int,A: int,C: int] :
% 5.41/5.63 ( ( B != zero_zero_int )
% 5.41/5.63 => ( ( divide_divide_int @ ( plus_plus_int @ A @ ( times_times_int @ C @ B ) ) @ B )
% 5.41/5.63 = ( plus_plus_int @ C @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % div_mult_self1
% 5.41/5.63 thf(fact_1284_nonzero__divide__mult__cancel__left,axiom,
% 5.41/5.63 ! [A: complex,B: complex] :
% 5.41/5.63 ( ( A != zero_zero_complex )
% 5.41/5.63 => ( ( divide1717551699836669952omplex @ A @ ( times_times_complex @ A @ B ) )
% 5.41/5.63 = ( divide1717551699836669952omplex @ one_one_complex @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nonzero_divide_mult_cancel_left
% 5.41/5.63 thf(fact_1285_nonzero__divide__mult__cancel__left,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( A != zero_zero_real )
% 5.41/5.63 => ( ( divide_divide_real @ A @ ( times_times_real @ A @ B ) )
% 5.41/5.63 = ( divide_divide_real @ one_one_real @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nonzero_divide_mult_cancel_left
% 5.41/5.63 thf(fact_1286_nonzero__divide__mult__cancel__left,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( A != zero_zero_rat )
% 5.41/5.63 => ( ( divide_divide_rat @ A @ ( times_times_rat @ A @ B ) )
% 5.41/5.63 = ( divide_divide_rat @ one_one_rat @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nonzero_divide_mult_cancel_left
% 5.41/5.63 thf(fact_1287_nonzero__divide__mult__cancel__right,axiom,
% 5.41/5.63 ! [B: complex,A: complex] :
% 5.41/5.63 ( ( B != zero_zero_complex )
% 5.41/5.63 => ( ( divide1717551699836669952omplex @ B @ ( times_times_complex @ A @ B ) )
% 5.41/5.63 = ( divide1717551699836669952omplex @ one_one_complex @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nonzero_divide_mult_cancel_right
% 5.41/5.63 thf(fact_1288_nonzero__divide__mult__cancel__right,axiom,
% 5.41/5.63 ! [B: real,A: real] :
% 5.41/5.63 ( ( B != zero_zero_real )
% 5.41/5.63 => ( ( divide_divide_real @ B @ ( times_times_real @ A @ B ) )
% 5.41/5.63 = ( divide_divide_real @ one_one_real @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nonzero_divide_mult_cancel_right
% 5.41/5.63 thf(fact_1289_nonzero__divide__mult__cancel__right,axiom,
% 5.41/5.63 ! [B: rat,A: rat] :
% 5.41/5.63 ( ( B != zero_zero_rat )
% 5.41/5.63 => ( ( divide_divide_rat @ B @ ( times_times_rat @ A @ B ) )
% 5.41/5.63 = ( divide_divide_rat @ one_one_rat @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nonzero_divide_mult_cancel_right
% 5.41/5.63 thf(fact_1290_power__mono__iff,axiom,
% 5.41/5.63 ! [A: real,B: real,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_real @ A @ B ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_mono_iff
% 5.41/5.63 thf(fact_1291_power__mono__iff,axiom,
% 5.41/5.63 ! [A: rat,B: rat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_rat @ A @ B ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_mono_iff
% 5.41/5.63 thf(fact_1292_power__mono__iff,axiom,
% 5.41/5.63 ! [A: nat,B: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_nat @ A @ B ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_mono_iff
% 5.41/5.63 thf(fact_1293_power__mono__iff,axiom,
% 5.41/5.63 ! [A: int,B: int,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.63 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_int @ A @ B ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_mono_iff
% 5.41/5.63 thf(fact_1294_lesseq__shift,axiom,
% 5.41/5.63 ( ord_less_eq_nat
% 5.41/5.63 = ( ^ [X3: nat,Y3: nat] : ( vEBT_VEBT_lesseq @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % lesseq_shift
% 5.41/5.63 thf(fact_1295_le__divide__eq__1__pos,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.63 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.41/5.63 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_divide_eq_1_pos
% 5.41/5.63 thf(fact_1296_le__divide__eq__1__pos,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.63 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.41/5.63 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_divide_eq_1_pos
% 5.41/5.63 thf(fact_1297_le__divide__eq__1__neg,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.63 => ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.41/5.63 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_divide_eq_1_neg
% 5.41/5.63 thf(fact_1298_le__divide__eq__1__neg,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.63 => ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.41/5.63 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_divide_eq_1_neg
% 5.41/5.63 thf(fact_1299_divide__le__eq__1__pos,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.63 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.41/5.63 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_eq_1_pos
% 5.41/5.63 thf(fact_1300_divide__le__eq__1__pos,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.63 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.41/5.63 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_eq_1_pos
% 5.41/5.63 thf(fact_1301_divide__le__eq__1__neg,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.63 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.41/5.63 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_eq_1_neg
% 5.41/5.63 thf(fact_1302_divide__le__eq__1__neg,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.63 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.41/5.63 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_le_eq_1_neg
% 5.41/5.63 thf(fact_1303_power__strict__decreasing__iff,axiom,
% 5.41/5.63 ! [B: real,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.63 => ( ( ord_less_real @ B @ one_one_real )
% 5.41/5.63 => ( ( ord_less_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.41/5.63 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_decreasing_iff
% 5.41/5.63 thf(fact_1304_power__strict__decreasing__iff,axiom,
% 5.41/5.63 ! [B: rat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.41/5.63 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.41/5.63 => ( ( ord_less_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.41/5.63 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_decreasing_iff
% 5.41/5.63 thf(fact_1305_power__strict__decreasing__iff,axiom,
% 5.41/5.63 ! [B: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.63 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.41/5.63 => ( ( ord_less_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.41/5.63 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_decreasing_iff
% 5.41/5.63 thf(fact_1306_power__strict__decreasing__iff,axiom,
% 5.41/5.63 ! [B: int,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.63 => ( ( ord_less_int @ B @ one_one_int )
% 5.41/5.63 => ( ( ord_less_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.41/5.63 = ( ord_less_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_strict_decreasing_iff
% 5.41/5.63 thf(fact_1307_zero__eq__power2,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_rat )
% 5.41/5.63 = ( A = zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_eq_power2
% 5.41/5.63 thf(fact_1308_zero__eq__power2,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_nat )
% 5.41/5.63 = ( A = zero_zero_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_eq_power2
% 5.41/5.63 thf(fact_1309_zero__eq__power2,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_real )
% 5.41/5.63 = ( A = zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_eq_power2
% 5.41/5.63 thf(fact_1310_zero__eq__power2,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_int )
% 5.41/5.63 = ( A = zero_zero_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_eq_power2
% 5.41/5.63 thf(fact_1311_zero__eq__power2,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_complex )
% 5.41/5.63 = ( A = zero_zero_complex ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_eq_power2
% 5.41/5.63 thf(fact_1312_bits__one__mod__two__eq__one,axiom,
% 5.41/5.63 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % bits_one_mod_two_eq_one
% 5.41/5.63 thf(fact_1313_bits__one__mod__two__eq__one,axiom,
% 5.41/5.63 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_int ) ).
% 5.41/5.63
% 5.41/5.63 % bits_one_mod_two_eq_one
% 5.41/5.63 thf(fact_1314_bits__one__mod__two__eq__one,axiom,
% 5.41/5.63 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_Code_integer ) ).
% 5.41/5.63
% 5.41/5.63 % bits_one_mod_two_eq_one
% 5.41/5.63 thf(fact_1315_one__mod__two__eq__one,axiom,
% 5.41/5.63 ( ( modulo_modulo_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_nat ) ).
% 5.41/5.63
% 5.41/5.63 % one_mod_two_eq_one
% 5.41/5.63 thf(fact_1316_one__mod__two__eq__one,axiom,
% 5.41/5.63 ( ( modulo_modulo_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_int ) ).
% 5.41/5.63
% 5.41/5.63 % one_mod_two_eq_one
% 5.41/5.63 thf(fact_1317_one__mod__two__eq__one,axiom,
% 5.41/5.63 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_Code_integer ) ).
% 5.41/5.63
% 5.41/5.63 % one_mod_two_eq_one
% 5.41/5.63 thf(fact_1318_add__self__mod__2,axiom,
% 5.41/5.63 ! [M: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ M @ M ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % add_self_mod_2
% 5.41/5.63 thf(fact_1319_bits__1__div__2,axiom,
% 5.41/5.63 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % bits_1_div_2
% 5.41/5.63 thf(fact_1320_bits__1__div__2,axiom,
% 5.41/5.63 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % bits_1_div_2
% 5.41/5.63 thf(fact_1321_one__div__two__eq__zero,axiom,
% 5.41/5.63 ( ( divide_divide_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % one_div_two_eq_zero
% 5.41/5.63 thf(fact_1322_one__div__two__eq__zero,axiom,
% 5.41/5.63 ( ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % one_div_two_eq_zero
% 5.41/5.63 thf(fact_1323_power2__less__eq__zero__iff,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real )
% 5.41/5.63 = ( A = zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_less_eq_zero_iff
% 5.41/5.63 thf(fact_1324_power2__less__eq__zero__iff,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat )
% 5.41/5.63 = ( A = zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_less_eq_zero_iff
% 5.41/5.63 thf(fact_1325_power2__less__eq__zero__iff,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int )
% 5.41/5.63 = ( A = zero_zero_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_less_eq_zero_iff
% 5.41/5.63 thf(fact_1326_power2__eq__iff__nonneg,axiom,
% 5.41/5.63 ! [X: real,Y: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.63 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.63 => ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( X = Y ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_eq_iff_nonneg
% 5.41/5.63 thf(fact_1327_power2__eq__iff__nonneg,axiom,
% 5.41/5.63 ! [X: rat,Y: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.63 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.63 => ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( X = Y ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_eq_iff_nonneg
% 5.41/5.63 thf(fact_1328_power2__eq__iff__nonneg,axiom,
% 5.41/5.63 ! [X: nat,Y: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.41/5.63 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.41/5.63 => ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( X = Y ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_eq_iff_nonneg
% 5.41/5.63 thf(fact_1329_power2__eq__iff__nonneg,axiom,
% 5.41/5.63 ! [X: int,Y: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.63 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.63 => ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( X = Y ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power2_eq_iff_nonneg
% 5.41/5.63 thf(fact_1330_power__decreasing__iff,axiom,
% 5.41/5.63 ! [B: real,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.63 => ( ( ord_less_real @ B @ one_one_real )
% 5.41/5.63 => ( ( ord_less_eq_real @ ( power_power_real @ B @ M ) @ ( power_power_real @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_decreasing_iff
% 5.41/5.63 thf(fact_1331_power__decreasing__iff,axiom,
% 5.41/5.63 ! [B: rat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.41/5.63 => ( ( ord_less_rat @ B @ one_one_rat )
% 5.41/5.63 => ( ( ord_less_eq_rat @ ( power_power_rat @ B @ M ) @ ( power_power_rat @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_decreasing_iff
% 5.41/5.63 thf(fact_1332_power__decreasing__iff,axiom,
% 5.41/5.63 ! [B: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.63 => ( ( ord_less_nat @ B @ one_one_nat )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( power_power_nat @ B @ M ) @ ( power_power_nat @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_decreasing_iff
% 5.41/5.63 thf(fact_1333_power__decreasing__iff,axiom,
% 5.41/5.63 ! [B: int,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.63 => ( ( ord_less_int @ B @ one_one_int )
% 5.41/5.63 => ( ( ord_less_eq_int @ ( power_power_int @ B @ M ) @ ( power_power_int @ B @ N ) )
% 5.41/5.63 = ( ord_less_eq_nat @ N @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_decreasing_iff
% 5.41/5.63 thf(fact_1334_zero__less__power2,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( A != zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_less_power2
% 5.41/5.63 thf(fact_1335_zero__less__power2,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( A != zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_less_power2
% 5.41/5.63 thf(fact_1336_zero__less__power2,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( A != zero_zero_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_less_power2
% 5.41/5.63 thf(fact_1337_sum__power2__eq__zero__iff,axiom,
% 5.41/5.63 ! [X: rat,Y: rat] :
% 5.41/5.63 ( ( ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = zero_zero_rat )
% 5.41/5.63 = ( ( X = zero_zero_rat )
% 5.41/5.63 & ( Y = zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % sum_power2_eq_zero_iff
% 5.41/5.63 thf(fact_1338_sum__power2__eq__zero__iff,axiom,
% 5.41/5.63 ! [X: real,Y: real] :
% 5.41/5.63 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = zero_zero_real )
% 5.41/5.63 = ( ( X = zero_zero_real )
% 5.41/5.63 & ( Y = zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % sum_power2_eq_zero_iff
% 5.41/5.63 thf(fact_1339_sum__power2__eq__zero__iff,axiom,
% 5.41/5.63 ! [X: int,Y: int] :
% 5.41/5.63 ( ( ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = zero_zero_int )
% 5.41/5.63 = ( ( X = zero_zero_int )
% 5.41/5.63 & ( Y = zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % sum_power2_eq_zero_iff
% 5.41/5.63 thf(fact_1340_mod2__gr__0,axiom,
% 5.41/5.63 ! [M: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.63 = ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.63 = one_one_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod2_gr_0
% 5.41/5.63 thf(fact_1341_real__arch__pow,axiom,
% 5.41/5.63 ! [X: real,Y: real] :
% 5.41/5.63 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.63 => ? [N3: nat] : ( ord_less_real @ Y @ ( power_power_real @ X @ N3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % real_arch_pow
% 5.41/5.63 thf(fact_1342_less__eq__real__def,axiom,
% 5.41/5.63 ( ord_less_eq_real
% 5.41/5.63 = ( ^ [X3: real,Y3: real] :
% 5.41/5.63 ( ( ord_less_real @ X3 @ Y3 )
% 5.41/5.63 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_eq_real_def
% 5.41/5.63 thf(fact_1343_real__arch__pow__inv,axiom,
% 5.41/5.63 ! [Y: real,X: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.63 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.63 => ? [N3: nat] : ( ord_less_real @ ( power_power_real @ X @ N3 ) @ Y ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % real_arch_pow_inv
% 5.41/5.63 thf(fact_1344_complete__real,axiom,
% 5.41/5.63 ! [S2: set_real] :
% 5.41/5.63 ( ? [X4: real] : ( member_real @ X4 @ S2 )
% 5.41/5.63 => ( ? [Z4: real] :
% 5.41/5.63 ! [X6: real] :
% 5.41/5.63 ( ( member_real @ X6 @ S2 )
% 5.41/5.63 => ( ord_less_eq_real @ X6 @ Z4 ) )
% 5.41/5.63 => ? [Y5: real] :
% 5.41/5.63 ( ! [X4: real] :
% 5.41/5.63 ( ( member_real @ X4 @ S2 )
% 5.41/5.63 => ( ord_less_eq_real @ X4 @ Y5 ) )
% 5.41/5.63 & ! [Z4: real] :
% 5.41/5.63 ( ! [X6: real] :
% 5.41/5.63 ( ( member_real @ X6 @ S2 )
% 5.41/5.63 => ( ord_less_eq_real @ X6 @ Z4 ) )
% 5.41/5.63 => ( ord_less_eq_real @ Y5 @ Z4 ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % complete_real
% 5.41/5.63 thf(fact_1345_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.63 => ( ord_le3102999989581377725nteger @ ( modulo364778990260209775nteger @ A @ B ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.41/5.63 thf(fact_1346_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.63 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ A @ B ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.41/5.63 thf(fact_1347_unique__euclidean__semiring__numeral__class_Omod__less__eq__dividend,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.63 => ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ A ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.mod_less_eq_dividend
% 5.41/5.63 thf(fact_1348_mod__eq__0D,axiom,
% 5.41/5.63 ! [M: nat,D: nat] :
% 5.41/5.63 ( ( ( modulo_modulo_nat @ M @ D )
% 5.41/5.63 = zero_zero_nat )
% 5.41/5.63 => ? [Q3: nat] :
% 5.41/5.63 ( M
% 5.41/5.63 = ( times_times_nat @ D @ Q3 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_eq_0D
% 5.41/5.63 thf(fact_1349_mod__diff__right__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( minus_minus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_right_eq
% 5.41/5.63 thf(fact_1350_mod__diff__right__eq,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_right_eq
% 5.41/5.63 thf(fact_1351_mod__diff__left__eq,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_left_eq
% 5.41/5.63 thf(fact_1352_mod__diff__left__eq,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_left_eq
% 5.41/5.63 thf(fact_1353_mod__diff__cong,axiom,
% 5.41/5.63 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.41/5.63 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.63 = ( modulo_modulo_int @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo_modulo_int @ B @ C )
% 5.41/5.63 = ( modulo_modulo_int @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_cong
% 5.41/5.63 thf(fact_1354_mod__diff__cong,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.41/5.63 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_cong
% 5.41/5.63 thf(fact_1355_mod__diff__eq,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( minus_minus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_eq
% 5.41/5.63 thf(fact_1356_mod__diff__eq,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_diff_eq
% 5.41/5.63 thf(fact_1357_diffs0__imp__equal,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( ( minus_minus_nat @ M @ N )
% 5.41/5.63 = zero_zero_nat )
% 5.41/5.63 => ( ( ( minus_minus_nat @ N @ M )
% 5.41/5.63 = zero_zero_nat )
% 5.41/5.63 => ( M = N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diffs0_imp_equal
% 5.41/5.63 thf(fact_1358_zero__reorient,axiom,
% 5.41/5.63 ! [X: complex] :
% 5.41/5.63 ( ( zero_zero_complex = X )
% 5.41/5.63 = ( X = zero_zero_complex ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_reorient
% 5.41/5.63 thf(fact_1359_zero__reorient,axiom,
% 5.41/5.63 ! [X: real] :
% 5.41/5.63 ( ( zero_zero_real = X )
% 5.41/5.63 = ( X = zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_reorient
% 5.41/5.63 thf(fact_1360_zero__reorient,axiom,
% 5.41/5.63 ! [X: rat] :
% 5.41/5.63 ( ( zero_zero_rat = X )
% 5.41/5.63 = ( X = zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_reorient
% 5.41/5.63 thf(fact_1361_zero__reorient,axiom,
% 5.41/5.63 ! [X: nat] :
% 5.41/5.63 ( ( zero_zero_nat = X )
% 5.41/5.63 = ( X = zero_zero_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_reorient
% 5.41/5.63 thf(fact_1362_zero__reorient,axiom,
% 5.41/5.63 ! [X: int] :
% 5.41/5.63 ( ( zero_zero_int = X )
% 5.41/5.63 = ( X = zero_zero_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_reorient
% 5.41/5.63 thf(fact_1363_diff__commute,axiom,
% 5.41/5.63 ! [I: nat,J: nat,K: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ I @ J ) @ K )
% 5.41/5.63 = ( minus_minus_nat @ ( minus_minus_nat @ I @ K ) @ J ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_commute
% 5.41/5.63 thf(fact_1364_diff__right__commute,axiom,
% 5.41/5.63 ! [A: real,C: real,B: real] :
% 5.41/5.63 ( ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B )
% 5.41/5.63 = ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_right_commute
% 5.41/5.63 thf(fact_1365_diff__right__commute,axiom,
% 5.41/5.63 ! [A: rat,C: rat,B: rat] :
% 5.41/5.63 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B )
% 5.41/5.63 = ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_right_commute
% 5.41/5.63 thf(fact_1366_diff__right__commute,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ C ) @ B )
% 5.41/5.63 = ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_right_commute
% 5.41/5.63 thf(fact_1367_diff__right__commute,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B )
% 5.41/5.63 = ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_right_commute
% 5.41/5.63 thf(fact_1368_eq__iff__diff__eq__0,axiom,
% 5.41/5.63 ( ( ^ [Y4: complex,Z2: complex] : ( Y4 = Z2 ) )
% 5.41/5.63 = ( ^ [A3: complex,B2: complex] :
% 5.41/5.63 ( ( minus_minus_complex @ A3 @ B2 )
% 5.41/5.63 = zero_zero_complex ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_iff_diff_eq_0
% 5.41/5.63 thf(fact_1369_eq__iff__diff__eq__0,axiom,
% 5.41/5.63 ( ( ^ [Y4: real,Z2: real] : ( Y4 = Z2 ) )
% 5.41/5.63 = ( ^ [A3: real,B2: real] :
% 5.41/5.63 ( ( minus_minus_real @ A3 @ B2 )
% 5.41/5.63 = zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_iff_diff_eq_0
% 5.41/5.63 thf(fact_1370_eq__iff__diff__eq__0,axiom,
% 5.41/5.63 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 5.41/5.63 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.63 ( ( minus_minus_rat @ A3 @ B2 )
% 5.41/5.63 = zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_iff_diff_eq_0
% 5.41/5.63 thf(fact_1371_eq__iff__diff__eq__0,axiom,
% 5.41/5.63 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.41/5.63 = ( ^ [A3: int,B2: int] :
% 5.41/5.63 ( ( minus_minus_int @ A3 @ B2 )
% 5.41/5.63 = zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_iff_diff_eq_0
% 5.41/5.63 thf(fact_1372_diff__eq__diff__eq,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.63 ( ( ( minus_minus_real @ A @ B )
% 5.41/5.63 = ( minus_minus_real @ C @ D ) )
% 5.41/5.63 => ( ( A = B )
% 5.41/5.63 = ( C = D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_eq
% 5.41/5.63 thf(fact_1373_diff__eq__diff__eq,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.41/5.63 = ( minus_minus_rat @ C @ D ) )
% 5.41/5.63 => ( ( A = B )
% 5.41/5.63 = ( C = D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_eq
% 5.41/5.63 thf(fact_1374_diff__eq__diff__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.41/5.63 = ( minus_minus_int @ C @ D ) )
% 5.41/5.63 => ( ( A = B )
% 5.41/5.63 = ( C = D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_eq
% 5.41/5.63 thf(fact_1375_minus__nat_Odiff__0,axiom,
% 5.41/5.63 ! [M: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ M @ zero_zero_nat )
% 5.41/5.63 = M ) ).
% 5.41/5.63
% 5.41/5.63 % minus_nat.diff_0
% 5.41/5.63 thf(fact_1376_mod__geq,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ~ ( ord_less_nat @ M @ N )
% 5.41/5.63 => ( ( modulo_modulo_nat @ M @ N )
% 5.41/5.63 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_geq
% 5.41/5.63 thf(fact_1377_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.41/5.63 ! [B: nat,A: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.63 => ( ord_less_nat @ ( modulo_modulo_nat @ A @ B ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.41/5.63 thf(fact_1378_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.41/5.63 ! [B: int,A: int] :
% 5.41/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.63 => ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.41/5.63 thf(fact_1379_unique__euclidean__semiring__numeral__class_Opos__mod__bound,axiom,
% 5.41/5.63 ! [B: code_integer,A: code_integer] :
% 5.41/5.63 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.63 => ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ B ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.pos_mod_bound
% 5.41/5.63 thf(fact_1380_mod__if,axiom,
% 5.41/5.63 ( modulo_modulo_nat
% 5.41/5.63 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( ord_less_nat @ M3 @ N2 ) @ M3 @ ( modulo_modulo_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_if
% 5.41/5.63 thf(fact_1381_le__mod__geq,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.63 => ( ( modulo_modulo_nat @ M @ N )
% 5.41/5.63 = ( modulo_modulo_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_mod_geq
% 5.41/5.63 thf(fact_1382_mod__eq__self__iff__div__eq__0,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( ( modulo_modulo_nat @ A @ B )
% 5.41/5.63 = A )
% 5.41/5.63 = ( ( divide_divide_nat @ A @ B )
% 5.41/5.63 = zero_zero_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_eq_self_iff_div_eq_0
% 5.41/5.63 thf(fact_1383_mod__eq__self__iff__div__eq__0,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.63 = A )
% 5.41/5.63 = ( ( divide_divide_int @ A @ B )
% 5.41/5.63 = zero_zero_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_eq_self_iff_div_eq_0
% 5.41/5.63 thf(fact_1384_mod__eq__self__iff__div__eq__0,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.41/5.63 = A )
% 5.41/5.63 = ( ( divide6298287555418463151nteger @ A @ B )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_eq_self_iff_div_eq_0
% 5.41/5.63 thf(fact_1385_le__iff__diff__le__0,axiom,
% 5.41/5.63 ( ord_less_eq_real
% 5.41/5.63 = ( ^ [A3: real,B2: real] : ( ord_less_eq_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_iff_diff_le_0
% 5.41/5.63 thf(fact_1386_le__iff__diff__le__0,axiom,
% 5.41/5.63 ( ord_less_eq_rat
% 5.41/5.63 = ( ^ [A3: rat,B2: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_iff_diff_le_0
% 5.41/5.63 thf(fact_1387_le__iff__diff__le__0,axiom,
% 5.41/5.63 ( ord_less_eq_int
% 5.41/5.63 = ( ^ [A3: int,B2: int] : ( ord_less_eq_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_iff_diff_le_0
% 5.41/5.63 thf(fact_1388_less__iff__diff__less__0,axiom,
% 5.41/5.63 ( ord_less_real
% 5.41/5.63 = ( ^ [A3: real,B2: real] : ( ord_less_real @ ( minus_minus_real @ A3 @ B2 ) @ zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_iff_diff_less_0
% 5.41/5.63 thf(fact_1389_less__iff__diff__less__0,axiom,
% 5.41/5.63 ( ord_less_rat
% 5.41/5.63 = ( ^ [A3: rat,B2: rat] : ( ord_less_rat @ ( minus_minus_rat @ A3 @ B2 ) @ zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_iff_diff_less_0
% 5.41/5.63 thf(fact_1390_less__iff__diff__less__0,axiom,
% 5.41/5.63 ( ord_less_int
% 5.41/5.63 = ( ^ [A3: int,B2: int] : ( ord_less_int @ ( minus_minus_int @ A3 @ B2 ) @ zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_iff_diff_less_0
% 5.41/5.63 thf(fact_1391_mod__less__divisor,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ord_less_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_less_divisor
% 5.41/5.63 thf(fact_1392_diff__less,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.63 => ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ M ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_less
% 5.41/5.63 thf(fact_1393_diff__add__0,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ N @ ( plus_plus_nat @ N @ M ) )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_0
% 5.41/5.63 thf(fact_1394_realpow__pos__nth__unique,axiom,
% 5.41/5.63 ! [N: nat,A: real] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.63 => ? [X6: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ X6 )
% 5.41/5.63 & ( ( power_power_real @ X6 @ N )
% 5.41/5.63 = A )
% 5.41/5.63 & ! [Y2: real] :
% 5.41/5.63 ( ( ( ord_less_real @ zero_zero_real @ Y2 )
% 5.41/5.63 & ( ( power_power_real @ Y2 @ N )
% 5.41/5.63 = A ) )
% 5.41/5.63 => ( Y2 = X6 ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % realpow_pos_nth_unique
% 5.41/5.63 thf(fact_1395_realpow__pos__nth,axiom,
% 5.41/5.63 ! [N: nat,A: real] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.63 => ? [R2: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.41/5.63 & ( ( power_power_real @ R2 @ N )
% 5.41/5.63 = A ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % realpow_pos_nth
% 5.41/5.63 thf(fact_1396_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.41/5.63 ! [B: code_integer,A: code_integer] :
% 5.41/5.63 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.63 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.41/5.63 thf(fact_1397_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.41/5.63 ! [B: nat,A: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.63 => ( ord_less_eq_nat @ zero_zero_nat @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.41/5.63 thf(fact_1398_unique__euclidean__semiring__numeral__class_Opos__mod__sign,axiom,
% 5.41/5.63 ! [B: int,A: int] :
% 5.41/5.63 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.63 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.pos_mod_sign
% 5.41/5.63 thf(fact_1399_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.63 => ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.41/5.63 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.41/5.63 = A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.mod_less
% 5.41/5.63 thf(fact_1400_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.63 => ( ( ord_less_nat @ A @ B )
% 5.41/5.63 => ( ( modulo_modulo_nat @ A @ B )
% 5.41/5.63 = A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.mod_less
% 5.41/5.63 thf(fact_1401_unique__euclidean__semiring__numeral__class_Omod__less,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.63 => ( ( ord_less_int @ A @ B )
% 5.41/5.63 => ( ( modulo_modulo_int @ A @ B )
% 5.41/5.63 = A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % unique_euclidean_semiring_numeral_class.mod_less
% 5.41/5.63 thf(fact_1402_cong__exp__iff__simps_I2_J,axiom,
% 5.41/5.63 ! [N: num,Q2: num] :
% 5.41/5.63 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.63 = zero_zero_nat )
% 5.41/5.63 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.41/5.63 = zero_zero_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(2)
% 5.41/5.63 thf(fact_1403_cong__exp__iff__simps_I2_J,axiom,
% 5.41/5.63 ! [N: num,Q2: num] :
% 5.41/5.63 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.63 = zero_zero_int )
% 5.41/5.63 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.41/5.63 = zero_zero_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(2)
% 5.41/5.63 thf(fact_1404_cong__exp__iff__simps_I2_J,axiom,
% 5.41/5.63 ! [N: num,Q2: num] :
% 5.41/5.63 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.63 = zero_z3403309356797280102nteger )
% 5.41/5.63 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(2)
% 5.41/5.63 thf(fact_1405_cong__exp__iff__simps_I1_J,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) )
% 5.41/5.63 = zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(1)
% 5.41/5.63 thf(fact_1406_cong__exp__iff__simps_I1_J,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) )
% 5.41/5.63 = zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(1)
% 5.41/5.63 thf(fact_1407_cong__exp__iff__simps_I1_J,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) )
% 5.41/5.63 = zero_z3403309356797280102nteger ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(1)
% 5.41/5.63 thf(fact_1408_minus__div__mult__eq__mod,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ A @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.41/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_div_mult_eq_mod
% 5.41/5.63 thf(fact_1409_minus__div__mult__eq__mod,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( minus_minus_int @ A @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.41/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_div_mult_eq_mod
% 5.41/5.63 thf(fact_1410_minus__div__mult__eq__mod,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_div_mult_eq_mod
% 5.41/5.63 thf(fact_1411_minus__mod__eq__div__mult,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.63 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mod_eq_div_mult
% 5.41/5.63 thf(fact_1412_minus__mod__eq__div__mult,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.63 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mod_eq_div_mult
% 5.41/5.63 thf(fact_1413_minus__mod__eq__div__mult,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.41/5.63 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mod_eq_div_mult
% 5.41/5.63 thf(fact_1414_minus__mod__eq__mult__div,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.63 = ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mod_eq_mult_div
% 5.41/5.63 thf(fact_1415_minus__mod__eq__mult__div,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.63 = ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mod_eq_mult_div
% 5.41/5.63 thf(fact_1416_minus__mod__eq__mult__div,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.41/5.63 = ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mod_eq_mult_div
% 5.41/5.63 thf(fact_1417_minus__mult__div__eq__mod,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ A @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.41/5.63 = ( modulo_modulo_nat @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mult_div_eq_mod
% 5.41/5.63 thf(fact_1418_minus__mult__div__eq__mod,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( minus_minus_int @ A @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.41/5.63 = ( modulo_modulo_int @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mult_div_eq_mod
% 5.41/5.63 thf(fact_1419_minus__mult__div__eq__mod,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( minus_8373710615458151222nteger @ A @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % minus_mult_div_eq_mod
% 5.41/5.63 thf(fact_1420_add__divide__eq__if__simps_I4_J,axiom,
% 5.41/5.63 ! [Z: complex,A: complex,B: complex] :
% 5.41/5.63 ( ( ( Z = zero_zero_complex )
% 5.41/5.63 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.41/5.63 = A ) )
% 5.41/5.63 & ( ( Z != zero_zero_complex )
% 5.41/5.63 => ( ( minus_minus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.41/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_divide_eq_if_simps(4)
% 5.41/5.63 thf(fact_1421_add__divide__eq__if__simps_I4_J,axiom,
% 5.41/5.63 ! [Z: real,A: real,B: real] :
% 5.41/5.63 ( ( ( Z = zero_zero_real )
% 5.41/5.63 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.41/5.63 = A ) )
% 5.41/5.63 & ( ( Z != zero_zero_real )
% 5.41/5.63 => ( ( minus_minus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.41/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_divide_eq_if_simps(4)
% 5.41/5.63 thf(fact_1422_add__divide__eq__if__simps_I4_J,axiom,
% 5.41/5.63 ! [Z: rat,A: rat,B: rat] :
% 5.41/5.63 ( ( ( Z = zero_zero_rat )
% 5.41/5.63 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.41/5.63 = A ) )
% 5.41/5.63 & ( ( Z != zero_zero_rat )
% 5.41/5.63 => ( ( minus_minus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.41/5.63 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_divide_eq_if_simps(4)
% 5.41/5.63 thf(fact_1423_diff__frac__eq,axiom,
% 5.41/5.63 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.41/5.63 ( ( Y != zero_zero_complex )
% 5.41/5.63 => ( ( Z != zero_zero_complex )
% 5.41/5.63 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.41/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_frac_eq
% 5.41/5.63 thf(fact_1424_diff__frac__eq,axiom,
% 5.41/5.63 ! [Y: real,Z: real,X: real,W: real] :
% 5.41/5.63 ( ( Y != zero_zero_real )
% 5.41/5.63 => ( ( Z != zero_zero_real )
% 5.41/5.63 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.41/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_frac_eq
% 5.41/5.63 thf(fact_1425_diff__frac__eq,axiom,
% 5.41/5.63 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.41/5.63 ( ( Y != zero_zero_rat )
% 5.41/5.63 => ( ( Z != zero_zero_rat )
% 5.41/5.63 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.41/5.63 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_frac_eq
% 5.41/5.63 thf(fact_1426_diff__divide__eq__iff,axiom,
% 5.41/5.63 ! [Z: complex,X: complex,Y: complex] :
% 5.41/5.63 ( ( Z != zero_zero_complex )
% 5.41/5.63 => ( ( minus_minus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.41/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_divide_eq_iff
% 5.41/5.63 thf(fact_1427_diff__divide__eq__iff,axiom,
% 5.41/5.63 ! [Z: real,X: real,Y: real] :
% 5.41/5.63 ( ( Z != zero_zero_real )
% 5.41/5.63 => ( ( minus_minus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.41/5.63 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_divide_eq_iff
% 5.41/5.63 thf(fact_1428_diff__divide__eq__iff,axiom,
% 5.41/5.63 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.63 ( ( Z != zero_zero_rat )
% 5.41/5.63 => ( ( minus_minus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.41/5.63 = ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_divide_eq_iff
% 5.41/5.63 thf(fact_1429_divide__diff__eq__iff,axiom,
% 5.41/5.63 ! [Z: complex,X: complex,Y: complex] :
% 5.41/5.63 ( ( Z != zero_zero_complex )
% 5.41/5.63 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.41/5.63 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_diff_eq_iff
% 5.41/5.63 thf(fact_1430_divide__diff__eq__iff,axiom,
% 5.41/5.63 ! [Z: real,X: real,Y: real] :
% 5.41/5.63 ( ( Z != zero_zero_real )
% 5.41/5.63 => ( ( minus_minus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.41/5.63 = ( divide_divide_real @ ( minus_minus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_diff_eq_iff
% 5.41/5.63 thf(fact_1431_divide__diff__eq__iff,axiom,
% 5.41/5.63 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.63 ( ( Z != zero_zero_rat )
% 5.41/5.63 => ( ( minus_minus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.41/5.63 = ( divide_divide_rat @ ( minus_minus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divide_diff_eq_iff
% 5.41/5.63 thf(fact_1432_modulo__nat__def,axiom,
% 5.41/5.63 ( modulo_modulo_nat
% 5.41/5.63 = ( ^ [M3: nat,N2: nat] : ( minus_minus_nat @ M3 @ ( times_times_nat @ ( divide_divide_nat @ M3 @ N2 ) @ N2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % modulo_nat_def
% 5.41/5.63 thf(fact_1433_mod__le__divisor,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_le_divisor
% 5.41/5.63 thf(fact_1434_nat__diff__split__asm,axiom,
% 5.41/5.63 ! [P: nat > $o,A: nat,B: nat] :
% 5.41/5.63 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.41/5.63 = ( ~ ( ( ( ord_less_nat @ A @ B )
% 5.41/5.63 & ~ ( P @ zero_zero_nat ) )
% 5.41/5.63 | ? [D2: nat] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( plus_plus_nat @ B @ D2 ) )
% 5.41/5.63 & ~ ( P @ D2 ) ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_diff_split_asm
% 5.41/5.63 thf(fact_1435_nat__diff__split,axiom,
% 5.41/5.63 ! [P: nat > $o,A: nat,B: nat] :
% 5.41/5.63 ( ( P @ ( minus_minus_nat @ A @ B ) )
% 5.41/5.63 = ( ( ( ord_less_nat @ A @ B )
% 5.41/5.63 => ( P @ zero_zero_nat ) )
% 5.41/5.63 & ! [D2: nat] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( plus_plus_nat @ B @ D2 ) )
% 5.41/5.63 => ( P @ D2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % nat_diff_split
% 5.41/5.63 thf(fact_1436_power__0__left,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ( N = zero_zero_nat )
% 5.41/5.63 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.41/5.63 = one_one_rat ) )
% 5.41/5.63 & ( ( N != zero_zero_nat )
% 5.41/5.63 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.41/5.63 = zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_0_left
% 5.41/5.63 thf(fact_1437_power__0__left,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ( N = zero_zero_nat )
% 5.41/5.63 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.41/5.63 = one_one_nat ) )
% 5.41/5.63 & ( ( N != zero_zero_nat )
% 5.41/5.63 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.41/5.63 = zero_zero_nat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_0_left
% 5.41/5.63 thf(fact_1438_power__0__left,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ( N = zero_zero_nat )
% 5.41/5.63 => ( ( power_power_real @ zero_zero_real @ N )
% 5.41/5.63 = one_one_real ) )
% 5.41/5.63 & ( ( N != zero_zero_nat )
% 5.41/5.63 => ( ( power_power_real @ zero_zero_real @ N )
% 5.41/5.63 = zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_0_left
% 5.41/5.63 thf(fact_1439_power__0__left,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ( N = zero_zero_nat )
% 5.41/5.63 => ( ( power_power_int @ zero_zero_int @ N )
% 5.41/5.63 = one_one_int ) )
% 5.41/5.63 & ( ( N != zero_zero_nat )
% 5.41/5.63 => ( ( power_power_int @ zero_zero_int @ N )
% 5.41/5.63 = zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_0_left
% 5.41/5.63 thf(fact_1440_power__0__left,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ( N = zero_zero_nat )
% 5.41/5.63 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.41/5.63 = one_one_complex ) )
% 5.41/5.63 & ( ( N != zero_zero_nat )
% 5.41/5.63 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.41/5.63 = zero_zero_complex ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_0_left
% 5.41/5.63 thf(fact_1441_zero__power,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( power_power_rat @ zero_zero_rat @ N )
% 5.41/5.63 = zero_zero_rat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_power
% 5.41/5.63 thf(fact_1442_zero__power,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( power_power_nat @ zero_zero_nat @ N )
% 5.41/5.63 = zero_zero_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_power
% 5.41/5.63 thf(fact_1443_zero__power,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( power_power_real @ zero_zero_real @ N )
% 5.41/5.63 = zero_zero_real ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_power
% 5.41/5.63 thf(fact_1444_zero__power,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( power_power_int @ zero_zero_int @ N )
% 5.41/5.63 = zero_zero_int ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_power
% 5.41/5.63 thf(fact_1445_zero__power,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 => ( ( power_power_complex @ zero_zero_complex @ N )
% 5.41/5.63 = zero_zero_complex ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_power
% 5.41/5.63 thf(fact_1446_mod__mult__eq,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_eq
% 5.41/5.63 thf(fact_1447_mod__mult__eq,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_eq
% 5.41/5.63 thf(fact_1448_mod__mult__eq,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_eq
% 5.41/5.63 thf(fact_1449_mod__mult__cong,axiom,
% 5.41/5.63 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.41/5.63 ( ( ( modulo_modulo_nat @ A @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_cong
% 5.41/5.63 thf(fact_1450_mod__mult__cong,axiom,
% 5.41/5.63 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.41/5.63 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.63 = ( modulo_modulo_int @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo_modulo_int @ B @ C )
% 5.41/5.63 = ( modulo_modulo_int @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( times_times_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_cong
% 5.41/5.63 thf(fact_1451_mod__mult__cong,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.41/5.63 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_cong
% 5.41/5.63 thf(fact_1452_mod__mult__mult2,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.41/5.63 = ( times_times_nat @ ( modulo_modulo_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_mult2
% 5.41/5.63 thf(fact_1453_mod__mult__mult2,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.63 = ( times_times_int @ ( modulo_modulo_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_mult2
% 5.41/5.63 thf(fact_1454_mod__mult__mult2,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.41/5.63 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_mult2
% 5.41/5.63 thf(fact_1455_mult__mod__right,axiom,
% 5.41/5.63 ! [C: nat,A: nat,B: nat] :
% 5.41/5.63 ( ( times_times_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_mod_right
% 5.41/5.63 thf(fact_1456_mult__mod__right,axiom,
% 5.41/5.63 ! [C: int,A: int,B: int] :
% 5.41/5.63 ( ( times_times_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.63 = ( modulo_modulo_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_mod_right
% 5.41/5.63 thf(fact_1457_mult__mod__right,axiom,
% 5.41/5.63 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.63 ( ( times_3573771949741848930nteger @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_mod_right
% 5.41/5.63 thf(fact_1458_mod__mult__left__eq,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_left_eq
% 5.41/5.63 thf(fact_1459_mod__mult__left__eq,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( times_times_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_left_eq
% 5.41/5.63 thf(fact_1460_mod__mult__left__eq,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_left_eq
% 5.41/5.63 thf(fact_1461_mod__mult__right__eq,axiom,
% 5.41/5.63 ! [A: nat,B: nat,C: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( times_times_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_right_eq
% 5.41/5.63 thf(fact_1462_mod__mult__right__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( times_times_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_right_eq
% 5.41/5.63 thf(fact_1463_mod__mult__right__eq,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_mult_right_eq
% 5.41/5.63 thf(fact_1464_mod__add__eq,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_eq
% 5.41/5.63 thf(fact_1465_mod__add__eq,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_eq
% 5.41/5.63 thf(fact_1466_mod__add__eq,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_eq
% 5.41/5.63 thf(fact_1467_mod__add__cong,axiom,
% 5.41/5.63 ! [A: nat,C: nat,A4: nat,B: nat,B4: nat] :
% 5.41/5.63 ( ( ( modulo_modulo_nat @ A @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo_modulo_nat @ B @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_cong
% 5.41/5.63 thf(fact_1468_mod__add__cong,axiom,
% 5.41/5.63 ! [A: int,C: int,A4: int,B: int,B4: int] :
% 5.41/5.63 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.63 = ( modulo_modulo_int @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo_modulo_int @ B @ C )
% 5.41/5.63 = ( modulo_modulo_int @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_cong
% 5.41/5.63 thf(fact_1469_mod__add__cong,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,A4: code_integer,B: code_integer,B4: code_integer] :
% 5.41/5.63 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ A4 @ C ) )
% 5.41/5.63 => ( ( ( modulo364778990260209775nteger @ B @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ B4 @ C ) )
% 5.41/5.63 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A4 @ B4 ) @ C ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_cong
% 5.41/5.63 thf(fact_1470_mod__add__left__eq,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_left_eq
% 5.41/5.63 thf(fact_1471_mod__add__left__eq,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_left_eq
% 5.41/5.63 thf(fact_1472_mod__add__left__eq,axiom,
% 5.41/5.63 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ B ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_left_eq
% 5.41/5.63 thf(fact_1473_mod__add__right__eq,axiom,
% 5.41/5.63 ! [A: nat,B: nat,C: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( plus_plus_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_nat @ ( plus_plus_nat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_right_eq
% 5.41/5.63 thf(fact_1474_mod__add__right__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( plus_plus_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo_modulo_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_right_eq
% 5.41/5.63 thf(fact_1475_mod__add__right__eq,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % mod_add_right_eq
% 5.41/5.63 thf(fact_1476_power__mod,axiom,
% 5.41/5.63 ! [A: nat,B: nat,N: nat] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( power_power_nat @ ( modulo_modulo_nat @ A @ B ) @ N ) @ B )
% 5.41/5.63 = ( modulo_modulo_nat @ ( power_power_nat @ A @ N ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_mod
% 5.41/5.63 thf(fact_1477_power__mod,axiom,
% 5.41/5.63 ! [A: int,B: int,N: nat] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( power_power_int @ ( modulo_modulo_int @ A @ B ) @ N ) @ B )
% 5.41/5.63 = ( modulo_modulo_int @ ( power_power_int @ A @ N ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_mod
% 5.41/5.63 thf(fact_1478_power__mod,axiom,
% 5.41/5.63 ! [A: code_integer,B: code_integer,N: nat] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( modulo364778990260209775nteger @ A @ B ) @ N ) @ B )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ A @ N ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % power_mod
% 5.41/5.63 thf(fact_1479_diff__mono,axiom,
% 5.41/5.63 ! [A: real,B: real,D: real,C: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.63 => ( ( ord_less_eq_real @ D @ C )
% 5.41/5.63 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_mono
% 5.41/5.63 thf(fact_1480_diff__mono,axiom,
% 5.41/5.63 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.63 => ( ( ord_less_eq_rat @ D @ C )
% 5.41/5.63 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_mono
% 5.41/5.63 thf(fact_1481_diff__mono,axiom,
% 5.41/5.63 ! [A: int,B: int,D: int,C: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.63 => ( ( ord_less_eq_int @ D @ C )
% 5.41/5.63 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_mono
% 5.41/5.63 thf(fact_1482_diff__left__mono,axiom,
% 5.41/5.63 ! [B: real,A: real,C: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ B @ A )
% 5.41/5.63 => ( ord_less_eq_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_left_mono
% 5.41/5.63 thf(fact_1483_diff__left__mono,axiom,
% 5.41/5.63 ! [B: rat,A: rat,C: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.63 => ( ord_less_eq_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_left_mono
% 5.41/5.63 thf(fact_1484_diff__left__mono,axiom,
% 5.41/5.63 ! [B: int,A: int,C: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.63 => ( ord_less_eq_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_left_mono
% 5.41/5.63 thf(fact_1485_diff__right__mono,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.63 => ( ord_less_eq_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_right_mono
% 5.41/5.63 thf(fact_1486_diff__right__mono,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.63 => ( ord_less_eq_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_right_mono
% 5.41/5.63 thf(fact_1487_diff__right__mono,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.63 => ( ord_less_eq_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_right_mono
% 5.41/5.63 thf(fact_1488_diff__eq__diff__less__eq,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.63 ( ( ( minus_minus_real @ A @ B )
% 5.41/5.63 = ( minus_minus_real @ C @ D ) )
% 5.41/5.63 => ( ( ord_less_eq_real @ A @ B )
% 5.41/5.63 = ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_less_eq
% 5.41/5.63 thf(fact_1489_diff__eq__diff__less__eq,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.41/5.63 = ( minus_minus_rat @ C @ D ) )
% 5.41/5.63 => ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.63 = ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_less_eq
% 5.41/5.63 thf(fact_1490_diff__eq__diff__less__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.41/5.63 = ( minus_minus_int @ C @ D ) )
% 5.41/5.63 => ( ( ord_less_eq_int @ A @ B )
% 5.41/5.63 = ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_less_eq
% 5.41/5.63 thf(fact_1491_diff__strict__mono,axiom,
% 5.41/5.63 ! [A: real,B: real,D: real,C: real] :
% 5.41/5.63 ( ( ord_less_real @ A @ B )
% 5.41/5.63 => ( ( ord_less_real @ D @ C )
% 5.41/5.63 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_mono
% 5.41/5.63 thf(fact_1492_diff__strict__mono,axiom,
% 5.41/5.63 ! [A: rat,B: rat,D: rat,C: rat] :
% 5.41/5.63 ( ( ord_less_rat @ A @ B )
% 5.41/5.63 => ( ( ord_less_rat @ D @ C )
% 5.41/5.63 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_mono
% 5.41/5.63 thf(fact_1493_diff__strict__mono,axiom,
% 5.41/5.63 ! [A: int,B: int,D: int,C: int] :
% 5.41/5.63 ( ( ord_less_int @ A @ B )
% 5.41/5.63 => ( ( ord_less_int @ D @ C )
% 5.41/5.63 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_mono
% 5.41/5.63 thf(fact_1494_diff__eq__diff__less,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.63 ( ( ( minus_minus_real @ A @ B )
% 5.41/5.63 = ( minus_minus_real @ C @ D ) )
% 5.41/5.63 => ( ( ord_less_real @ A @ B )
% 5.41/5.63 = ( ord_less_real @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_less
% 5.41/5.63 thf(fact_1495_diff__eq__diff__less,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.41/5.63 = ( minus_minus_rat @ C @ D ) )
% 5.41/5.63 => ( ( ord_less_rat @ A @ B )
% 5.41/5.63 = ( ord_less_rat @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_less
% 5.41/5.63 thf(fact_1496_diff__eq__diff__less,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.41/5.63 = ( minus_minus_int @ C @ D ) )
% 5.41/5.63 => ( ( ord_less_int @ A @ B )
% 5.41/5.63 = ( ord_less_int @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_diff_less
% 5.41/5.63 thf(fact_1497_diff__strict__left__mono,axiom,
% 5.41/5.63 ! [B: real,A: real,C: real] :
% 5.41/5.63 ( ( ord_less_real @ B @ A )
% 5.41/5.63 => ( ord_less_real @ ( minus_minus_real @ C @ A ) @ ( minus_minus_real @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_left_mono
% 5.41/5.63 thf(fact_1498_diff__strict__left__mono,axiom,
% 5.41/5.63 ! [B: rat,A: rat,C: rat] :
% 5.41/5.63 ( ( ord_less_rat @ B @ A )
% 5.41/5.63 => ( ord_less_rat @ ( minus_minus_rat @ C @ A ) @ ( minus_minus_rat @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_left_mono
% 5.41/5.63 thf(fact_1499_diff__strict__left__mono,axiom,
% 5.41/5.63 ! [B: int,A: int,C: int] :
% 5.41/5.63 ( ( ord_less_int @ B @ A )
% 5.41/5.63 => ( ord_less_int @ ( minus_minus_int @ C @ A ) @ ( minus_minus_int @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_left_mono
% 5.41/5.63 thf(fact_1500_diff__strict__right__mono,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( ord_less_real @ A @ B )
% 5.41/5.63 => ( ord_less_real @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_right_mono
% 5.41/5.63 thf(fact_1501_diff__strict__right__mono,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( ord_less_rat @ A @ B )
% 5.41/5.63 => ( ord_less_rat @ ( minus_minus_rat @ A @ C ) @ ( minus_minus_rat @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_right_mono
% 5.41/5.63 thf(fact_1502_diff__strict__right__mono,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( ord_less_int @ A @ B )
% 5.41/5.63 => ( ord_less_int @ ( minus_minus_int @ A @ C ) @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_strict_right_mono
% 5.41/5.63 thf(fact_1503_left__diff__distrib,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( times_times_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib
% 5.41/5.63 thf(fact_1504_left__diff__distrib,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib
% 5.41/5.63 thf(fact_1505_left__diff__distrib,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( times_times_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib
% 5.41/5.63 thf(fact_1506_right__diff__distrib,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib
% 5.41/5.63 thf(fact_1507_right__diff__distrib,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib
% 5.41/5.63 thf(fact_1508_right__diff__distrib,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib
% 5.41/5.63 thf(fact_1509_left__diff__distrib_H,axiom,
% 5.41/5.63 ! [B: real,C: real,A: real] :
% 5.41/5.63 ( ( times_times_real @ ( minus_minus_real @ B @ C ) @ A )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ B @ A ) @ ( times_times_real @ C @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib'
% 5.41/5.63 thf(fact_1510_left__diff__distrib_H,axiom,
% 5.41/5.63 ! [B: rat,C: rat,A: rat] :
% 5.41/5.63 ( ( times_times_rat @ ( minus_minus_rat @ B @ C ) @ A )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ B @ A ) @ ( times_times_rat @ C @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib'
% 5.41/5.63 thf(fact_1511_left__diff__distrib_H,axiom,
% 5.41/5.63 ! [B: nat,C: nat,A: nat] :
% 5.41/5.63 ( ( times_times_nat @ ( minus_minus_nat @ B @ C ) @ A )
% 5.41/5.63 = ( minus_minus_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib'
% 5.41/5.63 thf(fact_1512_left__diff__distrib_H,axiom,
% 5.41/5.63 ! [B: int,C: int,A: int] :
% 5.41/5.63 ( ( times_times_int @ ( minus_minus_int @ B @ C ) @ A )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % left_diff_distrib'
% 5.41/5.63 thf(fact_1513_right__diff__distrib_H,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( times_times_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.41/5.63 = ( minus_minus_real @ ( times_times_real @ A @ B ) @ ( times_times_real @ A @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib'
% 5.41/5.63 thf(fact_1514_right__diff__distrib_H,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( times_times_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.41/5.63 = ( minus_minus_rat @ ( times_times_rat @ A @ B ) @ ( times_times_rat @ A @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib'
% 5.41/5.63 thf(fact_1515_right__diff__distrib_H,axiom,
% 5.41/5.63 ! [A: nat,B: nat,C: nat] :
% 5.41/5.63 ( ( times_times_nat @ A @ ( minus_minus_nat @ B @ C ) )
% 5.41/5.63 = ( minus_minus_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib'
% 5.41/5.63 thf(fact_1516_right__diff__distrib_H,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( times_times_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.41/5.63 = ( minus_minus_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % right_diff_distrib'
% 5.41/5.63 thf(fact_1517_group__cancel_Osub1,axiom,
% 5.41/5.63 ! [A2: real,K: real,A: real,B: real] :
% 5.41/5.63 ( ( A2
% 5.41/5.63 = ( plus_plus_real @ K @ A ) )
% 5.41/5.63 => ( ( minus_minus_real @ A2 @ B )
% 5.41/5.63 = ( plus_plus_real @ K @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % group_cancel.sub1
% 5.41/5.63 thf(fact_1518_group__cancel_Osub1,axiom,
% 5.41/5.63 ! [A2: rat,K: rat,A: rat,B: rat] :
% 5.41/5.63 ( ( A2
% 5.41/5.63 = ( plus_plus_rat @ K @ A ) )
% 5.41/5.63 => ( ( minus_minus_rat @ A2 @ B )
% 5.41/5.63 = ( plus_plus_rat @ K @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % group_cancel.sub1
% 5.41/5.63 thf(fact_1519_group__cancel_Osub1,axiom,
% 5.41/5.63 ! [A2: int,K: int,A: int,B: int] :
% 5.41/5.63 ( ( A2
% 5.41/5.63 = ( plus_plus_int @ K @ A ) )
% 5.41/5.63 => ( ( minus_minus_int @ A2 @ B )
% 5.41/5.63 = ( plus_plus_int @ K @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % group_cancel.sub1
% 5.41/5.63 thf(fact_1520_diff__eq__eq,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( ( minus_minus_real @ A @ B )
% 5.41/5.63 = C )
% 5.41/5.63 = ( A
% 5.41/5.63 = ( plus_plus_real @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_eq
% 5.41/5.63 thf(fact_1521_diff__eq__eq,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( ( minus_minus_rat @ A @ B )
% 5.41/5.63 = C )
% 5.41/5.63 = ( A
% 5.41/5.63 = ( plus_plus_rat @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_eq
% 5.41/5.63 thf(fact_1522_diff__eq__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( ( minus_minus_int @ A @ B )
% 5.41/5.63 = C )
% 5.41/5.63 = ( A
% 5.41/5.63 = ( plus_plus_int @ C @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_eq_eq
% 5.41/5.63 thf(fact_1523_eq__diff__eq,axiom,
% 5.41/5.63 ! [A: real,C: real,B: real] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( minus_minus_real @ C @ B ) )
% 5.41/5.63 = ( ( plus_plus_real @ A @ B )
% 5.41/5.63 = C ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_diff_eq
% 5.41/5.63 thf(fact_1524_eq__diff__eq,axiom,
% 5.41/5.63 ! [A: rat,C: rat,B: rat] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( minus_minus_rat @ C @ B ) )
% 5.41/5.63 = ( ( plus_plus_rat @ A @ B )
% 5.41/5.63 = C ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_diff_eq
% 5.41/5.63 thf(fact_1525_eq__diff__eq,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int] :
% 5.41/5.63 ( ( A
% 5.41/5.63 = ( minus_minus_int @ C @ B ) )
% 5.41/5.63 = ( ( plus_plus_int @ A @ B )
% 5.41/5.63 = C ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_diff_eq
% 5.41/5.63 thf(fact_1526_add__diff__eq,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( plus_plus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.41/5.63 = ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_diff_eq
% 5.41/5.63 thf(fact_1527_add__diff__eq,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( plus_plus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.41/5.63 = ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_diff_eq
% 5.41/5.63 thf(fact_1528_add__diff__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( plus_plus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.41/5.63 = ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_diff_eq
% 5.41/5.63 thf(fact_1529_diff__diff__eq2,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( minus_minus_real @ A @ ( minus_minus_real @ B @ C ) )
% 5.41/5.63 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_eq2
% 5.41/5.63 thf(fact_1530_diff__diff__eq2,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( minus_minus_rat @ A @ ( minus_minus_rat @ B @ C ) )
% 5.41/5.63 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_eq2
% 5.41/5.63 thf(fact_1531_diff__diff__eq2,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( minus_minus_int @ A @ ( minus_minus_int @ B @ C ) )
% 5.41/5.63 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_eq2
% 5.41/5.63 thf(fact_1532_diff__add__eq,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_eq
% 5.41/5.63 thf(fact_1533_diff__add__eq,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_eq
% 5.41/5.63 thf(fact_1534_diff__add__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_eq
% 5.41/5.63 thf(fact_1535_diff__add__eq__diff__diff__swap,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.41/5.63 = ( minus_minus_real @ ( minus_minus_real @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_eq_diff_diff_swap
% 5.41/5.63 thf(fact_1536_diff__add__eq__diff__diff__swap,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.63 = ( minus_minus_rat @ ( minus_minus_rat @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_eq_diff_diff_swap
% 5.41/5.63 thf(fact_1537_diff__add__eq__diff__diff__swap,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.41/5.63 = ( minus_minus_int @ ( minus_minus_int @ A @ C ) @ B ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_eq_diff_diff_swap
% 5.41/5.63 thf(fact_1538_add__implies__diff,axiom,
% 5.41/5.63 ! [C: real,B: real,A: real] :
% 5.41/5.63 ( ( ( plus_plus_real @ C @ B )
% 5.41/5.63 = A )
% 5.41/5.63 => ( C
% 5.41/5.63 = ( minus_minus_real @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_implies_diff
% 5.41/5.63 thf(fact_1539_add__implies__diff,axiom,
% 5.41/5.63 ! [C: rat,B: rat,A: rat] :
% 5.41/5.63 ( ( ( plus_plus_rat @ C @ B )
% 5.41/5.63 = A )
% 5.41/5.63 => ( C
% 5.41/5.63 = ( minus_minus_rat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_implies_diff
% 5.41/5.63 thf(fact_1540_add__implies__diff,axiom,
% 5.41/5.63 ! [C: nat,B: nat,A: nat] :
% 5.41/5.63 ( ( ( plus_plus_nat @ C @ B )
% 5.41/5.63 = A )
% 5.41/5.63 => ( C
% 5.41/5.63 = ( minus_minus_nat @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_implies_diff
% 5.41/5.63 thf(fact_1541_add__implies__diff,axiom,
% 5.41/5.63 ! [C: int,B: int,A: int] :
% 5.41/5.63 ( ( ( plus_plus_int @ C @ B )
% 5.41/5.63 = A )
% 5.41/5.63 => ( C
% 5.41/5.63 = ( minus_minus_int @ A @ B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_implies_diff
% 5.41/5.63 thf(fact_1542_diff__diff__eq,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( minus_minus_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_real @ A @ ( plus_plus_real @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_eq
% 5.41/5.63 thf(fact_1543_diff__diff__eq,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( minus_minus_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_eq
% 5.41/5.63 thf(fact_1544_diff__diff__eq,axiom,
% 5.41/5.63 ! [A: nat,B: nat,C: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( minus_minus_nat @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_eq
% 5.41/5.63 thf(fact_1545_diff__diff__eq,axiom,
% 5.41/5.63 ! [A: int,B: int,C: int] :
% 5.41/5.63 ( ( minus_minus_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_int @ A @ ( plus_plus_int @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_diff_eq
% 5.41/5.63 thf(fact_1546_add__diff__add,axiom,
% 5.41/5.63 ! [A: real,C: real,B: real,D: real] :
% 5.41/5.63 ( ( minus_minus_real @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) )
% 5.41/5.63 = ( plus_plus_real @ ( minus_minus_real @ A @ B ) @ ( minus_minus_real @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_diff_add
% 5.41/5.63 thf(fact_1547_add__diff__add,axiom,
% 5.41/5.63 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.41/5.63 ( ( minus_minus_rat @ ( plus_plus_rat @ A @ C ) @ ( plus_plus_rat @ B @ D ) )
% 5.41/5.63 = ( plus_plus_rat @ ( minus_minus_rat @ A @ B ) @ ( minus_minus_rat @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_diff_add
% 5.41/5.63 thf(fact_1548_add__diff__add,axiom,
% 5.41/5.63 ! [A: int,C: int,B: int,D: int] :
% 5.41/5.63 ( ( minus_minus_int @ ( plus_plus_int @ A @ C ) @ ( plus_plus_int @ B @ D ) )
% 5.41/5.63 = ( plus_plus_int @ ( minus_minus_int @ A @ B ) @ ( minus_minus_int @ C @ D ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % add_diff_add
% 5.41/5.63 thf(fact_1549_mod__less__eq__dividend,axiom,
% 5.41/5.63 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ N ) @ M ) ).
% 5.41/5.63
% 5.41/5.63 % mod_less_eq_dividend
% 5.41/5.63 thf(fact_1550_diff__divide__distrib,axiom,
% 5.41/5.63 ! [A: complex,B: complex,C: complex] :
% 5.41/5.63 ( ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ C ) @ ( divide1717551699836669952omplex @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_divide_distrib
% 5.41/5.63 thf(fact_1551_diff__divide__distrib,axiom,
% 5.41/5.63 ! [A: real,B: real,C: real] :
% 5.41/5.63 ( ( divide_divide_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_divide_distrib
% 5.41/5.63 thf(fact_1552_diff__divide__distrib,axiom,
% 5.41/5.63 ! [A: rat,B: rat,C: rat] :
% 5.41/5.63 ( ( divide_divide_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.41/5.63 = ( minus_minus_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_divide_distrib
% 5.41/5.63 thf(fact_1553_diff__less__mono2,axiom,
% 5.41/5.63 ! [M: nat,N: nat,L2: nat] :
% 5.41/5.63 ( ( ord_less_nat @ M @ N )
% 5.41/5.63 => ( ( ord_less_nat @ M @ L2 )
% 5.41/5.63 => ( ord_less_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_less_mono2
% 5.41/5.63 thf(fact_1554_less__imp__diff__less,axiom,
% 5.41/5.63 ! [J: nat,K: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ J @ K )
% 5.41/5.63 => ( ord_less_nat @ ( minus_minus_nat @ J @ N ) @ K ) ) ).
% 5.41/5.63
% 5.41/5.63 % less_imp_diff_less
% 5.41/5.63 thf(fact_1555_eq__diff__iff,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.63 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.63 => ( ( ( minus_minus_nat @ M @ K )
% 5.41/5.63 = ( minus_minus_nat @ N @ K ) )
% 5.41/5.63 = ( M = N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % eq_diff_iff
% 5.41/5.63 thf(fact_1556_le__diff__iff,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.63 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.41/5.63 = ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_diff_iff
% 5.41/5.63 thf(fact_1557_Nat_Odiff__diff__eq,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.63 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.63 => ( ( minus_minus_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.41/5.63 = ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.diff_diff_eq
% 5.41/5.63 thf(fact_1558_diff__le__mono,axiom,
% 5.41/5.63 ! [M: nat,N: nat,L2: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.63 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ L2 ) @ ( minus_minus_nat @ N @ L2 ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_le_mono
% 5.41/5.63 thf(fact_1559_diff__le__self,axiom,
% 5.41/5.63 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ M ) ).
% 5.41/5.63
% 5.41/5.63 % diff_le_self
% 5.41/5.63 thf(fact_1560_le__diff__iff_H,axiom,
% 5.41/5.63 ! [A: nat,C: nat,B: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ A @ C )
% 5.41/5.63 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.63 => ( ( ord_less_eq_nat @ ( minus_minus_nat @ C @ A ) @ ( minus_minus_nat @ C @ B ) )
% 5.41/5.63 = ( ord_less_eq_nat @ B @ A ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % le_diff_iff'
% 5.41/5.63 thf(fact_1561_diff__le__mono2,axiom,
% 5.41/5.63 ! [M: nat,N: nat,L2: nat] :
% 5.41/5.63 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.63 => ( ord_less_eq_nat @ ( minus_minus_nat @ L2 @ N ) @ ( minus_minus_nat @ L2 @ M ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_le_mono2
% 5.41/5.63 thf(fact_1562_Nat_Odiff__cancel,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ K @ M ) @ ( plus_plus_nat @ K @ N ) )
% 5.41/5.63 = ( minus_minus_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % Nat.diff_cancel
% 5.41/5.63 thf(fact_1563_diff__cancel2,axiom,
% 5.41/5.63 ! [M: nat,K: nat,N: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) )
% 5.41/5.63 = ( minus_minus_nat @ M @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_cancel2
% 5.41/5.63 thf(fact_1564_diff__add__inverse,axiom,
% 5.41/5.63 ! [N: nat,M: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ N @ M ) @ N )
% 5.41/5.63 = M ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_inverse
% 5.41/5.63 thf(fact_1565_diff__add__inverse2,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ N )
% 5.41/5.63 = M ) ).
% 5.41/5.63
% 5.41/5.63 % diff_add_inverse2
% 5.41/5.63 thf(fact_1566_diff__mult__distrib,axiom,
% 5.41/5.63 ! [M: nat,N: nat,K: nat] :
% 5.41/5.63 ( ( times_times_nat @ ( minus_minus_nat @ M @ N ) @ K )
% 5.41/5.63 = ( minus_minus_nat @ ( times_times_nat @ M @ K ) @ ( times_times_nat @ N @ K ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_mult_distrib
% 5.41/5.63 thf(fact_1567_diff__mult__distrib2,axiom,
% 5.41/5.63 ! [K: nat,M: nat,N: nat] :
% 5.41/5.63 ( ( times_times_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.63 = ( minus_minus_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % diff_mult_distrib2
% 5.41/5.63 thf(fact_1568_zero__le,axiom,
% 5.41/5.63 ! [X: nat] : ( ord_less_eq_nat @ zero_zero_nat @ X ) ).
% 5.41/5.63
% 5.41/5.63 % zero_le
% 5.41/5.63 thf(fact_1569_le__numeral__extra_I3_J,axiom,
% 5.41/5.63 ord_less_eq_real @ zero_zero_real @ zero_zero_real ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(3)
% 5.41/5.63 thf(fact_1570_le__numeral__extra_I3_J,axiom,
% 5.41/5.63 ord_less_eq_rat @ zero_zero_rat @ zero_zero_rat ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(3)
% 5.41/5.63 thf(fact_1571_le__numeral__extra_I3_J,axiom,
% 5.41/5.63 ord_less_eq_nat @ zero_zero_nat @ zero_zero_nat ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(3)
% 5.41/5.63 thf(fact_1572_le__numeral__extra_I3_J,axiom,
% 5.41/5.63 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.41/5.63
% 5.41/5.63 % le_numeral_extra(3)
% 5.41/5.63 thf(fact_1573_gr__zeroI,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( N != zero_zero_nat )
% 5.41/5.63 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % gr_zeroI
% 5.41/5.63 thf(fact_1574_not__less__zero,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % not_less_zero
% 5.41/5.63 thf(fact_1575_gr__implies__not__zero,axiom,
% 5.41/5.63 ! [M: nat,N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ M @ N )
% 5.41/5.63 => ( N != zero_zero_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % gr_implies_not_zero
% 5.41/5.63 thf(fact_1576_zero__less__iff__neq__zero,axiom,
% 5.41/5.63 ! [N: nat] :
% 5.41/5.63 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.63 = ( N != zero_zero_nat ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_less_iff_neq_zero
% 5.41/5.63 thf(fact_1577_less__numeral__extra_I3_J,axiom,
% 5.41/5.63 ~ ( ord_less_real @ zero_zero_real @ zero_zero_real ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(3)
% 5.41/5.63 thf(fact_1578_less__numeral__extra_I3_J,axiom,
% 5.41/5.63 ~ ( ord_less_rat @ zero_zero_rat @ zero_zero_rat ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(3)
% 5.41/5.63 thf(fact_1579_less__numeral__extra_I3_J,axiom,
% 5.41/5.63 ~ ( ord_less_nat @ zero_zero_nat @ zero_zero_nat ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(3)
% 5.41/5.63 thf(fact_1580_less__numeral__extra_I3_J,axiom,
% 5.41/5.63 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.41/5.63
% 5.41/5.63 % less_numeral_extra(3)
% 5.41/5.63 thf(fact_1581_field__lbound__gt__zero,axiom,
% 5.41/5.63 ! [D1: real,D22: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ D1 )
% 5.41/5.63 => ( ( ord_less_real @ zero_zero_real @ D22 )
% 5.41/5.63 => ? [E2: real] :
% 5.41/5.63 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.41/5.63 & ( ord_less_real @ E2 @ D1 )
% 5.41/5.63 & ( ord_less_real @ E2 @ D22 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % field_lbound_gt_zero
% 5.41/5.63 thf(fact_1582_field__lbound__gt__zero,axiom,
% 5.41/5.63 ! [D1: rat,D22: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ D1 )
% 5.41/5.63 => ( ( ord_less_rat @ zero_zero_rat @ D22 )
% 5.41/5.63 => ? [E2: rat] :
% 5.41/5.63 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.41/5.63 & ( ord_less_rat @ E2 @ D1 )
% 5.41/5.63 & ( ord_less_rat @ E2 @ D22 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % field_lbound_gt_zero
% 5.41/5.63 thf(fact_1583_zero__neq__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( zero_zero_complex
% 5.41/5.63 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_numeral
% 5.41/5.63 thf(fact_1584_zero__neq__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( zero_zero_real
% 5.41/5.63 != ( numeral_numeral_real @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_numeral
% 5.41/5.63 thf(fact_1585_zero__neq__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( zero_zero_rat
% 5.41/5.63 != ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_numeral
% 5.41/5.63 thf(fact_1586_zero__neq__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( zero_zero_nat
% 5.41/5.63 != ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_numeral
% 5.41/5.63 thf(fact_1587_zero__neq__numeral,axiom,
% 5.41/5.63 ! [N: num] :
% 5.41/5.63 ( zero_zero_int
% 5.41/5.63 != ( numeral_numeral_int @ N ) ) ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_numeral
% 5.41/5.63 thf(fact_1588_cong__exp__iff__simps_I9_J,axiom,
% 5.41/5.63 ! [M: num,Q2: num,N: num] :
% 5.41/5.63 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.63 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.41/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(9)
% 5.41/5.63 thf(fact_1589_cong__exp__iff__simps_I9_J,axiom,
% 5.41/5.63 ! [M: num,Q2: num,N: num] :
% 5.41/5.63 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.63 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.41/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(9)
% 5.41/5.63 thf(fact_1590_cong__exp__iff__simps_I9_J,axiom,
% 5.41/5.63 ! [M: num,Q2: num,N: num] :
% 5.41/5.63 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.63 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(9)
% 5.41/5.63 thf(fact_1591_cong__exp__iff__simps_I4_J,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ one ) )
% 5.41/5.63 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(4)
% 5.41/5.63 thf(fact_1592_cong__exp__iff__simps_I4_J,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ one ) )
% 5.41/5.63 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(4)
% 5.41/5.63 thf(fact_1593_cong__exp__iff__simps_I4_J,axiom,
% 5.41/5.63 ! [M: num,N: num] :
% 5.41/5.63 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ one ) )
% 5.41/5.63 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % cong_exp_iff_simps(4)
% 5.41/5.63 thf(fact_1594_mult__not__zero,axiom,
% 5.41/5.63 ! [A: complex,B: complex] :
% 5.41/5.63 ( ( ( times_times_complex @ A @ B )
% 5.41/5.63 != zero_zero_complex )
% 5.41/5.63 => ( ( A != zero_zero_complex )
% 5.41/5.63 & ( B != zero_zero_complex ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_not_zero
% 5.41/5.63 thf(fact_1595_mult__not__zero,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ( times_times_real @ A @ B )
% 5.41/5.63 != zero_zero_real )
% 5.41/5.63 => ( ( A != zero_zero_real )
% 5.41/5.63 & ( B != zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_not_zero
% 5.41/5.63 thf(fact_1596_mult__not__zero,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ( times_times_rat @ A @ B )
% 5.41/5.63 != zero_zero_rat )
% 5.41/5.63 => ( ( A != zero_zero_rat )
% 5.41/5.63 & ( B != zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_not_zero
% 5.41/5.63 thf(fact_1597_mult__not__zero,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( ( times_times_nat @ A @ B )
% 5.41/5.63 != zero_zero_nat )
% 5.41/5.63 => ( ( A != zero_zero_nat )
% 5.41/5.63 & ( B != zero_zero_nat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_not_zero
% 5.41/5.63 thf(fact_1598_mult__not__zero,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( ( times_times_int @ A @ B )
% 5.41/5.63 != zero_zero_int )
% 5.41/5.63 => ( ( A != zero_zero_int )
% 5.41/5.63 & ( B != zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_not_zero
% 5.41/5.63 thf(fact_1599_divisors__zero,axiom,
% 5.41/5.63 ! [A: complex,B: complex] :
% 5.41/5.63 ( ( ( times_times_complex @ A @ B )
% 5.41/5.63 = zero_zero_complex )
% 5.41/5.63 => ( ( A = zero_zero_complex )
% 5.41/5.63 | ( B = zero_zero_complex ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divisors_zero
% 5.41/5.63 thf(fact_1600_divisors__zero,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( ( times_times_real @ A @ B )
% 5.41/5.63 = zero_zero_real )
% 5.41/5.63 => ( ( A = zero_zero_real )
% 5.41/5.63 | ( B = zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divisors_zero
% 5.41/5.63 thf(fact_1601_divisors__zero,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( ( times_times_rat @ A @ B )
% 5.41/5.63 = zero_zero_rat )
% 5.41/5.63 => ( ( A = zero_zero_rat )
% 5.41/5.63 | ( B = zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divisors_zero
% 5.41/5.63 thf(fact_1602_divisors__zero,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( ( times_times_nat @ A @ B )
% 5.41/5.63 = zero_zero_nat )
% 5.41/5.63 => ( ( A = zero_zero_nat )
% 5.41/5.63 | ( B = zero_zero_nat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divisors_zero
% 5.41/5.63 thf(fact_1603_divisors__zero,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( ( times_times_int @ A @ B )
% 5.41/5.63 = zero_zero_int )
% 5.41/5.63 => ( ( A = zero_zero_int )
% 5.41/5.63 | ( B = zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % divisors_zero
% 5.41/5.63 thf(fact_1604_no__zero__divisors,axiom,
% 5.41/5.63 ! [A: complex,B: complex] :
% 5.41/5.63 ( ( A != zero_zero_complex )
% 5.41/5.63 => ( ( B != zero_zero_complex )
% 5.41/5.63 => ( ( times_times_complex @ A @ B )
% 5.41/5.63 != zero_zero_complex ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % no_zero_divisors
% 5.41/5.63 thf(fact_1605_no__zero__divisors,axiom,
% 5.41/5.63 ! [A: real,B: real] :
% 5.41/5.63 ( ( A != zero_zero_real )
% 5.41/5.63 => ( ( B != zero_zero_real )
% 5.41/5.63 => ( ( times_times_real @ A @ B )
% 5.41/5.63 != zero_zero_real ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % no_zero_divisors
% 5.41/5.63 thf(fact_1606_no__zero__divisors,axiom,
% 5.41/5.63 ! [A: rat,B: rat] :
% 5.41/5.63 ( ( A != zero_zero_rat )
% 5.41/5.63 => ( ( B != zero_zero_rat )
% 5.41/5.63 => ( ( times_times_rat @ A @ B )
% 5.41/5.63 != zero_zero_rat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % no_zero_divisors
% 5.41/5.63 thf(fact_1607_no__zero__divisors,axiom,
% 5.41/5.63 ! [A: nat,B: nat] :
% 5.41/5.63 ( ( A != zero_zero_nat )
% 5.41/5.63 => ( ( B != zero_zero_nat )
% 5.41/5.63 => ( ( times_times_nat @ A @ B )
% 5.41/5.63 != zero_zero_nat ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % no_zero_divisors
% 5.41/5.63 thf(fact_1608_no__zero__divisors,axiom,
% 5.41/5.63 ! [A: int,B: int] :
% 5.41/5.63 ( ( A != zero_zero_int )
% 5.41/5.63 => ( ( B != zero_zero_int )
% 5.41/5.63 => ( ( times_times_int @ A @ B )
% 5.41/5.63 != zero_zero_int ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % no_zero_divisors
% 5.41/5.63 thf(fact_1609_mult__left__cancel,axiom,
% 5.41/5.63 ! [C: complex,A: complex,B: complex] :
% 5.41/5.63 ( ( C != zero_zero_complex )
% 5.41/5.63 => ( ( ( times_times_complex @ C @ A )
% 5.41/5.63 = ( times_times_complex @ C @ B ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_left_cancel
% 5.41/5.63 thf(fact_1610_mult__left__cancel,axiom,
% 5.41/5.63 ! [C: real,A: real,B: real] :
% 5.41/5.63 ( ( C != zero_zero_real )
% 5.41/5.63 => ( ( ( times_times_real @ C @ A )
% 5.41/5.63 = ( times_times_real @ C @ B ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_left_cancel
% 5.41/5.63 thf(fact_1611_mult__left__cancel,axiom,
% 5.41/5.63 ! [C: rat,A: rat,B: rat] :
% 5.41/5.63 ( ( C != zero_zero_rat )
% 5.41/5.63 => ( ( ( times_times_rat @ C @ A )
% 5.41/5.63 = ( times_times_rat @ C @ B ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_left_cancel
% 5.41/5.63 thf(fact_1612_mult__left__cancel,axiom,
% 5.41/5.63 ! [C: nat,A: nat,B: nat] :
% 5.41/5.63 ( ( C != zero_zero_nat )
% 5.41/5.63 => ( ( ( times_times_nat @ C @ A )
% 5.41/5.63 = ( times_times_nat @ C @ B ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_left_cancel
% 5.41/5.63 thf(fact_1613_mult__left__cancel,axiom,
% 5.41/5.63 ! [C: int,A: int,B: int] :
% 5.41/5.63 ( ( C != zero_zero_int )
% 5.41/5.63 => ( ( ( times_times_int @ C @ A )
% 5.41/5.63 = ( times_times_int @ C @ B ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_left_cancel
% 5.41/5.63 thf(fact_1614_mult__right__cancel,axiom,
% 5.41/5.63 ! [C: complex,A: complex,B: complex] :
% 5.41/5.63 ( ( C != zero_zero_complex )
% 5.41/5.63 => ( ( ( times_times_complex @ A @ C )
% 5.41/5.63 = ( times_times_complex @ B @ C ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_right_cancel
% 5.41/5.63 thf(fact_1615_mult__right__cancel,axiom,
% 5.41/5.63 ! [C: real,A: real,B: real] :
% 5.41/5.63 ( ( C != zero_zero_real )
% 5.41/5.63 => ( ( ( times_times_real @ A @ C )
% 5.41/5.63 = ( times_times_real @ B @ C ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_right_cancel
% 5.41/5.63 thf(fact_1616_mult__right__cancel,axiom,
% 5.41/5.63 ! [C: rat,A: rat,B: rat] :
% 5.41/5.63 ( ( C != zero_zero_rat )
% 5.41/5.63 => ( ( ( times_times_rat @ A @ C )
% 5.41/5.63 = ( times_times_rat @ B @ C ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_right_cancel
% 5.41/5.63 thf(fact_1617_mult__right__cancel,axiom,
% 5.41/5.63 ! [C: nat,A: nat,B: nat] :
% 5.41/5.63 ( ( C != zero_zero_nat )
% 5.41/5.63 => ( ( ( times_times_nat @ A @ C )
% 5.41/5.63 = ( times_times_nat @ B @ C ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_right_cancel
% 5.41/5.63 thf(fact_1618_mult__right__cancel,axiom,
% 5.41/5.63 ! [C: int,A: int,B: int] :
% 5.41/5.63 ( ( C != zero_zero_int )
% 5.41/5.63 => ( ( ( times_times_int @ A @ C )
% 5.41/5.63 = ( times_times_int @ B @ C ) )
% 5.41/5.63 = ( A = B ) ) ) ).
% 5.41/5.63
% 5.41/5.63 % mult_right_cancel
% 5.41/5.63 thf(fact_1619_comm__monoid__add__class_Oadd__0,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % comm_monoid_add_class.add_0
% 5.41/5.63 thf(fact_1620_comm__monoid__add__class_Oadd__0,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % comm_monoid_add_class.add_0
% 5.41/5.63 thf(fact_1621_comm__monoid__add__class_Oadd__0,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % comm_monoid_add_class.add_0
% 5.41/5.63 thf(fact_1622_comm__monoid__add__class_Oadd__0,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( plus_plus_nat @ zero_zero_nat @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % comm_monoid_add_class.add_0
% 5.41/5.63 thf(fact_1623_comm__monoid__add__class_Oadd__0,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % comm_monoid_add_class.add_0
% 5.41/5.63 thf(fact_1624_add_Ocomm__neutral,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.comm_neutral
% 5.41/5.63 thf(fact_1625_add_Ocomm__neutral,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.comm_neutral
% 5.41/5.63 thf(fact_1626_add_Ocomm__neutral,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.comm_neutral
% 5.41/5.63 thf(fact_1627_add_Ocomm__neutral,axiom,
% 5.41/5.63 ! [A: nat] :
% 5.41/5.63 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.comm_neutral
% 5.41/5.63 thf(fact_1628_add_Ocomm__neutral,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.comm_neutral
% 5.41/5.63 thf(fact_1629_add_Ogroup__left__neutral,axiom,
% 5.41/5.63 ! [A: complex] :
% 5.41/5.63 ( ( plus_plus_complex @ zero_zero_complex @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.group_left_neutral
% 5.41/5.63 thf(fact_1630_add_Ogroup__left__neutral,axiom,
% 5.41/5.63 ! [A: real] :
% 5.41/5.63 ( ( plus_plus_real @ zero_zero_real @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.group_left_neutral
% 5.41/5.63 thf(fact_1631_add_Ogroup__left__neutral,axiom,
% 5.41/5.63 ! [A: rat] :
% 5.41/5.63 ( ( plus_plus_rat @ zero_zero_rat @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.group_left_neutral
% 5.41/5.63 thf(fact_1632_add_Ogroup__left__neutral,axiom,
% 5.41/5.63 ! [A: int] :
% 5.41/5.63 ( ( plus_plus_int @ zero_zero_int @ A )
% 5.41/5.63 = A ) ).
% 5.41/5.63
% 5.41/5.63 % add.group_left_neutral
% 5.41/5.63 thf(fact_1633_zero__neq__one,axiom,
% 5.41/5.63 zero_zero_complex != one_one_complex ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_one
% 5.41/5.63 thf(fact_1634_zero__neq__one,axiom,
% 5.41/5.63 zero_zero_real != one_one_real ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_one
% 5.41/5.63 thf(fact_1635_zero__neq__one,axiom,
% 5.41/5.63 zero_zero_rat != one_one_rat ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_one
% 5.41/5.63 thf(fact_1636_zero__neq__one,axiom,
% 5.41/5.63 zero_zero_nat != one_one_nat ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_one
% 5.41/5.63 thf(fact_1637_zero__neq__one,axiom,
% 5.41/5.63 zero_zero_int != one_one_int ).
% 5.41/5.63
% 5.41/5.63 % zero_neq_one
% 5.41/5.63 thf(fact_1638_power__not__zero,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( A != zero_zero_rat )
% 5.41/5.64 => ( ( power_power_rat @ A @ N )
% 5.41/5.64 != zero_zero_rat ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_not_zero
% 5.41/5.64 thf(fact_1639_power__not__zero,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( A != zero_zero_nat )
% 5.41/5.64 => ( ( power_power_nat @ A @ N )
% 5.41/5.64 != zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_not_zero
% 5.41/5.64 thf(fact_1640_power__not__zero,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( A != zero_zero_real )
% 5.41/5.64 => ( ( power_power_real @ A @ N )
% 5.41/5.64 != zero_zero_real ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_not_zero
% 5.41/5.64 thf(fact_1641_power__not__zero,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( A != zero_zero_int )
% 5.41/5.64 => ( ( power_power_int @ A @ N )
% 5.41/5.64 != zero_zero_int ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_not_zero
% 5.41/5.64 thf(fact_1642_power__not__zero,axiom,
% 5.41/5.64 ! [A: complex,N: nat] :
% 5.41/5.64 ( ( A != zero_zero_complex )
% 5.41/5.64 => ( ( power_power_complex @ A @ N )
% 5.41/5.64 != zero_zero_complex ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_not_zero
% 5.41/5.64 thf(fact_1643_num_Osize_I4_J,axiom,
% 5.41/5.64 ( ( size_size_num @ one )
% 5.41/5.64 = zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % num.size(4)
% 5.41/5.64 thf(fact_1644_bot__nat__0_Oextremum__strict,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ~ ( ord_less_nat @ A @ zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % bot_nat_0.extremum_strict
% 5.41/5.64 thf(fact_1645_gr0I,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ( ( N != zero_zero_nat )
% 5.41/5.64 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % gr0I
% 5.41/5.64 thf(fact_1646_not__gr0,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ( ( ~ ( ord_less_nat @ zero_zero_nat @ N ) )
% 5.41/5.64 = ( N = zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % not_gr0
% 5.41/5.64 thf(fact_1647_not__less0,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % not_less0
% 5.41/5.64 thf(fact_1648_less__zeroE,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ~ ( ord_less_nat @ N @ zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % less_zeroE
% 5.41/5.64 thf(fact_1649_gr__implies__not0,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( N != zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % gr_implies_not0
% 5.41/5.64 thf(fact_1650_infinite__descent0,axiom,
% 5.41/5.64 ! [P: nat > $o,N: nat] :
% 5.41/5.64 ( ( P @ zero_zero_nat )
% 5.41/5.64 => ( ! [N3: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.41/5.64 => ( ~ ( P @ N3 )
% 5.41/5.64 => ? [M2: nat] :
% 5.41/5.64 ( ( ord_less_nat @ M2 @ N3 )
% 5.41/5.64 & ~ ( P @ M2 ) ) ) )
% 5.41/5.64 => ( P @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % infinite_descent0
% 5.41/5.64 thf(fact_1651_less__eq__nat_Osimps_I1_J,axiom,
% 5.41/5.64 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ N ) ).
% 5.41/5.64
% 5.41/5.64 % less_eq_nat.simps(1)
% 5.41/5.64 thf(fact_1652_bot__nat__0_Oextremum__unique,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.41/5.64 = ( A = zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % bot_nat_0.extremum_unique
% 5.41/5.64 thf(fact_1653_bot__nat__0_Oextremum__uniqueI,axiom,
% 5.41/5.64 ! [A: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.41/5.64 => ( A = zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % bot_nat_0.extremum_uniqueI
% 5.41/5.64 thf(fact_1654_le__0__eq,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ N @ zero_zero_nat )
% 5.41/5.64 = ( N = zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_0_eq
% 5.41/5.64 thf(fact_1655_plus__nat_Oadd__0,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ zero_zero_nat @ N )
% 5.41/5.64 = N ) ).
% 5.41/5.64
% 5.41/5.64 % plus_nat.add_0
% 5.41/5.64 thf(fact_1656_add__eq__self__zero,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ( ( plus_plus_nat @ M @ N )
% 5.41/5.64 = M )
% 5.41/5.64 => ( N = zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_eq_self_zero
% 5.41/5.64 thf(fact_1657_nat__mult__eq__cancel__disj,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ( times_times_nat @ K @ M )
% 5.41/5.64 = ( times_times_nat @ K @ N ) )
% 5.41/5.64 = ( ( K = zero_zero_nat )
% 5.41/5.64 | ( M = N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_mult_eq_cancel_disj
% 5.41/5.64 thf(fact_1658_mult__0,axiom,
% 5.41/5.64 ! [N: nat] :
% 5.41/5.64 ( ( times_times_nat @ zero_zero_nat @ N )
% 5.41/5.64 = zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % mult_0
% 5.41/5.64 thf(fact_1659_nat__mod__eq__iff,axiom,
% 5.41/5.64 ! [X: nat,N: nat,Y: nat] :
% 5.41/5.64 ( ( ( modulo_modulo_nat @ X @ N )
% 5.41/5.64 = ( modulo_modulo_nat @ Y @ N ) )
% 5.41/5.64 = ( ? [Q1: nat,Q22: nat] :
% 5.41/5.64 ( ( plus_plus_nat @ X @ ( times_times_nat @ N @ Q1 ) )
% 5.41/5.64 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q22 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_mod_eq_iff
% 5.41/5.64 thf(fact_1660_pos__zdiv__mult__2,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.64 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % pos_zdiv_mult_2
% 5.41/5.64 thf(fact_1661_neg__zdiv__mult__2,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.64 = ( divide_divide_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % neg_zdiv_mult_2
% 5.41/5.64 thf(fact_1662_frac__le__eq,axiom,
% 5.41/5.64 ! [Y: real,Z: real,X: real,W: real] :
% 5.41/5.64 ( ( Y != zero_zero_real )
% 5.41/5.64 => ( ( Z != zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.41/5.64 = ( ord_less_eq_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % frac_le_eq
% 5.41/5.64 thf(fact_1663_frac__le__eq,axiom,
% 5.41/5.64 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.41/5.64 ( ( Y != zero_zero_rat )
% 5.41/5.64 => ( ( Z != zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.41/5.64 = ( ord_less_eq_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % frac_le_eq
% 5.41/5.64 thf(fact_1664_frac__less__eq,axiom,
% 5.41/5.64 ! [Y: real,Z: real,X: real,W: real] :
% 5.41/5.64 ( ( Y != zero_zero_real )
% 5.41/5.64 => ( ( Z != zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.41/5.64 = ( ord_less_real @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) @ zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % frac_less_eq
% 5.41/5.64 thf(fact_1665_frac__less__eq,axiom,
% 5.41/5.64 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.41/5.64 ( ( Y != zero_zero_rat )
% 5.41/5.64 => ( ( Z != zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.41/5.64 = ( ord_less_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) @ zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % frac_less_eq
% 5.41/5.64 thf(fact_1666_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.41/5.64 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.64 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ C )
% 5.41/5.64 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.41/5.64 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.41/5.64 thf(fact_1667_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.41/5.64 ! [C: nat,A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ B @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) @ ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.41/5.64 thf(fact_1668_unique__euclidean__semiring__numeral__class_Omod__mult2__eq,axiom,
% 5.41/5.64 ! [C: int,A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % unique_euclidean_semiring_numeral_class.mod_mult2_eq
% 5.41/5.64 thf(fact_1669_not__iless0,axiom,
% 5.41/5.64 ! [N: extended_enat] :
% 5.41/5.64 ~ ( ord_le72135733267957522d_enat @ N @ zero_z5237406670263579293d_enat ) ).
% 5.41/5.64
% 5.41/5.64 % not_iless0
% 5.41/5.64 thf(fact_1670_enat__0__less__mult__iff,axiom,
% 5.41/5.64 ! [M: extended_enat,N: extended_enat] :
% 5.41/5.64 ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ ( times_7803423173614009249d_enat @ M @ N ) )
% 5.41/5.64 = ( ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ M )
% 5.41/5.64 & ( ord_le72135733267957522d_enat @ zero_z5237406670263579293d_enat @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % enat_0_less_mult_iff
% 5.41/5.64 thf(fact_1671_power__diff,axiom,
% 5.41/5.64 ! [A: complex,N: nat,M: nat] :
% 5.41/5.64 ( ( A != zero_zero_complex )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( power_power_complex @ A @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = ( divide1717551699836669952omplex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_diff
% 5.41/5.64 thf(fact_1672_power__diff,axiom,
% 5.41/5.64 ! [A: real,N: nat,M: nat] :
% 5.41/5.64 ( ( A != zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( power_power_real @ A @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = ( divide_divide_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_diff
% 5.41/5.64 thf(fact_1673_power__diff,axiom,
% 5.41/5.64 ! [A: rat,N: nat,M: nat] :
% 5.41/5.64 ( ( A != zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( power_power_rat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = ( divide_divide_rat @ ( power_power_rat @ A @ M ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_diff
% 5.41/5.64 thf(fact_1674_power__diff,axiom,
% 5.41/5.64 ! [A: nat,N: nat,M: nat] :
% 5.41/5.64 ( ( A != zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_diff
% 5.41/5.64 thf(fact_1675_power__diff,axiom,
% 5.41/5.64 ! [A: int,N: nat,M: nat] :
% 5.41/5.64 ( ( A != zero_zero_int )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_diff
% 5.41/5.64 thf(fact_1676_split__mod,axiom,
% 5.41/5.64 ! [P: nat > $o,M: nat,N: nat] :
% 5.41/5.64 ( ( P @ ( modulo_modulo_nat @ M @ N ) )
% 5.41/5.64 = ( ( ( N = zero_zero_nat )
% 5.41/5.64 => ( P @ M ) )
% 5.41/5.64 & ( ( N != zero_zero_nat )
% 5.41/5.64 => ! [I5: nat,J3: nat] :
% 5.41/5.64 ( ( ord_less_nat @ J3 @ N )
% 5.41/5.64 => ( ( M
% 5.41/5.64 = ( plus_plus_nat @ ( times_times_nat @ N @ I5 ) @ J3 ) )
% 5.41/5.64 => ( P @ J3 ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mod
% 5.41/5.64 thf(fact_1677_i0__lb,axiom,
% 5.41/5.64 ! [N: extended_enat] : ( ord_le2932123472753598470d_enat @ zero_z5237406670263579293d_enat @ N ) ).
% 5.41/5.64
% 5.41/5.64 % i0_lb
% 5.41/5.64 thf(fact_1678_ile0__eq,axiom,
% 5.41/5.64 ! [N: extended_enat] :
% 5.41/5.64 ( ( ord_le2932123472753598470d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.41/5.64 = ( N = zero_z5237406670263579293d_enat ) ) ).
% 5.41/5.64
% 5.41/5.64 % ile0_eq
% 5.41/5.64 thf(fact_1679_divmod__digit__1_I2_J,axiom,
% 5.41/5.64 ! [A: code_integer,B: code_integer] :
% 5.41/5.64 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.64 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.64 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.64 => ( ( minus_8373710615458151222nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.64 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divmod_digit_1(2)
% 5.41/5.64 thf(fact_1680_divmod__digit__1_I2_J,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.64 => ( ( minus_minus_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.64 = ( modulo_modulo_nat @ A @ B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divmod_digit_1(2)
% 5.41/5.64 thf(fact_1681_divmod__digit__1_I2_J,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.64 => ( ( minus_minus_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.64 = ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divmod_digit_1(2)
% 5.41/5.64 thf(fact_1682_power__eq__iff__eq__base,axiom,
% 5.41/5.64 ! [N: nat,A: real,B: real] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ( ( power_power_real @ A @ N )
% 5.41/5.64 = ( power_power_real @ B @ N ) )
% 5.41/5.64 = ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_iff_eq_base
% 5.41/5.64 thf(fact_1683_power__eq__iff__eq__base,axiom,
% 5.41/5.64 ! [N: nat,A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ( ( power_power_rat @ A @ N )
% 5.41/5.64 = ( power_power_rat @ B @ N ) )
% 5.41/5.64 = ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_iff_eq_base
% 5.41/5.64 thf(fact_1684_power__eq__iff__eq__base,axiom,
% 5.41/5.64 ! [N: nat,A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ( ( power_power_nat @ A @ N )
% 5.41/5.64 = ( power_power_nat @ B @ N ) )
% 5.41/5.64 = ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_iff_eq_base
% 5.41/5.64 thf(fact_1685_power__eq__iff__eq__base,axiom,
% 5.41/5.64 ! [N: nat,A: int,B: int] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ( ( power_power_int @ A @ N )
% 5.41/5.64 = ( power_power_int @ B @ N ) )
% 5.41/5.64 = ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_iff_eq_base
% 5.41/5.64 thf(fact_1686_power__eq__imp__eq__base,axiom,
% 5.41/5.64 ! [A: real,N: nat,B: real] :
% 5.41/5.64 ( ( ( power_power_real @ A @ N )
% 5.41/5.64 = ( power_power_real @ B @ N ) )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_imp_eq_base
% 5.41/5.64 thf(fact_1687_power__eq__imp__eq__base,axiom,
% 5.41/5.64 ! [A: rat,N: nat,B: rat] :
% 5.41/5.64 ( ( ( power_power_rat @ A @ N )
% 5.41/5.64 = ( power_power_rat @ B @ N ) )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_imp_eq_base
% 5.41/5.64 thf(fact_1688_power__eq__imp__eq__base,axiom,
% 5.41/5.64 ! [A: nat,N: nat,B: nat] :
% 5.41/5.64 ( ( ( power_power_nat @ A @ N )
% 5.41/5.64 = ( power_power_nat @ B @ N ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_imp_eq_base
% 5.41/5.64 thf(fact_1689_power__eq__imp__eq__base,axiom,
% 5.41/5.64 ! [A: int,N: nat,B: int] :
% 5.41/5.64 ( ( ( power_power_int @ A @ N )
% 5.41/5.64 = ( power_power_int @ B @ N ) )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( A = B ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_imp_eq_base
% 5.41/5.64 thf(fact_1690_mult__eq__if,axiom,
% 5.41/5.64 ( times_times_nat
% 5.41/5.64 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ N2 @ ( times_times_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_eq_if
% 5.41/5.64 thf(fact_1691_divmod__digit__0_I2_J,axiom,
% 5.41/5.64 ! [B: nat,A: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.64 => ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) )
% 5.41/5.64 = ( modulo_modulo_nat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divmod_digit_0(2)
% 5.41/5.64 thf(fact_1692_divmod__digit__0_I2_J,axiom,
% 5.41/5.64 ! [B: int,A: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.64 => ( ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) )
% 5.41/5.64 = ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divmod_digit_0(2)
% 5.41/5.64 thf(fact_1693_divmod__digit__0_I2_J,axiom,
% 5.41/5.64 ! [B: code_integer,A: code_integer] :
% 5.41/5.64 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.64 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.64 => ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) )
% 5.41/5.64 = ( modulo364778990260209775nteger @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divmod_digit_0(2)
% 5.41/5.64 thf(fact_1694_cong__exp__iff__simps_I8_J,axiom,
% 5.41/5.64 ! [M: num,Q2: num] :
% 5.41/5.64 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.64 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % cong_exp_iff_simps(8)
% 5.41/5.64 thf(fact_1695_cong__exp__iff__simps_I8_J,axiom,
% 5.41/5.64 ! [M: num,Q2: num] :
% 5.41/5.64 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.64 != ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % cong_exp_iff_simps(8)
% 5.41/5.64 thf(fact_1696_cong__exp__iff__simps_I8_J,axiom,
% 5.41/5.64 ! [M: num,Q2: num] :
% 5.41/5.64 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.64 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % cong_exp_iff_simps(8)
% 5.41/5.64 thf(fact_1697_cong__exp__iff__simps_I6_J,axiom,
% 5.41/5.64 ! [Q2: num,N: num] :
% 5.41/5.64 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.64 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % cong_exp_iff_simps(6)
% 5.41/5.64 thf(fact_1698_cong__exp__iff__simps_I6_J,axiom,
% 5.41/5.64 ! [Q2: num,N: num] :
% 5.41/5.64 ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.64 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % cong_exp_iff_simps(6)
% 5.41/5.64 thf(fact_1699_cong__exp__iff__simps_I6_J,axiom,
% 5.41/5.64 ! [Q2: num,N: num] :
% 5.41/5.64 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.64 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % cong_exp_iff_simps(6)
% 5.41/5.64 thf(fact_1700_scaling__mono,axiom,
% 5.41/5.64 ! [U: real,V: real,R: real,S: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ U @ V )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ R )
% 5.41/5.64 => ( ( ord_less_eq_real @ R @ S )
% 5.41/5.64 => ( ord_less_eq_real @ ( plus_plus_real @ U @ ( divide_divide_real @ ( times_times_real @ R @ ( minus_minus_real @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % scaling_mono
% 5.41/5.64 thf(fact_1701_scaling__mono,axiom,
% 5.41/5.64 ! [U: rat,V: rat,R: rat,S: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ U @ V )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ R )
% 5.41/5.64 => ( ( ord_less_eq_rat @ R @ S )
% 5.41/5.64 => ( ord_less_eq_rat @ ( plus_plus_rat @ U @ ( divide_divide_rat @ ( times_times_rat @ R @ ( minus_minus_rat @ V @ U ) ) @ S ) ) @ V ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % scaling_mono
% 5.41/5.64 thf(fact_1702_mod__eqE,axiom,
% 5.41/5.64 ! [A: int,C: int,B: int] :
% 5.41/5.64 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.64 = ( modulo_modulo_int @ B @ C ) )
% 5.41/5.64 => ~ ! [D3: int] :
% 5.41/5.64 ( B
% 5.41/5.64 != ( plus_plus_int @ A @ ( times_times_int @ C @ D3 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mod_eqE
% 5.41/5.64 thf(fact_1703_mod__eqE,axiom,
% 5.41/5.64 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.64 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.64 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.41/5.64 => ~ ! [D3: code_integer] :
% 5.41/5.64 ( B
% 5.41/5.64 != ( plus_p5714425477246183910nteger @ A @ ( times_3573771949741848930nteger @ C @ D3 ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mod_eqE
% 5.41/5.64 thf(fact_1704_div__add1__eq,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.64 = ( plus_plus_nat @ ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ A @ C ) @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_add1_eq
% 5.41/5.64 thf(fact_1705_div__add1__eq,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( plus_plus_int @ ( modulo_modulo_int @ A @ C ) @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_add1_eq
% 5.41/5.64 thf(fact_1706_div__add1__eq,axiom,
% 5.41/5.64 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.64 ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.41/5.64 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ C ) @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_add1_eq
% 5.41/5.64 thf(fact_1707_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.64 != zero_zero_nat )
% 5.41/5.64 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.41/5.64 != zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % exp_not_zero_imp_exp_diff_not_zero
% 5.41/5.64 thf(fact_1708_exp__not__zero__imp__exp__diff__not__zero,axiom,
% 5.41/5.64 ! [N: nat,M: nat] :
% 5.41/5.64 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.41/5.64 != zero_zero_int )
% 5.41/5.64 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) )
% 5.41/5.64 != zero_zero_int ) ) ).
% 5.41/5.64
% 5.41/5.64 % exp_not_zero_imp_exp_diff_not_zero
% 5.41/5.64 thf(fact_1709_power__diff__power__eq,axiom,
% 5.41/5.64 ! [A: nat,N: nat,M: nat] :
% 5.41/5.64 ( ( A != zero_zero_nat )
% 5.41/5.64 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.64 = ( power_power_nat @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.41/5.64 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( divide_divide_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.64 = ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_diff_power_eq
% 5.41/5.64 thf(fact_1710_power__diff__power__eq,axiom,
% 5.41/5.64 ! [A: int,N: nat,M: nat] :
% 5.41/5.64 ( ( A != zero_zero_int )
% 5.41/5.64 => ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.41/5.64 = ( power_power_int @ A @ ( minus_minus_nat @ M @ N ) ) ) )
% 5.41/5.64 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ( ( divide_divide_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) )
% 5.41/5.64 = ( divide_divide_int @ one_one_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_diff_power_eq
% 5.41/5.64 thf(fact_1711_power__eq__if,axiom,
% 5.41/5.64 ( power_power_complex
% 5.41/5.64 = ( ^ [P2: complex,M3: nat] : ( if_complex @ ( M3 = zero_zero_nat ) @ one_one_complex @ ( times_times_complex @ P2 @ ( power_power_complex @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_if
% 5.41/5.64 thf(fact_1712_power__eq__if,axiom,
% 5.41/5.64 ( power_power_real
% 5.41/5.64 = ( ^ [P2: real,M3: nat] : ( if_real @ ( M3 = zero_zero_nat ) @ one_one_real @ ( times_times_real @ P2 @ ( power_power_real @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_if
% 5.41/5.64 thf(fact_1713_power__eq__if,axiom,
% 5.41/5.64 ( power_power_rat
% 5.41/5.64 = ( ^ [P2: rat,M3: nat] : ( if_rat @ ( M3 = zero_zero_nat ) @ one_one_rat @ ( times_times_rat @ P2 @ ( power_power_rat @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_if
% 5.41/5.64 thf(fact_1714_power__eq__if,axiom,
% 5.41/5.64 ( power_power_nat
% 5.41/5.64 = ( ^ [P2: nat,M3: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ one_one_nat @ ( times_times_nat @ P2 @ ( power_power_nat @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_if
% 5.41/5.64 thf(fact_1715_power__eq__if,axiom,
% 5.41/5.64 ( power_power_int
% 5.41/5.64 = ( ^ [P2: int,M3: nat] : ( if_int @ ( M3 = zero_zero_nat ) @ one_one_int @ ( times_times_int @ P2 @ ( power_power_int @ P2 @ ( minus_minus_nat @ M3 @ one_one_nat ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_eq_if
% 5.41/5.64 thf(fact_1716_diff__le__eq,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.41/5.64 = ( ord_less_eq_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_le_eq
% 5.41/5.64 thf(fact_1717_diff__le__eq,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.41/5.64 = ( ord_less_eq_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_le_eq
% 5.41/5.64 thf(fact_1718_diff__le__eq,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.41/5.64 = ( ord_less_eq_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_le_eq
% 5.41/5.64 thf(fact_1719_le__diff__eq,axiom,
% 5.41/5.64 ! [A: real,C: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.41/5.64 = ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_diff_eq
% 5.41/5.64 thf(fact_1720_le__diff__eq,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.41/5.64 = ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_diff_eq
% 5.41/5.64 thf(fact_1721_le__diff__eq,axiom,
% 5.41/5.64 ! [A: int,C: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.41/5.64 = ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_diff_eq
% 5.41/5.64 thf(fact_1722_diff__add,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ A )
% 5.41/5.64 = B ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_add
% 5.41/5.64 thf(fact_1723_le__add__diff,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ord_less_eq_nat @ C @ ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_add_diff
% 5.41/5.64 thf(fact_1724_ordered__cancel__comm__monoid__diff__class_Ole__diff__conv2,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.41/5.64 = ( ord_less_eq_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.le_diff_conv2
% 5.41/5.64 thf(fact_1725_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.41/5.64 = ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc
% 5.41/5.64 thf(fact_1726_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ C @ B ) @ A )
% 5.41/5.64 = ( plus_plus_nat @ C @ ( minus_minus_nat @ B @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc
% 5.41/5.64 thf(fact_1727_ordered__cancel__comm__monoid__diff__class_Oadd__diff__assoc2,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C )
% 5.41/5.64 = ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.add_diff_assoc2
% 5.41/5.64 thf(fact_1728_ordered__cancel__comm__monoid__diff__class_Odiff__add__assoc2,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ B @ C ) @ A )
% 5.41/5.64 = ( plus_plus_nat @ ( minus_minus_nat @ B @ A ) @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.diff_add_assoc2
% 5.41/5.64 thf(fact_1729_ordered__cancel__comm__monoid__diff__class_Odiff__diff__right,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( minus_minus_nat @ C @ ( minus_minus_nat @ B @ A ) )
% 5.41/5.64 = ( minus_minus_nat @ ( plus_plus_nat @ C @ A ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.diff_diff_right
% 5.41/5.64 thf(fact_1730_ordered__cancel__comm__monoid__diff__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( plus_plus_nat @ A @ ( minus_minus_nat @ B @ A ) )
% 5.41/5.64 = B ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.add_diff_inverse
% 5.41/5.64 thf(fact_1731_ordered__cancel__comm__monoid__diff__class_Ole__imp__diff__is__add,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ( minus_minus_nat @ B @ A )
% 5.41/5.64 = C )
% 5.41/5.64 = ( B
% 5.41/5.64 = ( plus_plus_nat @ C @ A ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_cancel_comm_monoid_diff_class.le_imp_diff_is_add
% 5.41/5.64 thf(fact_1732_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: real,K: real,N: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_real @ I @ ( minus_minus_real @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_1733_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: rat,K: rat,N: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_rat @ I @ ( minus_minus_rat @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_1734_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: nat,K: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_nat @ I @ ( minus_minus_nat @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_1735_add__le__imp__le__diff,axiom,
% 5.41/5.64 ! [I: int,K: int,N: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.41/5.64 => ( ord_less_eq_int @ I @ ( minus_minus_int @ N @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_imp_le_diff
% 5.41/5.64 thf(fact_1736_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: real,K: real,N: real,J: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_real @ ( plus_plus_real @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_real @ N @ ( plus_plus_real @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_real @ ( minus_minus_real @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_1737_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: rat,K: rat,N: rat,J: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_rat @ ( plus_plus_rat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_rat @ N @ ( plus_plus_rat @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_rat @ ( minus_minus_rat @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_1738_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: nat,K: nat,N: nat,J: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ ( plus_plus_nat @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_nat @ ( minus_minus_nat @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_1739_add__le__add__imp__diff__le,axiom,
% 5.41/5.64 ! [I: int,K: int,N: int,J: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.41/5.64 => ( ( ord_less_eq_int @ ( plus_plus_int @ I @ K ) @ N )
% 5.41/5.64 => ( ( ord_less_eq_int @ N @ ( plus_plus_int @ J @ K ) )
% 5.41/5.64 => ( ord_less_eq_int @ ( minus_minus_int @ N @ K ) @ J ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_le_add_imp_diff_le
% 5.41/5.64 thf(fact_1740_power__minus__mult,axiom,
% 5.41/5.64 ! [N: nat,A: complex] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( times_times_complex @ ( power_power_complex @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.41/5.64 = ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_minus_mult
% 5.41/5.64 thf(fact_1741_power__minus__mult,axiom,
% 5.41/5.64 ! [N: nat,A: real] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( times_times_real @ ( power_power_real @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.41/5.64 = ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_minus_mult
% 5.41/5.64 thf(fact_1742_power__minus__mult,axiom,
% 5.41/5.64 ! [N: nat,A: rat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( times_times_rat @ ( power_power_rat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.41/5.64 = ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_minus_mult
% 5.41/5.64 thf(fact_1743_power__minus__mult,axiom,
% 5.41/5.64 ! [N: nat,A: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( times_times_nat @ ( power_power_nat @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.41/5.64 = ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_minus_mult
% 5.41/5.64 thf(fact_1744_power__minus__mult,axiom,
% 5.41/5.64 ! [N: nat,A: int] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ( times_times_int @ ( power_power_int @ A @ ( minus_minus_nat @ N @ one_one_nat ) ) @ A )
% 5.41/5.64 = ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_minus_mult
% 5.41/5.64 thf(fact_1745_less__diff__eq,axiom,
% 5.41/5.64 ! [A: real,C: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ ( minus_minus_real @ C @ B ) )
% 5.41/5.64 = ( ord_less_real @ ( plus_plus_real @ A @ B ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_eq
% 5.41/5.64 thf(fact_1746_less__diff__eq,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ ( minus_minus_rat @ C @ B ) )
% 5.41/5.64 = ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_eq
% 5.41/5.64 thf(fact_1747_less__diff__eq,axiom,
% 5.41/5.64 ! [A: int,C: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.41/5.64 = ( ord_less_int @ ( plus_plus_int @ A @ B ) @ C ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_eq
% 5.41/5.64 thf(fact_1748_diff__less__eq,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ ( minus_minus_real @ A @ B ) @ C )
% 5.41/5.64 = ( ord_less_real @ A @ ( plus_plus_real @ C @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_less_eq
% 5.41/5.64 thf(fact_1749_diff__less__eq,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( minus_minus_rat @ A @ B ) @ C )
% 5.41/5.64 = ( ord_less_rat @ A @ ( plus_plus_rat @ C @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_less_eq
% 5.41/5.64 thf(fact_1750_diff__less__eq,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.41/5.64 = ( ord_less_int @ A @ ( plus_plus_int @ C @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_less_eq
% 5.41/5.64 thf(fact_1751_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ~ ( ord_less_real @ A @ B )
% 5.41/5.64 => ( ( plus_plus_real @ B @ ( minus_minus_real @ A @ B ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_1752_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ~ ( ord_less_rat @ A @ B )
% 5.41/5.64 => ( ( plus_plus_rat @ B @ ( minus_minus_rat @ A @ B ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_1753_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ~ ( ord_less_nat @ A @ B )
% 5.41/5.64 => ( ( plus_plus_nat @ B @ ( minus_minus_nat @ A @ B ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_1754_linordered__semidom__class_Oadd__diff__inverse,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ~ ( ord_less_int @ A @ B )
% 5.41/5.64 => ( ( plus_plus_int @ B @ ( minus_minus_int @ A @ B ) )
% 5.41/5.64 = A ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_semidom_class.add_diff_inverse
% 5.41/5.64 thf(fact_1755_mult__diff__mult,axiom,
% 5.41/5.64 ! [X: real,Y: real,A: real,B: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( times_times_real @ X @ Y ) @ ( times_times_real @ A @ B ) )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ X @ ( minus_minus_real @ Y @ B ) ) @ ( times_times_real @ ( minus_minus_real @ X @ A ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_diff_mult
% 5.41/5.64 thf(fact_1756_mult__diff__mult,axiom,
% 5.41/5.64 ! [X: rat,Y: rat,A: rat,B: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( times_times_rat @ X @ Y ) @ ( times_times_rat @ A @ B ) )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ X @ ( minus_minus_rat @ Y @ B ) ) @ ( times_times_rat @ ( minus_minus_rat @ X @ A ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_diff_mult
% 5.41/5.64 thf(fact_1757_mult__diff__mult,axiom,
% 5.41/5.64 ! [X: int,Y: int,A: int,B: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( times_times_int @ X @ Y ) @ ( times_times_int @ A @ B ) )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ X @ ( minus_minus_int @ Y @ B ) ) @ ( times_times_int @ ( minus_minus_int @ X @ A ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_diff_mult
% 5.41/5.64 thf(fact_1758_square__diff__square__factored,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) )
% 5.41/5.64 = ( times_times_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ X @ Y ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_square_factored
% 5.41/5.64 thf(fact_1759_square__diff__square__factored,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) )
% 5.41/5.64 = ( times_times_rat @ ( plus_plus_rat @ X @ Y ) @ ( minus_minus_rat @ X @ Y ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_square_factored
% 5.41/5.64 thf(fact_1760_square__diff__square__factored,axiom,
% 5.41/5.64 ! [X: int,Y: int] :
% 5.41/5.64 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) )
% 5.41/5.64 = ( times_times_int @ ( plus_plus_int @ X @ Y ) @ ( minus_minus_int @ X @ Y ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % square_diff_square_factored
% 5.41/5.64 thf(fact_1761_eq__add__iff2,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.41/5.64 = ( C
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff2
% 5.41/5.64 thf(fact_1762_eq__add__iff2,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.41/5.64 = ( C
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff2
% 5.41/5.64 thf(fact_1763_eq__add__iff2,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.41/5.64 = ( C
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff2
% 5.41/5.64 thf(fact_1764_eq__add__iff1,axiom,
% 5.41/5.64 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.41/5.64 ( ( ( plus_plus_real @ ( times_times_real @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.41/5.64 = ( ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C )
% 5.41/5.64 = D ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff1
% 5.41/5.64 thf(fact_1765_eq__add__iff1,axiom,
% 5.41/5.64 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.41/5.64 ( ( ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.41/5.64 = ( ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C )
% 5.41/5.64 = D ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff1
% 5.41/5.64 thf(fact_1766_eq__add__iff1,axiom,
% 5.41/5.64 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.41/5.64 ( ( ( plus_plus_int @ ( times_times_int @ A @ E ) @ C )
% 5.41/5.64 = ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.41/5.64 = ( ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C )
% 5.41/5.64 = D ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_add_iff1
% 5.41/5.64 thf(fact_1767_power__strict__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,N: nat] :
% 5.41/5.64 ( ( ord_less_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_strict_mono
% 5.41/5.64 thf(fact_1768_power__strict__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,N: nat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_strict_mono
% 5.41/5.64 thf(fact_1769_power__strict__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_strict_mono
% 5.41/5.64 thf(fact_1770_power__strict__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,N: nat] :
% 5.41/5.64 ( ( ord_less_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.64 => ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_strict_mono
% 5.41/5.64 thf(fact_1771_mod__eq__nat1E,axiom,
% 5.41/5.64 ! [M: nat,Q2: nat,N: nat] :
% 5.41/5.64 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.41/5.64 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.64 => ~ ! [S3: nat] :
% 5.41/5.64 ( M
% 5.41/5.64 != ( plus_plus_nat @ N @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mod_eq_nat1E
% 5.41/5.64 thf(fact_1772_mod__eq__nat2E,axiom,
% 5.41/5.64 ! [M: nat,Q2: nat,N: nat] :
% 5.41/5.64 ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.41/5.64 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.64 => ~ ! [S3: nat] :
% 5.41/5.64 ( N
% 5.41/5.64 != ( plus_plus_nat @ M @ ( times_times_nat @ Q2 @ S3 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mod_eq_nat2E
% 5.41/5.64 thf(fact_1773_nat__mod__eq__lemma,axiom,
% 5.41/5.64 ! [X: nat,N: nat,Y: nat] :
% 5.41/5.64 ( ( ( modulo_modulo_nat @ X @ N )
% 5.41/5.64 = ( modulo_modulo_nat @ Y @ N ) )
% 5.41/5.64 => ( ( ord_less_eq_nat @ Y @ X )
% 5.41/5.64 => ? [Q3: nat] :
% 5.41/5.64 ( X
% 5.41/5.64 = ( plus_plus_nat @ Y @ ( times_times_nat @ N @ Q3 ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nat_mod_eq_lemma
% 5.41/5.64 thf(fact_1774_div__positive,axiom,
% 5.41/5.64 ! [B: nat,A: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.64 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_positive
% 5.41/5.64 thf(fact_1775_div__positive,axiom,
% 5.41/5.64 ! [B: int,A: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ A )
% 5.41/5.64 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % div_positive
% 5.41/5.64 thf(fact_1776_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ A @ B )
% 5.41/5.64 => ( ( divide_divide_nat @ A @ B )
% 5.41/5.64 = zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % unique_euclidean_semiring_numeral_class.div_less
% 5.41/5.64 thf(fact_1777_unique__euclidean__semiring__numeral__class_Odiv__less,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_int @ A @ B )
% 5.41/5.64 => ( ( divide_divide_int @ A @ B )
% 5.41/5.64 = zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % unique_euclidean_semiring_numeral_class.div_less
% 5.41/5.64 thf(fact_1778_diff__less__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ C @ A )
% 5.41/5.64 => ( ord_less_nat @ ( minus_minus_nat @ A @ C ) @ ( minus_minus_nat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % diff_less_mono
% 5.41/5.64 thf(fact_1779_less__diff__iff,axiom,
% 5.41/5.64 ! [K: nat,M: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.64 => ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.64 => ( ( ord_less_nat @ ( minus_minus_nat @ M @ K ) @ ( minus_minus_nat @ N @ K ) )
% 5.41/5.64 = ( ord_less_nat @ M @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_iff
% 5.41/5.64 thf(fact_1780_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.41/5.64 ! [C: nat,A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.41/5.64 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.41/5.64 thf(fact_1781_unique__euclidean__semiring__numeral__class_Odiv__mult2__eq,axiom,
% 5.41/5.64 ! [C: int,A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.64 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % unique_euclidean_semiring_numeral_class.div_mult2_eq
% 5.41/5.64 thf(fact_1782_add__diff__inverse__nat,axiom,
% 5.41/5.64 ! [M: nat,N: nat] :
% 5.41/5.64 ( ~ ( ord_less_nat @ M @ N )
% 5.41/5.64 => ( ( plus_plus_nat @ N @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.64 = M ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_diff_inverse_nat
% 5.41/5.64 thf(fact_1783_less__diff__conv,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.64 = ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ).
% 5.41/5.64
% 5.41/5.64 % less_diff_conv
% 5.41/5.64 thf(fact_1784_le__diff__conv,axiom,
% 5.41/5.64 ! [J: nat,K: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.41/5.64 = ( ord_less_eq_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % le_diff_conv
% 5.41/5.64 thf(fact_1785_Nat_Ole__diff__conv2,axiom,
% 5.41/5.64 ! [K: nat,J: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.64 => ( ( ord_less_eq_nat @ I @ ( minus_minus_nat @ J @ K ) )
% 5.41/5.64 = ( ord_less_eq_nat @ ( plus_plus_nat @ I @ K ) @ J ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.le_diff_conv2
% 5.41/5.64 thf(fact_1786_Nat_Odiff__add__assoc,axiom,
% 5.41/5.64 ! [K: nat,J: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ I @ J ) @ K )
% 5.41/5.64 = ( plus_plus_nat @ I @ ( minus_minus_nat @ J @ K ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.diff_add_assoc
% 5.41/5.64 thf(fact_1787_Nat_Odiff__add__assoc2,axiom,
% 5.41/5.64 ! [K: nat,J: nat,I: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.64 => ( ( minus_minus_nat @ ( plus_plus_nat @ J @ I ) @ K )
% 5.41/5.64 = ( plus_plus_nat @ ( minus_minus_nat @ J @ K ) @ I ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.diff_add_assoc2
% 5.41/5.64 thf(fact_1788_Nat_Ole__imp__diff__is__add,axiom,
% 5.41/5.64 ! [I: nat,J: nat,K: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.64 => ( ( ( minus_minus_nat @ J @ I )
% 5.41/5.64 = K )
% 5.41/5.64 = ( J
% 5.41/5.64 = ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % Nat.le_imp_diff_is_add
% 5.41/5.64 thf(fact_1789_dbl__def,axiom,
% 5.41/5.64 ( neg_numeral_dbl_real
% 5.41/5.64 = ( ^ [X3: real] : ( plus_plus_real @ X3 @ X3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % dbl_def
% 5.41/5.64 thf(fact_1790_dbl__def,axiom,
% 5.41/5.64 ( neg_numeral_dbl_rat
% 5.41/5.64 = ( ^ [X3: rat] : ( plus_plus_rat @ X3 @ X3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % dbl_def
% 5.41/5.64 thf(fact_1791_dbl__def,axiom,
% 5.41/5.64 ( neg_numeral_dbl_int
% 5.41/5.64 = ( ^ [X3: int] : ( plus_plus_int @ X3 @ X3 ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % dbl_def
% 5.41/5.64 thf(fact_1792_not__numeral__le__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_le_zero
% 5.41/5.64 thf(fact_1793_not__numeral__le__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_le_zero
% 5.41/5.64 thf(fact_1794_not__numeral__le__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_le_zero
% 5.41/5.64 thf(fact_1795_not__numeral__le__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_le_zero
% 5.41/5.64 thf(fact_1796_zero__le__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_numeral
% 5.41/5.64 thf(fact_1797_zero__le__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_numeral
% 5.41/5.64 thf(fact_1798_zero__le__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_eq_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_numeral
% 5.41/5.64 thf(fact_1799_zero__le__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_eq_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_numeral
% 5.41/5.64 thf(fact_1800_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.41/5.64 thf(fact_1801_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.41/5.64 thf(fact_1802_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.41/5.64 thf(fact_1803_ordered__comm__semiring__class_Ocomm__mult__left__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % ordered_comm_semiring_class.comm_mult_left_mono
% 5.41/5.64 thf(fact_1804_zero__le__mult__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_mult_iff
% 5.41/5.64 thf(fact_1805_zero__le__mult__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_mult_iff
% 5.41/5.64 thf(fact_1806_zero__le__mult__iff,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 & ( ord_less_eq_int @ B @ zero_zero_int ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_mult_iff
% 5.41/5.64 thf(fact_1807_mult__nonneg__nonpos2,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos2
% 5.41/5.64 thf(fact_1808_mult__nonneg__nonpos2,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos2
% 5.41/5.64 thf(fact_1809_mult__nonneg__nonpos2,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos2
% 5.41/5.64 thf(fact_1810_mult__nonneg__nonpos2,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos2
% 5.41/5.64 thf(fact_1811_mult__nonpos__nonneg,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonpos_nonneg
% 5.41/5.64 thf(fact_1812_mult__nonpos__nonneg,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonpos_nonneg
% 5.41/5.64 thf(fact_1813_mult__nonpos__nonneg,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonpos_nonneg
% 5.41/5.64 thf(fact_1814_mult__nonpos__nonneg,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonpos_nonneg
% 5.41/5.64 thf(fact_1815_mult__nonneg__nonpos,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos
% 5.41/5.64 thf(fact_1816_mult__nonneg__nonpos,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos
% 5.41/5.64 thf(fact_1817_mult__nonneg__nonpos,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos
% 5.41/5.64 thf(fact_1818_mult__nonneg__nonpos,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonpos
% 5.41/5.64 thf(fact_1819_mult__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonneg
% 5.41/5.64 thf(fact_1820_mult__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonneg
% 5.41/5.64 thf(fact_1821_mult__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ord_less_eq_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonneg
% 5.41/5.64 thf(fact_1822_mult__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonneg_nonneg
% 5.41/5.64 thf(fact_1823_split__mult__neg__le,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.41/5.64 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_eq_real @ zero_zero_real @ B ) ) )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mult_neg_le
% 5.41/5.64 thf(fact_1824_split__mult__neg__le,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.41/5.64 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mult_neg_le
% 5.41/5.64 thf(fact_1825_split__mult__neg__le,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 & ( ord_less_eq_nat @ B @ zero_zero_nat ) )
% 5.41/5.64 | ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.41/5.64 & ( ord_less_eq_nat @ zero_zero_nat @ B ) ) )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mult_neg_le
% 5.41/5.64 thf(fact_1826_split__mult__neg__le,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.41/5.64 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 & ( ord_less_eq_int @ zero_zero_int @ B ) ) )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mult_neg_le
% 5.41/5.64 thf(fact_1827_mult__le__0__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.41/5.64 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.41/5.64 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_le_0_iff
% 5.41/5.64 thf(fact_1828_mult__le__0__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.41/5.64 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.41/5.64 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_le_0_iff
% 5.41/5.64 thf(fact_1829_mult__le__0__iff,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.41/5.64 = ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 & ( ord_less_eq_int @ B @ zero_zero_int ) )
% 5.41/5.64 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 & ( ord_less_eq_int @ zero_zero_int @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_le_0_iff
% 5.41/5.64 thf(fact_1830_mult__right__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_right_mono
% 5.41/5.64 thf(fact_1831_mult__right__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_right_mono
% 5.41/5.64 thf(fact_1832_mult__right__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_right_mono
% 5.41/5.64 thf(fact_1833_mult__right__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_right_mono
% 5.41/5.64 thf(fact_1834_mult__right__mono__neg,axiom,
% 5.41/5.64 ! [B: real,A: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ B @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_right_mono_neg
% 5.41/5.64 thf(fact_1835_mult__right__mono__neg,axiom,
% 5.41/5.64 ! [B: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_right_mono_neg
% 5.41/5.64 thf(fact_1836_mult__right__mono__neg,axiom,
% 5.41/5.64 ! [B: int,A: int,C: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_right_mono_neg
% 5.41/5.64 thf(fact_1837_mult__left__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_left_mono
% 5.41/5.64 thf(fact_1838_mult__left__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_left_mono
% 5.41/5.64 thf(fact_1839_mult__left__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_left_mono
% 5.41/5.64 thf(fact_1840_mult__left__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_left_mono
% 5.41/5.64 thf(fact_1841_mult__nonpos__nonpos,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonpos_nonpos
% 5.41/5.64 thf(fact_1842_mult__nonpos__nonpos,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonpos_nonpos
% 5.41/5.64 thf(fact_1843_mult__nonpos__nonpos,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_nonpos_nonpos
% 5.41/5.64 thf(fact_1844_mult__left__mono__neg,axiom,
% 5.41/5.64 ! [B: real,A: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ B @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_left_mono_neg
% 5.41/5.64 thf(fact_1845_mult__left__mono__neg,axiom,
% 5.41/5.64 ! [B: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_left_mono_neg
% 5.41/5.64 thf(fact_1846_mult__left__mono__neg,axiom,
% 5.41/5.64 ! [B: int,A: int,C: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_left_mono_neg
% 5.41/5.64 thf(fact_1847_split__mult__pos__le,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.41/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mult_pos_le
% 5.41/5.64 thf(fact_1848_split__mult__pos__le,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.41/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mult_pos_le
% 5.41/5.64 thf(fact_1849_split__mult__pos__le,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 & ( ord_less_eq_int @ zero_zero_int @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 & ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.41/5.64 => ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % split_mult_pos_le
% 5.41/5.64 thf(fact_1850_zero__le__square,axiom,
% 5.41/5.64 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( times_times_real @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_square
% 5.41/5.64 thf(fact_1851_zero__le__square,axiom,
% 5.41/5.64 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( times_times_rat @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_square
% 5.41/5.64 thf(fact_1852_zero__le__square,axiom,
% 5.41/5.64 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( times_times_int @ A @ A ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_square
% 5.41/5.64 thf(fact_1853_mult__mono_H,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono'
% 5.41/5.64 thf(fact_1854_mult__mono_H,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono'
% 5.41/5.64 thf(fact_1855_mult__mono_H,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono'
% 5.41/5.64 thf(fact_1856_mult__mono_H,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono'
% 5.41/5.64 thf(fact_1857_mult__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono
% 5.41/5.64 thf(fact_1858_mult__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono
% 5.41/5.64 thf(fact_1859_mult__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono
% 5.41/5.64 thf(fact_1860_mult__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ C @ D )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_mono
% 5.41/5.64 thf(fact_1861_zero__less__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_numeral
% 5.41/5.64 thf(fact_1862_zero__less__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_numeral
% 5.41/5.64 thf(fact_1863_zero__less__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_numeral
% 5.41/5.64 thf(fact_1864_zero__less__numeral,axiom,
% 5.41/5.64 ! [N: num] : ( ord_less_int @ zero_zero_int @ ( numeral_numeral_int @ N ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_numeral
% 5.41/5.64 thf(fact_1865_not__numeral__less__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_real @ ( numeral_numeral_real @ N ) @ zero_zero_real ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_less_zero
% 5.41/5.64 thf(fact_1866_not__numeral__less__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ zero_zero_rat ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_less_zero
% 5.41/5.64 thf(fact_1867_not__numeral__less__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_nat @ ( numeral_numeral_nat @ N ) @ zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_less_zero
% 5.41/5.64 thf(fact_1868_not__numeral__less__zero,axiom,
% 5.41/5.64 ! [N: num] :
% 5.41/5.64 ~ ( ord_less_int @ ( numeral_numeral_int @ N ) @ zero_zero_int ) ).
% 5.41/5.64
% 5.41/5.64 % not_numeral_less_zero
% 5.41/5.64 thf(fact_1869_add__decreasing,axiom,
% 5.41/5.64 ! [A: real,C: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ C @ B )
% 5.41/5.64 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing
% 5.41/5.64 thf(fact_1870_add__decreasing,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ C @ B )
% 5.41/5.64 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing
% 5.41/5.64 thf(fact_1871_add__decreasing,axiom,
% 5.41/5.64 ! [A: nat,C: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_eq_nat @ C @ B )
% 5.41/5.64 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing
% 5.41/5.64 thf(fact_1872_add__decreasing,axiom,
% 5.41/5.64 ! [A: int,C: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_eq_int @ C @ B )
% 5.41/5.64 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing
% 5.41/5.64 thf(fact_1873_add__increasing,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ B @ C )
% 5.41/5.64 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing
% 5.41/5.64 thf(fact_1874_add__increasing,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.64 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing
% 5.41/5.64 thf(fact_1875_add__increasing,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.64 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing
% 5.41/5.64 thf(fact_1876_add__increasing,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ C )
% 5.41/5.64 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing
% 5.41/5.64 thf(fact_1877_add__decreasing2,axiom,
% 5.41/5.64 ! [C: real,A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ord_less_eq_real @ ( plus_plus_real @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing2
% 5.41/5.64 thf(fact_1878_add__decreasing2,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing2
% 5.41/5.64 thf(fact_1879_add__decreasing2,axiom,
% 5.41/5.64 ! [C: nat,A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ C @ zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing2
% 5.41/5.64 thf(fact_1880_add__decreasing2,axiom,
% 5.41/5.64 ! [C: int,A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_eq_int @ A @ B )
% 5.41/5.64 => ( ord_less_eq_int @ ( plus_plus_int @ A @ C ) @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_decreasing2
% 5.41/5.64 thf(fact_1881_add__increasing2,axiom,
% 5.41/5.64 ! [C: real,B: real,A: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ( ord_less_eq_real @ B @ A )
% 5.41/5.64 => ( ord_less_eq_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing2
% 5.41/5.64 thf(fact_1882_add__increasing2,axiom,
% 5.41/5.64 ! [C: rat,B: rat,A: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.64 => ( ord_less_eq_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing2
% 5.41/5.64 thf(fact_1883_add__increasing2,axiom,
% 5.41/5.64 ! [C: nat,B: nat,A: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.64 => ( ord_less_eq_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing2
% 5.41/5.64 thf(fact_1884_add__increasing2,axiom,
% 5.41/5.64 ! [C: int,B: int,A: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ A )
% 5.41/5.64 => ( ord_less_eq_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_increasing2
% 5.41/5.64 thf(fact_1885_add__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_nonneg
% 5.41/5.64 thf(fact_1886_add__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_nonneg
% 5.41/5.64 thf(fact_1887_add__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ord_less_eq_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_nonneg
% 5.41/5.64 thf(fact_1888_add__nonneg__nonneg,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_nonneg
% 5.41/5.64 thf(fact_1889_add__nonpos__nonpos,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_nonpos
% 5.41/5.64 thf(fact_1890_add__nonpos__nonpos,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_nonpos
% 5.41/5.64 thf(fact_1891_add__nonpos__nonpos,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.41/5.64 => ( ord_less_eq_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_nonpos
% 5.41/5.64 thf(fact_1892_add__nonpos__nonpos,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_eq_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_nonpos
% 5.41/5.64 thf(fact_1893_add__nonneg__eq__0__iff,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.64 => ( ( ( plus_plus_real @ X @ Y )
% 5.41/5.64 = zero_zero_real )
% 5.41/5.64 = ( ( X = zero_zero_real )
% 5.41/5.64 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_eq_0_iff
% 5.41/5.64 thf(fact_1894_add__nonneg__eq__0__iff,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.64 => ( ( ( plus_plus_rat @ X @ Y )
% 5.41/5.64 = zero_zero_rat )
% 5.41/5.64 = ( ( X = zero_zero_rat )
% 5.41/5.64 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_eq_0_iff
% 5.41/5.64 thf(fact_1895_add__nonneg__eq__0__iff,axiom,
% 5.41/5.64 ! [X: nat,Y: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.41/5.64 => ( ( ( plus_plus_nat @ X @ Y )
% 5.41/5.64 = zero_zero_nat )
% 5.41/5.64 = ( ( X = zero_zero_nat )
% 5.41/5.64 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_eq_0_iff
% 5.41/5.64 thf(fact_1896_add__nonneg__eq__0__iff,axiom,
% 5.41/5.64 ! [X: int,Y: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.64 => ( ( ( plus_plus_int @ X @ Y )
% 5.41/5.64 = zero_zero_int )
% 5.41/5.64 = ( ( X = zero_zero_int )
% 5.41/5.64 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonneg_eq_0_iff
% 5.41/5.64 thf(fact_1897_add__nonpos__eq__0__iff,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.41/5.64 => ( ( ( plus_plus_real @ X @ Y )
% 5.41/5.64 = zero_zero_real )
% 5.41/5.64 = ( ( X = zero_zero_real )
% 5.41/5.64 & ( Y = zero_zero_real ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_eq_0_iff
% 5.41/5.64 thf(fact_1898_add__nonpos__eq__0__iff,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.41/5.64 => ( ( ( plus_plus_rat @ X @ Y )
% 5.41/5.64 = zero_zero_rat )
% 5.41/5.64 = ( ( X = zero_zero_rat )
% 5.41/5.64 & ( Y = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_eq_0_iff
% 5.41/5.64 thf(fact_1899_add__nonpos__eq__0__iff,axiom,
% 5.41/5.64 ! [X: nat,Y: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ X @ zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_eq_nat @ Y @ zero_zero_nat )
% 5.41/5.64 => ( ( ( plus_plus_nat @ X @ Y )
% 5.41/5.64 = zero_zero_nat )
% 5.41/5.64 = ( ( X = zero_zero_nat )
% 5.41/5.64 & ( Y = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_eq_0_iff
% 5.41/5.64 thf(fact_1900_add__nonpos__eq__0__iff,axiom,
% 5.41/5.64 ! [X: int,Y: int] :
% 5.41/5.64 ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.41/5.64 => ( ( ( plus_plus_int @ X @ Y )
% 5.41/5.64 = zero_zero_int )
% 5.41/5.64 = ( ( X = zero_zero_int )
% 5.41/5.64 & ( Y = zero_zero_int ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_nonpos_eq_0_iff
% 5.41/5.64 thf(fact_1901_not__one__le__zero,axiom,
% 5.41/5.64 ~ ( ord_less_eq_real @ one_one_real @ zero_zero_real ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_le_zero
% 5.41/5.64 thf(fact_1902_not__one__le__zero,axiom,
% 5.41/5.64 ~ ( ord_less_eq_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_le_zero
% 5.41/5.64 thf(fact_1903_not__one__le__zero,axiom,
% 5.41/5.64 ~ ( ord_less_eq_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_le_zero
% 5.41/5.64 thf(fact_1904_not__one__le__zero,axiom,
% 5.41/5.64 ~ ( ord_less_eq_int @ one_one_int @ zero_zero_int ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_le_zero
% 5.41/5.64 thf(fact_1905_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.41/5.64
% 5.41/5.64 % linordered_nonzero_semiring_class.zero_le_one
% 5.41/5.64 thf(fact_1906_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.41/5.64
% 5.41/5.64 % linordered_nonzero_semiring_class.zero_le_one
% 5.41/5.64 thf(fact_1907_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.41/5.64
% 5.41/5.64 % linordered_nonzero_semiring_class.zero_le_one
% 5.41/5.64 thf(fact_1908_linordered__nonzero__semiring__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.41/5.64
% 5.41/5.64 % linordered_nonzero_semiring_class.zero_le_one
% 5.41/5.64 thf(fact_1909_zero__less__one__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_real @ zero_zero_real @ one_one_real ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one_class.zero_le_one
% 5.41/5.64 thf(fact_1910_zero__less__one__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_rat @ zero_zero_rat @ one_one_rat ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one_class.zero_le_one
% 5.41/5.64 thf(fact_1911_zero__less__one__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_nat @ zero_zero_nat @ one_one_nat ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one_class.zero_le_one
% 5.41/5.64 thf(fact_1912_zero__less__one__class_Ozero__le__one,axiom,
% 5.41/5.64 ord_less_eq_int @ zero_zero_int @ one_one_int ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one_class.zero_le_one
% 5.41/5.64 thf(fact_1913_mult__neg__neg,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_neg_neg
% 5.41/5.64 thf(fact_1914_mult__neg__neg,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_neg_neg
% 5.41/5.64 thf(fact_1915_mult__neg__neg,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_neg_neg
% 5.41/5.64 thf(fact_1916_not__square__less__zero,axiom,
% 5.41/5.64 ! [A: real] :
% 5.41/5.64 ~ ( ord_less_real @ ( times_times_real @ A @ A ) @ zero_zero_real ) ).
% 5.41/5.64
% 5.41/5.64 % not_square_less_zero
% 5.41/5.64 thf(fact_1917_not__square__less__zero,axiom,
% 5.41/5.64 ! [A: rat] :
% 5.41/5.64 ~ ( ord_less_rat @ ( times_times_rat @ A @ A ) @ zero_zero_rat ) ).
% 5.41/5.64
% 5.41/5.64 % not_square_less_zero
% 5.41/5.64 thf(fact_1918_not__square__less__zero,axiom,
% 5.41/5.64 ! [A: int] :
% 5.41/5.64 ~ ( ord_less_int @ ( times_times_int @ A @ A ) @ zero_zero_int ) ).
% 5.41/5.64
% 5.41/5.64 % not_square_less_zero
% 5.41/5.64 thf(fact_1919_mult__less__0__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real )
% 5.41/5.64 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.41/5.64 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_0_iff
% 5.41/5.64 thf(fact_1920_mult__less__0__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat )
% 5.41/5.64 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.41/5.64 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_0_iff
% 5.41/5.64 thf(fact_1921_mult__less__0__iff,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int )
% 5.41/5.64 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 & ( ord_less_int @ B @ zero_zero_int ) )
% 5.41/5.64 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.64 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_0_iff
% 5.41/5.64 thf(fact_1922_mult__neg__pos,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_neg_pos
% 5.41/5.64 thf(fact_1923_mult__neg__pos,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_neg_pos
% 5.41/5.64 thf(fact_1924_mult__neg__pos,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_neg_pos
% 5.41/5.64 thf(fact_1925_mult__neg__pos,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_neg_pos
% 5.41/5.64 thf(fact_1926_mult__pos__neg,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg
% 5.41/5.64 thf(fact_1927_mult__pos__neg,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg
% 5.41/5.64 thf(fact_1928_mult__pos__neg,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.41/5.64 => ( ord_less_nat @ ( times_times_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg
% 5.41/5.64 thf(fact_1929_mult__pos__neg,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg
% 5.41/5.64 thf(fact_1930_mult__pos__pos,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_pos
% 5.41/5.64 thf(fact_1931_mult__pos__pos,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_pos
% 5.41/5.64 thf(fact_1932_mult__pos__pos,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_pos
% 5.41/5.64 thf(fact_1933_mult__pos__pos,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_pos
% 5.41/5.64 thf(fact_1934_mult__pos__neg2,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ B @ A ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg2
% 5.41/5.64 thf(fact_1935_mult__pos__neg2,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ B @ A ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg2
% 5.41/5.64 thf(fact_1936_mult__pos__neg2,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.41/5.64 => ( ord_less_nat @ ( times_times_nat @ B @ A ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg2
% 5.41/5.64 thf(fact_1937_mult__pos__neg2,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ B @ A ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_pos_neg2
% 5.41/5.64 thf(fact_1938_zero__less__mult__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.41/5.64 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_iff
% 5.41/5.64 thf(fact_1939_zero__less__mult__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.41/5.64 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_iff
% 5.41/5.64 thf(fact_1940_zero__less__mult__iff,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 & ( ord_less_int @ zero_zero_int @ B ) )
% 5.41/5.64 | ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.64 & ( ord_less_int @ B @ zero_zero_int ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_iff
% 5.41/5.64 thf(fact_1941_zero__less__mult__pos,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos
% 5.41/5.64 thf(fact_1942_zero__less__mult__pos,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos
% 5.41/5.64 thf(fact_1943_zero__less__mult__pos,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ A @ B ) )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos
% 5.41/5.64 thf(fact_1944_zero__less__mult__pos,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ A @ B ) )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos
% 5.41/5.64 thf(fact_1945_zero__less__mult__pos2,axiom,
% 5.41/5.64 ! [B: real,A: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ B @ A ) )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos2
% 5.41/5.64 thf(fact_1946_zero__less__mult__pos2,axiom,
% 5.41/5.64 ! [B: rat,A: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ B @ A ) )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos2
% 5.41/5.64 thf(fact_1947_zero__less__mult__pos2,axiom,
% 5.41/5.64 ! [B: nat,A: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ ( times_times_nat @ B @ A ) )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ord_less_nat @ zero_zero_nat @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos2
% 5.41/5.64 thf(fact_1948_zero__less__mult__pos2,axiom,
% 5.41/5.64 ! [B: int,A: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ ( times_times_int @ B @ A ) )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ord_less_int @ zero_zero_int @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_mult_pos2
% 5.41/5.64 thf(fact_1949_mult__less__cancel__left__neg,axiom,
% 5.41/5.64 ! [C: real,A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.64 = ( ord_less_real @ B @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_neg
% 5.41/5.64 thf(fact_1950_mult__less__cancel__left__neg,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.64 = ( ord_less_rat @ B @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_neg
% 5.41/5.64 thf(fact_1951_mult__less__cancel__left__neg,axiom,
% 5.41/5.64 ! [C: int,A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.64 = ( ord_less_int @ B @ A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_neg
% 5.41/5.64 thf(fact_1952_mult__less__cancel__left__pos,axiom,
% 5.41/5.64 ! [C: real,A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.64 = ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_pos
% 5.41/5.64 thf(fact_1953_mult__less__cancel__left__pos,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.64 = ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_pos
% 5.41/5.64 thf(fact_1954_mult__less__cancel__left__pos,axiom,
% 5.41/5.64 ! [C: int,A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.64 = ( ord_less_int @ A @ B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_pos
% 5.41/5.64 thf(fact_1955_mult__strict__left__mono__neg,axiom,
% 5.41/5.64 ! [B: real,A: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ B @ A )
% 5.41/5.64 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_left_mono_neg
% 5.41/5.64 thf(fact_1956_mult__strict__left__mono__neg,axiom,
% 5.41/5.64 ! [B: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ B @ A )
% 5.41/5.64 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_left_mono_neg
% 5.41/5.64 thf(fact_1957_mult__strict__left__mono__neg,axiom,
% 5.41/5.64 ! [B: int,A: int,C: int] :
% 5.41/5.64 ( ( ord_less_int @ B @ A )
% 5.41/5.64 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_left_mono_neg
% 5.41/5.64 thf(fact_1958_mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_left_mono
% 5.41/5.64 thf(fact_1959_mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_left_mono
% 5.41/5.64 thf(fact_1960_mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_left_mono
% 5.41/5.64 thf(fact_1961_mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_left_mono
% 5.41/5.64 thf(fact_1962_mult__less__cancel__left__disj,axiom,
% 5.41/5.64 ! [C: real,A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.64 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 & ( ord_less_real @ A @ B ) )
% 5.41/5.64 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.64 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_disj
% 5.41/5.64 thf(fact_1963_mult__less__cancel__left__disj,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.64 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 & ( ord_less_rat @ A @ B ) )
% 5.41/5.64 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_disj
% 5.41/5.64 thf(fact_1964_mult__less__cancel__left__disj,axiom,
% 5.41/5.64 ! [C: int,A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.64 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.64 & ( ord_less_int @ A @ B ) )
% 5.41/5.64 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.64 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_left_disj
% 5.41/5.64 thf(fact_1965_mult__strict__right__mono__neg,axiom,
% 5.41/5.64 ! [B: real,A: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ B @ A )
% 5.41/5.64 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_right_mono_neg
% 5.41/5.64 thf(fact_1966_mult__strict__right__mono__neg,axiom,
% 5.41/5.64 ! [B: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ B @ A )
% 5.41/5.64 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_right_mono_neg
% 5.41/5.64 thf(fact_1967_mult__strict__right__mono__neg,axiom,
% 5.41/5.64 ! [B: int,A: int,C: int] :
% 5.41/5.64 ( ( ord_less_int @ B @ A )
% 5.41/5.64 => ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_right_mono_neg
% 5.41/5.64 thf(fact_1968_mult__strict__right__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_right_mono
% 5.41/5.64 thf(fact_1969_mult__strict__right__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_right_mono
% 5.41/5.64 thf(fact_1970_mult__strict__right__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_right_mono
% 5.41/5.64 thf(fact_1971_mult__strict__right__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_strict_right_mono
% 5.41/5.64 thf(fact_1972_mult__less__cancel__right__disj,axiom,
% 5.41/5.64 ! [A: real,C: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.41/5.64 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 & ( ord_less_real @ A @ B ) )
% 5.41/5.64 | ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.64 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_right_disj
% 5.41/5.64 thf(fact_1973_mult__less__cancel__right__disj,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.64 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 & ( ord_less_rat @ A @ B ) )
% 5.41/5.64 | ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_right_disj
% 5.41/5.64 thf(fact_1974_mult__less__cancel__right__disj,axiom,
% 5.41/5.64 ! [A: int,C: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.64 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.64 & ( ord_less_int @ A @ B ) )
% 5.41/5.64 | ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.64 & ( ord_less_int @ B @ A ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % mult_less_cancel_right_disj
% 5.41/5.64 thf(fact_1975_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.41/5.64 thf(fact_1976_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.41/5.64 thf(fact_1977_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.64 => ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.41/5.64 thf(fact_1978_linordered__comm__semiring__strict__class_Ocomm__mult__strict__left__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.64 => ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % linordered_comm_semiring_strict_class.comm_mult_strict_left_mono
% 5.41/5.64 thf(fact_1979_pos__add__strict,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_real @ B @ C )
% 5.41/5.64 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % pos_add_strict
% 5.41/5.64 thf(fact_1980_pos__add__strict,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_rat @ B @ C )
% 5.41/5.64 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % pos_add_strict
% 5.41/5.64 thf(fact_1981_pos__add__strict,axiom,
% 5.41/5.64 ! [A: nat,B: nat,C: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ B @ C )
% 5.41/5.64 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % pos_add_strict
% 5.41/5.64 thf(fact_1982_pos__add__strict,axiom,
% 5.41/5.64 ! [A: int,B: int,C: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_int @ B @ C )
% 5.41/5.64 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % pos_add_strict
% 5.41/5.64 thf(fact_1983_canonically__ordered__monoid__add__class_OlessE,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ B )
% 5.41/5.64 => ~ ! [C2: nat] :
% 5.41/5.64 ( ( B
% 5.41/5.64 = ( plus_plus_nat @ A @ C2 ) )
% 5.41/5.64 => ( C2 = zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % canonically_ordered_monoid_add_class.lessE
% 5.41/5.64 thf(fact_1984_add__pos__pos,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_pos_pos
% 5.41/5.64 thf(fact_1985_add__pos__pos,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_pos_pos
% 5.41/5.64 thf(fact_1986_add__pos__pos,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.64 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_pos_pos
% 5.41/5.64 thf(fact_1987_add__pos__pos,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.64 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_pos_pos
% 5.41/5.64 thf(fact_1988_add__neg__neg,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_neg_neg
% 5.41/5.64 thf(fact_1989_add__neg__neg,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_neg_neg
% 5.41/5.64 thf(fact_1990_add__neg__neg,axiom,
% 5.41/5.64 ! [A: nat,B: nat] :
% 5.41/5.64 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.41/5.64 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.41/5.64 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_neg_neg
% 5.41/5.64 thf(fact_1991_add__neg__neg,axiom,
% 5.41/5.64 ! [A: int,B: int] :
% 5.41/5.64 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.64 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_neg_neg
% 5.41/5.64 thf(fact_1992_add__less__zeroD,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.64 | ( ord_less_real @ Y @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_zeroD
% 5.41/5.64 thf(fact_1993_add__less__zeroD,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( plus_plus_rat @ X @ Y ) @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.41/5.64 | ( ord_less_rat @ Y @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_zeroD
% 5.41/5.64 thf(fact_1994_add__less__zeroD,axiom,
% 5.41/5.64 ! [X: int,Y: int] :
% 5.41/5.64 ( ( ord_less_int @ ( plus_plus_int @ X @ Y ) @ zero_zero_int )
% 5.41/5.64 => ( ( ord_less_int @ X @ zero_zero_int )
% 5.41/5.64 | ( ord_less_int @ Y @ zero_zero_int ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % add_less_zeroD
% 5.41/5.64 thf(fact_1995_less__numeral__extra_I1_J,axiom,
% 5.41/5.64 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.41/5.64
% 5.41/5.64 % less_numeral_extra(1)
% 5.41/5.64 thf(fact_1996_less__numeral__extra_I1_J,axiom,
% 5.41/5.64 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.41/5.64
% 5.41/5.64 % less_numeral_extra(1)
% 5.41/5.64 thf(fact_1997_less__numeral__extra_I1_J,axiom,
% 5.41/5.64 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.41/5.64
% 5.41/5.64 % less_numeral_extra(1)
% 5.41/5.64 thf(fact_1998_less__numeral__extra_I1_J,axiom,
% 5.41/5.64 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.41/5.64
% 5.41/5.64 % less_numeral_extra(1)
% 5.41/5.64 thf(fact_1999_zero__less__one,axiom,
% 5.41/5.64 ord_less_real @ zero_zero_real @ one_one_real ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one
% 5.41/5.64 thf(fact_2000_zero__less__one,axiom,
% 5.41/5.64 ord_less_rat @ zero_zero_rat @ one_one_rat ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one
% 5.41/5.64 thf(fact_2001_zero__less__one,axiom,
% 5.41/5.64 ord_less_nat @ zero_zero_nat @ one_one_nat ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one
% 5.41/5.64 thf(fact_2002_zero__less__one,axiom,
% 5.41/5.64 ord_less_int @ zero_zero_int @ one_one_int ).
% 5.41/5.64
% 5.41/5.64 % zero_less_one
% 5.41/5.64 thf(fact_2003_not__one__less__zero,axiom,
% 5.41/5.64 ~ ( ord_less_real @ one_one_real @ zero_zero_real ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_less_zero
% 5.41/5.64 thf(fact_2004_not__one__less__zero,axiom,
% 5.41/5.64 ~ ( ord_less_rat @ one_one_rat @ zero_zero_rat ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_less_zero
% 5.41/5.64 thf(fact_2005_not__one__less__zero,axiom,
% 5.41/5.64 ~ ( ord_less_nat @ one_one_nat @ zero_zero_nat ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_less_zero
% 5.41/5.64 thf(fact_2006_not__one__less__zero,axiom,
% 5.41/5.64 ~ ( ord_less_int @ one_one_int @ zero_zero_int ) ).
% 5.41/5.64
% 5.41/5.64 % not_one_less_zero
% 5.41/5.64 thf(fact_2007_divide__right__mono__neg,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( divide_divide_real @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_right_mono_neg
% 5.41/5.64 thf(fact_2008_divide__right__mono__neg,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( divide_divide_rat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_right_mono_neg
% 5.41/5.64 thf(fact_2009_divide__nonpos__nonpos,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonpos_nonpos
% 5.41/5.64 thf(fact_2010_divide__nonpos__nonpos,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonpos_nonpos
% 5.41/5.64 thf(fact_2011_divide__nonpos__nonneg,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.64 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonpos_nonneg
% 5.41/5.64 thf(fact_2012_divide__nonpos__nonneg,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.64 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonpos_nonneg
% 5.41/5.64 thf(fact_2013_divide__nonneg__nonpos,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.64 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.41/5.64 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonneg_nonpos
% 5.41/5.64 thf(fact_2014_divide__nonneg__nonpos,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.64 => ( ( ord_less_eq_rat @ Y @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonneg_nonpos
% 5.41/5.64 thf(fact_2015_divide__nonneg__nonneg,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonneg_nonneg
% 5.41/5.64 thf(fact_2016_divide__nonneg__nonneg,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_nonneg_nonneg
% 5.41/5.64 thf(fact_2017_zero__le__divide__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_eq_real @ zero_zero_real @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_eq_real @ B @ zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_divide_iff
% 5.41/5.64 thf(fact_2018_zero__le__divide__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_eq_rat @ zero_zero_rat @ B ) )
% 5.41/5.64 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_eq_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_divide_iff
% 5.41/5.64 thf(fact_2019_divide__right__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_right_mono
% 5.41/5.64 thf(fact_2020_divide__right__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_right_mono
% 5.41/5.64 thf(fact_2021_divide__le__0__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.41/5.64 = ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_eq_real @ B @ zero_zero_real ) )
% 5.41/5.64 | ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_eq_real @ zero_zero_real @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_le_0_iff
% 5.41/5.64 thf(fact_2022_divide__le__0__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.41/5.64 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_eq_rat @ B @ zero_zero_rat ) )
% 5.41/5.64 | ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_eq_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_le_0_iff
% 5.41/5.64 thf(fact_2023_divide__neg__neg,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_neg_neg
% 5.41/5.64 thf(fact_2024_divide__neg__neg,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_neg_neg
% 5.41/5.64 thf(fact_2025_divide__neg__pos,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.64 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_neg_pos
% 5.41/5.64 thf(fact_2026_divide__neg__pos,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_rat @ X @ zero_zero_rat )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.64 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_neg_pos
% 5.41/5.64 thf(fact_2027_divide__pos__neg,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.64 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_pos_neg
% 5.41/5.64 thf(fact_2028_divide__pos__neg,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.41/5.64 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_pos_neg
% 5.41/5.64 thf(fact_2029_divide__pos__pos,axiom,
% 5.41/5.64 ! [X: real,Y: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_pos_pos
% 5.41/5.64 thf(fact_2030_divide__pos__pos,axiom,
% 5.41/5.64 ! [X: rat,Y: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_pos_pos
% 5.41/5.64 thf(fact_2031_divide__less__0__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ ( divide_divide_real @ A @ B ) @ zero_zero_real )
% 5.41/5.64 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_real @ B @ zero_zero_real ) )
% 5.41/5.64 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_real @ zero_zero_real @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_less_0_iff
% 5.41/5.64 thf(fact_2032_divide__less__0__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( divide_divide_rat @ A @ B ) @ zero_zero_rat )
% 5.41/5.64 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_rat @ B @ zero_zero_rat ) )
% 5.41/5.64 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_rat @ zero_zero_rat @ B ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_less_0_iff
% 5.41/5.64 thf(fact_2033_divide__less__cancel,axiom,
% 5.41/5.64 ! [A: real,C: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.41/5.64 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_real @ A @ B ) )
% 5.41/5.64 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ B @ A ) )
% 5.41/5.64 & ( C != zero_zero_real ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_less_cancel
% 5.41/5.64 thf(fact_2034_divide__less__cancel,axiom,
% 5.41/5.64 ! [A: rat,C: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.64 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_rat @ A @ B ) )
% 5.41/5.64 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ B @ A ) )
% 5.41/5.64 & ( C != zero_zero_rat ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_less_cancel
% 5.41/5.64 thf(fact_2035_zero__less__divide__iff,axiom,
% 5.41/5.64 ! [A: real,B: real] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 & ( ord_less_real @ zero_zero_real @ B ) )
% 5.41/5.64 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.64 & ( ord_less_real @ B @ zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_divide_iff
% 5.41/5.64 thf(fact_2036_zero__less__divide__iff,axiom,
% 5.41/5.64 ! [A: rat,B: rat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.64 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 & ( ord_less_rat @ zero_zero_rat @ B ) )
% 5.41/5.64 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.64 & ( ord_less_rat @ B @ zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_divide_iff
% 5.41/5.64 thf(fact_2037_divide__strict__right__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.64 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_strict_right_mono
% 5.41/5.64 thf(fact_2038_divide__strict__right__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.64 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_strict_right_mono
% 5.41/5.64 thf(fact_2039_divide__strict__right__mono__neg,axiom,
% 5.41/5.64 ! [B: real,A: real,C: real] :
% 5.41/5.64 ( ( ord_less_real @ B @ A )
% 5.41/5.64 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.64 => ( ord_less_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_strict_right_mono_neg
% 5.41/5.64 thf(fact_2040_divide__strict__right__mono__neg,axiom,
% 5.41/5.64 ! [B: rat,A: rat,C: rat] :
% 5.41/5.64 ( ( ord_less_rat @ B @ A )
% 5.41/5.64 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.64 => ( ord_less_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_strict_right_mono_neg
% 5.41/5.64 thf(fact_2041_zero__le__power,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_power
% 5.41/5.64 thf(fact_2042_zero__le__power,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_power
% 5.41/5.64 thf(fact_2043_zero__le__power,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ord_less_eq_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_power
% 5.41/5.64 thf(fact_2044_zero__le__power,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_le_power
% 5.41/5.64 thf(fact_2045_power__mono,axiom,
% 5.41/5.64 ! [A: real,B: real,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mono
% 5.41/5.64 thf(fact_2046_power__mono,axiom,
% 5.41/5.64 ! [A: rat,B: rat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mono
% 5.41/5.64 thf(fact_2047_power__mono,axiom,
% 5.41/5.64 ! [A: nat,B: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mono
% 5.41/5.64 thf(fact_2048_power__mono,axiom,
% 5.41/5.64 ! [A: int,B: int,N: nat] :
% 5.41/5.64 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.64 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % power_mono
% 5.41/5.64 thf(fact_2049_zero__less__power,axiom,
% 5.41/5.64 ! [A: real,N: nat] :
% 5.41/5.64 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.64 => ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_power
% 5.41/5.64 thf(fact_2050_zero__less__power,axiom,
% 5.41/5.64 ! [A: rat,N: nat] :
% 5.41/5.64 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.64 => ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_power
% 5.41/5.64 thf(fact_2051_zero__less__power,axiom,
% 5.41/5.64 ! [A: nat,N: nat] :
% 5.41/5.64 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.64 => ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_power
% 5.41/5.64 thf(fact_2052_zero__less__power,axiom,
% 5.41/5.64 ! [A: int,N: nat] :
% 5.41/5.64 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.64 => ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % zero_less_power
% 5.41/5.64 thf(fact_2053_frac__eq__eq,axiom,
% 5.41/5.64 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.41/5.64 ( ( Y != zero_zero_complex )
% 5.41/5.64 => ( ( Z != zero_zero_complex )
% 5.41/5.64 => ( ( ( divide1717551699836669952omplex @ X @ Y )
% 5.41/5.64 = ( divide1717551699836669952omplex @ W @ Z ) )
% 5.41/5.64 = ( ( times_times_complex @ X @ Z )
% 5.41/5.64 = ( times_times_complex @ W @ Y ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % frac_eq_eq
% 5.41/5.64 thf(fact_2054_frac__eq__eq,axiom,
% 5.41/5.64 ! [Y: real,Z: real,X: real,W: real] :
% 5.41/5.64 ( ( Y != zero_zero_real )
% 5.41/5.64 => ( ( Z != zero_zero_real )
% 5.41/5.64 => ( ( ( divide_divide_real @ X @ Y )
% 5.41/5.64 = ( divide_divide_real @ W @ Z ) )
% 5.41/5.64 = ( ( times_times_real @ X @ Z )
% 5.41/5.64 = ( times_times_real @ W @ Y ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % frac_eq_eq
% 5.41/5.64 thf(fact_2055_frac__eq__eq,axiom,
% 5.41/5.64 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.41/5.64 ( ( Y != zero_zero_rat )
% 5.41/5.64 => ( ( Z != zero_zero_rat )
% 5.41/5.64 => ( ( ( divide_divide_rat @ X @ Y )
% 5.41/5.64 = ( divide_divide_rat @ W @ Z ) )
% 5.41/5.64 = ( ( times_times_rat @ X @ Z )
% 5.41/5.64 = ( times_times_rat @ W @ Y ) ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % frac_eq_eq
% 5.41/5.64 thf(fact_2056_divide__eq__eq,axiom,
% 5.41/5.64 ! [B: complex,C: complex,A: complex] :
% 5.41/5.64 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.41/5.64 = A )
% 5.41/5.64 = ( ( ( C != zero_zero_complex )
% 5.41/5.64 => ( B
% 5.41/5.64 = ( times_times_complex @ A @ C ) ) )
% 5.41/5.64 & ( ( C = zero_zero_complex )
% 5.41/5.64 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_eq_eq
% 5.41/5.64 thf(fact_2057_divide__eq__eq,axiom,
% 5.41/5.64 ! [B: real,C: real,A: real] :
% 5.41/5.64 ( ( ( divide_divide_real @ B @ C )
% 5.41/5.64 = A )
% 5.41/5.64 = ( ( ( C != zero_zero_real )
% 5.41/5.64 => ( B
% 5.41/5.64 = ( times_times_real @ A @ C ) ) )
% 5.41/5.64 & ( ( C = zero_zero_real )
% 5.41/5.64 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_eq_eq
% 5.41/5.64 thf(fact_2058_divide__eq__eq,axiom,
% 5.41/5.64 ! [B: rat,C: rat,A: rat] :
% 5.41/5.64 ( ( ( divide_divide_rat @ B @ C )
% 5.41/5.64 = A )
% 5.41/5.64 = ( ( ( C != zero_zero_rat )
% 5.41/5.64 => ( B
% 5.41/5.64 = ( times_times_rat @ A @ C ) ) )
% 5.41/5.64 & ( ( C = zero_zero_rat )
% 5.41/5.64 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_eq_eq
% 5.41/5.64 thf(fact_2059_eq__divide__eq,axiom,
% 5.41/5.64 ! [A: complex,B: complex,C: complex] :
% 5.41/5.64 ( ( A
% 5.41/5.64 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.64 = ( ( ( C != zero_zero_complex )
% 5.41/5.64 => ( ( times_times_complex @ A @ C )
% 5.41/5.64 = B ) )
% 5.41/5.64 & ( ( C = zero_zero_complex )
% 5.41/5.64 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_divide_eq
% 5.41/5.64 thf(fact_2060_eq__divide__eq,axiom,
% 5.41/5.64 ! [A: real,B: real,C: real] :
% 5.41/5.64 ( ( A
% 5.41/5.64 = ( divide_divide_real @ B @ C ) )
% 5.41/5.64 = ( ( ( C != zero_zero_real )
% 5.41/5.64 => ( ( times_times_real @ A @ C )
% 5.41/5.64 = B ) )
% 5.41/5.64 & ( ( C = zero_zero_real )
% 5.41/5.64 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_divide_eq
% 5.41/5.64 thf(fact_2061_eq__divide__eq,axiom,
% 5.41/5.64 ! [A: rat,B: rat,C: rat] :
% 5.41/5.64 ( ( A
% 5.41/5.64 = ( divide_divide_rat @ B @ C ) )
% 5.41/5.64 = ( ( ( C != zero_zero_rat )
% 5.41/5.64 => ( ( times_times_rat @ A @ C )
% 5.41/5.64 = B ) )
% 5.41/5.64 & ( ( C = zero_zero_rat )
% 5.41/5.64 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_divide_eq
% 5.41/5.64 thf(fact_2062_divide__eq__imp,axiom,
% 5.41/5.64 ! [C: complex,B: complex,A: complex] :
% 5.41/5.64 ( ( C != zero_zero_complex )
% 5.41/5.64 => ( ( B
% 5.41/5.64 = ( times_times_complex @ A @ C ) )
% 5.41/5.64 => ( ( divide1717551699836669952omplex @ B @ C )
% 5.41/5.64 = A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_eq_imp
% 5.41/5.64 thf(fact_2063_divide__eq__imp,axiom,
% 5.41/5.64 ! [C: real,B: real,A: real] :
% 5.41/5.64 ( ( C != zero_zero_real )
% 5.41/5.64 => ( ( B
% 5.41/5.64 = ( times_times_real @ A @ C ) )
% 5.41/5.64 => ( ( divide_divide_real @ B @ C )
% 5.41/5.64 = A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_eq_imp
% 5.41/5.64 thf(fact_2064_divide__eq__imp,axiom,
% 5.41/5.64 ! [C: rat,B: rat,A: rat] :
% 5.41/5.64 ( ( C != zero_zero_rat )
% 5.41/5.64 => ( ( B
% 5.41/5.64 = ( times_times_rat @ A @ C ) )
% 5.41/5.64 => ( ( divide_divide_rat @ B @ C )
% 5.41/5.64 = A ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % divide_eq_imp
% 5.41/5.64 thf(fact_2065_eq__divide__imp,axiom,
% 5.41/5.64 ! [C: complex,A: complex,B: complex] :
% 5.41/5.64 ( ( C != zero_zero_complex )
% 5.41/5.64 => ( ( ( times_times_complex @ A @ C )
% 5.41/5.64 = B )
% 5.41/5.64 => ( A
% 5.41/5.64 = ( divide1717551699836669952omplex @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_divide_imp
% 5.41/5.64 thf(fact_2066_eq__divide__imp,axiom,
% 5.41/5.64 ! [C: real,A: real,B: real] :
% 5.41/5.64 ( ( C != zero_zero_real )
% 5.41/5.64 => ( ( ( times_times_real @ A @ C )
% 5.41/5.64 = B )
% 5.41/5.64 => ( A
% 5.41/5.64 = ( divide_divide_real @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_divide_imp
% 5.41/5.64 thf(fact_2067_eq__divide__imp,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B: rat] :
% 5.41/5.64 ( ( C != zero_zero_rat )
% 5.41/5.64 => ( ( ( times_times_rat @ A @ C )
% 5.41/5.64 = B )
% 5.41/5.64 => ( A
% 5.41/5.64 = ( divide_divide_rat @ B @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % eq_divide_imp
% 5.41/5.64 thf(fact_2068_nonzero__divide__eq__eq,axiom,
% 5.41/5.64 ! [C: complex,B: complex,A: complex] :
% 5.41/5.64 ( ( C != zero_zero_complex )
% 5.41/5.64 => ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.41/5.64 = A )
% 5.41/5.64 = ( B
% 5.41/5.64 = ( times_times_complex @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nonzero_divide_eq_eq
% 5.41/5.64 thf(fact_2069_nonzero__divide__eq__eq,axiom,
% 5.41/5.64 ! [C: real,B: real,A: real] :
% 5.41/5.64 ( ( C != zero_zero_real )
% 5.41/5.64 => ( ( ( divide_divide_real @ B @ C )
% 5.41/5.64 = A )
% 5.41/5.64 = ( B
% 5.41/5.64 = ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nonzero_divide_eq_eq
% 5.41/5.64 thf(fact_2070_nonzero__divide__eq__eq,axiom,
% 5.41/5.64 ! [C: rat,B: rat,A: rat] :
% 5.41/5.64 ( ( C != zero_zero_rat )
% 5.41/5.64 => ( ( ( divide_divide_rat @ B @ C )
% 5.41/5.64 = A )
% 5.41/5.64 = ( B
% 5.41/5.64 = ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nonzero_divide_eq_eq
% 5.41/5.64 thf(fact_2071_nonzero__eq__divide__eq,axiom,
% 5.41/5.64 ! [C: complex,A: complex,B: complex] :
% 5.41/5.64 ( ( C != zero_zero_complex )
% 5.41/5.64 => ( ( A
% 5.41/5.64 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.64 = ( ( times_times_complex @ A @ C )
% 5.41/5.64 = B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nonzero_eq_divide_eq
% 5.41/5.64 thf(fact_2072_nonzero__eq__divide__eq,axiom,
% 5.41/5.64 ! [C: real,A: real,B: real] :
% 5.41/5.64 ( ( C != zero_zero_real )
% 5.41/5.64 => ( ( A
% 5.41/5.64 = ( divide_divide_real @ B @ C ) )
% 5.41/5.64 = ( ( times_times_real @ A @ C )
% 5.41/5.64 = B ) ) ) ).
% 5.41/5.64
% 5.41/5.64 % nonzero_eq_divide_eq
% 5.41/5.64 thf(fact_2073_nonzero__eq__divide__eq,axiom,
% 5.41/5.64 ! [C: rat,A: rat,B: rat] :
% 5.41/5.64 ( ( C != zero_zero_rat )
% 5.41/5.64 => ( ( A
% 5.41/5.65 = ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ( times_times_rat @ A @ C )
% 5.41/5.65 = B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nonzero_eq_divide_eq
% 5.41/5.65 thf(fact_2074_right__inverse__eq,axiom,
% 5.41/5.65 ! [B: complex,A: complex] :
% 5.41/5.65 ( ( B != zero_zero_complex )
% 5.41/5.65 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.41/5.65 = one_one_complex )
% 5.41/5.65 = ( A = B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % right_inverse_eq
% 5.41/5.65 thf(fact_2075_right__inverse__eq,axiom,
% 5.41/5.65 ! [B: real,A: real] :
% 5.41/5.65 ( ( B != zero_zero_real )
% 5.41/5.65 => ( ( ( divide_divide_real @ A @ B )
% 5.41/5.65 = one_one_real )
% 5.41/5.65 = ( A = B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % right_inverse_eq
% 5.41/5.65 thf(fact_2076_right__inverse__eq,axiom,
% 5.41/5.65 ! [B: rat,A: rat] :
% 5.41/5.65 ( ( B != zero_zero_rat )
% 5.41/5.65 => ( ( ( divide_divide_rat @ A @ B )
% 5.41/5.65 = one_one_rat )
% 5.41/5.65 = ( A = B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % right_inverse_eq
% 5.41/5.65 thf(fact_2077_not__exp__less__eq__0__int,axiom,
% 5.41/5.65 ! [N: nat] :
% 5.41/5.65 ~ ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ zero_zero_int ) ).
% 5.41/5.65
% 5.41/5.65 % not_exp_less_eq_0_int
% 5.41/5.65 thf(fact_2078_power__0,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( power_power_rat @ A @ zero_zero_nat )
% 5.41/5.65 = one_one_rat ) ).
% 5.41/5.65
% 5.41/5.65 % power_0
% 5.41/5.65 thf(fact_2079_power__0,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( power_power_nat @ A @ zero_zero_nat )
% 5.41/5.65 = one_one_nat ) ).
% 5.41/5.65
% 5.41/5.65 % power_0
% 5.41/5.65 thf(fact_2080_power__0,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( power_power_real @ A @ zero_zero_nat )
% 5.41/5.65 = one_one_real ) ).
% 5.41/5.65
% 5.41/5.65 % power_0
% 5.41/5.65 thf(fact_2081_power__0,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( power_power_int @ A @ zero_zero_nat )
% 5.41/5.65 = one_one_int ) ).
% 5.41/5.65
% 5.41/5.65 % power_0
% 5.41/5.65 thf(fact_2082_power__0,axiom,
% 5.41/5.65 ! [A: complex] :
% 5.41/5.65 ( ( power_power_complex @ A @ zero_zero_nat )
% 5.41/5.65 = one_one_complex ) ).
% 5.41/5.65
% 5.41/5.65 % power_0
% 5.41/5.65 thf(fact_2083_divmod__digit__0_I1_J,axiom,
% 5.41/5.65 ! [B: nat,A: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.65 => ( ( ord_less_nat @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.65 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.65 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_0(1)
% 5.41/5.65 thf(fact_2084_divmod__digit__0_I1_J,axiom,
% 5.41/5.65 ! [B: int,A: int] :
% 5.41/5.65 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.65 => ( ( ord_less_int @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.65 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.65 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_0(1)
% 5.41/5.65 thf(fact_2085_divmod__digit__0_I1_J,axiom,
% 5.41/5.65 ! [B: code_integer,A: code_integer] :
% 5.41/5.65 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.65 => ( ( ord_le6747313008572928689nteger @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) @ B )
% 5.41/5.65 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.65 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_0(1)
% 5.41/5.65 thf(fact_2086_ex__least__nat__le,axiom,
% 5.41/5.65 ! [P: nat > $o,N: nat] :
% 5.41/5.65 ( ( P @ N )
% 5.41/5.65 => ( ~ ( P @ zero_zero_nat )
% 5.41/5.65 => ? [K3: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ K3 @ N )
% 5.41/5.65 & ! [I2: nat] :
% 5.41/5.65 ( ( ord_less_nat @ I2 @ K3 )
% 5.41/5.65 => ~ ( P @ I2 ) )
% 5.41/5.65 & ( P @ K3 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ex_least_nat_le
% 5.41/5.65 thf(fact_2087_less__imp__add__positive,axiom,
% 5.41/5.65 ! [I: nat,J: nat] :
% 5.41/5.65 ( ( ord_less_nat @ I @ J )
% 5.41/5.65 => ? [K3: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ K3 )
% 5.41/5.65 & ( ( plus_plus_nat @ I @ K3 )
% 5.41/5.65 = J ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_imp_add_positive
% 5.41/5.65 thf(fact_2088_mult__less__mono1,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat] :
% 5.41/5.65 ( ( ord_less_nat @ I @ J )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.65 => ( ord_less_nat @ ( times_times_nat @ I @ K ) @ ( times_times_nat @ J @ K ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_mono1
% 5.41/5.65 thf(fact_2089_mult__less__mono2,axiom,
% 5.41/5.65 ! [I: nat,J: nat,K: nat] :
% 5.41/5.65 ( ( ord_less_nat @ I @ J )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.65 => ( ord_less_nat @ ( times_times_nat @ K @ I ) @ ( times_times_nat @ K @ J ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_mono2
% 5.41/5.65 thf(fact_2090_nat__mult__less__cancel1,axiom,
% 5.41/5.65 ! [K: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.65 => ( ( ord_less_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.65 = ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_mult_less_cancel1
% 5.41/5.65 thf(fact_2091_nat__mult__eq__cancel1,axiom,
% 5.41/5.65 ! [K: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.65 => ( ( ( times_times_nat @ K @ M )
% 5.41/5.65 = ( times_times_nat @ K @ N ) )
% 5.41/5.65 = ( M = N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_mult_eq_cancel1
% 5.41/5.65 thf(fact_2092_Euclidean__Division_Odiv__eq__0__iff,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( ( divide_divide_nat @ M @ N )
% 5.41/5.65 = zero_zero_nat )
% 5.41/5.65 = ( ( ord_less_nat @ M @ N )
% 5.41/5.65 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % Euclidean_Division.div_eq_0_iff
% 5.41/5.65 thf(fact_2093_nat__power__less__imp__less,axiom,
% 5.41/5.65 ! [I: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ I )
% 5.41/5.65 => ( ( ord_less_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.41/5.65 => ( ord_less_nat @ M @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_power_less_imp_less
% 5.41/5.65 thf(fact_2094_bits__stable__imp__add__self,axiom,
% 5.41/5.65 ! [A: nat] :
% 5.41/5.65 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = A )
% 5.41/5.65 => ( ( plus_plus_nat @ A @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 = zero_zero_nat ) ) ).
% 5.41/5.65
% 5.41/5.65 % bits_stable_imp_add_self
% 5.41/5.65 thf(fact_2095_bits__stable__imp__add__self,axiom,
% 5.41/5.65 ! [A: int] :
% 5.41/5.65 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.65 = A )
% 5.41/5.65 => ( ( plus_plus_int @ A @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.41/5.65 = zero_zero_int ) ) ).
% 5.41/5.65
% 5.41/5.65 % bits_stable_imp_add_self
% 5.41/5.65 thf(fact_2096_bits__stable__imp__add__self,axiom,
% 5.41/5.65 ! [A: code_integer] :
% 5.41/5.65 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.65 = A )
% 5.41/5.65 => ( ( plus_p5714425477246183910nteger @ A @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.41/5.65 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.65
% 5.41/5.65 % bits_stable_imp_add_self
% 5.41/5.65 thf(fact_2097_mult__eq__self__implies__10,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( M
% 5.41/5.65 = ( times_times_nat @ M @ N ) )
% 5.41/5.65 => ( ( N = one_one_nat )
% 5.41/5.65 | ( M = zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_eq_self_implies_10
% 5.41/5.65 thf(fact_2098_pow_Osimps_I1_J,axiom,
% 5.41/5.65 ! [X: num] :
% 5.41/5.65 ( ( pow @ X @ one )
% 5.41/5.65 = X ) ).
% 5.41/5.65
% 5.41/5.65 % pow.simps(1)
% 5.41/5.65 thf(fact_2099_mod__double__modulus,axiom,
% 5.41/5.65 ! [M: code_integer,X: code_integer] :
% 5.41/5.65 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ M )
% 5.41/5.65 => ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.41/5.65 => ( ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.65 = ( modulo364778990260209775nteger @ X @ M ) )
% 5.41/5.65 | ( ( modulo364778990260209775nteger @ X @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ X @ M ) @ M ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_double_modulus
% 5.41/5.65 thf(fact_2100_mod__double__modulus,axiom,
% 5.41/5.65 ! [M: nat,X: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.41/5.65 => ( ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.65 = ( modulo_modulo_nat @ X @ M ) )
% 5.41/5.65 | ( ( modulo_modulo_nat @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.65 = ( plus_plus_nat @ ( modulo_modulo_nat @ X @ M ) @ M ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_double_modulus
% 5.41/5.65 thf(fact_2101_mod__double__modulus,axiom,
% 5.41/5.65 ! [M: int,X: int] :
% 5.41/5.65 ( ( ord_less_int @ zero_zero_int @ M )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.65 => ( ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.65 = ( modulo_modulo_int @ X @ M ) )
% 5.41/5.65 | ( ( modulo_modulo_int @ X @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.65 = ( plus_plus_int @ ( modulo_modulo_int @ X @ M ) @ M ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_double_modulus
% 5.41/5.65 thf(fact_2102_mult__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,A: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ( ( modulo_modulo_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.65 = ( times_times_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_exp_mod_exp_eq
% 5.41/5.65 thf(fact_2103_mult__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,A: int] :
% 5.41/5.65 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ( ( modulo_modulo_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.65 = ( times_times_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_exp_mod_exp_eq
% 5.41/5.65 thf(fact_2104_mult__exp__mod__exp__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,A: code_integer] :
% 5.41/5.65 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ( ( modulo364778990260209775nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.65 = ( times_3573771949741848930nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_exp_mod_exp_eq
% 5.41/5.65 thf(fact_2105_div__mult1__eq,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat] :
% 5.41/5.65 ( ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( modulo_modulo_nat @ B @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult1_eq
% 5.41/5.65 thf(fact_2106_div__mult1__eq,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int] :
% 5.41/5.65 ( ( divide_divide_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.65 = ( plus_plus_int @ ( times_times_int @ A @ ( divide_divide_int @ B @ C ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( modulo_modulo_int @ B @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult1_eq
% 5.41/5.65 thf(fact_2107_div__mult1__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.65 ( ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( modulo364778990260209775nteger @ B @ C ) ) @ C ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult1_eq
% 5.41/5.65 thf(fact_2108_mult__div__mod__eq,axiom,
% 5.41/5.65 ! [B: nat,A: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult_div_mod_eq
% 5.41/5.65 thf(fact_2109_mult__div__mod__eq,axiom,
% 5.41/5.65 ! [B: int,A: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult_div_mod_eq
% 5.41/5.65 thf(fact_2110_mult__div__mod__eq,axiom,
% 5.41/5.65 ! [B: code_integer,A: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mult_div_mod_eq
% 5.41/5.65 thf(fact_2111_mod__mult__div__eq,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_div_eq
% 5.41/5.65 thf(fact_2112_mod__mult__div__eq,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_div_eq
% 5.41/5.65 thf(fact_2113_mod__mult__div__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult_div_eq
% 5.41/5.65 thf(fact_2114_mod__div__mult__eq,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( modulo_modulo_nat @ A @ B ) @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_mult_eq
% 5.41/5.65 thf(fact_2115_mod__div__mult__eq,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( modulo_modulo_int @ A @ B ) @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_mult_eq
% 5.41/5.65 thf(fact_2116_mod__div__mult__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ B ) @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_mult_eq
% 5.41/5.65 thf(fact_2117_div__mult__mod__eq,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult_mod_eq
% 5.41/5.65 thf(fact_2118_div__mult__mod__eq,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult_mod_eq
% 5.41/5.65 thf(fact_2119_div__mult__mod__eq,axiom,
% 5.41/5.65 ! [A: code_integer,B: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.41/5.65 = A ) ).
% 5.41/5.65
% 5.41/5.65 % div_mult_mod_eq
% 5.41/5.65 thf(fact_2120_mod__div__decomp,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( A
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_decomp
% 5.41/5.65 thf(fact_2121_mod__div__decomp,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( A
% 5.41/5.65 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_decomp
% 5.41/5.65 thf(fact_2122_mod__div__decomp,axiom,
% 5.41/5.65 ! [A: code_integer,B: code_integer] :
% 5.41/5.65 ( A
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_div_decomp
% 5.41/5.65 thf(fact_2123_cancel__div__mod__rules_I1_J,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ B ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(1)
% 5.41/5.65 thf(fact_2124_cancel__div__mod__rules_I1_J,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A @ B ) @ B ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.41/5.65 = ( plus_plus_int @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(1)
% 5.41/5.65 thf(fact_2125_cancel__div__mod__rules_I1_J,axiom,
% 5.41/5.65 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ B ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(1)
% 5.41/5.65 thf(fact_2126_cancel__div__mod__rules_I2_J,axiom,
% 5.41/5.65 ! [B: nat,A: nat,C: nat] :
% 5.41/5.65 ( ( plus_plus_nat @ ( plus_plus_nat @ ( times_times_nat @ B @ ( divide_divide_nat @ A @ B ) ) @ ( modulo_modulo_nat @ A @ B ) ) @ C )
% 5.41/5.65 = ( plus_plus_nat @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(2)
% 5.41/5.65 thf(fact_2127_cancel__div__mod__rules_I2_J,axiom,
% 5.41/5.65 ! [B: int,A: int,C: int] :
% 5.41/5.65 ( ( plus_plus_int @ ( plus_plus_int @ ( times_times_int @ B @ ( divide_divide_int @ A @ B ) ) @ ( modulo_modulo_int @ A @ B ) ) @ C )
% 5.41/5.65 = ( plus_plus_int @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(2)
% 5.41/5.65 thf(fact_2128_cancel__div__mod__rules_I2_J,axiom,
% 5.41/5.65 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.65 ( ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ A @ B ) ) @ ( modulo364778990260209775nteger @ A @ B ) ) @ C )
% 5.41/5.65 = ( plus_p5714425477246183910nteger @ A @ C ) ) ).
% 5.41/5.65
% 5.41/5.65 % cancel_div_mod_rules(2)
% 5.41/5.65 thf(fact_2129_ordered__ring__class_Ole__add__iff1,axiom,
% 5.41/5.65 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_ring_class.le_add_iff1
% 5.41/5.65 thf(fact_2130_ordered__ring__class_Ole__add__iff1,axiom,
% 5.41/5.65 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_ring_class.le_add_iff1
% 5.41/5.65 thf(fact_2131_ordered__ring__class_Ole__add__iff1,axiom,
% 5.41/5.65 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_ring_class.le_add_iff1
% 5.41/5.65 thf(fact_2132_ordered__ring__class_Ole__add__iff2,axiom,
% 5.41/5.65 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_eq_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_ring_class.le_add_iff2
% 5.41/5.65 thf(fact_2133_ordered__ring__class_Ole__add__iff2,axiom,
% 5.41/5.65 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_eq_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_ring_class.le_add_iff2
% 5.41/5.65 thf(fact_2134_ordered__ring__class_Ole__add__iff2,axiom,
% 5.41/5.65 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_eq_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % ordered_ring_class.le_add_iff2
% 5.41/5.65 thf(fact_2135_less__add__iff2,axiom,
% 5.41/5.65 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.41/5.65 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_real @ C @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_add_iff2
% 5.41/5.65 thf(fact_2136_less__add__iff2,axiom,
% 5.41/5.65 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_rat @ C @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_add_iff2
% 5.41/5.65 thf(fact_2137_less__add__iff2,axiom,
% 5.41/5.65 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.41/5.65 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_int @ C @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ B @ A ) @ E ) @ D ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_add_iff2
% 5.41/5.65 thf(fact_2138_less__add__iff1,axiom,
% 5.41/5.65 ! [A: real,E: real,C: real,B: real,D: real] :
% 5.41/5.65 ( ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ A @ E ) @ C ) @ ( plus_plus_real @ ( times_times_real @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ ( minus_minus_real @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_add_iff1
% 5.41/5.65 thf(fact_2139_less__add__iff1,axiom,
% 5.41/5.65 ! [A: rat,E: rat,C: rat,B: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ E ) @ C ) @ ( plus_plus_rat @ ( times_times_rat @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ ( minus_minus_rat @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_add_iff1
% 5.41/5.65 thf(fact_2140_less__add__iff1,axiom,
% 5.41/5.65 ! [A: int,E: int,C: int,B: int,D: int] :
% 5.41/5.65 ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ A @ E ) @ C ) @ ( plus_plus_int @ ( times_times_int @ B @ E ) @ D ) )
% 5.41/5.65 = ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ ( minus_minus_int @ A @ B ) @ E ) @ C ) @ D ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_add_iff1
% 5.41/5.65 thf(fact_2141_square__diff__one__factored,axiom,
% 5.41/5.65 ! [X: complex] :
% 5.41/5.65 ( ( minus_minus_complex @ ( times_times_complex @ X @ X ) @ one_one_complex )
% 5.41/5.65 = ( times_times_complex @ ( plus_plus_complex @ X @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % square_diff_one_factored
% 5.41/5.65 thf(fact_2142_square__diff__one__factored,axiom,
% 5.41/5.65 ! [X: real] :
% 5.41/5.65 ( ( minus_minus_real @ ( times_times_real @ X @ X ) @ one_one_real )
% 5.41/5.65 = ( times_times_real @ ( plus_plus_real @ X @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % square_diff_one_factored
% 5.41/5.65 thf(fact_2143_square__diff__one__factored,axiom,
% 5.41/5.65 ! [X: rat] :
% 5.41/5.65 ( ( minus_minus_rat @ ( times_times_rat @ X @ X ) @ one_one_rat )
% 5.41/5.65 = ( times_times_rat @ ( plus_plus_rat @ X @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % square_diff_one_factored
% 5.41/5.65 thf(fact_2144_square__diff__one__factored,axiom,
% 5.41/5.65 ! [X: int] :
% 5.41/5.65 ( ( minus_minus_int @ ( times_times_int @ X @ X ) @ one_one_int )
% 5.41/5.65 = ( times_times_int @ ( plus_plus_int @ X @ one_one_int ) @ ( minus_minus_int @ X @ one_one_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % square_diff_one_factored
% 5.41/5.65 thf(fact_2145_mod__mult2__eq,axiom,
% 5.41/5.65 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.65 ( ( modulo_modulo_nat @ M @ ( times_times_nat @ N @ Q2 ) )
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ N @ ( modulo_modulo_nat @ ( divide_divide_nat @ M @ N ) @ Q2 ) ) @ ( modulo_modulo_nat @ M @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mod_mult2_eq
% 5.41/5.65 thf(fact_2146_less__diff__conv2,axiom,
% 5.41/5.65 ! [K: nat,J: nat,I: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.65 => ( ( ord_less_nat @ ( minus_minus_nat @ J @ K ) @ I )
% 5.41/5.65 = ( ord_less_nat @ J @ ( plus_plus_nat @ I @ K ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_diff_conv2
% 5.41/5.65 thf(fact_2147_nat__eq__add__iff1,axiom,
% 5.41/5.65 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.65 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M )
% 5.41/5.65 = N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_eq_add_iff1
% 5.41/5.65 thf(fact_2148_nat__eq__add__iff2,axiom,
% 5.41/5.65 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.65 => ( ( ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M )
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( M
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_eq_add_iff2
% 5.41/5.65 thf(fact_2149_nat__le__add__iff1,axiom,
% 5.41/5.65 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.65 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_le_add_iff1
% 5.41/5.65 thf(fact_2150_nat__le__add__iff2,axiom,
% 5.41/5.65 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.65 => ( ( ord_less_eq_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( ord_less_eq_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_le_add_iff2
% 5.41/5.65 thf(fact_2151_nat__diff__add__eq1,axiom,
% 5.41/5.65 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.65 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_diff_add_eq1
% 5.41/5.65 thf(fact_2152_nat__diff__add__eq2,axiom,
% 5.41/5.65 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.65 => ( ( minus_minus_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( minus_minus_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_diff_add_eq2
% 5.41/5.65 thf(fact_2153_mult__less__le__imp__less,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B )
% 5.41/5.65 => ( ( ord_less_eq_real @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_le_imp_less
% 5.41/5.65 thf(fact_2154_mult__less__le__imp__less,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B )
% 5.41/5.65 => ( ( ord_less_eq_rat @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_le_imp_less
% 5.41/5.65 thf(fact_2155_mult__less__le__imp__less,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ B )
% 5.41/5.65 => ( ( ord_less_eq_nat @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_le_imp_less
% 5.41/5.65 thf(fact_2156_mult__less__le__imp__less,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B )
% 5.41/5.65 => ( ( ord_less_eq_int @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_le_imp_less
% 5.41/5.65 thf(fact_2157_mult__le__less__imp__less,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.65 => ( ( ord_less_real @ C @ D )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_less_imp_less
% 5.41/5.65 thf(fact_2158_mult__le__less__imp__less,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.65 => ( ( ord_less_rat @ C @ D )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_less_imp_less
% 5.41/5.65 thf(fact_2159_mult__le__less__imp__less,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.65 => ( ( ord_less_nat @ C @ D )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_less_imp_less
% 5.41/5.65 thf(fact_2160_mult__le__less__imp__less,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.65 => ( ( ord_less_int @ C @ D )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_less_imp_less
% 5.41/5.65 thf(fact_2161_mult__right__le__imp__le,axiom,
% 5.41/5.65 ! [A: real,C: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_le_imp_le
% 5.41/5.65 thf(fact_2162_mult__right__le__imp__le,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_le_imp_le
% 5.41/5.65 thf(fact_2163_mult__right__le__imp__le,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_le_imp_le
% 5.41/5.65 thf(fact_2164_mult__right__le__imp__le,axiom,
% 5.41/5.65 ! [A: int,C: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_le_imp_le
% 5.41/5.65 thf(fact_2165_mult__left__le__imp__le,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le_imp_le
% 5.41/5.65 thf(fact_2166_mult__left__le__imp__le,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le_imp_le
% 5.41/5.65 thf(fact_2167_mult__left__le__imp__le,axiom,
% 5.41/5.65 ! [C: nat,A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le_imp_le
% 5.41/5.65 thf(fact_2168_mult__left__le__imp__le,axiom,
% 5.41/5.65 ! [C: int,A: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le_imp_le
% 5.41/5.65 thf(fact_2169_mult__le__cancel__left__pos,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.65 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left_pos
% 5.41/5.65 thf(fact_2170_mult__le__cancel__left__pos,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 = ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left_pos
% 5.41/5.65 thf(fact_2171_mult__le__cancel__left__pos,axiom,
% 5.41/5.65 ! [C: int,A: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.65 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left_pos
% 5.41/5.65 thf(fact_2172_mult__le__cancel__left__neg,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.65 = ( ord_less_eq_real @ B @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left_neg
% 5.41/5.65 thf(fact_2173_mult__le__cancel__left__neg,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 = ( ord_less_eq_rat @ B @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left_neg
% 5.41/5.65 thf(fact_2174_mult__le__cancel__left__neg,axiom,
% 5.41/5.65 ! [C: int,A: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.65 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left_neg
% 5.41/5.65 thf(fact_2175_mult__less__cancel__right,axiom,
% 5.41/5.65 ! [A: real,C: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right
% 5.41/5.65 thf(fact_2176_mult__less__cancel__right,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right
% 5.41/5.65 thf(fact_2177_mult__less__cancel__right,axiom,
% 5.41/5.65 ! [A: int,C: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right
% 5.41/5.65 thf(fact_2178_mult__strict__mono_H,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B )
% 5.41/5.65 => ( ( ord_less_real @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono'
% 5.41/5.65 thf(fact_2179_mult__strict__mono_H,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B )
% 5.41/5.65 => ( ( ord_less_rat @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono'
% 5.41/5.65 thf(fact_2180_mult__strict__mono_H,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ B )
% 5.41/5.65 => ( ( ord_less_nat @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono'
% 5.41/5.65 thf(fact_2181_mult__strict__mono_H,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B )
% 5.41/5.65 => ( ( ord_less_int @ C @ D )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono'
% 5.41/5.65 thf(fact_2182_mult__right__less__imp__less,axiom,
% 5.41/5.65 ! [A: real,C: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_less_imp_less
% 5.41/5.65 thf(fact_2183_mult__right__less__imp__less,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_less_imp_less
% 5.41/5.65 thf(fact_2184_mult__right__less__imp__less,axiom,
% 5.41/5.65 ! [A: nat,C: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_less_imp_less
% 5.41/5.65 thf(fact_2185_mult__right__less__imp__less,axiom,
% 5.41/5.65 ! [A: int,C: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_less_imp_less
% 5.41/5.65 thf(fact_2186_mult__less__cancel__left,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left
% 5.41/5.65 thf(fact_2187_mult__less__cancel__left,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left
% 5.41/5.65 thf(fact_2188_mult__less__cancel__left,axiom,
% 5.41/5.65 ! [C: int,A: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left
% 5.41/5.65 thf(fact_2189_mult__strict__mono,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B )
% 5.41/5.65 => ( ( ord_less_real @ C @ D )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono
% 5.41/5.65 thf(fact_2190_mult__strict__mono,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B )
% 5.41/5.65 => ( ( ord_less_rat @ C @ D )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono
% 5.41/5.65 thf(fact_2191_mult__strict__mono,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ B )
% 5.41/5.65 => ( ( ord_less_nat @ C @ D )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono
% 5.41/5.65 thf(fact_2192_mult__strict__mono,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ B )
% 5.41/5.65 => ( ( ord_less_int @ C @ D )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_strict_mono
% 5.41/5.65 thf(fact_2193_mult__left__less__imp__less,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_less_imp_less
% 5.41/5.65 thf(fact_2194_mult__left__less__imp__less,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_less_imp_less
% 5.41/5.65 thf(fact_2195_mult__left__less__imp__less,axiom,
% 5.41/5.65 ! [C: nat,A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_nat @ ( times_times_nat @ C @ A ) @ ( times_times_nat @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ C )
% 5.41/5.65 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_less_imp_less
% 5.41/5.65 thf(fact_2196_mult__left__less__imp__less,axiom,
% 5.41/5.65 ! [C: int,A: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_less_imp_less
% 5.41/5.65 thf(fact_2197_mult__le__cancel__right,axiom,
% 5.41/5.65 ! [A: real,C: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right
% 5.41/5.65 thf(fact_2198_mult__le__cancel__right,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right
% 5.41/5.65 thf(fact_2199_mult__le__cancel__right,axiom,
% 5.41/5.65 ! [A: int,C: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right
% 5.41/5.65 thf(fact_2200_mult__le__cancel__left,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left
% 5.41/5.65 thf(fact_2201_mult__le__cancel__left,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left
% 5.41/5.65 thf(fact_2202_mult__le__cancel__left,axiom,
% 5.41/5.65 ! [C: int,A: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_eq_int @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left
% 5.41/5.65 thf(fact_2203_add__strict__increasing2,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_real @ B @ C )
% 5.41/5.65 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing2
% 5.41/5.65 thf(fact_2204_add__strict__increasing2,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_rat @ B @ C )
% 5.41/5.65 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing2
% 5.41/5.65 thf(fact_2205_add__strict__increasing2,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ B @ C )
% 5.41/5.65 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing2
% 5.41/5.65 thf(fact_2206_add__strict__increasing2,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_int @ B @ C )
% 5.41/5.65 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing2
% 5.41/5.65 thf(fact_2207_add__strict__increasing,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ B @ C )
% 5.41/5.65 => ( ord_less_real @ B @ ( plus_plus_real @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing
% 5.41/5.65 thf(fact_2208_add__strict__increasing,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.65 => ( ord_less_rat @ B @ ( plus_plus_rat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing
% 5.41/5.65 thf(fact_2209_add__strict__increasing,axiom,
% 5.41/5.65 ! [A: nat,B: nat,C: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.65 => ( ord_less_nat @ B @ ( plus_plus_nat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing
% 5.41/5.65 thf(fact_2210_add__strict__increasing,axiom,
% 5.41/5.65 ! [A: int,B: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ B @ C )
% 5.41/5.65 => ( ord_less_int @ B @ ( plus_plus_int @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_strict_increasing
% 5.41/5.65 thf(fact_2211_add__pos__nonneg,axiom,
% 5.41/5.65 ! [A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.65 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_pos_nonneg
% 5.41/5.65 thf(fact_2212_add__pos__nonneg,axiom,
% 5.41/5.65 ! [A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.65 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_pos_nonneg
% 5.41/5.65 thf(fact_2213_add__pos__nonneg,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_pos_nonneg
% 5.41/5.65 thf(fact_2214_add__pos__nonneg,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.65 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_pos_nonneg
% 5.41/5.65 thf(fact_2215_add__nonpos__neg,axiom,
% 5.41/5.65 ! [A: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_real @ B @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonpos_neg
% 5.41/5.65 thf(fact_2216_add__nonpos__neg,axiom,
% 5.41/5.65 ! [A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_rat @ B @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonpos_neg
% 5.41/5.65 thf(fact_2217_add__nonpos__neg,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ zero_zero_nat )
% 5.41/5.65 => ( ( ord_less_nat @ B @ zero_zero_nat )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonpos_neg
% 5.41/5.65 thf(fact_2218_add__nonpos__neg,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.65 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonpos_neg
% 5.41/5.65 thf(fact_2219_add__nonneg__pos,axiom,
% 5.41/5.65 ! [A: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.65 => ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonneg_pos
% 5.41/5.65 thf(fact_2220_add__nonneg__pos,axiom,
% 5.41/5.65 ! [A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ B )
% 5.41/5.65 => ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonneg_pos
% 5.41/5.65 thf(fact_2221_add__nonneg__pos,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonneg_pos
% 5.41/5.65 thf(fact_2222_add__nonneg__pos,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.65 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_nonneg_pos
% 5.41/5.65 thf(fact_2223_add__neg__nonpos,axiom,
% 5.41/5.65 ! [A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_eq_real @ B @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ A @ B ) @ zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_neg_nonpos
% 5.41/5.65 thf(fact_2224_add__neg__nonpos,axiom,
% 5.41/5.65 ! [A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_eq_rat @ B @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ A @ B ) @ zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_neg_nonpos
% 5.41/5.65 thf(fact_2225_add__neg__nonpos,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_nat @ A @ zero_zero_nat )
% 5.41/5.65 => ( ( ord_less_eq_nat @ B @ zero_zero_nat )
% 5.41/5.65 => ( ord_less_nat @ ( plus_plus_nat @ A @ B ) @ zero_zero_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_neg_nonpos
% 5.41/5.65 thf(fact_2226_add__neg__nonpos,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.65 => ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_neg_nonpos
% 5.41/5.65 thf(fact_2227_field__le__epsilon,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ! [E2: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.41/5.65 => ( ord_less_eq_real @ X @ ( plus_plus_real @ Y @ E2 ) ) )
% 5.41/5.65 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.65
% 5.41/5.65 % field_le_epsilon
% 5.41/5.65 thf(fact_2228_field__le__epsilon,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ! [E2: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.41/5.65 => ( ord_less_eq_rat @ X @ ( plus_plus_rat @ Y @ E2 ) ) )
% 5.41/5.65 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.41/5.65
% 5.41/5.65 % field_le_epsilon
% 5.41/5.65 thf(fact_2229_divide__nonpos__pos,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonpos_pos
% 5.41/5.65 thf(fact_2230_divide__nonpos__pos,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonpos_pos
% 5.41/5.65 thf(fact_2231_divide__nonpos__neg,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonpos_neg
% 5.41/5.65 thf(fact_2232_divide__nonpos__neg,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ X @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonpos_neg
% 5.41/5.65 thf(fact_2233_divide__nonneg__pos,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonneg_pos
% 5.41/5.65 thf(fact_2234_divide__nonneg__pos,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonneg_pos
% 5.41/5.65 thf(fact_2235_divide__nonneg__neg,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.65 => ( ( ord_less_real @ Y @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonneg_neg
% 5.41/5.65 thf(fact_2236_divide__nonneg__neg,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.65 => ( ( ord_less_rat @ Y @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_nonneg_neg
% 5.41/5.65 thf(fact_2237_divide__le__cancel,axiom,
% 5.41/5.65 ! [A: real,C: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ C ) @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_cancel
% 5.41/5.65 thf(fact_2238_divide__le__cancel,axiom,
% 5.41/5.65 ! [A: rat,C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ C ) @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ B ) )
% 5.41/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_cancel
% 5.41/5.65 thf(fact_2239_frac__less2,axiom,
% 5.41/5.65 ! [X: real,Y: real,W: real,Z: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.65 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.41/5.65 => ( ( ord_less_real @ W @ Z )
% 5.41/5.65 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % frac_less2
% 5.41/5.65 thf(fact_2240_frac__less2,axiom,
% 5.41/5.65 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.41/5.65 => ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.41/5.65 => ( ( ord_less_rat @ W @ Z )
% 5.41/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % frac_less2
% 5.41/5.65 thf(fact_2241_frac__less,axiom,
% 5.41/5.65 ! [X: real,Y: real,W: real,Z: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.65 => ( ( ord_less_real @ X @ Y )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.41/5.65 => ( ( ord_less_eq_real @ W @ Z )
% 5.41/5.65 => ( ord_less_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % frac_less
% 5.41/5.65 thf(fact_2242_frac__less,axiom,
% 5.41/5.65 ! [X: rat,Y: rat,W: rat,Z: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.65 => ( ( ord_less_rat @ X @ Y )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.41/5.65 => ( ( ord_less_eq_rat @ W @ Z )
% 5.41/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % frac_less
% 5.41/5.65 thf(fact_2243_frac__le,axiom,
% 5.41/5.65 ! [Y: real,X: real,W: real,Z: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ W )
% 5.41/5.65 => ( ( ord_less_eq_real @ W @ Z )
% 5.41/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Z ) @ ( divide_divide_real @ Y @ W ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % frac_le
% 5.41/5.65 thf(fact_2244_frac__le,axiom,
% 5.41/5.65 ! [Y: rat,X: rat,W: rat,Z: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ W )
% 5.41/5.65 => ( ( ord_less_eq_rat @ W @ Z )
% 5.41/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Z ) @ ( divide_divide_rat @ Y @ W ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % frac_le
% 5.41/5.65 thf(fact_2245_sum__squares__le__zero__iff,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real )
% 5.41/5.65 = ( ( X = zero_zero_real )
% 5.41/5.65 & ( Y = zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_le_zero_iff
% 5.41/5.65 thf(fact_2246_sum__squares__le__zero__iff,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat )
% 5.41/5.65 = ( ( X = zero_zero_rat )
% 5.41/5.65 & ( Y = zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_le_zero_iff
% 5.41/5.65 thf(fact_2247_sum__squares__le__zero__iff,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int )
% 5.41/5.65 = ( ( X = zero_zero_int )
% 5.41/5.65 & ( Y = zero_zero_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_le_zero_iff
% 5.41/5.65 thf(fact_2248_sum__squares__ge__zero,axiom,
% 5.41/5.65 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_ge_zero
% 5.41/5.65 thf(fact_2249_sum__squares__ge__zero,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_ge_zero
% 5.41/5.65 thf(fact_2250_sum__squares__ge__zero,axiom,
% 5.41/5.65 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_ge_zero
% 5.41/5.65 thf(fact_2251_mult__left__le,axiom,
% 5.41/5.65 ! [C: real,A: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ C @ one_one_real )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le
% 5.41/5.65 thf(fact_2252_mult__left__le,axiom,
% 5.41/5.65 ! [C: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ C @ one_one_rat )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le
% 5.41/5.65 thf(fact_2253_mult__left__le,axiom,
% 5.41/5.65 ! [C: nat,A: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ C @ one_one_nat )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ C ) @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le
% 5.41/5.65 thf(fact_2254_mult__left__le,axiom,
% 5.41/5.65 ! [C: int,A: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ C @ one_one_int )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ A ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le
% 5.41/5.65 thf(fact_2255_mult__le__one,axiom,
% 5.41/5.65 ! [A: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ one_one_real )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.65 => ( ( ord_less_eq_real @ B @ one_one_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ B ) @ one_one_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_one
% 5.41/5.65 thf(fact_2256_mult__le__one,axiom,
% 5.41/5.65 ! [A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.65 => ( ( ord_less_eq_rat @ B @ one_one_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ B ) @ one_one_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_one
% 5.41/5.65 thf(fact_2257_mult__le__one,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.65 => ( ( ord_less_eq_nat @ B @ one_one_nat )
% 5.41/5.65 => ( ord_less_eq_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_one
% 5.41/5.65 thf(fact_2258_mult__le__one,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ A @ one_one_int )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.65 => ( ( ord_less_eq_int @ B @ one_one_int )
% 5.41/5.65 => ( ord_less_eq_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_one
% 5.41/5.65 thf(fact_2259_mult__right__le__one__le,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ X @ Y ) @ X ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_le_one_le
% 5.41/5.65 thf(fact_2260_mult__right__le__one__le,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ X @ Y ) @ X ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_le_one_le
% 5.41/5.65 thf(fact_2261_mult__right__le__one__le,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.65 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.41/5.65 => ( ord_less_eq_int @ ( times_times_int @ X @ Y ) @ X ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_right_le_one_le
% 5.41/5.65 thf(fact_2262_mult__left__le__one__le,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ Y @ X ) @ X ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le_one_le
% 5.41/5.65 thf(fact_2263_mult__left__le__one__le,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ( ord_less_eq_rat @ Y @ one_one_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ Y @ X ) @ X ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le_one_le
% 5.41/5.65 thf(fact_2264_mult__left__le__one__le,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.65 => ( ( ord_less_eq_int @ Y @ one_one_int )
% 5.41/5.65 => ( ord_less_eq_int @ ( times_times_int @ Y @ X ) @ X ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_left_le_one_le
% 5.41/5.65 thf(fact_2265_power__less__imp__less__base,axiom,
% 5.41/5.65 ! [A: real,N: nat,B: real] :
% 5.41/5.65 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.65 => ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_less_imp_less_base
% 5.41/5.65 thf(fact_2266_power__less__imp__less__base,axiom,
% 5.41/5.65 ! [A: rat,N: nat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.65 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_less_imp_less_base
% 5.41/5.65 thf(fact_2267_power__less__imp__less__base,axiom,
% 5.41/5.65 ! [A: nat,N: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.65 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_less_imp_less_base
% 5.41/5.65 thf(fact_2268_power__less__imp__less__base,axiom,
% 5.41/5.65 ! [A: int,N: nat,B: int] :
% 5.41/5.65 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.65 => ( ord_less_int @ A @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_less_imp_less_base
% 5.41/5.65 thf(fact_2269_sum__squares__gt__zero__iff,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) )
% 5.41/5.65 = ( ( X != zero_zero_real )
% 5.41/5.65 | ( Y != zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_gt_zero_iff
% 5.41/5.65 thf(fact_2270_sum__squares__gt__zero__iff,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) )
% 5.41/5.65 = ( ( X != zero_zero_rat )
% 5.41/5.65 | ( Y != zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_gt_zero_iff
% 5.41/5.65 thf(fact_2271_sum__squares__gt__zero__iff,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) )
% 5.41/5.65 = ( ( X != zero_zero_int )
% 5.41/5.65 | ( Y != zero_zero_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % sum_squares_gt_zero_iff
% 5.41/5.65 thf(fact_2272_not__sum__squares__lt__zero,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ~ ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) @ zero_zero_real ) ).
% 5.41/5.65
% 5.41/5.65 % not_sum_squares_lt_zero
% 5.41/5.65 thf(fact_2273_not__sum__squares__lt__zero,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ~ ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ X ) @ ( times_times_rat @ Y @ Y ) ) @ zero_zero_rat ) ).
% 5.41/5.65
% 5.41/5.65 % not_sum_squares_lt_zero
% 5.41/5.65 thf(fact_2274_not__sum__squares__lt__zero,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ~ ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ X @ X ) @ ( times_times_int @ Y @ Y ) ) @ zero_zero_int ) ).
% 5.41/5.65
% 5.41/5.65 % not_sum_squares_lt_zero
% 5.41/5.65 thf(fact_2275_zero__less__two,axiom,
% 5.41/5.65 ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ one_one_real ) ).
% 5.41/5.65
% 5.41/5.65 % zero_less_two
% 5.41/5.65 thf(fact_2276_zero__less__two,axiom,
% 5.41/5.65 ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ one_one_rat ) ).
% 5.41/5.65
% 5.41/5.65 % zero_less_two
% 5.41/5.65 thf(fact_2277_zero__less__two,axiom,
% 5.41/5.65 ord_less_nat @ zero_zero_nat @ ( plus_plus_nat @ one_one_nat @ one_one_nat ) ).
% 5.41/5.65
% 5.41/5.65 % zero_less_two
% 5.41/5.65 thf(fact_2278_zero__less__two,axiom,
% 5.41/5.65 ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ one_one_int ) ).
% 5.41/5.65
% 5.41/5.65 % zero_less_two
% 5.41/5.65 thf(fact_2279_divide__less__eq,axiom,
% 5.41/5.65 ! [B: real,C: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_less_eq
% 5.41/5.65 thf(fact_2280_divide__less__eq,axiom,
% 5.41/5.65 ! [B: rat,C: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_less_eq
% 5.41/5.65 thf(fact_2281_less__divide__eq,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_divide_eq
% 5.41/5.65 thf(fact_2282_less__divide__eq,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_divide_eq
% 5.41/5.65 thf(fact_2283_neg__divide__less__eq,axiom,
% 5.41/5.65 ! [C: real,B: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_divide_less_eq
% 5.41/5.65 thf(fact_2284_neg__divide__less__eq,axiom,
% 5.41/5.65 ! [C: rat,B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_divide_less_eq
% 5.41/5.65 thf(fact_2285_neg__less__divide__eq,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_less_divide_eq
% 5.41/5.65 thf(fact_2286_neg__less__divide__eq,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_less_divide_eq
% 5.41/5.65 thf(fact_2287_pos__divide__less__eq,axiom,
% 5.41/5.65 ! [C: real,B: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_divide_less_eq
% 5.41/5.65 thf(fact_2288_pos__divide__less__eq,axiom,
% 5.41/5.65 ! [C: rat,B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_divide_less_eq
% 5.41/5.65 thf(fact_2289_pos__less__divide__eq,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ord_less_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ord_less_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_less_divide_eq
% 5.41/5.65 thf(fact_2290_pos__less__divide__eq,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_less_divide_eq
% 5.41/5.65 thf(fact_2291_mult__imp__div__pos__less,axiom,
% 5.41/5.65 ! [Y: real,X: real,Z: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ( ord_less_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.41/5.65 => ( ord_less_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_div_pos_less
% 5.41/5.65 thf(fact_2292_mult__imp__div__pos__less,axiom,
% 5.41/5.65 ! [Y: rat,X: rat,Z: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ( ord_less_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.41/5.65 => ( ord_less_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_div_pos_less
% 5.41/5.65 thf(fact_2293_mult__imp__less__div__pos,axiom,
% 5.41/5.65 ! [Y: real,Z: real,X: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ( ord_less_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.41/5.65 => ( ord_less_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_less_div_pos
% 5.41/5.65 thf(fact_2294_mult__imp__less__div__pos,axiom,
% 5.41/5.65 ! [Y: rat,Z: rat,X: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ( ord_less_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.41/5.65 => ( ord_less_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_less_div_pos
% 5.41/5.65 thf(fact_2295_divide__strict__left__mono,axiom,
% 5.41/5.65 ! [B: real,A: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ B @ A )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.41/5.65 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_strict_left_mono
% 5.41/5.65 thf(fact_2296_divide__strict__left__mono,axiom,
% 5.41/5.65 ! [B: rat,A: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ B @ A )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.65 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_strict_left_mono
% 5.41/5.65 thf(fact_2297_divide__strict__left__mono__neg,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ A @ B )
% 5.41/5.65 => ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.41/5.65 => ( ord_less_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_strict_left_mono_neg
% 5.41/5.65 thf(fact_2298_divide__strict__left__mono__neg,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ A @ B )
% 5.41/5.65 => ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.65 => ( ord_less_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_strict_left_mono_neg
% 5.41/5.65 thf(fact_2299_divide__less__eq__1,axiom,
% 5.41/5.65 ! [B: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 & ( ord_less_real @ B @ A ) )
% 5.41/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.65 & ( ord_less_real @ A @ B ) )
% 5.41/5.65 | ( A = zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_less_eq_1
% 5.41/5.65 thf(fact_2300_divide__less__eq__1,axiom,
% 5.41/5.65 ! [B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 & ( ord_less_rat @ B @ A ) )
% 5.41/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.65 & ( ord_less_rat @ A @ B ) )
% 5.41/5.65 | ( A = zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_less_eq_1
% 5.41/5.65 thf(fact_2301_less__divide__eq__1,axiom,
% 5.41/5.65 ! [B: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 & ( ord_less_real @ A @ B ) )
% 5.41/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.65 & ( ord_less_real @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_divide_eq_1
% 5.41/5.65 thf(fact_2302_less__divide__eq__1,axiom,
% 5.41/5.65 ! [B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 & ( ord_less_rat @ A @ B ) )
% 5.41/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.65 & ( ord_less_rat @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_divide_eq_1
% 5.41/5.65 thf(fact_2303_power__le__one,axiom,
% 5.41/5.65 ! [A: real,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ one_one_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_le_one
% 5.41/5.65 thf(fact_2304_power__le__one,axiom,
% 5.41/5.65 ! [A: rat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ one_one_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_le_one
% 5.41/5.65 thf(fact_2305_power__le__one,axiom,
% 5.41/5.65 ! [A: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.41/5.65 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N ) @ one_one_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_le_one
% 5.41/5.65 thf(fact_2306_power__le__one,axiom,
% 5.41/5.65 ! [A: int,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.41/5.65 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ one_one_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_le_one
% 5.41/5.65 thf(fact_2307_divide__eq__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [B: complex,C: complex,W: num] :
% 5.41/5.65 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.41/5.65 = ( numera6690914467698888265omplex @ W ) )
% 5.41/5.65 = ( ( ( C != zero_zero_complex )
% 5.41/5.65 => ( B
% 5.41/5.65 = ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C ) ) )
% 5.41/5.65 & ( ( C = zero_zero_complex )
% 5.41/5.65 => ( ( numera6690914467698888265omplex @ W )
% 5.41/5.65 = zero_zero_complex ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_eq_eq_numeral(1)
% 5.41/5.65 thf(fact_2308_divide__eq__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [B: real,C: real,W: num] :
% 5.41/5.65 ( ( ( divide_divide_real @ B @ C )
% 5.41/5.65 = ( numeral_numeral_real @ W ) )
% 5.41/5.65 = ( ( ( C != zero_zero_real )
% 5.41/5.65 => ( B
% 5.41/5.65 = ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.41/5.65 & ( ( C = zero_zero_real )
% 5.41/5.65 => ( ( numeral_numeral_real @ W )
% 5.41/5.65 = zero_zero_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_eq_eq_numeral(1)
% 5.41/5.65 thf(fact_2309_divide__eq__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [B: rat,C: rat,W: num] :
% 5.41/5.65 ( ( ( divide_divide_rat @ B @ C )
% 5.41/5.65 = ( numeral_numeral_rat @ W ) )
% 5.41/5.65 = ( ( ( C != zero_zero_rat )
% 5.41/5.65 => ( B
% 5.41/5.65 = ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.41/5.65 & ( ( C = zero_zero_rat )
% 5.41/5.65 => ( ( numeral_numeral_rat @ W )
% 5.41/5.65 = zero_zero_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_eq_eq_numeral(1)
% 5.41/5.65 thf(fact_2310_eq__divide__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [W: num,B: complex,C: complex] :
% 5.41/5.65 ( ( ( numera6690914467698888265omplex @ W )
% 5.41/5.65 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.65 = ( ( ( C != zero_zero_complex )
% 5.41/5.65 => ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ C )
% 5.41/5.65 = B ) )
% 5.41/5.65 & ( ( C = zero_zero_complex )
% 5.41/5.65 => ( ( numera6690914467698888265omplex @ W )
% 5.41/5.65 = zero_zero_complex ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % eq_divide_eq_numeral(1)
% 5.41/5.65 thf(fact_2311_eq__divide__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [W: num,B: real,C: real] :
% 5.41/5.65 ( ( ( numeral_numeral_real @ W )
% 5.41/5.65 = ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ( ( C != zero_zero_real )
% 5.41/5.65 => ( ( times_times_real @ ( numeral_numeral_real @ W ) @ C )
% 5.41/5.65 = B ) )
% 5.41/5.65 & ( ( C = zero_zero_real )
% 5.41/5.65 => ( ( numeral_numeral_real @ W )
% 5.41/5.65 = zero_zero_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % eq_divide_eq_numeral(1)
% 5.41/5.65 thf(fact_2312_eq__divide__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [W: num,B: rat,C: rat] :
% 5.41/5.65 ( ( ( numeral_numeral_rat @ W )
% 5.41/5.65 = ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( C != zero_zero_rat )
% 5.41/5.65 => ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C )
% 5.41/5.65 = B ) )
% 5.41/5.65 & ( ( C = zero_zero_rat )
% 5.41/5.65 => ( ( numeral_numeral_rat @ W )
% 5.41/5.65 = zero_zero_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % eq_divide_eq_numeral(1)
% 5.41/5.65 thf(fact_2313_divide__add__eq__iff,axiom,
% 5.41/5.65 ! [Z: complex,X: complex,Y: complex] :
% 5.41/5.65 ( ( Z != zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Z ) @ Y )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_add_eq_iff
% 5.41/5.65 thf(fact_2314_divide__add__eq__iff,axiom,
% 5.41/5.65 ! [Z: real,X: real,Y: real] :
% 5.41/5.65 ( ( Z != zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Z ) @ Y )
% 5.41/5.65 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_add_eq_iff
% 5.41/5.65 thf(fact_2315_divide__add__eq__iff,axiom,
% 5.41/5.65 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.65 ( ( Z != zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Z ) @ Y )
% 5.41/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_add_eq_iff
% 5.41/5.65 thf(fact_2316_add__divide__eq__iff,axiom,
% 5.41/5.65 ! [Z: complex,X: complex,Y: complex] :
% 5.41/5.65 ( ( Z != zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ X @ ( divide1717551699836669952omplex @ Y @ Z ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_iff
% 5.41/5.65 thf(fact_2317_add__divide__eq__iff,axiom,
% 5.41/5.65 ! [Z: real,X: real,Y: real] :
% 5.41/5.65 ( ( Z != zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ X @ ( divide_divide_real @ Y @ Z ) )
% 5.41/5.65 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_iff
% 5.41/5.65 thf(fact_2318_add__divide__eq__iff,axiom,
% 5.41/5.65 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.65 ( ( Z != zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ X @ ( divide_divide_rat @ Y @ Z ) )
% 5.41/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ Y ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_iff
% 5.41/5.65 thf(fact_2319_add__num__frac,axiom,
% 5.41/5.65 ! [Y: complex,Z: complex,X: complex] :
% 5.41/5.65 ( ( Y != zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ Z @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_num_frac
% 5.41/5.65 thf(fact_2320_add__num__frac,axiom,
% 5.41/5.65 ! [Y: real,Z: real,X: real] :
% 5.41/5.65 ( ( Y != zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ Z @ ( divide_divide_real @ X @ Y ) )
% 5.41/5.65 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_num_frac
% 5.41/5.65 thf(fact_2321_add__num__frac,axiom,
% 5.41/5.65 ! [Y: rat,Z: rat,X: rat] :
% 5.41/5.65 ( ( Y != zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ Z @ ( divide_divide_rat @ X @ Y ) )
% 5.41/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_num_frac
% 5.41/5.65 thf(fact_2322_add__frac__num,axiom,
% 5.41/5.65 ! [Y: complex,X: complex,Z: complex] :
% 5.41/5.65 ( ( Y != zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ Z )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ X @ ( times_times_complex @ Z @ Y ) ) @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_frac_num
% 5.41/5.65 thf(fact_2323_add__frac__num,axiom,
% 5.41/5.65 ! [Y: real,X: real,Z: real] :
% 5.41/5.65 ( ( Y != zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ Z )
% 5.41/5.65 = ( divide_divide_real @ ( plus_plus_real @ X @ ( times_times_real @ Z @ Y ) ) @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_frac_num
% 5.41/5.65 thf(fact_2324_add__frac__num,axiom,
% 5.41/5.65 ! [Y: rat,X: rat,Z: rat] :
% 5.41/5.65 ( ( Y != zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ Z )
% 5.41/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ X @ ( times_times_rat @ Z @ Y ) ) @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_frac_num
% 5.41/5.65 thf(fact_2325_add__frac__eq,axiom,
% 5.41/5.65 ! [Y: complex,Z: complex,X: complex,W: complex] :
% 5.41/5.65 ( ( Y != zero_zero_complex )
% 5.41/5.65 => ( ( Z != zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ X @ Y ) @ ( divide1717551699836669952omplex @ W @ Z ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ X @ Z ) @ ( times_times_complex @ W @ Y ) ) @ ( times_times_complex @ Y @ Z ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_frac_eq
% 5.41/5.65 thf(fact_2326_add__frac__eq,axiom,
% 5.41/5.65 ! [Y: real,Z: real,X: real,W: real] :
% 5.41/5.65 ( ( Y != zero_zero_real )
% 5.41/5.65 => ( ( Z != zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ X @ Y ) @ ( divide_divide_real @ W @ Z ) )
% 5.41/5.65 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ W @ Y ) ) @ ( times_times_real @ Y @ Z ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_frac_eq
% 5.41/5.65 thf(fact_2327_add__frac__eq,axiom,
% 5.41/5.65 ! [Y: rat,Z: rat,X: rat,W: rat] :
% 5.41/5.65 ( ( Y != zero_zero_rat )
% 5.41/5.65 => ( ( Z != zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ X @ Y ) @ ( divide_divide_rat @ W @ Z ) )
% 5.41/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ W @ Y ) ) @ ( times_times_rat @ Y @ Z ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_frac_eq
% 5.41/5.65 thf(fact_2328_add__divide__eq__if__simps_I1_J,axiom,
% 5.41/5.65 ! [Z: complex,A: complex,B: complex] :
% 5.41/5.65 ( ( ( Z = zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.41/5.65 = A ) )
% 5.41/5.65 & ( ( Z != zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ A @ ( divide1717551699836669952omplex @ B @ Z ) )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( times_times_complex @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_if_simps(1)
% 5.41/5.65 thf(fact_2329_add__divide__eq__if__simps_I1_J,axiom,
% 5.41/5.65 ! [Z: real,A: real,B: real] :
% 5.41/5.65 ( ( ( Z = zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.41/5.65 = A ) )
% 5.41/5.65 & ( ( Z != zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ A @ ( divide_divide_real @ B @ Z ) )
% 5.41/5.65 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_if_simps(1)
% 5.41/5.65 thf(fact_2330_add__divide__eq__if__simps_I1_J,axiom,
% 5.41/5.65 ! [Z: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ( Z = zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.41/5.65 = A ) )
% 5.41/5.65 & ( ( Z != zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ A @ ( divide_divide_rat @ B @ Z ) )
% 5.41/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ ( times_times_rat @ A @ Z ) @ B ) @ Z ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_if_simps(1)
% 5.41/5.65 thf(fact_2331_add__divide__eq__if__simps_I2_J,axiom,
% 5.41/5.65 ! [Z: complex,A: complex,B: complex] :
% 5.41/5.65 ( ( ( Z = zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.41/5.65 = B ) )
% 5.41/5.65 & ( ( Z != zero_zero_complex )
% 5.41/5.65 => ( ( plus_plus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.41/5.65 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_if_simps(2)
% 5.41/5.65 thf(fact_2332_add__divide__eq__if__simps_I2_J,axiom,
% 5.41/5.65 ! [Z: real,A: real,B: real] :
% 5.41/5.65 ( ( ( Z = zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.41/5.65 = B ) )
% 5.41/5.65 & ( ( Z != zero_zero_real )
% 5.41/5.65 => ( ( plus_plus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.41/5.65 = ( divide_divide_real @ ( plus_plus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_if_simps(2)
% 5.41/5.65 thf(fact_2333_add__divide__eq__if__simps_I2_J,axiom,
% 5.41/5.65 ! [Z: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ( Z = zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.41/5.65 = B ) )
% 5.41/5.65 & ( ( Z != zero_zero_rat )
% 5.41/5.65 => ( ( plus_plus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.41/5.65 = ( divide_divide_rat @ ( plus_plus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % add_divide_eq_if_simps(2)
% 5.41/5.65 thf(fact_2334_div__add__self2,axiom,
% 5.41/5.65 ! [B: nat,A: nat] :
% 5.41/5.65 ( ( B != zero_zero_nat )
% 5.41/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ B )
% 5.41/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_add_self2
% 5.41/5.65 thf(fact_2335_div__add__self2,axiom,
% 5.41/5.65 ! [B: int,A: int] :
% 5.41/5.65 ( ( B != zero_zero_int )
% 5.41/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ B )
% 5.41/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_add_self2
% 5.41/5.65 thf(fact_2336_div__add__self1,axiom,
% 5.41/5.65 ! [B: nat,A: nat] :
% 5.41/5.65 ( ( B != zero_zero_nat )
% 5.41/5.65 => ( ( divide_divide_nat @ ( plus_plus_nat @ B @ A ) @ B )
% 5.41/5.65 = ( plus_plus_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_add_self1
% 5.41/5.65 thf(fact_2337_div__add__self1,axiom,
% 5.41/5.65 ! [B: int,A: int] :
% 5.41/5.65 ( ( B != zero_zero_int )
% 5.41/5.65 => ( ( divide_divide_int @ ( plus_plus_int @ B @ A ) @ B )
% 5.41/5.65 = ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_add_self1
% 5.41/5.65 thf(fact_2338_bounded__Max__nat,axiom,
% 5.41/5.65 ! [P: nat > $o,X: nat,M5: nat] :
% 5.41/5.65 ( ( P @ X )
% 5.41/5.65 => ( ! [X6: nat] :
% 5.41/5.65 ( ( P @ X6 )
% 5.41/5.65 => ( ord_less_eq_nat @ X6 @ M5 ) )
% 5.41/5.65 => ~ ! [M4: nat] :
% 5.41/5.65 ( ( P @ M4 )
% 5.41/5.65 => ~ ! [X4: nat] :
% 5.41/5.65 ( ( P @ X4 )
% 5.41/5.65 => ( ord_less_eq_nat @ X4 @ M4 ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % bounded_Max_nat
% 5.41/5.65 thf(fact_2339_length__pos__if__in__set,axiom,
% 5.41/5.65 ! [X: complex,Xs: list_complex] :
% 5.41/5.65 ( ( member_complex @ X @ ( set_complex2 @ Xs ) )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_s3451745648224563538omplex @ Xs ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % length_pos_if_in_set
% 5.41/5.65 thf(fact_2340_length__pos__if__in__set,axiom,
% 5.41/5.65 ! [X: real,Xs: list_real] :
% 5.41/5.65 ( ( member_real @ X @ ( set_real2 @ Xs ) )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_real @ Xs ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % length_pos_if_in_set
% 5.41/5.65 thf(fact_2341_length__pos__if__in__set,axiom,
% 5.41/5.65 ! [X: set_nat,Xs: list_set_nat] :
% 5.41/5.65 ( ( member_set_nat @ X @ ( set_set_nat2 @ Xs ) )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_s3254054031482475050et_nat @ Xs ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % length_pos_if_in_set
% 5.41/5.65 thf(fact_2342_length__pos__if__in__set,axiom,
% 5.41/5.65 ! [X: vEBT_VEBT,Xs: list_VEBT_VEBT] :
% 5.41/5.65 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % length_pos_if_in_set
% 5.41/5.65 thf(fact_2343_length__pos__if__in__set,axiom,
% 5.41/5.65 ! [X: $o,Xs: list_o] :
% 5.41/5.65 ( ( member_o @ X @ ( set_o2 @ Xs ) )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_o @ Xs ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % length_pos_if_in_set
% 5.41/5.65 thf(fact_2344_length__pos__if__in__set,axiom,
% 5.41/5.65 ! [X: nat,Xs: list_nat] :
% 5.41/5.65 ( ( member_nat @ X @ ( set_nat2 @ Xs ) )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_nat @ Xs ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % length_pos_if_in_set
% 5.41/5.65 thf(fact_2345_length__pos__if__in__set,axiom,
% 5.41/5.65 ! [X: int,Xs: list_int] :
% 5.41/5.65 ( ( member_int @ X @ ( set_int2 @ Xs ) )
% 5.41/5.65 => ( ord_less_nat @ zero_zero_nat @ ( size_size_list_int @ Xs ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % length_pos_if_in_set
% 5.41/5.65 thf(fact_2346_nat__mult__le__cancel1,axiom,
% 5.41/5.65 ! [K: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.65 => ( ( ord_less_eq_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.65 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_mult_le_cancel1
% 5.41/5.65 thf(fact_2347_div__greater__zero__iff,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.65 = ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.65 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_greater_zero_iff
% 5.41/5.65 thf(fact_2348_div__le__mono2,axiom,
% 5.41/5.65 ! [M: nat,N: nat,K: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.65 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.65 => ( ord_less_eq_nat @ ( divide_divide_nat @ K @ N ) @ ( divide_divide_nat @ K @ M ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_le_mono2
% 5.41/5.65 thf(fact_2349_nat__mult__div__cancel1,axiom,
% 5.41/5.65 ! [K: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.65 => ( ( divide_divide_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.65 = ( divide_divide_nat @ M @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_mult_div_cancel1
% 5.41/5.65 thf(fact_2350_div__less__iff__less__mult,axiom,
% 5.41/5.65 ! [Q2: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.41/5.65 => ( ( ord_less_nat @ ( divide_divide_nat @ M @ Q2 ) @ N )
% 5.41/5.65 = ( ord_less_nat @ M @ ( times_times_nat @ N @ Q2 ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_less_iff_less_mult
% 5.41/5.65 thf(fact_2351_div__less__dividend,axiom,
% 5.41/5.65 ! [N: nat,M: nat] :
% 5.41/5.65 ( ( ord_less_nat @ one_one_nat @ N )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.65 => ( ord_less_nat @ ( divide_divide_nat @ M @ N ) @ M ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_less_dividend
% 5.41/5.65 thf(fact_2352_div__eq__dividend__iff,axiom,
% 5.41/5.65 ! [M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.65 => ( ( ( divide_divide_nat @ M @ N )
% 5.41/5.65 = M )
% 5.41/5.65 = ( N = one_one_nat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % div_eq_dividend_iff
% 5.41/5.65 thf(fact_2353_divmod__digit__1_I1_J,axiom,
% 5.41/5.65 ! [A: code_integer,B: code_integer] :
% 5.41/5.65 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.65 => ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.65 => ( ( ord_le3102999989581377725nteger @ B @ ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.65 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_Code_integer )
% 5.41/5.65 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_1(1)
% 5.41/5.65 thf(fact_2354_divmod__digit__1_I1_J,axiom,
% 5.41/5.65 ! [A: nat,B: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ B )
% 5.41/5.65 => ( ( ord_less_eq_nat @ B @ ( modulo_modulo_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.65 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_nat )
% 5.41/5.65 = ( divide_divide_nat @ A @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_1(1)
% 5.41/5.65 thf(fact_2355_divmod__digit__1_I1_J,axiom,
% 5.41/5.65 ! [A: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.65 => ( ( ord_less_eq_int @ B @ ( modulo_modulo_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) )
% 5.41/5.65 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) @ one_one_int )
% 5.41/5.65 = ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divmod_digit_1(1)
% 5.41/5.65 thf(fact_2356_power2__commute,axiom,
% 5.41/5.65 ! [X: complex,Y: complex] :
% 5.41/5.65 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_complex @ ( minus_minus_complex @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_commute
% 5.41/5.65 thf(fact_2357_power2__commute,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_real @ ( minus_minus_real @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_commute
% 5.41/5.65 thf(fact_2358_power2__commute,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_rat @ ( minus_minus_rat @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_commute
% 5.41/5.65 thf(fact_2359_power2__commute,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_int @ ( minus_minus_int @ Y @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_commute
% 5.41/5.65 thf(fact_2360_nat__less__add__iff2,axiom,
% 5.41/5.65 ! [I: nat,J: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.65 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( ord_less_nat @ M @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ J @ I ) @ U ) @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_less_add_iff2
% 5.41/5.65 thf(fact_2361_nat__less__add__iff1,axiom,
% 5.41/5.65 ! [J: nat,I: nat,U: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.65 => ( ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ I @ U ) @ M ) @ ( plus_plus_nat @ ( times_times_nat @ J @ U ) @ N ) )
% 5.41/5.65 = ( ord_less_nat @ ( plus_plus_nat @ ( times_times_nat @ ( minus_minus_nat @ I @ J ) @ U ) @ M ) @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % nat_less_add_iff1
% 5.41/5.65 thf(fact_2362_field__le__mult__one__interval,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ! [Z5: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ Z5 )
% 5.41/5.65 => ( ( ord_less_real @ Z5 @ one_one_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ Z5 @ X ) @ Y ) ) )
% 5.41/5.65 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.65
% 5.41/5.65 % field_le_mult_one_interval
% 5.41/5.65 thf(fact_2363_field__le__mult__one__interval,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ! [Z5: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ Z5 )
% 5.41/5.65 => ( ( ord_less_rat @ Z5 @ one_one_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ Z5 @ X ) @ Y ) ) )
% 5.41/5.65 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.41/5.65
% 5.41/5.65 % field_le_mult_one_interval
% 5.41/5.65 thf(fact_2364_mult__less__cancel__right2,axiom,
% 5.41/5.65 ! [A: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ ( times_times_real @ A @ C ) @ C )
% 5.41/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ A @ one_one_real ) )
% 5.41/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right2
% 5.41/5.65 thf(fact_2365_mult__less__cancel__right2,axiom,
% 5.41/5.65 ! [A: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.41/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.41/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right2
% 5.41/5.65 thf(fact_2366_mult__less__cancel__right2,axiom,
% 5.41/5.65 ! [A: int,C: int] :
% 5.41/5.65 ( ( ord_less_int @ ( times_times_int @ A @ C ) @ C )
% 5.41/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ A @ one_one_int ) )
% 5.41/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right2
% 5.41/5.65 thf(fact_2367_mult__less__cancel__right1,axiom,
% 5.41/5.65 ! [C: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ C @ ( times_times_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ one_one_real @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right1
% 5.41/5.65 thf(fact_2368_mult__less__cancel__right1,axiom,
% 5.41/5.65 ! [C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right1
% 5.41/5.65 thf(fact_2369_mult__less__cancel__right1,axiom,
% 5.41/5.65 ! [C: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ C @ ( times_times_int @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ one_one_int @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_right1
% 5.41/5.65 thf(fact_2370_mult__less__cancel__left2,axiom,
% 5.41/5.65 ! [C: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ ( times_times_real @ C @ A ) @ C )
% 5.41/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ A @ one_one_real ) )
% 5.41/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ one_one_real @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left2
% 5.41/5.65 thf(fact_2371_mult__less__cancel__left2,axiom,
% 5.41/5.65 ! [C: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.41/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ A @ one_one_rat ) )
% 5.41/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ one_one_rat @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left2
% 5.41/5.65 thf(fact_2372_mult__less__cancel__left2,axiom,
% 5.41/5.65 ! [C: int,A: int] :
% 5.41/5.65 ( ( ord_less_int @ ( times_times_int @ C @ A ) @ C )
% 5.41/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ A @ one_one_int ) )
% 5.41/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ one_one_int @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left2
% 5.41/5.65 thf(fact_2373_mult__less__cancel__left1,axiom,
% 5.41/5.65 ! [C: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ C @ ( times_times_real @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ one_one_real @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ B @ one_one_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left1
% 5.41/5.65 thf(fact_2374_mult__less__cancel__left1,axiom,
% 5.41/5.65 ! [C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ one_one_rat @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ B @ one_one_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left1
% 5.41/5.65 thf(fact_2375_mult__less__cancel__left1,axiom,
% 5.41/5.65 ! [C: int,B: int] :
% 5.41/5.65 ( ( ord_less_int @ C @ ( times_times_int @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_int @ one_one_int @ B ) )
% 5.41/5.65 & ( ( ord_less_eq_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_int @ B @ one_one_int ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_less_cancel_left1
% 5.41/5.65 thf(fact_2376_mult__le__cancel__right2,axiom,
% 5.41/5.65 ! [A: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ C )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.41/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right2
% 5.41/5.65 thf(fact_2377_mult__le__cancel__right2,axiom,
% 5.41/5.65 ! [A: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ C )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.41/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right2
% 5.41/5.65 thf(fact_2378_mult__le__cancel__right2,axiom,
% 5.41/5.65 ! [A: int,C: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( times_times_int @ A @ C ) @ C )
% 5.41/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.41/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right2
% 5.41/5.65 thf(fact_2379_mult__le__cancel__right1,axiom,
% 5.41/5.65 ! [C: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ C @ ( times_times_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.41/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right1
% 5.41/5.65 thf(fact_2380_mult__le__cancel__right1,axiom,
% 5.41/5.65 ! [C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.41/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right1
% 5.41/5.65 thf(fact_2381_mult__le__cancel__right1,axiom,
% 5.41/5.65 ! [C: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ C @ ( times_times_int @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.41/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_right1
% 5.41/5.65 thf(fact_2382_mult__le__cancel__left2,axiom,
% 5.41/5.65 ! [C: real,A: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( times_times_real @ C @ A ) @ C )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ A @ one_one_real ) )
% 5.41/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ one_one_real @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left2
% 5.41/5.65 thf(fact_2383_mult__le__cancel__left2,axiom,
% 5.41/5.65 ! [C: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( times_times_rat @ C @ A ) @ C )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ one_one_rat ) )
% 5.41/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ one_one_rat @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left2
% 5.41/5.65 thf(fact_2384_mult__le__cancel__left2,axiom,
% 5.41/5.65 ! [C: int,A: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( times_times_int @ C @ A ) @ C )
% 5.41/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ A @ one_one_int ) )
% 5.41/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_eq_int @ one_one_int @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left2
% 5.41/5.65 thf(fact_2385_mult__le__cancel__left1,axiom,
% 5.41/5.65 ! [C: real,B: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ C @ ( times_times_real @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ one_one_real @ B ) )
% 5.41/5.65 & ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ B @ one_one_real ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left1
% 5.41/5.65 thf(fact_2386_mult__le__cancel__left1,axiom,
% 5.41/5.65 ! [C: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ C @ ( times_times_rat @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ one_one_rat @ B ) )
% 5.41/5.65 & ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ one_one_rat ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left1
% 5.41/5.65 thf(fact_2387_mult__le__cancel__left1,axiom,
% 5.41/5.65 ! [C: int,B: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ C @ ( times_times_int @ C @ B ) )
% 5.41/5.65 = ( ( ( ord_less_int @ zero_zero_int @ C )
% 5.41/5.65 => ( ord_less_eq_int @ one_one_int @ B ) )
% 5.41/5.65 & ( ( ord_less_int @ C @ zero_zero_int )
% 5.41/5.65 => ( ord_less_eq_int @ B @ one_one_int ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_le_cancel_left1
% 5.41/5.65 thf(fact_2388_divide__left__mono__neg,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.65 => ( ( ord_less_eq_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.41/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_left_mono_neg
% 5.41/5.65 thf(fact_2389_divide__left__mono__neg,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.65 => ( ( ord_less_eq_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_left_mono_neg
% 5.41/5.65 thf(fact_2390_mult__imp__le__div__pos,axiom,
% 5.41/5.65 ! [Y: real,Z: real,X: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ Y ) @ X )
% 5.41/5.65 => ( ord_less_eq_real @ Z @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_le_div_pos
% 5.41/5.65 thf(fact_2391_mult__imp__le__div__pos,axiom,
% 5.41/5.65 ! [Y: rat,Z: rat,X: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ Y ) @ X )
% 5.41/5.65 => ( ord_less_eq_rat @ Z @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_le_div_pos
% 5.41/5.65 thf(fact_2392_mult__imp__div__pos__le,axiom,
% 5.41/5.65 ! [Y: real,X: real,Z: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ( ord_less_eq_real @ X @ ( times_times_real @ Z @ Y ) )
% 5.41/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ X @ Y ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_div_pos_le
% 5.41/5.65 thf(fact_2393_mult__imp__div__pos__le,axiom,
% 5.41/5.65 ! [Y: rat,X: rat,Z: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ( ord_less_eq_rat @ X @ ( times_times_rat @ Z @ Y ) )
% 5.41/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ X @ Y ) @ Z ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % mult_imp_div_pos_le
% 5.41/5.65 thf(fact_2394_pos__le__divide__eq,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_le_divide_eq
% 5.41/5.65 thf(fact_2395_pos__le__divide__eq,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_le_divide_eq
% 5.41/5.65 thf(fact_2396_pos__divide__le__eq,axiom,
% 5.41/5.65 ! [C: real,B: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_divide_le_eq
% 5.41/5.65 thf(fact_2397_pos__divide__le__eq,axiom,
% 5.41/5.65 ! [C: rat,B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos_divide_le_eq
% 5.41/5.65 thf(fact_2398_neg__le__divide__eq,axiom,
% 5.41/5.65 ! [C: real,A: real,B: real] :
% 5.41/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_le_divide_eq
% 5.41/5.65 thf(fact_2399_neg__le__divide__eq,axiom,
% 5.41/5.65 ! [C: rat,A: rat,B: rat] :
% 5.41/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_le_divide_eq
% 5.41/5.65 thf(fact_2400_neg__divide__le__eq,axiom,
% 5.41/5.65 ! [C: real,B: real,A: real] :
% 5.41/5.65 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_divide_le_eq
% 5.41/5.65 thf(fact_2401_neg__divide__le__eq,axiom,
% 5.41/5.65 ! [C: rat,B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.41/5.65 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % neg_divide_le_eq
% 5.41/5.65 thf(fact_2402_divide__left__mono,axiom,
% 5.41/5.65 ! [B: real,A: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ B @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ ( times_times_real @ A @ B ) )
% 5.41/5.65 => ( ord_less_eq_real @ ( divide_divide_real @ C @ A ) @ ( divide_divide_real @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_left_mono
% 5.41/5.65 thf(fact_2403_divide__left__mono,axiom,
% 5.41/5.65 ! [B: rat,A: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.65 => ( ord_less_eq_rat @ ( divide_divide_rat @ C @ A ) @ ( divide_divide_rat @ C @ B ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_left_mono
% 5.41/5.65 thf(fact_2404_le__divide__eq,axiom,
% 5.41/5.65 ! [A: real,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_divide_eq
% 5.41/5.65 thf(fact_2405_le__divide__eq,axiom,
% 5.41/5.65 ! [A: rat,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_divide_eq
% 5.41/5.65 thf(fact_2406_divide__le__eq,axiom,
% 5.41/5.65 ! [B: real,C: real,A: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ A )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ B @ ( times_times_real @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_eq
% 5.41/5.65 thf(fact_2407_divide__le__eq,axiom,
% 5.41/5.65 ! [B: rat,C: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ A )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_eq
% 5.41/5.65 thf(fact_2408_le__divide__eq__1,axiom,
% 5.41/5.65 ! [B: real,A: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ one_one_real @ ( divide_divide_real @ B @ A ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 & ( ord_less_eq_real @ A @ B ) )
% 5.41/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.65 & ( ord_less_eq_real @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_divide_eq_1
% 5.41/5.65 thf(fact_2409_le__divide__eq__1,axiom,
% 5.41/5.65 ! [B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ one_one_rat @ ( divide_divide_rat @ B @ A ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 & ( ord_less_eq_rat @ A @ B ) )
% 5.41/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.65 & ( ord_less_eq_rat @ B @ A ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_divide_eq_1
% 5.41/5.65 thf(fact_2410_divide__le__eq__1,axiom,
% 5.41/5.65 ! [B: real,A: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ A ) @ one_one_real )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 & ( ord_less_eq_real @ B @ A ) )
% 5.41/5.65 | ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.65 & ( ord_less_eq_real @ A @ B ) )
% 5.41/5.65 | ( A = zero_zero_real ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_eq_1
% 5.41/5.65 thf(fact_2411_divide__le__eq__1,axiom,
% 5.41/5.65 ! [B: rat,A: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ A ) @ one_one_rat )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 & ( ord_less_eq_rat @ B @ A ) )
% 5.41/5.65 | ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.65 & ( ord_less_eq_rat @ A @ B ) )
% 5.41/5.65 | ( A = zero_zero_rat ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_eq_1
% 5.41/5.65 thf(fact_2412_convex__bound__le,axiom,
% 5.41/5.65 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ X @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ Y @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.41/5.65 => ( ( ( plus_plus_real @ U @ V )
% 5.41/5.65 = one_one_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % convex_bound_le
% 5.41/5.65 thf(fact_2413_convex__bound__le,axiom,
% 5.41/5.65 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ X @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ Y @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.41/5.65 => ( ( ( plus_plus_rat @ U @ V )
% 5.41/5.65 = one_one_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % convex_bound_le
% 5.41/5.65 thf(fact_2414_convex__bound__le,axiom,
% 5.41/5.65 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ X @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ Y @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.41/5.65 => ( ( ( plus_plus_int @ U @ V )
% 5.41/5.65 = one_one_int )
% 5.41/5.65 => ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % convex_bound_le
% 5.41/5.65 thf(fact_2415_divide__less__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [B: real,C: real,W: num] :
% 5.41/5.65 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_less_eq_numeral(1)
% 5.41/5.65 thf(fact_2416_divide__less__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [B: rat,C: rat,W: num] :
% 5.41/5.65 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_less_eq_numeral(1)
% 5.41/5.65 thf(fact_2417_less__divide__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [W: num,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_divide_eq_numeral(1)
% 5.41/5.65 thf(fact_2418_less__divide__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [W: num,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_divide_eq_numeral(1)
% 5.41/5.65 thf(fact_2419_power__Suc__less,axiom,
% 5.41/5.65 ! [A: real,N: nat] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_real @ A @ one_one_real )
% 5.41/5.65 => ( ord_less_real @ ( times_times_real @ A @ ( power_power_real @ A @ N ) ) @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_Suc_less
% 5.41/5.65 thf(fact_2420_power__Suc__less,axiom,
% 5.41/5.65 ! [A: rat,N: nat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.41/5.65 => ( ord_less_rat @ ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_Suc_less
% 5.41/5.65 thf(fact_2421_power__Suc__less,axiom,
% 5.41/5.65 ! [A: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.41/5.65 => ( ord_less_nat @ ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_Suc_less
% 5.41/5.65 thf(fact_2422_power__Suc__less,axiom,
% 5.41/5.65 ! [A: int,N: nat] :
% 5.41/5.65 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_int @ A @ one_one_int )
% 5.41/5.65 => ( ord_less_int @ ( times_times_int @ A @ ( power_power_int @ A @ N ) ) @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_Suc_less
% 5.41/5.65 thf(fact_2423_power__strict__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: real] :
% 5.41/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_real @ A @ one_one_real )
% 5.41/5.65 => ( ord_less_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_strict_decreasing
% 5.41/5.65 thf(fact_2424_power__strict__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: rat] :
% 5.41/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.41/5.65 => ( ord_less_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_strict_decreasing
% 5.41/5.65 thf(fact_2425_power__strict__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: nat] :
% 5.41/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.41/5.65 => ( ord_less_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_strict_decreasing
% 5.41/5.65 thf(fact_2426_power__strict__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: int] :
% 5.41/5.65 ( ( ord_less_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_int @ A @ one_one_int )
% 5.41/5.65 => ( ord_less_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_strict_decreasing
% 5.41/5.65 thf(fact_2427_power__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: real] :
% 5.41/5.65 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( power_power_real @ A @ N4 ) @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_decreasing
% 5.41/5.65 thf(fact_2428_power__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: rat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N4 ) @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_decreasing
% 5.41/5.65 thf(fact_2429_power__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.65 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.41/5.65 => ( ord_less_eq_nat @ ( power_power_nat @ A @ N4 ) @ ( power_power_nat @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_decreasing
% 5.41/5.65 thf(fact_2430_power__decreasing,axiom,
% 5.41/5.65 ! [N: nat,N4: nat,A: int] :
% 5.41/5.65 ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.41/5.65 => ( ord_less_eq_int @ ( power_power_int @ A @ N4 ) @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power_decreasing
% 5.41/5.65 thf(fact_2431_zero__power2,axiom,
% 5.41/5.65 ( ( power_power_rat @ zero_zero_rat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = zero_zero_rat ) ).
% 5.41/5.65
% 5.41/5.65 % zero_power2
% 5.41/5.65 thf(fact_2432_zero__power2,axiom,
% 5.41/5.65 ( ( power_power_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = zero_zero_nat ) ).
% 5.41/5.65
% 5.41/5.65 % zero_power2
% 5.41/5.65 thf(fact_2433_zero__power2,axiom,
% 5.41/5.65 ( ( power_power_real @ zero_zero_real @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = zero_zero_real ) ).
% 5.41/5.65
% 5.41/5.65 % zero_power2
% 5.41/5.65 thf(fact_2434_zero__power2,axiom,
% 5.41/5.65 ( ( power_power_int @ zero_zero_int @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = zero_zero_int ) ).
% 5.41/5.65
% 5.41/5.65 % zero_power2
% 5.41/5.65 thf(fact_2435_zero__power2,axiom,
% 5.41/5.65 ( ( power_power_complex @ zero_zero_complex @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = zero_zero_complex ) ).
% 5.41/5.65
% 5.41/5.65 % zero_power2
% 5.41/5.65 thf(fact_2436_self__le__power,axiom,
% 5.41/5.65 ! [A: real,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_real @ one_one_real @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_eq_real @ A @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % self_le_power
% 5.41/5.65 thf(fact_2437_self__le__power,axiom,
% 5.41/5.65 ! [A: rat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ one_one_rat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_eq_rat @ A @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % self_le_power
% 5.41/5.65 thf(fact_2438_self__le__power,axiom,
% 5.41/5.65 ! [A: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ one_one_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_eq_nat @ A @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % self_le_power
% 5.41/5.65 thf(fact_2439_self__le__power,axiom,
% 5.41/5.65 ! [A: int,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_int @ one_one_int @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_eq_int @ A @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % self_le_power
% 5.41/5.65 thf(fact_2440_one__less__power,axiom,
% 5.41/5.65 ! [A: real,N: nat] :
% 5.41/5.65 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % one_less_power
% 5.41/5.65 thf(fact_2441_one__less__power,axiom,
% 5.41/5.65 ! [A: rat,N: nat] :
% 5.41/5.65 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % one_less_power
% 5.41/5.65 thf(fact_2442_one__less__power,axiom,
% 5.41/5.65 ! [A: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % one_less_power
% 5.41/5.65 thf(fact_2443_one__less__power,axiom,
% 5.41/5.65 ! [A: int,N: nat] :
% 5.41/5.65 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.65 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % one_less_power
% 5.41/5.65 thf(fact_2444_pos2,axiom,
% 5.41/5.65 ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ).
% 5.41/5.65
% 5.41/5.65 % pos2
% 5.41/5.65 thf(fact_2445_less__eq__div__iff__mult__less__eq,axiom,
% 5.41/5.65 ! [Q2: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ Q2 )
% 5.41/5.65 => ( ( ord_less_eq_nat @ M @ ( divide_divide_nat @ N @ Q2 ) )
% 5.41/5.65 = ( ord_less_eq_nat @ ( times_times_nat @ M @ Q2 ) @ N ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % less_eq_div_iff_mult_less_eq
% 5.41/5.65 thf(fact_2446_dividend__less__times__div,axiom,
% 5.41/5.65 ! [N: nat,M: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ N @ ( divide_divide_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % dividend_less_times_div
% 5.41/5.65 thf(fact_2447_dividend__less__div__times,axiom,
% 5.41/5.65 ! [N: nat,M: nat] :
% 5.41/5.65 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.65 => ( ord_less_nat @ M @ ( plus_plus_nat @ N @ ( times_times_nat @ ( divide_divide_nat @ M @ N ) @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % dividend_less_div_times
% 5.41/5.65 thf(fact_2448_split__div,axiom,
% 5.41/5.65 ! [P: nat > $o,M: nat,N: nat] :
% 5.41/5.65 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.65 = ( ( ( N = zero_zero_nat )
% 5.41/5.65 => ( P @ zero_zero_nat ) )
% 5.41/5.65 & ( ( N != zero_zero_nat )
% 5.41/5.65 => ! [I5: nat,J3: nat] :
% 5.41/5.65 ( ( ord_less_nat @ J3 @ N )
% 5.41/5.65 => ( ( M
% 5.41/5.65 = ( plus_plus_nat @ ( times_times_nat @ N @ I5 ) @ J3 ) )
% 5.41/5.65 => ( P @ I5 ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % split_div
% 5.41/5.65 thf(fact_2449_diff__le__diff__pow,axiom,
% 5.41/5.65 ! [K: nat,M: nat,N: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.65 => ( ord_less_eq_nat @ ( minus_minus_nat @ M @ N ) @ ( minus_minus_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % diff_le_diff_pow
% 5.41/5.65 thf(fact_2450_le__divide__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [W: num,B: real,C: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ ( divide_divide_real @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( numeral_numeral_real @ W ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_divide_eq_numeral(1)
% 5.41/5.65 thf(fact_2451_le__divide__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [W: num,B: rat,C: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( numeral_numeral_rat @ W ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % le_divide_eq_numeral(1)
% 5.41/5.65 thf(fact_2452_divide__le__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [B: real,C: real,W: num] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( numeral_numeral_real @ W ) )
% 5.41/5.65 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ord_less_eq_real @ B @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.65 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.65 => ( ord_less_eq_real @ zero_zero_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_eq_numeral(1)
% 5.41/5.65 thf(fact_2453_divide__le__eq__numeral_I1_J,axiom,
% 5.41/5.65 ! [B: rat,C: rat,W: num] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( numeral_numeral_rat @ W ) )
% 5.41/5.65 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.65 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ C ) @ B ) )
% 5.41/5.65 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.65 => ( ord_less_eq_rat @ zero_zero_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % divide_le_eq_numeral(1)
% 5.41/5.65 thf(fact_2454_convex__bound__lt,axiom,
% 5.41/5.65 ! [X: real,A: real,Y: real,U: real,V: real] :
% 5.41/5.65 ( ( ord_less_real @ X @ A )
% 5.41/5.65 => ( ( ord_less_real @ Y @ A )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ U )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ V )
% 5.41/5.65 => ( ( ( plus_plus_real @ U @ V )
% 5.41/5.65 = one_one_real )
% 5.41/5.65 => ( ord_less_real @ ( plus_plus_real @ ( times_times_real @ U @ X ) @ ( times_times_real @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % convex_bound_lt
% 5.41/5.65 thf(fact_2455_convex__bound__lt,axiom,
% 5.41/5.65 ! [X: rat,A: rat,Y: rat,U: rat,V: rat] :
% 5.41/5.65 ( ( ord_less_rat @ X @ A )
% 5.41/5.65 => ( ( ord_less_rat @ Y @ A )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ U )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ V )
% 5.41/5.65 => ( ( ( plus_plus_rat @ U @ V )
% 5.41/5.65 = one_one_rat )
% 5.41/5.65 => ( ord_less_rat @ ( plus_plus_rat @ ( times_times_rat @ U @ X ) @ ( times_times_rat @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % convex_bound_lt
% 5.41/5.65 thf(fact_2456_convex__bound__lt,axiom,
% 5.41/5.65 ! [X: int,A: int,Y: int,U: int,V: int] :
% 5.41/5.65 ( ( ord_less_int @ X @ A )
% 5.41/5.65 => ( ( ord_less_int @ Y @ A )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ V )
% 5.41/5.65 => ( ( ( plus_plus_int @ U @ V )
% 5.41/5.65 = one_one_int )
% 5.41/5.65 => ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ U @ X ) @ ( times_times_int @ V @ Y ) ) @ A ) ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % convex_bound_lt
% 5.41/5.65 thf(fact_2457_half__gt__zero,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.65 => ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % half_gt_zero
% 5.41/5.65 thf(fact_2458_half__gt__zero,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.65 => ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % half_gt_zero
% 5.41/5.65 thf(fact_2459_half__gt__zero__iff,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ( ( ord_less_real @ zero_zero_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.65 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.41/5.65
% 5.41/5.65 % half_gt_zero_iff
% 5.41/5.65 thf(fact_2460_half__gt__zero__iff,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ( ( ord_less_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.65
% 5.41/5.65 % half_gt_zero_iff
% 5.41/5.65 thf(fact_2461_zero__le__power2,axiom,
% 5.41/5.65 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % zero_le_power2
% 5.41/5.65 thf(fact_2462_zero__le__power2,axiom,
% 5.41/5.65 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % zero_le_power2
% 5.41/5.65 thf(fact_2463_zero__le__power2,axiom,
% 5.41/5.65 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % zero_le_power2
% 5.41/5.65 thf(fact_2464_power2__eq__imp__eq,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( X = Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_eq_imp_eq
% 5.41/5.65 thf(fact_2465_power2__eq__imp__eq,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( X = Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_eq_imp_eq
% 5.41/5.65 thf(fact_2466_power2__eq__imp__eq,axiom,
% 5.41/5.65 ! [X: nat,Y: nat] :
% 5.41/5.65 ( ( ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ X )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.41/5.65 => ( X = Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_eq_imp_eq
% 5.41/5.65 thf(fact_2467_power2__eq__imp__eq,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.65 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.65 => ( X = Y ) ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_eq_imp_eq
% 5.41/5.65 thf(fact_2468_power2__le__imp__le,axiom,
% 5.41/5.65 ! [X: real,Y: real] :
% 5.41/5.65 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.65 => ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_le_imp_le
% 5.41/5.65 thf(fact_2469_power2__le__imp__le,axiom,
% 5.41/5.65 ! [X: rat,Y: rat] :
% 5.41/5.65 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.65 => ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_le_imp_le
% 5.41/5.65 thf(fact_2470_power2__le__imp__le,axiom,
% 5.41/5.65 ! [X: nat,Y: nat] :
% 5.41/5.65 ( ( ord_less_eq_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.41/5.65 => ( ord_less_eq_nat @ X @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_le_imp_le
% 5.41/5.65 thf(fact_2471_power2__le__imp__le,axiom,
% 5.41/5.65 ! [X: int,Y: int] :
% 5.41/5.65 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.65 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.65 => ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.41/5.65
% 5.41/5.65 % power2_le_imp_le
% 5.41/5.65 thf(fact_2472_power2__less__0,axiom,
% 5.41/5.65 ! [A: real] :
% 5.41/5.65 ~ ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_real ) ).
% 5.41/5.65
% 5.41/5.65 % power2_less_0
% 5.41/5.65 thf(fact_2473_power2__less__0,axiom,
% 5.41/5.65 ! [A: rat] :
% 5.41/5.65 ~ ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_0
% 5.41/5.66 thf(fact_2474_power2__less__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ~ ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_0
% 5.41/5.66 thf(fact_2475_exp__add__not__zero__imp__left,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.66 != zero_zero_nat )
% 5.41/5.66 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.41/5.66 != zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % exp_add_not_zero_imp_left
% 5.41/5.66 thf(fact_2476_exp__add__not__zero__imp__left,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.66 != zero_zero_int )
% 5.41/5.66 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.41/5.66 != zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % exp_add_not_zero_imp_left
% 5.41/5.66 thf(fact_2477_exp__add__not__zero__imp__right,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.66 != zero_zero_nat )
% 5.41/5.66 => ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.66 != zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % exp_add_not_zero_imp_right
% 5.41/5.66 thf(fact_2478_exp__add__not__zero__imp__right,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.66 != zero_zero_int )
% 5.41/5.66 => ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.41/5.66 != zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % exp_add_not_zero_imp_right
% 5.41/5.66 thf(fact_2479_div__exp__mod__exp__eq,axiom,
% 5.41/5.66 ! [A: nat,N: nat,M: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.66 = ( divide_divide_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_exp_mod_exp_eq
% 5.41/5.66 thf(fact_2480_div__exp__mod__exp__eq,axiom,
% 5.41/5.66 ! [A: int,N: nat,M: nat] :
% 5.41/5.66 ( ( modulo_modulo_int @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.66 = ( divide_divide_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_exp_mod_exp_eq
% 5.41/5.66 thf(fact_2481_div__exp__mod__exp__eq,axiom,
% 5.41/5.66 ! [A: code_integer,N: nat,M: nat] :
% 5.41/5.66 ( ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.66 = ( divide6298287555418463151nteger @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_exp_mod_exp_eq
% 5.41/5.66 thf(fact_2482_power2__less__imp__less,axiom,
% 5.41/5.66 ! [X: real,Y: real] :
% 5.41/5.66 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.66 => ( ord_less_real @ X @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_imp_less
% 5.41/5.66 thf(fact_2483_power2__less__imp__less,axiom,
% 5.41/5.66 ! [X: rat,Y: rat] :
% 5.41/5.66 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 => ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.66 => ( ord_less_rat @ X @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_imp_less
% 5.41/5.66 thf(fact_2484_power2__less__imp__less,axiom,
% 5.41/5.66 ! [X: nat,Y: nat] :
% 5.41/5.66 ( ( ord_less_nat @ ( power_power_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 => ( ( ord_less_eq_nat @ zero_zero_nat @ Y )
% 5.41/5.66 => ( ord_less_nat @ X @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_imp_less
% 5.41/5.66 thf(fact_2485_power2__less__imp__less,axiom,
% 5.41/5.66 ! [X: int,Y: int] :
% 5.41/5.66 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.66 => ( ord_less_int @ X @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_less_imp_less
% 5.41/5.66 thf(fact_2486_sum__power2__ge__zero,axiom,
% 5.41/5.66 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_ge_zero
% 5.41/5.66 thf(fact_2487_sum__power2__ge__zero,axiom,
% 5.41/5.66 ! [X: rat,Y: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_ge_zero
% 5.41/5.66 thf(fact_2488_sum__power2__ge__zero,axiom,
% 5.41/5.66 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_ge_zero
% 5.41/5.66 thf(fact_2489_sum__power2__le__zero__iff,axiom,
% 5.41/5.66 ! [X: real,Y: real] :
% 5.41/5.66 ( ( ord_less_eq_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real )
% 5.41/5.66 = ( ( X = zero_zero_real )
% 5.41/5.66 & ( Y = zero_zero_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_le_zero_iff
% 5.41/5.66 thf(fact_2490_sum__power2__le__zero__iff,axiom,
% 5.41/5.66 ! [X: rat,Y: rat] :
% 5.41/5.66 ( ( ord_less_eq_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat )
% 5.41/5.66 = ( ( X = zero_zero_rat )
% 5.41/5.66 & ( Y = zero_zero_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_le_zero_iff
% 5.41/5.66 thf(fact_2491_sum__power2__le__zero__iff,axiom,
% 5.41/5.66 ! [X: int,Y: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int )
% 5.41/5.66 = ( ( X = zero_zero_int )
% 5.41/5.66 & ( Y = zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_le_zero_iff
% 5.41/5.66 thf(fact_2492_not__sum__power2__lt__zero,axiom,
% 5.41/5.66 ! [X: real,Y: real] :
% 5.41/5.66 ~ ( ord_less_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % not_sum_power2_lt_zero
% 5.41/5.66 thf(fact_2493_not__sum__power2__lt__zero,axiom,
% 5.41/5.66 ! [X: rat,Y: rat] :
% 5.41/5.66 ~ ( ord_less_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % not_sum_power2_lt_zero
% 5.41/5.66 thf(fact_2494_not__sum__power2__lt__zero,axiom,
% 5.41/5.66 ! [X: int,Y: int] :
% 5.41/5.66 ~ ( ord_less_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % not_sum_power2_lt_zero
% 5.41/5.66 thf(fact_2495_sum__power2__gt__zero__iff,axiom,
% 5.41/5.66 ! [X: real,Y: real] :
% 5.41/5.66 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.66 = ( ( X != zero_zero_real )
% 5.41/5.66 | ( Y != zero_zero_real ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_gt_zero_iff
% 5.41/5.66 thf(fact_2496_sum__power2__gt__zero__iff,axiom,
% 5.41/5.66 ! [X: rat,Y: rat] :
% 5.41/5.66 ( ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.66 = ( ( X != zero_zero_rat )
% 5.41/5.66 | ( Y != zero_zero_rat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_gt_zero_iff
% 5.41/5.66 thf(fact_2497_sum__power2__gt__zero__iff,axiom,
% 5.41/5.66 ! [X: int,Y: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.66 = ( ( X != zero_zero_int )
% 5.41/5.66 | ( Y != zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % sum_power2_gt_zero_iff
% 5.41/5.66 thf(fact_2498_zero__le__even__power_H,axiom,
% 5.41/5.66 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_even_power'
% 5.41/5.66 thf(fact_2499_zero__le__even__power_H,axiom,
% 5.41/5.66 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_even_power'
% 5.41/5.66 thf(fact_2500_zero__le__even__power_H,axiom,
% 5.41/5.66 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_le_even_power'
% 5.41/5.66 thf(fact_2501_power2__diff,axiom,
% 5.41/5.66 ! [X: complex,Y: complex] :
% 5.41/5.66 ( ( power_power_complex @ ( minus_minus_complex @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( minus_minus_complex @ ( plus_plus_complex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_diff
% 5.41/5.66 thf(fact_2502_power2__diff,axiom,
% 5.41/5.66 ! [X: real,Y: real] :
% 5.41/5.66 ( ( power_power_real @ ( minus_minus_real @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( minus_minus_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_diff
% 5.41/5.66 thf(fact_2503_power2__diff,axiom,
% 5.41/5.66 ! [X: rat,Y: rat] :
% 5.41/5.66 ( ( power_power_rat @ ( minus_minus_rat @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( minus_minus_rat @ ( plus_plus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_diff
% 5.41/5.66 thf(fact_2504_power2__diff,axiom,
% 5.41/5.66 ! [X: int,Y: int] :
% 5.41/5.66 ( ( power_power_int @ ( minus_minus_int @ X @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( minus_minus_int @ ( plus_plus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X ) @ Y ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % power2_diff
% 5.41/5.66 thf(fact_2505_invar__vebt_Ointros_I4_J,axiom,
% 5.41/5.66 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.41/5.66 ( ! [X6: vEBT_VEBT] :
% 5.41/5.66 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.66 => ( vEBT_invar_vebt @ X6 @ N ) )
% 5.41/5.66 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.41/5.66 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.41/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.66 => ( ( M = N )
% 5.41/5.66 => ( ( Deg
% 5.41/5.66 = ( plus_plus_nat @ N @ M ) )
% 5.41/5.66 => ( ! [I4: nat] :
% 5.41/5.66 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.66 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X2 ) )
% 5.41/5.66 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.41/5.66 => ( ( ( Mi = Ma )
% 5.41/5.66 => ! [X6: vEBT_VEBT] :
% 5.41/5.66 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.66 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) ) )
% 5.41/5.66 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.41/5.66 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.41/5.66 => ( ( ( Mi != Ma )
% 5.41/5.66 => ! [I4: nat] :
% 5.41/5.66 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.66 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.41/5.66 = I4 )
% 5.41/5.66 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.41/5.66 & ! [X6: nat] :
% 5.41/5.66 ( ( ( ( vEBT_VEBT_high @ X6 @ N )
% 5.41/5.66 = I4 )
% 5.41/5.66 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X6 @ N ) ) )
% 5.41/5.66 => ( ( ord_less_nat @ Mi @ X6 )
% 5.41/5.66 & ( ord_less_eq_nat @ X6 @ Ma ) ) ) ) ) )
% 5.41/5.66 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % invar_vebt.intros(4)
% 5.41/5.66 thf(fact_2506_pred__list__to__short,axiom,
% 5.41/5.66 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.66 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = none_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pred_list_to_short
% 5.41/5.66 thf(fact_2507_succ__list__to__short,axiom,
% 5.41/5.66 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.66 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = none_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % succ_list_to_short
% 5.41/5.66 thf(fact_2508_not__mod__2__eq__0__eq__1,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 != zero_zero_nat )
% 5.41/5.66 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = one_one_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_0_eq_1
% 5.41/5.66 thf(fact_2509_not__mod__2__eq__0__eq__1,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 != zero_zero_int )
% 5.41/5.66 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 = one_one_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_0_eq_1
% 5.41/5.66 thf(fact_2510_not__mod__2__eq__0__eq__1,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 != zero_z3403309356797280102nteger )
% 5.41/5.66 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 = one_one_Code_integer ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_0_eq_1
% 5.41/5.66 thf(fact_2511_not__mod__2__eq__1__eq__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 != one_one_nat )
% 5.41/5.66 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_1_eq_0
% 5.41/5.66 thf(fact_2512_not__mod__2__eq__1__eq__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 != one_one_int )
% 5.41/5.66 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_1_eq_0
% 5.41/5.66 thf(fact_2513_not__mod__2__eq__1__eq__0,axiom,
% 5.41/5.66 ! [A: code_integer] :
% 5.41/5.66 ( ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 != one_one_Code_integer )
% 5.41/5.66 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod_2_eq_1_eq_0
% 5.41/5.66 thf(fact_2514_pred__max,axiom,
% 5.41/5.66 ! [Deg: nat,Ma: nat,X: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ord_less_nat @ Ma @ X )
% 5.41/5.66 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( some_nat @ Ma ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pred_max
% 5.41/5.66 thf(fact_2515_succ__min,axiom,
% 5.41/5.66 ! [Deg: nat,X: nat,Mi: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ord_less_nat @ X @ Mi )
% 5.41/5.66 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( some_nat @ Mi ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % succ_min
% 5.41/5.66 thf(fact_2516_del__x__not__mi__newnode__not__nil,axiom,
% 5.41/5.66 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ( ord_less_nat @ Mi @ X )
% 5.41/5.66 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( Newnode
% 5.41/5.66 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( Newlist
% 5.41/5.66 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_not_mi_newnode_not_nil
% 5.41/5.66 thf(fact_2517_greater__shift,axiom,
% 5.41/5.66 ( ord_less_nat
% 5.41/5.66 = ( ^ [Y3: nat,X3: nat] : ( vEBT_VEBT_greater @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % greater_shift
% 5.41/5.66 thf(fact_2518_less__shift,axiom,
% 5.41/5.66 ( ord_less_nat
% 5.41/5.66 = ( ^ [X3: nat,Y3: nat] : ( vEBT_VEBT_less @ ( some_nat @ X3 ) @ ( some_nat @ Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_shift
% 5.41/5.66 thf(fact_2519_helpyd,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.41/5.66 = ( some_nat @ Y ) )
% 5.41/5.66 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % helpyd
% 5.41/5.66 thf(fact_2520_VEBT_Oinject_I1_J,axiom,
% 5.41/5.66 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,Y11: option4927543243414619207at_nat,Y12: nat,Y13: list_VEBT_VEBT,Y14: vEBT_VEBT] :
% 5.41/5.66 ( ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.41/5.66 = ( vEBT_Node @ Y11 @ Y12 @ Y13 @ Y14 ) )
% 5.41/5.66 = ( ( X11 = Y11 )
% 5.41/5.66 & ( X12 = Y12 )
% 5.41/5.66 & ( X13 = Y13 )
% 5.41/5.66 & ( X14 = Y14 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % VEBT.inject(1)
% 5.41/5.66 thf(fact_2521_idiff__0__right,axiom,
% 5.41/5.66 ! [N: extended_enat] :
% 5.41/5.66 ( ( minus_3235023915231533773d_enat @ N @ zero_z5237406670263579293d_enat )
% 5.41/5.66 = N ) ).
% 5.41/5.66
% 5.41/5.66 % idiff_0_right
% 5.41/5.66 thf(fact_2522_idiff__0,axiom,
% 5.41/5.66 ! [N: extended_enat] :
% 5.41/5.66 ( ( minus_3235023915231533773d_enat @ zero_z5237406670263579293d_enat @ N )
% 5.41/5.66 = zero_z5237406670263579293d_enat ) ).
% 5.41/5.66
% 5.41/5.66 % idiff_0
% 5.41/5.66 thf(fact_2523_succ__corr,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.41/5.66 = ( some_nat @ Sx ) )
% 5.41/5.66 = ( vEBT_is_succ_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % succ_corr
% 5.41/5.66 thf(fact_2524_pred__corr,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat,Px: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.41/5.66 = ( some_nat @ Px ) )
% 5.41/5.66 = ( vEBT_is_pred_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X @ Px ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pred_corr
% 5.41/5.66 thf(fact_2525_succ__correct,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.41/5.66 = ( some_nat @ Sx ) )
% 5.41/5.66 = ( vEBT_is_succ_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % succ_correct
% 5.41/5.66 thf(fact_2526_pred__correct,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat,Sx: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.41/5.66 = ( some_nat @ Sx ) )
% 5.41/5.66 = ( vEBT_is_pred_in_set @ ( vEBT_set_vebt @ T ) @ X @ Sx ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pred_correct
% 5.41/5.66 thf(fact_2527_geqmaxNone,axiom,
% 5.41/5.66 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.41/5.66 => ( ( ord_less_eq_nat @ Ma @ X )
% 5.41/5.66 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = none_nat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % geqmaxNone
% 5.41/5.66 thf(fact_2528_helpypredd,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat,Y: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.41/5.66 = ( some_nat @ Y ) )
% 5.41/5.66 => ( ord_less_nat @ Y @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % helpypredd
% 5.41/5.66 thf(fact_2529_summaxma,axiom,
% 5.41/5.66 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( the_nat @ ( vEBT_vebt_maxt @ Summary ) )
% 5.41/5.66 = ( vEBT_VEBT_high @ Ma @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % summaxma
% 5.41/5.66 thf(fact_2530_mod__neg__neg__trivial,axiom,
% 5.41/5.66 ! [K: int,L2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ L2 @ K )
% 5.41/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.41/5.66 = K ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mod_neg_neg_trivial
% 5.41/5.66 thf(fact_2531_mod__pos__pos__trivial,axiom,
% 5.41/5.66 ! [K: int,L2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.66 => ( ( ord_less_int @ K @ L2 )
% 5.41/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.41/5.66 = K ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mod_pos_pos_trivial
% 5.41/5.66 thf(fact_2532_zmod__numeral__Bit0,axiom,
% 5.41/5.66 ! [V: num,W: num] :
% 5.41/5.66 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.41/5.66 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmod_numeral_Bit0
% 5.41/5.66 thf(fact_2533_div__neg__neg__trivial,axiom,
% 5.41/5.66 ! [K: int,L2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ L2 @ K )
% 5.41/5.66 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.66 = zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_neg_neg_trivial
% 5.41/5.66 thf(fact_2534_div__pos__pos__trivial,axiom,
% 5.41/5.66 ! [K: int,L2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.66 => ( ( ord_less_int @ K @ L2 )
% 5.41/5.66 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.66 = zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_pos_pos_trivial
% 5.41/5.66 thf(fact_2535_local_Opower__def,axiom,
% 5.41/5.66 ( vEBT_VEBT_power
% 5.41/5.66 = ( vEBT_V4262088993061758097ft_nat @ power_power_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % local.power_def
% 5.41/5.66 thf(fact_2536_split__zdiv,axiom,
% 5.41/5.66 ! [P: int > $o,N: int,K: int] :
% 5.41/5.66 ( ( P @ ( divide_divide_int @ N @ K ) )
% 5.41/5.66 = ( ( ( K = zero_zero_int )
% 5.41/5.66 => ( P @ zero_zero_int ) )
% 5.41/5.66 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.66 => ! [I5: int,J3: int] :
% 5.41/5.66 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.41/5.66 & ( ord_less_int @ J3 @ K )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.41/5.66 => ( P @ I5 ) ) )
% 5.41/5.66 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.66 => ! [I5: int,J3: int] :
% 5.41/5.66 ( ( ( ord_less_int @ K @ J3 )
% 5.41/5.66 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.41/5.66 => ( P @ I5 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_zdiv
% 5.41/5.66 thf(fact_2537_split__zmod,axiom,
% 5.41/5.66 ! [P: int > $o,N: int,K: int] :
% 5.41/5.66 ( ( P @ ( modulo_modulo_int @ N @ K ) )
% 5.41/5.66 = ( ( ( K = zero_zero_int )
% 5.41/5.66 => ( P @ N ) )
% 5.41/5.66 & ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.66 => ! [I5: int,J3: int] :
% 5.41/5.66 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.41/5.66 & ( ord_less_int @ J3 @ K )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.41/5.66 => ( P @ J3 ) ) )
% 5.41/5.66 & ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.66 => ! [I5: int,J3: int] :
% 5.41/5.66 ( ( ( ord_less_int @ K @ J3 )
% 5.41/5.66 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.41/5.66 => ( P @ J3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_zmod
% 5.41/5.66 thf(fact_2538_zdiv__mono1,axiom,
% 5.41/5.66 ! [A: int,A4: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ A @ A4 )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A4 @ B ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_mono1
% 5.41/5.66 thf(fact_2539_zdiv__mono2,axiom,
% 5.41/5.66 ! [A: int,B4: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.41/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.41/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ A @ B4 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_mono2
% 5.41/5.66 thf(fact_2540_div__pos__geq,axiom,
% 5.41/5.66 ! [L2: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.41/5.66 => ( ( ord_less_eq_int @ L2 @ K )
% 5.41/5.66 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.66 = ( plus_plus_int @ ( divide_divide_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) @ one_one_int ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_pos_geq
% 5.41/5.66 thf(fact_2541_mod__pos__geq,axiom,
% 5.41/5.66 ! [L2: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.41/5.66 => ( ( ord_less_eq_int @ L2 @ K )
% 5.41/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.41/5.66 = ( modulo_modulo_int @ ( minus_minus_int @ K @ L2 ) @ L2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mod_pos_geq
% 5.41/5.66 thf(fact_2542_q__pos__lemma,axiom,
% 5.41/5.66 ! [B4: int,Q4: int,R3: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 5.41/5.66 => ( ( ord_less_int @ R3 @ B4 )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.41/5.66 => ( ord_less_eq_int @ zero_zero_int @ Q4 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % q_pos_lemma
% 5.41/5.66 thf(fact_2543_neg__mod__conj,axiom,
% 5.41/5.66 ! [B: int,A: int] :
% 5.41/5.66 ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_eq_int @ ( modulo_modulo_int @ A @ B ) @ zero_zero_int )
% 5.41/5.66 & ( ord_less_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % neg_mod_conj
% 5.41/5.66 thf(fact_2544_pos__mod__conj,axiom,
% 5.41/5.66 ! [B: int,A: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.66 & ( ord_less_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pos_mod_conj
% 5.41/5.66 thf(fact_2545_zdiv__eq__0__iff,axiom,
% 5.41/5.66 ! [I: int,K: int] :
% 5.41/5.66 ( ( ( divide_divide_int @ I @ K )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 = ( ( K = zero_zero_int )
% 5.41/5.66 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.41/5.66 & ( ord_less_int @ I @ K ) )
% 5.41/5.66 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.41/5.66 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_eq_0_iff
% 5.41/5.66 thf(fact_2546_int__div__neg__eq,axiom,
% 5.41/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.41/5.66 ( ( A
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ B @ R )
% 5.41/5.66 => ( ( divide_divide_int @ A @ B )
% 5.41/5.66 = Q2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_div_neg_eq
% 5.41/5.66 thf(fact_2547_int__div__pos__eq,axiom,
% 5.41/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.41/5.66 ( ( A
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.41/5.66 => ( ( ord_less_int @ R @ B )
% 5.41/5.66 => ( ( divide_divide_int @ A @ B )
% 5.41/5.66 = Q2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_div_pos_eq
% 5.41/5.66 thf(fact_2548_int__mod__neg__eq,axiom,
% 5.41/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.41/5.66 ( ( A
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ B @ R )
% 5.41/5.66 => ( ( modulo_modulo_int @ A @ B )
% 5.41/5.66 = R ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_mod_neg_eq
% 5.41/5.66 thf(fact_2549_int__mod__pos__eq,axiom,
% 5.41/5.66 ! [A: int,B: int,Q2: int,R: int] :
% 5.41/5.66 ( ( A
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.41/5.66 => ( ( ord_less_int @ R @ B )
% 5.41/5.66 => ( ( modulo_modulo_int @ A @ B )
% 5.41/5.66 = R ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_mod_pos_eq
% 5.41/5.66 thf(fact_2550_zdiv__mono1__neg,axiom,
% 5.41/5.66 ! [A: int,A4: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ A @ A4 )
% 5.41/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A4 @ B ) @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_mono1_neg
% 5.41/5.66 thf(fact_2551_zdiv__mono2__neg,axiom,
% 5.41/5.66 ! [A: int,B4: int,B: int] :
% 5.41/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.41/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.41/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B4 ) @ ( divide_divide_int @ A @ B ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_mono2_neg
% 5.41/5.66 thf(fact_2552_div__int__pos__iff,axiom,
% 5.41/5.66 ! [K: int,L2: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) )
% 5.41/5.66 = ( ( K = zero_zero_int )
% 5.41/5.66 | ( L2 = zero_zero_int )
% 5.41/5.66 | ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.66 & ( ord_less_eq_int @ zero_zero_int @ L2 ) )
% 5.41/5.66 | ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.66 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_int_pos_iff
% 5.41/5.66 thf(fact_2553_split__neg__lemma,axiom,
% 5.41/5.66 ! [K: int,P: int > int > $o,N: int] :
% 5.41/5.66 ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.66 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.41/5.66 = ( ! [I5: int,J3: int] :
% 5.41/5.66 ( ( ( ord_less_int @ K @ J3 )
% 5.41/5.66 & ( ord_less_eq_int @ J3 @ zero_zero_int )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.41/5.66 => ( P @ I5 @ J3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_neg_lemma
% 5.41/5.66 thf(fact_2554_split__pos__lemma,axiom,
% 5.41/5.66 ! [K: int,P: int > int > $o,N: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.66 => ( ( P @ ( divide_divide_int @ N @ K ) @ ( modulo_modulo_int @ N @ K ) )
% 5.41/5.66 = ( ! [I5: int,J3: int] :
% 5.41/5.66 ( ( ( ord_less_eq_int @ zero_zero_int @ J3 )
% 5.41/5.66 & ( ord_less_int @ J3 @ K )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ K @ I5 ) @ J3 ) ) )
% 5.41/5.66 => ( P @ I5 @ J3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_pos_lemma
% 5.41/5.66 thf(fact_2555_div__positive__int,axiom,
% 5.41/5.66 ! [L2: int,K: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ L2 @ K )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.41/5.66 => ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ K @ L2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_positive_int
% 5.41/5.66 thf(fact_2556_zdiv__mono2__lemma,axiom,
% 5.41/5.66 ! [B: int,Q2: int,R: int,B4: int,Q4: int,R3: int] :
% 5.41/5.66 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 5.41/5.66 => ( ( ord_less_int @ R3 @ B4 )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.41/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.41/5.66 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_mono2_lemma
% 5.41/5.66 thf(fact_2557_zmod__trivial__iff,axiom,
% 5.41/5.66 ! [I: int,K: int] :
% 5.41/5.66 ( ( ( modulo_modulo_int @ I @ K )
% 5.41/5.66 = I )
% 5.41/5.66 = ( ( K = zero_zero_int )
% 5.41/5.66 | ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.41/5.66 & ( ord_less_int @ I @ K ) )
% 5.41/5.66 | ( ( ord_less_eq_int @ I @ zero_zero_int )
% 5.41/5.66 & ( ord_less_int @ K @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmod_trivial_iff
% 5.41/5.66 thf(fact_2558_div__neg__pos__less0,axiom,
% 5.41/5.66 ! [A: int,B: int] :
% 5.41/5.66 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.66 => ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_neg_pos_less0
% 5.41/5.66 thf(fact_2559_int__div__less__self,axiom,
% 5.41/5.66 ! [X: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ X )
% 5.41/5.66 => ( ( ord_less_int @ one_one_int @ K )
% 5.41/5.66 => ( ord_less_int @ ( divide_divide_int @ X @ K ) @ X ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_div_less_self
% 5.41/5.66 thf(fact_2560_div__nonneg__neg__le0,axiom,
% 5.41/5.66 ! [A: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.66 => ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_nonneg_neg_le0
% 5.41/5.66 thf(fact_2561_div__nonpos__pos__le0,axiom,
% 5.41/5.66 ! [A: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.66 => ( ord_less_eq_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div_nonpos_pos_le0
% 5.41/5.66 thf(fact_2562_neg__imp__zdiv__neg__iff,axiom,
% 5.41/5.66 ! [B: int,A: int] :
% 5.41/5.66 ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.41/5.66 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % neg_imp_zdiv_neg_iff
% 5.41/5.66 thf(fact_2563_pos__imp__zdiv__neg__iff,axiom,
% 5.41/5.66 ! [B: int,A: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.66 => ( ( ord_less_int @ ( divide_divide_int @ A @ B ) @ zero_zero_int )
% 5.41/5.66 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pos_imp_zdiv_neg_iff
% 5.41/5.66 thf(fact_2564_pos__imp__zdiv__pos__iff,axiom,
% 5.41/5.66 ! [K: int,I: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ I @ K ) )
% 5.41/5.66 = ( ord_less_eq_int @ K @ I ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pos_imp_zdiv_pos_iff
% 5.41/5.66 thf(fact_2565_zdiv__mono2__neg__lemma,axiom,
% 5.41/5.66 ! [B: int,Q2: int,R: int,B4: int,Q4: int,R3: int] :
% 5.41/5.66 ( ( ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R )
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) )
% 5.41/5.66 => ( ( ord_less_int @ ( plus_plus_int @ ( times_times_int @ B4 @ Q4 ) @ R3 ) @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ R @ B )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ B4 )
% 5.41/5.66 => ( ( ord_less_eq_int @ B4 @ B )
% 5.41/5.66 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_mono2_neg_lemma
% 5.41/5.66 thf(fact_2566_unique__quotient__lemma,axiom,
% 5.41/5.66 ! [B: int,Q4: int,R3: int,Q2: int,R: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ R3 )
% 5.41/5.66 => ( ( ord_less_int @ R3 @ B )
% 5.41/5.66 => ( ( ord_less_int @ R @ B )
% 5.41/5.66 => ( ord_less_eq_int @ Q4 @ Q2 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unique_quotient_lemma
% 5.41/5.66 thf(fact_2567_neg__imp__zdiv__nonneg__iff,axiom,
% 5.41/5.66 ! [B: int,A: int] :
% 5.41/5.66 ( ( ord_less_int @ B @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.41/5.66 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % neg_imp_zdiv_nonneg_iff
% 5.41/5.66 thf(fact_2568_pos__imp__zdiv__nonneg__iff,axiom,
% 5.41/5.66 ! [B: int,A: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.66 => ( ( ord_less_eq_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.41/5.66 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pos_imp_zdiv_nonneg_iff
% 5.41/5.66 thf(fact_2569_neg__mod__sign,axiom,
% 5.41/5.66 ! [L2: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.41/5.66 => ( ord_less_eq_int @ ( modulo_modulo_int @ K @ L2 ) @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % neg_mod_sign
% 5.41/5.66 thf(fact_2570_Euclidean__Division_Opos__mod__sign,axiom,
% 5.41/5.66 ! [L2: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.41/5.66 => ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Euclidean_Division.pos_mod_sign
% 5.41/5.66 thf(fact_2571_nonneg1__imp__zdiv__pos__iff,axiom,
% 5.41/5.66 ! [A: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ ( divide_divide_int @ A @ B ) )
% 5.41/5.66 = ( ( ord_less_eq_int @ B @ A )
% 5.41/5.66 & ( ord_less_int @ zero_zero_int @ B ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nonneg1_imp_zdiv_pos_iff
% 5.41/5.66 thf(fact_2572_neg__mod__bound,axiom,
% 5.41/5.66 ! [L2: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.41/5.66 => ( ord_less_int @ L2 @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % neg_mod_bound
% 5.41/5.66 thf(fact_2573_Euclidean__Division_Opos__mod__bound,axiom,
% 5.41/5.66 ! [L2: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.41/5.66 => ( ord_less_int @ ( modulo_modulo_int @ K @ L2 ) @ L2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % Euclidean_Division.pos_mod_bound
% 5.41/5.66 thf(fact_2574_unique__quotient__lemma__neg,axiom,
% 5.41/5.66 ! [B: int,Q4: int,R3: int,Q2: int,R: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ ( times_times_int @ B @ Q4 ) @ R3 ) @ ( plus_plus_int @ ( times_times_int @ B @ Q2 ) @ R ) )
% 5.41/5.66 => ( ( ord_less_eq_int @ R @ zero_zero_int )
% 5.41/5.66 => ( ( ord_less_int @ B @ R )
% 5.41/5.66 => ( ( ord_less_int @ B @ R3 )
% 5.41/5.66 => ( ord_less_eq_int @ Q2 @ Q4 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % unique_quotient_lemma_neg
% 5.41/5.66 thf(fact_2575_mod__pos__neg__trivial,axiom,
% 5.41/5.66 ! [K: int,L2: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.66 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.41/5.66 => ( ( modulo_modulo_int @ K @ L2 )
% 5.41/5.66 = ( plus_plus_int @ K @ L2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mod_pos_neg_trivial
% 5.41/5.66 thf(fact_2576_zmod__zmult2__eq,axiom,
% 5.41/5.66 ! [C: int,A: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.66 => ( ( modulo_modulo_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ B @ ( modulo_modulo_int @ ( divide_divide_int @ A @ B ) @ C ) ) @ ( modulo_modulo_int @ A @ B ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmod_zmult2_eq
% 5.41/5.66 thf(fact_2577_zdiv__zmult2__eq,axiom,
% 5.41/5.66 ! [C: int,A: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ C )
% 5.41/5.66 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.66 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zdiv_zmult2_eq
% 5.41/5.66 thf(fact_2578_zmod__le__nonneg__dividend,axiom,
% 5.41/5.66 ! [M: int,K: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.41/5.66 => ( ord_less_eq_int @ ( modulo_modulo_int @ M @ K ) @ M ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmod_le_nonneg_dividend
% 5.41/5.66 thf(fact_2579_zero__one__enat__neq_I1_J,axiom,
% 5.41/5.66 zero_z5237406670263579293d_enat != one_on7984719198319812577d_enat ).
% 5.41/5.66
% 5.41/5.66 % zero_one_enat_neq(1)
% 5.41/5.66 thf(fact_2580_zmod__eq__0D,axiom,
% 5.41/5.66 ! [M: int,D: int] :
% 5.41/5.66 ( ( ( modulo_modulo_int @ M @ D )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 => ? [Q3: int] :
% 5.41/5.66 ( M
% 5.41/5.66 = ( times_times_int @ D @ Q3 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmod_eq_0D
% 5.41/5.66 thf(fact_2581_zmod__eq__0__iff,axiom,
% 5.41/5.66 ! [M: int,D: int] :
% 5.41/5.66 ( ( ( modulo_modulo_int @ M @ D )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 = ( ? [Q5: int] :
% 5.41/5.66 ( M
% 5.41/5.66 = ( times_times_int @ D @ Q5 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmod_eq_0_iff
% 5.41/5.66 thf(fact_2582_imult__is__0,axiom,
% 5.41/5.66 ! [M: extended_enat,N: extended_enat] :
% 5.41/5.66 ( ( ( times_7803423173614009249d_enat @ M @ N )
% 5.41/5.66 = zero_z5237406670263579293d_enat )
% 5.41/5.66 = ( ( M = zero_z5237406670263579293d_enat )
% 5.41/5.66 | ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % imult_is_0
% 5.41/5.66 thf(fact_2583_iadd__is__0,axiom,
% 5.41/5.66 ! [M: extended_enat,N: extended_enat] :
% 5.41/5.66 ( ( ( plus_p3455044024723400733d_enat @ M @ N )
% 5.41/5.66 = zero_z5237406670263579293d_enat )
% 5.41/5.66 = ( ( M = zero_z5237406670263579293d_enat )
% 5.41/5.66 & ( N = zero_z5237406670263579293d_enat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % iadd_is_0
% 5.41/5.66 thf(fact_2584_neg__zmod__mult__2,axiom,
% 5.41/5.66 ! [A: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.66 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.66 = ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( plus_plus_int @ B @ one_one_int ) @ A ) ) @ one_one_int ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % neg_zmod_mult_2
% 5.41/5.66 thf(fact_2585_add__diff__assoc__enat,axiom,
% 5.41/5.66 ! [Z: extended_enat,Y: extended_enat,X: extended_enat] :
% 5.41/5.66 ( ( ord_le2932123472753598470d_enat @ Z @ Y )
% 5.41/5.66 => ( ( plus_p3455044024723400733d_enat @ X @ ( minus_3235023915231533773d_enat @ Y @ Z ) )
% 5.41/5.66 = ( minus_3235023915231533773d_enat @ ( plus_p3455044024723400733d_enat @ X @ Y ) @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_diff_assoc_enat
% 5.41/5.66 thf(fact_2586_pos__zmod__mult__2,axiom,
% 5.41/5.66 ! [A: int,B: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.66 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.66 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ B @ A ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pos_zmod_mult_2
% 5.41/5.66 thf(fact_2587_nat__induct2,axiom,
% 5.41/5.66 ! [P: nat > $o,N: nat] :
% 5.41/5.66 ( ( P @ zero_zero_nat )
% 5.41/5.66 => ( ( P @ one_one_nat )
% 5.41/5.66 => ( ! [N3: nat] :
% 5.41/5.66 ( ( P @ N3 )
% 5.41/5.66 => ( P @ ( plus_plus_nat @ N3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.66 => ( P @ N ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_induct2
% 5.41/5.66 thf(fact_2588_VEBT__internal_Oexp__split__high__low_I1_J,axiom,
% 5.41/5.66 ! [X: nat,N: nat,M: nat] :
% 5.41/5.66 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.66 => ( ord_less_nat @ ( vEBT_VEBT_high @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % VEBT_internal.exp_split_high_low(1)
% 5.41/5.66 thf(fact_2589_VEBT__internal_Oexp__split__high__low_I2_J,axiom,
% 5.41/5.66 ! [X: nat,N: nat,M: nat] :
% 5.41/5.66 ( ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ N @ M ) ) )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.66 => ( ord_less_nat @ ( vEBT_VEBT_low @ X @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % VEBT_internal.exp_split_high_low(2)
% 5.41/5.66 thf(fact_2590_del__x__mi__lets__in__not__minNull,axiom,
% 5.41/5.66 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.41/5.66 ( ( ( X = Mi )
% 5.41/5.66 & ( ord_less_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( Xn
% 5.41/5.66 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( Newnode
% 5.41/5.66 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 => ( ( Newlist
% 5.41/5.66 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.41/5.66 => ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_mi_lets_in_not_minNull
% 5.41/5.66 thf(fact_2591_real__average__minus__first,axiom,
% 5.41/5.66 ! [A: real,B: real] :
% 5.41/5.66 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.41/5.66 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % real_average_minus_first
% 5.41/5.66 thf(fact_2592_real__average__minus__second,axiom,
% 5.41/5.66 ! [B: real,A: real] :
% 5.41/5.66 ( ( minus_minus_real @ ( divide_divide_real @ ( plus_plus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ A )
% 5.41/5.66 = ( divide_divide_real @ ( minus_minus_real @ B @ A ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % real_average_minus_second
% 5.41/5.66 thf(fact_2593_insert__simp__norm,axiom,
% 5.41/5.66 ! [X: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( ord_less_nat @ Mi @ X )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( X != Ma )
% 5.41/5.66 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( ord_max_nat @ X @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % insert_simp_norm
% 5.41/5.66 thf(fact_2594_insert__simp__excp,axiom,
% 5.41/5.66 ! [Mi: nat,Deg: nat,TreeList2: list_VEBT_VEBT,X: nat,Ma: nat,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ord_less_nat @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( ord_less_nat @ X @ Mi )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( X != Ma )
% 5.41/5.66 => ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ ( ord_max_nat @ Mi @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ Mi @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % insert_simp_excp
% 5.41/5.66 thf(fact_2595_zle__add1__eq__le,axiom,
% 5.41/5.66 ! [W: int,Z: int] :
% 5.41/5.66 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.41/5.66 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.41/5.66
% 5.41/5.66 % zle_add1_eq_le
% 5.41/5.66 thf(fact_2596_divmod__step__eq,axiom,
% 5.41/5.66 ! [L2: num,R: nat,Q2: nat] :
% 5.41/5.66 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 5.41/5.66 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.41/5.66 = ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ one_one_nat ) @ ( minus_minus_nat @ R @ ( numeral_numeral_nat @ L2 ) ) ) ) )
% 5.41/5.66 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L2 ) @ R )
% 5.41/5.66 => ( ( unique5026877609467782581ep_nat @ L2 @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.41/5.66 = ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divmod_step_eq
% 5.41/5.66 thf(fact_2597_divmod__step__eq,axiom,
% 5.41/5.66 ! [L2: num,R: int,Q2: int] :
% 5.41/5.66 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 5.41/5.66 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.66 = ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ one_one_int ) @ ( minus_minus_int @ R @ ( numeral_numeral_int @ L2 ) ) ) ) )
% 5.41/5.66 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ L2 ) @ R )
% 5.41/5.66 => ( ( unique5024387138958732305ep_int @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.66 = ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divmod_step_eq
% 5.41/5.66 thf(fact_2598_divmod__step__eq,axiom,
% 5.41/5.66 ! [L2: num,R: code_integer,Q2: code_integer] :
% 5.41/5.66 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 5.41/5.66 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.41/5.66 = ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R @ ( numera6620942414471956472nteger @ L2 ) ) ) ) )
% 5.41/5.66 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L2 ) @ R )
% 5.41/5.66 => ( ( unique4921790084139445826nteger @ L2 @ ( produc1086072967326762835nteger @ Q2 @ R ) )
% 5.41/5.66 = ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q2 ) @ R ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % divmod_step_eq
% 5.41/5.66 thf(fact_2599_mintlistlength,axiom,
% 5.41/5.66 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_nat @ Mi @ Ma )
% 5.41/5.66 & ? [M4: nat] :
% 5.41/5.66 ( ( ( some_nat @ M4 )
% 5.41/5.66 = ( vEBT_vebt_mint @ Summary ) )
% 5.41/5.66 & ( ord_less_nat @ M4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mintlistlength
% 5.41/5.66 thf(fact_2600_option_Ocollapse,axiom,
% 5.41/5.66 ! [Option: option_nat] :
% 5.41/5.66 ( ( Option != none_nat )
% 5.41/5.66 => ( ( some_nat @ ( the_nat @ Option ) )
% 5.41/5.66 = Option ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.collapse
% 5.41/5.66 thf(fact_2601_option_Ocollapse,axiom,
% 5.41/5.66 ! [Option: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( Option != none_P5556105721700978146at_nat )
% 5.41/5.66 => ( ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) )
% 5.41/5.66 = Option ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.collapse
% 5.41/5.66 thf(fact_2602_option_Ocollapse,axiom,
% 5.41/5.66 ! [Option: option_num] :
% 5.41/5.66 ( ( Option != none_num )
% 5.41/5.66 => ( ( some_num @ ( the_num @ Option ) )
% 5.41/5.66 = Option ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.collapse
% 5.41/5.66 thf(fact_2603_minNullmin,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT] :
% 5.41/5.66 ( ( vEBT_VEBT_minNull @ T )
% 5.41/5.66 => ( ( vEBT_vebt_mint @ T )
% 5.41/5.66 = none_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % minNullmin
% 5.41/5.66 thf(fact_2604_minminNull,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT] :
% 5.41/5.66 ( ( ( vEBT_vebt_mint @ T )
% 5.41/5.66 = none_nat )
% 5.41/5.66 => ( vEBT_VEBT_minNull @ T ) ) ).
% 5.41/5.66
% 5.41/5.66 % minminNull
% 5.41/5.66 thf(fact_2605_mint__member,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,Maxi: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_mint @ T )
% 5.41/5.66 = ( some_nat @ Maxi ) )
% 5.41/5.66 => ( vEBT_vebt_member @ T @ Maxi ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mint_member
% 5.41/5.66 thf(fact_2606_option_Oinject,axiom,
% 5.41/5.66 ! [X22: nat,Y22: nat] :
% 5.41/5.66 ( ( ( some_nat @ X22 )
% 5.41/5.66 = ( some_nat @ Y22 ) )
% 5.41/5.66 = ( X22 = Y22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.inject
% 5.41/5.66 thf(fact_2607_option_Oinject,axiom,
% 5.41/5.66 ! [X22: product_prod_nat_nat,Y22: product_prod_nat_nat] :
% 5.41/5.66 ( ( ( some_P7363390416028606310at_nat @ X22 )
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ Y22 ) )
% 5.41/5.66 = ( X22 = Y22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.inject
% 5.41/5.66 thf(fact_2608_option_Oinject,axiom,
% 5.41/5.66 ! [X22: num,Y22: num] :
% 5.41/5.66 ( ( ( some_num @ X22 )
% 5.41/5.66 = ( some_num @ Y22 ) )
% 5.41/5.66 = ( X22 = Y22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.inject
% 5.41/5.66 thf(fact_2609_mint__corr__help,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,Mini: nat,X: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_mint @ T )
% 5.41/5.66 = ( some_nat @ Mini ) )
% 5.41/5.66 => ( ( vEBT_vebt_member @ T @ X )
% 5.41/5.66 => ( ord_less_eq_nat @ Mini @ X ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mint_corr_help
% 5.41/5.66 thf(fact_2610_mint__corr,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( vEBT_vebt_mint @ T )
% 5.41/5.66 = ( some_nat @ X ) )
% 5.41/5.66 => ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mint_corr
% 5.41/5.66 thf(fact_2611_mint__sound,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( vEBT_VEBT_min_in_set @ ( vEBT_VEBT_set_vebt @ T ) @ X )
% 5.41/5.66 => ( ( vEBT_vebt_mint @ T )
% 5.41/5.66 = ( some_nat @ X ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mint_sound
% 5.41/5.66 thf(fact_2612_double__eq__0__iff,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( ( plus_plus_real @ A @ A )
% 5.41/5.66 = zero_zero_real )
% 5.41/5.66 = ( A = zero_zero_real ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_eq_0_iff
% 5.41/5.66 thf(fact_2613_double__eq__0__iff,axiom,
% 5.41/5.66 ! [A: rat] :
% 5.41/5.66 ( ( ( plus_plus_rat @ A @ A )
% 5.41/5.66 = zero_zero_rat )
% 5.41/5.66 = ( A = zero_zero_rat ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_eq_0_iff
% 5.41/5.66 thf(fact_2614_double__eq__0__iff,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( ( plus_plus_int @ A @ A )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 = ( A = zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % double_eq_0_iff
% 5.41/5.66 thf(fact_2615_del__single__cont,axiom,
% 5.41/5.66 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ( X = Mi )
% 5.41/5.66 & ( X = Ma ) )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_single_cont
% 5.41/5.66 thf(fact_2616_misiz,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat,M: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ( ( some_nat @ M )
% 5.41/5.66 = ( vEBT_vebt_mint @ T ) )
% 5.41/5.66 => ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % misiz
% 5.41/5.66 thf(fact_2617_not__None__eq,axiom,
% 5.41/5.66 ! [X: option_nat] :
% 5.41/5.66 ( ( X != none_nat )
% 5.41/5.66 = ( ? [Y3: nat] :
% 5.41/5.66 ( X
% 5.41/5.66 = ( some_nat @ Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_None_eq
% 5.41/5.66 thf(fact_2618_not__None__eq,axiom,
% 5.41/5.66 ! [X: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( X != none_P5556105721700978146at_nat )
% 5.41/5.66 = ( ? [Y3: product_prod_nat_nat] :
% 5.41/5.66 ( X
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_None_eq
% 5.41/5.66 thf(fact_2619_not__None__eq,axiom,
% 5.41/5.66 ! [X: option_num] :
% 5.41/5.66 ( ( X != none_num )
% 5.41/5.66 = ( ? [Y3: num] :
% 5.41/5.66 ( X
% 5.41/5.66 = ( some_num @ Y3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_None_eq
% 5.41/5.66 thf(fact_2620_not__Some__eq,axiom,
% 5.41/5.66 ! [X: option_nat] :
% 5.41/5.66 ( ( ! [Y3: nat] :
% 5.41/5.66 ( X
% 5.41/5.66 != ( some_nat @ Y3 ) ) )
% 5.41/5.66 = ( X = none_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_Some_eq
% 5.41/5.66 thf(fact_2621_not__Some__eq,axiom,
% 5.41/5.66 ! [X: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( ! [Y3: product_prod_nat_nat] :
% 5.41/5.66 ( X
% 5.41/5.66 != ( some_P7363390416028606310at_nat @ Y3 ) ) )
% 5.41/5.66 = ( X = none_P5556105721700978146at_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_Some_eq
% 5.41/5.66 thf(fact_2622_not__Some__eq,axiom,
% 5.41/5.66 ! [X: option_num] :
% 5.41/5.66 ( ( ! [Y3: num] :
% 5.41/5.66 ( X
% 5.41/5.66 != ( some_num @ Y3 ) ) )
% 5.41/5.66 = ( X = none_num ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_Some_eq
% 5.41/5.66 thf(fact_2623_max__nat_Oeq__neutr__iff,axiom,
% 5.41/5.66 ! [A: nat,B: nat] :
% 5.41/5.66 ( ( ( ord_max_nat @ A @ B )
% 5.41/5.66 = zero_zero_nat )
% 5.41/5.66 = ( ( A = zero_zero_nat )
% 5.41/5.66 & ( B = zero_zero_nat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_nat.eq_neutr_iff
% 5.41/5.66 thf(fact_2624_max__nat_Oleft__neutral,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( ord_max_nat @ zero_zero_nat @ A )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % max_nat.left_neutral
% 5.41/5.66 thf(fact_2625_max__nat_Oneutr__eq__iff,axiom,
% 5.41/5.66 ! [A: nat,B: nat] :
% 5.41/5.66 ( ( zero_zero_nat
% 5.41/5.66 = ( ord_max_nat @ A @ B ) )
% 5.41/5.66 = ( ( A = zero_zero_nat )
% 5.41/5.66 & ( B = zero_zero_nat ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_nat.neutr_eq_iff
% 5.41/5.66 thf(fact_2626_max__nat_Oright__neutral,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( ord_max_nat @ A @ zero_zero_nat )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % max_nat.right_neutral
% 5.41/5.66 thf(fact_2627_max__0L,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_max_nat @ zero_zero_nat @ N )
% 5.41/5.66 = N ) ).
% 5.41/5.66
% 5.41/5.66 % max_0L
% 5.41/5.66 thf(fact_2628_max__0R,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_max_nat @ N @ zero_zero_nat )
% 5.41/5.66 = N ) ).
% 5.41/5.66
% 5.41/5.66 % max_0R
% 5.41/5.66 thf(fact_2629_max__number__of_I1_J,axiom,
% 5.41/5.66 ! [U: num,V: num] :
% 5.41/5.66 ( ( ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.41/5.66 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.41/5.66 = ( numera1916890842035813515d_enat @ V ) ) )
% 5.41/5.66 & ( ~ ( ord_le2932123472753598470d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.41/5.66 => ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ U ) @ ( numera1916890842035813515d_enat @ V ) )
% 5.41/5.66 = ( numera1916890842035813515d_enat @ U ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_number_of(1)
% 5.41/5.66 thf(fact_2630_max__number__of_I1_J,axiom,
% 5.41/5.66 ! [U: num,V: num] :
% 5.41/5.66 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.66 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.66 = ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.66 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.66 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.66 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_number_of(1)
% 5.41/5.66 thf(fact_2631_max__number__of_I1_J,axiom,
% 5.41/5.66 ! [U: num,V: num] :
% 5.41/5.66 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.66 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.66 = ( numeral_numeral_real @ V ) ) )
% 5.41/5.66 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.66 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.66 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_number_of(1)
% 5.41/5.66 thf(fact_2632_max__number__of_I1_J,axiom,
% 5.41/5.66 ! [U: num,V: num] :
% 5.41/5.66 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.66 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.66 = ( numeral_numeral_rat @ V ) ) )
% 5.41/5.66 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.66 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.66 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_number_of(1)
% 5.41/5.66 thf(fact_2633_max__number__of_I1_J,axiom,
% 5.41/5.66 ! [U: num,V: num] :
% 5.41/5.66 ( ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.66 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.66 = ( numeral_numeral_nat @ V ) ) )
% 5.41/5.66 & ( ~ ( ord_less_eq_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.66 => ( ( ord_max_nat @ ( numeral_numeral_nat @ U ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.66 = ( numeral_numeral_nat @ U ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_number_of(1)
% 5.41/5.66 thf(fact_2634_max__number__of_I1_J,axiom,
% 5.41/5.66 ! [U: num,V: num] :
% 5.41/5.66 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.66 = ( numeral_numeral_int @ V ) ) )
% 5.41/5.66 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.66 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.66 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_number_of(1)
% 5.41/5.66 thf(fact_2635_max__0__1_I3_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.41/5.66 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(3)
% 5.41/5.66 thf(fact_2636_max__0__1_I3_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ X ) )
% 5.41/5.66 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(3)
% 5.41/5.66 thf(fact_2637_max__0__1_I3_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_real @ zero_zero_real @ ( numeral_numeral_real @ X ) )
% 5.41/5.66 = ( numeral_numeral_real @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(3)
% 5.41/5.66 thf(fact_2638_max__0__1_I3_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_rat @ zero_zero_rat @ ( numeral_numeral_rat @ X ) )
% 5.41/5.66 = ( numeral_numeral_rat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(3)
% 5.41/5.66 thf(fact_2639_max__0__1_I3_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_nat @ zero_zero_nat @ ( numeral_numeral_nat @ X ) )
% 5.41/5.66 = ( numeral_numeral_nat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(3)
% 5.41/5.66 thf(fact_2640_max__0__1_I3_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_int @ zero_zero_int @ ( numeral_numeral_int @ X ) )
% 5.41/5.66 = ( numeral_numeral_int @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(3)
% 5.41/5.66 thf(fact_2641_max__0__1_I4_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ zero_z5237406670263579293d_enat )
% 5.41/5.66 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(4)
% 5.41/5.66 thf(fact_2642_max__0__1_I4_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ zero_z3403309356797280102nteger )
% 5.41/5.66 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(4)
% 5.41/5.66 thf(fact_2643_max__0__1_I4_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ zero_zero_real )
% 5.41/5.66 = ( numeral_numeral_real @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(4)
% 5.41/5.66 thf(fact_2644_max__0__1_I4_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ zero_zero_rat )
% 5.41/5.66 = ( numeral_numeral_rat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(4)
% 5.41/5.66 thf(fact_2645_max__0__1_I4_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ zero_zero_nat )
% 5.41/5.66 = ( numeral_numeral_nat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(4)
% 5.41/5.66 thf(fact_2646_max__0__1_I4_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ zero_zero_int )
% 5.41/5.66 = ( numeral_numeral_int @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(4)
% 5.41/5.66 thf(fact_2647_max__0__1_I1_J,axiom,
% 5.41/5.66 ( ( ord_max_real @ zero_zero_real @ one_one_real )
% 5.41/5.66 = one_one_real ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(1)
% 5.41/5.66 thf(fact_2648_max__0__1_I1_J,axiom,
% 5.41/5.66 ( ( ord_max_rat @ zero_zero_rat @ one_one_rat )
% 5.41/5.66 = one_one_rat ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(1)
% 5.41/5.66 thf(fact_2649_max__0__1_I1_J,axiom,
% 5.41/5.66 ( ( ord_max_nat @ zero_zero_nat @ one_one_nat )
% 5.41/5.66 = one_one_nat ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(1)
% 5.41/5.66 thf(fact_2650_max__0__1_I1_J,axiom,
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ one_on7984719198319812577d_enat )
% 5.41/5.66 = one_on7984719198319812577d_enat ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(1)
% 5.41/5.66 thf(fact_2651_max__0__1_I1_J,axiom,
% 5.41/5.66 ( ( ord_max_int @ zero_zero_int @ one_one_int )
% 5.41/5.66 = one_one_int ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(1)
% 5.41/5.66 thf(fact_2652_max__0__1_I1_J,axiom,
% 5.41/5.66 ( ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer )
% 5.41/5.66 = one_one_Code_integer ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(1)
% 5.41/5.66 thf(fact_2653_max__0__1_I2_J,axiom,
% 5.41/5.66 ( ( ord_max_real @ one_one_real @ zero_zero_real )
% 5.41/5.66 = one_one_real ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(2)
% 5.41/5.66 thf(fact_2654_max__0__1_I2_J,axiom,
% 5.41/5.66 ( ( ord_max_rat @ one_one_rat @ zero_zero_rat )
% 5.41/5.66 = one_one_rat ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(2)
% 5.41/5.66 thf(fact_2655_max__0__1_I2_J,axiom,
% 5.41/5.66 ( ( ord_max_nat @ one_one_nat @ zero_zero_nat )
% 5.41/5.66 = one_one_nat ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(2)
% 5.41/5.66 thf(fact_2656_max__0__1_I2_J,axiom,
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ zero_z5237406670263579293d_enat )
% 5.41/5.66 = one_on7984719198319812577d_enat ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(2)
% 5.41/5.66 thf(fact_2657_max__0__1_I2_J,axiom,
% 5.41/5.66 ( ( ord_max_int @ one_one_int @ zero_zero_int )
% 5.41/5.66 = one_one_int ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(2)
% 5.41/5.66 thf(fact_2658_max__0__1_I2_J,axiom,
% 5.41/5.66 ( ( ord_max_Code_integer @ one_one_Code_integer @ zero_z3403309356797280102nteger )
% 5.41/5.66 = one_one_Code_integer ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(2)
% 5.41/5.66 thf(fact_2659_max__0__1_I5_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ one_on7984719198319812577d_enat @ ( numera1916890842035813515d_enat @ X ) )
% 5.41/5.66 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(5)
% 5.41/5.66 thf(fact_2660_max__0__1_I5_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_Code_integer @ one_one_Code_integer @ ( numera6620942414471956472nteger @ X ) )
% 5.41/5.66 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(5)
% 5.41/5.66 thf(fact_2661_max__0__1_I5_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_real @ one_one_real @ ( numeral_numeral_real @ X ) )
% 5.41/5.66 = ( numeral_numeral_real @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(5)
% 5.41/5.66 thf(fact_2662_max__0__1_I5_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_rat @ one_one_rat @ ( numeral_numeral_rat @ X ) )
% 5.41/5.66 = ( numeral_numeral_rat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(5)
% 5.41/5.66 thf(fact_2663_max__0__1_I5_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_nat @ one_one_nat @ ( numeral_numeral_nat @ X ) )
% 5.41/5.66 = ( numeral_numeral_nat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(5)
% 5.41/5.66 thf(fact_2664_max__0__1_I5_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_int @ one_one_int @ ( numeral_numeral_int @ X ) )
% 5.41/5.66 = ( numeral_numeral_int @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(5)
% 5.41/5.66 thf(fact_2665_max__0__1_I6_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ ( numera1916890842035813515d_enat @ X ) @ one_on7984719198319812577d_enat )
% 5.41/5.66 = ( numera1916890842035813515d_enat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(6)
% 5.41/5.66 thf(fact_2666_max__0__1_I6_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ X ) @ one_one_Code_integer )
% 5.41/5.66 = ( numera6620942414471956472nteger @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(6)
% 5.41/5.66 thf(fact_2667_max__0__1_I6_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_real @ ( numeral_numeral_real @ X ) @ one_one_real )
% 5.41/5.66 = ( numeral_numeral_real @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(6)
% 5.41/5.66 thf(fact_2668_max__0__1_I6_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat )
% 5.41/5.66 = ( numeral_numeral_rat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(6)
% 5.41/5.66 thf(fact_2669_max__0__1_I6_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat )
% 5.41/5.66 = ( numeral_numeral_nat @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(6)
% 5.41/5.66 thf(fact_2670_max__0__1_I6_J,axiom,
% 5.41/5.66 ! [X: num] :
% 5.41/5.66 ( ( ord_max_int @ ( numeral_numeral_int @ X ) @ one_one_int )
% 5.41/5.66 = ( numeral_numeral_int @ X ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_0_1(6)
% 5.41/5.66 thf(fact_2671_zle__diff1__eq,axiom,
% 5.41/5.66 ! [W: int,Z: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ W @ ( minus_minus_int @ Z @ one_one_int ) )
% 5.41/5.66 = ( ord_less_int @ W @ Z ) ) ).
% 5.41/5.66
% 5.41/5.66 % zle_diff1_eq
% 5.41/5.66 thf(fact_2672_max__add__distrib__left,axiom,
% 5.41/5.66 ! [X: real,Y: real,Z: real] :
% 5.41/5.66 ( ( plus_plus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_real @ ( plus_plus_real @ X @ Z ) @ ( plus_plus_real @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_left
% 5.41/5.66 thf(fact_2673_max__add__distrib__left,axiom,
% 5.41/5.66 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.66 ( ( plus_plus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_rat @ ( plus_plus_rat @ X @ Z ) @ ( plus_plus_rat @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_left
% 5.41/5.66 thf(fact_2674_max__add__distrib__left,axiom,
% 5.41/5.66 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_nat @ ( plus_plus_nat @ X @ Z ) @ ( plus_plus_nat @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_left
% 5.41/5.66 thf(fact_2675_max__add__distrib__left,axiom,
% 5.41/5.66 ! [X: int,Y: int,Z: int] :
% 5.41/5.66 ( ( plus_plus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_int @ ( plus_plus_int @ X @ Z ) @ ( plus_plus_int @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_left
% 5.41/5.66 thf(fact_2676_max__add__distrib__left,axiom,
% 5.41/5.66 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.41/5.66 ( ( plus_p5714425477246183910nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Z ) @ ( plus_p5714425477246183910nteger @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_left
% 5.41/5.66 thf(fact_2677_max__add__distrib__right,axiom,
% 5.41/5.66 ! [X: real,Y: real,Z: real] :
% 5.41/5.66 ( ( plus_plus_real @ X @ ( ord_max_real @ Y @ Z ) )
% 5.41/5.66 = ( ord_max_real @ ( plus_plus_real @ X @ Y ) @ ( plus_plus_real @ X @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_right
% 5.41/5.66 thf(fact_2678_max__add__distrib__right,axiom,
% 5.41/5.66 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.66 ( ( plus_plus_rat @ X @ ( ord_max_rat @ Y @ Z ) )
% 5.41/5.66 = ( ord_max_rat @ ( plus_plus_rat @ X @ Y ) @ ( plus_plus_rat @ X @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_right
% 5.41/5.66 thf(fact_2679_max__add__distrib__right,axiom,
% 5.41/5.66 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ X @ ( ord_max_nat @ Y @ Z ) )
% 5.41/5.66 = ( ord_max_nat @ ( plus_plus_nat @ X @ Y ) @ ( plus_plus_nat @ X @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_right
% 5.41/5.66 thf(fact_2680_max__add__distrib__right,axiom,
% 5.41/5.66 ! [X: int,Y: int,Z: int] :
% 5.41/5.66 ( ( plus_plus_int @ X @ ( ord_max_int @ Y @ Z ) )
% 5.41/5.66 = ( ord_max_int @ ( plus_plus_int @ X @ Y ) @ ( plus_plus_int @ X @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_right
% 5.41/5.66 thf(fact_2681_max__add__distrib__right,axiom,
% 5.41/5.66 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.41/5.66 ( ( plus_p5714425477246183910nteger @ X @ ( ord_max_Code_integer @ Y @ Z ) )
% 5.41/5.66 = ( ord_max_Code_integer @ ( plus_p5714425477246183910nteger @ X @ Y ) @ ( plus_p5714425477246183910nteger @ X @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_add_distrib_right
% 5.41/5.66 thf(fact_2682_max__diff__distrib__left,axiom,
% 5.41/5.66 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.41/5.66 ( ( minus_8373710615458151222nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_Code_integer @ ( minus_8373710615458151222nteger @ X @ Z ) @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_diff_distrib_left
% 5.41/5.66 thf(fact_2683_max__diff__distrib__left,axiom,
% 5.41/5.66 ! [X: real,Y: real,Z: real] :
% 5.41/5.66 ( ( minus_minus_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_real @ ( minus_minus_real @ X @ Z ) @ ( minus_minus_real @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_diff_distrib_left
% 5.41/5.66 thf(fact_2684_max__diff__distrib__left,axiom,
% 5.41/5.66 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.66 ( ( minus_minus_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_rat @ ( minus_minus_rat @ X @ Z ) @ ( minus_minus_rat @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_diff_distrib_left
% 5.41/5.66 thf(fact_2685_max__diff__distrib__left,axiom,
% 5.41/5.66 ! [X: int,Y: int,Z: int] :
% 5.41/5.66 ( ( minus_minus_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.41/5.66 = ( ord_max_int @ ( minus_minus_int @ X @ Z ) @ ( minus_minus_int @ Y @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_diff_distrib_left
% 5.41/5.66 thf(fact_2686_nat__add__max__left,axiom,
% 5.41/5.66 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.41/5.66 = ( ord_max_nat @ ( plus_plus_nat @ M @ Q2 ) @ ( plus_plus_nat @ N @ Q2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_add_max_left
% 5.41/5.66 thf(fact_2687_nat__add__max__right,axiom,
% 5.41/5.66 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.41/5.66 = ( ord_max_nat @ ( plus_plus_nat @ M @ N ) @ ( plus_plus_nat @ M @ Q2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_add_max_right
% 5.41/5.66 thf(fact_2688_nat__mult__max__left,axiom,
% 5.41/5.66 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.66 ( ( times_times_nat @ ( ord_max_nat @ M @ N ) @ Q2 )
% 5.41/5.66 = ( ord_max_nat @ ( times_times_nat @ M @ Q2 ) @ ( times_times_nat @ N @ Q2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_mult_max_left
% 5.41/5.66 thf(fact_2689_nat__mult__max__right,axiom,
% 5.41/5.66 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.66 ( ( times_times_nat @ M @ ( ord_max_nat @ N @ Q2 ) )
% 5.41/5.66 = ( ord_max_nat @ ( times_times_nat @ M @ N ) @ ( times_times_nat @ M @ Q2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_mult_max_right
% 5.41/5.66 thf(fact_2690_nat__minus__add__max,axiom,
% 5.41/5.66 ! [N: nat,M: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ ( minus_minus_nat @ N @ M ) @ M )
% 5.41/5.66 = ( ord_max_nat @ N @ M ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_minus_add_max
% 5.41/5.66 thf(fact_2691_minus__int__code_I1_J,axiom,
% 5.41/5.66 ! [K: int] :
% 5.41/5.66 ( ( minus_minus_int @ K @ zero_zero_int )
% 5.41/5.66 = K ) ).
% 5.41/5.66
% 5.41/5.66 % minus_int_code(1)
% 5.41/5.66 thf(fact_2692_int__distrib_I3_J,axiom,
% 5.41/5.66 ! [Z1: int,Z22: int,W: int] :
% 5.41/5.66 ( ( times_times_int @ ( minus_minus_int @ Z1 @ Z22 ) @ W )
% 5.41/5.66 = ( minus_minus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_distrib(3)
% 5.41/5.66 thf(fact_2693_int__distrib_I4_J,axiom,
% 5.41/5.66 ! [W: int,Z1: int,Z22: int] :
% 5.41/5.66 ( ( times_times_int @ W @ ( minus_minus_int @ Z1 @ Z22 ) )
% 5.41/5.66 = ( minus_minus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_distrib(4)
% 5.41/5.66 thf(fact_2694_option_Odistinct_I1_J,axiom,
% 5.41/5.66 ! [X22: nat] :
% 5.41/5.66 ( none_nat
% 5.41/5.66 != ( some_nat @ X22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.distinct(1)
% 5.41/5.66 thf(fact_2695_option_Odistinct_I1_J,axiom,
% 5.41/5.66 ! [X22: product_prod_nat_nat] :
% 5.41/5.66 ( none_P5556105721700978146at_nat
% 5.41/5.66 != ( some_P7363390416028606310at_nat @ X22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.distinct(1)
% 5.41/5.66 thf(fact_2696_option_Odistinct_I1_J,axiom,
% 5.41/5.66 ! [X22: num] :
% 5.41/5.66 ( none_num
% 5.41/5.66 != ( some_num @ X22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.distinct(1)
% 5.41/5.66 thf(fact_2697_option_OdiscI,axiom,
% 5.41/5.66 ! [Option: option_nat,X22: nat] :
% 5.41/5.66 ( ( Option
% 5.41/5.66 = ( some_nat @ X22 ) )
% 5.41/5.66 => ( Option != none_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.discI
% 5.41/5.66 thf(fact_2698_option_OdiscI,axiom,
% 5.41/5.66 ! [Option: option4927543243414619207at_nat,X22: product_prod_nat_nat] :
% 5.41/5.66 ( ( Option
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ X22 ) )
% 5.41/5.66 => ( Option != none_P5556105721700978146at_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.discI
% 5.41/5.66 thf(fact_2699_option_OdiscI,axiom,
% 5.41/5.66 ! [Option: option_num,X22: num] :
% 5.41/5.66 ( ( Option
% 5.41/5.66 = ( some_num @ X22 ) )
% 5.41/5.66 => ( Option != none_num ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.discI
% 5.41/5.66 thf(fact_2700_option_Oexhaust,axiom,
% 5.41/5.66 ! [Y: option_nat] :
% 5.41/5.66 ( ( Y != none_nat )
% 5.41/5.66 => ~ ! [X23: nat] :
% 5.41/5.66 ( Y
% 5.41/5.66 != ( some_nat @ X23 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.exhaust
% 5.41/5.66 thf(fact_2701_option_Oexhaust,axiom,
% 5.41/5.66 ! [Y: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( Y != none_P5556105721700978146at_nat )
% 5.41/5.66 => ~ ! [X23: product_prod_nat_nat] :
% 5.41/5.66 ( Y
% 5.41/5.66 != ( some_P7363390416028606310at_nat @ X23 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.exhaust
% 5.41/5.66 thf(fact_2702_option_Oexhaust,axiom,
% 5.41/5.66 ! [Y: option_num] :
% 5.41/5.66 ( ( Y != none_num )
% 5.41/5.66 => ~ ! [X23: num] :
% 5.41/5.66 ( Y
% 5.41/5.66 != ( some_num @ X23 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.exhaust
% 5.41/5.66 thf(fact_2703_split__option__ex,axiom,
% 5.41/5.66 ( ( ^ [P3: option_nat > $o] :
% 5.41/5.66 ? [X7: option_nat] : ( P3 @ X7 ) )
% 5.41/5.66 = ( ^ [P4: option_nat > $o] :
% 5.41/5.66 ( ( P4 @ none_nat )
% 5.41/5.66 | ? [X3: nat] : ( P4 @ ( some_nat @ X3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_option_ex
% 5.41/5.66 thf(fact_2704_split__option__ex,axiom,
% 5.41/5.66 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.41/5.66 ? [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 5.41/5.66 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.41/5.66 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.41/5.66 | ? [X3: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_option_ex
% 5.41/5.66 thf(fact_2705_split__option__ex,axiom,
% 5.41/5.66 ( ( ^ [P3: option_num > $o] :
% 5.41/5.66 ? [X7: option_num] : ( P3 @ X7 ) )
% 5.41/5.66 = ( ^ [P4: option_num > $o] :
% 5.41/5.66 ( ( P4 @ none_num )
% 5.41/5.66 | ? [X3: num] : ( P4 @ ( some_num @ X3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_option_ex
% 5.41/5.66 thf(fact_2706_split__option__all,axiom,
% 5.41/5.66 ( ( ^ [P3: option_nat > $o] :
% 5.41/5.66 ! [X7: option_nat] : ( P3 @ X7 ) )
% 5.41/5.66 = ( ^ [P4: option_nat > $o] :
% 5.41/5.66 ( ( P4 @ none_nat )
% 5.41/5.66 & ! [X3: nat] : ( P4 @ ( some_nat @ X3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_option_all
% 5.41/5.66 thf(fact_2707_split__option__all,axiom,
% 5.41/5.66 ( ( ^ [P3: option4927543243414619207at_nat > $o] :
% 5.41/5.66 ! [X7: option4927543243414619207at_nat] : ( P3 @ X7 ) )
% 5.41/5.66 = ( ^ [P4: option4927543243414619207at_nat > $o] :
% 5.41/5.66 ( ( P4 @ none_P5556105721700978146at_nat )
% 5.41/5.66 & ! [X3: product_prod_nat_nat] : ( P4 @ ( some_P7363390416028606310at_nat @ X3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_option_all
% 5.41/5.66 thf(fact_2708_split__option__all,axiom,
% 5.41/5.66 ( ( ^ [P3: option_num > $o] :
% 5.41/5.66 ! [X7: option_num] : ( P3 @ X7 ) )
% 5.41/5.66 = ( ^ [P4: option_num > $o] :
% 5.41/5.66 ( ( P4 @ none_num )
% 5.41/5.66 & ! [X3: num] : ( P4 @ ( some_num @ X3 ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % split_option_all
% 5.41/5.66 thf(fact_2709_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option_nat,P: option_nat > option_nat > $o,Y: option_nat] :
% 5.41/5.66 ( ( ( X = none_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: nat,B5: nat] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_nat @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_nat @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2710_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option_nat,P: option_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( ( X = none_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: nat,B5: product_prod_nat_nat] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_nat @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2711_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option_nat,P: option_nat > option_num > $o,Y: option_num] :
% 5.41/5.66 ( ( ( X = none_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_num )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: nat,B5: num] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_nat @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_num @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2712_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_nat > $o,Y: option_nat] :
% 5.41/5.66 ( ( ( X = none_P5556105721700978146at_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: product_prod_nat_nat,B5: nat] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_nat @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2713_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( ( X = none_P5556105721700978146at_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2714_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option4927543243414619207at_nat,P: option4927543243414619207at_nat > option_num > $o,Y: option_num] :
% 5.41/5.66 ( ( ( X = none_P5556105721700978146at_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_num )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: product_prod_nat_nat,B5: num] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_num @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2715_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option_num,P: option_num > option_nat > $o,Y: option_nat] :
% 5.41/5.66 ( ( ( X = none_num )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: num,B5: nat] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_num @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_nat @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2716_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option_num,P: option_num > option4927543243414619207at_nat > $o,Y: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( ( X = none_num )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_P5556105721700978146at_nat )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: num,B5: product_prod_nat_nat] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_num @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2717_combine__options__cases,axiom,
% 5.41/5.66 ! [X: option_num,P: option_num > option_num > $o,Y: option_num] :
% 5.41/5.66 ( ( ( X = none_num )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ( ( Y = none_num )
% 5.41/5.66 => ( P @ X @ Y ) )
% 5.41/5.66 => ( ! [A5: num,B5: num] :
% 5.41/5.66 ( ( X
% 5.41/5.66 = ( some_num @ A5 ) )
% 5.41/5.66 => ( ( Y
% 5.41/5.66 = ( some_num @ B5 ) )
% 5.41/5.66 => ( P @ X @ Y ) ) )
% 5.41/5.66 => ( P @ X @ Y ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % combine_options_cases
% 5.41/5.66 thf(fact_2718_less__eq__int__code_I1_J,axiom,
% 5.41/5.66 ord_less_eq_int @ zero_zero_int @ zero_zero_int ).
% 5.41/5.66
% 5.41/5.66 % less_eq_int_code(1)
% 5.41/5.66 thf(fact_2719_less__int__code_I1_J,axiom,
% 5.41/5.66 ~ ( ord_less_int @ zero_zero_int @ zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % less_int_code(1)
% 5.41/5.66 thf(fact_2720_times__int__code_I1_J,axiom,
% 5.41/5.66 ! [K: int] :
% 5.41/5.66 ( ( times_times_int @ K @ zero_zero_int )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % times_int_code(1)
% 5.41/5.66 thf(fact_2721_times__int__code_I2_J,axiom,
% 5.41/5.66 ! [L2: int] :
% 5.41/5.66 ( ( times_times_int @ zero_zero_int @ L2 )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % times_int_code(2)
% 5.41/5.66 thf(fact_2722_plus__int__code_I1_J,axiom,
% 5.41/5.66 ! [K: int] :
% 5.41/5.66 ( ( plus_plus_int @ K @ zero_zero_int )
% 5.41/5.66 = K ) ).
% 5.41/5.66
% 5.41/5.66 % plus_int_code(1)
% 5.41/5.66 thf(fact_2723_plus__int__code_I2_J,axiom,
% 5.41/5.66 ! [L2: int] :
% 5.41/5.66 ( ( plus_plus_int @ zero_zero_int @ L2 )
% 5.41/5.66 = L2 ) ).
% 5.41/5.66
% 5.41/5.66 % plus_int_code(2)
% 5.41/5.66 thf(fact_2724_int__le__induct,axiom,
% 5.41/5.66 ! [I: int,K: int,P: int > $o] :
% 5.41/5.66 ( ( ord_less_eq_int @ I @ K )
% 5.41/5.66 => ( ( P @ K )
% 5.41/5.66 => ( ! [I4: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ I4 @ K )
% 5.41/5.66 => ( ( P @ I4 )
% 5.41/5.66 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.41/5.66 => ( P @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_le_induct
% 5.41/5.66 thf(fact_2725_int__less__induct,axiom,
% 5.41/5.66 ! [I: int,K: int,P: int > $o] :
% 5.41/5.66 ( ( ord_less_int @ I @ K )
% 5.41/5.66 => ( ( P @ ( minus_minus_int @ K @ one_one_int ) )
% 5.41/5.66 => ( ! [I4: int] :
% 5.41/5.66 ( ( ord_less_int @ I4 @ K )
% 5.41/5.66 => ( ( P @ I4 )
% 5.41/5.66 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.41/5.66 => ( P @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_less_induct
% 5.41/5.66 thf(fact_2726_int__distrib_I2_J,axiom,
% 5.41/5.66 ! [W: int,Z1: int,Z22: int] :
% 5.41/5.66 ( ( times_times_int @ W @ ( plus_plus_int @ Z1 @ Z22 ) )
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ W @ Z1 ) @ ( times_times_int @ W @ Z22 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_distrib(2)
% 5.41/5.66 thf(fact_2727_int__distrib_I1_J,axiom,
% 5.41/5.66 ! [Z1: int,Z22: int,W: int] :
% 5.41/5.66 ( ( times_times_int @ ( plus_plus_int @ Z1 @ Z22 ) @ W )
% 5.41/5.66 = ( plus_plus_int @ ( times_times_int @ Z1 @ W ) @ ( times_times_int @ Z22 @ W ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_distrib(1)
% 5.41/5.66 thf(fact_2728_option_Osel,axiom,
% 5.41/5.66 ! [X22: nat] :
% 5.41/5.66 ( ( the_nat @ ( some_nat @ X22 ) )
% 5.41/5.66 = X22 ) ).
% 5.41/5.66
% 5.41/5.66 % option.sel
% 5.41/5.66 thf(fact_2729_option_Osel,axiom,
% 5.41/5.66 ! [X22: product_prod_nat_nat] :
% 5.41/5.66 ( ( the_Pr8591224930841456533at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.41/5.66 = X22 ) ).
% 5.41/5.66
% 5.41/5.66 % option.sel
% 5.41/5.66 thf(fact_2730_option_Osel,axiom,
% 5.41/5.66 ! [X22: num] :
% 5.41/5.66 ( ( the_num @ ( some_num @ X22 ) )
% 5.41/5.66 = X22 ) ).
% 5.41/5.66
% 5.41/5.66 % option.sel
% 5.41/5.66 thf(fact_2731_option_Oexpand,axiom,
% 5.41/5.66 ! [Option: option_nat,Option2: option_nat] :
% 5.41/5.66 ( ( ( Option = none_nat )
% 5.41/5.66 = ( Option2 = none_nat ) )
% 5.41/5.66 => ( ( ( Option != none_nat )
% 5.41/5.66 => ( ( Option2 != none_nat )
% 5.41/5.66 => ( ( the_nat @ Option )
% 5.41/5.66 = ( the_nat @ Option2 ) ) ) )
% 5.41/5.66 => ( Option = Option2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.expand
% 5.41/5.66 thf(fact_2732_option_Oexpand,axiom,
% 5.41/5.66 ! [Option: option4927543243414619207at_nat,Option2: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( ( Option = none_P5556105721700978146at_nat )
% 5.41/5.66 = ( Option2 = none_P5556105721700978146at_nat ) )
% 5.41/5.66 => ( ( ( Option != none_P5556105721700978146at_nat )
% 5.41/5.66 => ( ( Option2 != none_P5556105721700978146at_nat )
% 5.41/5.66 => ( ( the_Pr8591224930841456533at_nat @ Option )
% 5.41/5.66 = ( the_Pr8591224930841456533at_nat @ Option2 ) ) ) )
% 5.41/5.66 => ( Option = Option2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.expand
% 5.41/5.66 thf(fact_2733_option_Oexpand,axiom,
% 5.41/5.66 ! [Option: option_num,Option2: option_num] :
% 5.41/5.66 ( ( ( Option = none_num )
% 5.41/5.66 = ( Option2 = none_num ) )
% 5.41/5.66 => ( ( ( Option != none_num )
% 5.41/5.66 => ( ( Option2 != none_num )
% 5.41/5.66 => ( ( the_num @ Option )
% 5.41/5.66 = ( the_num @ Option2 ) ) ) )
% 5.41/5.66 => ( Option = Option2 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.expand
% 5.41/5.66 thf(fact_2734_invar__vebt_Ointros_I2_J,axiom,
% 5.41/5.66 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.41/5.66 ( ! [X6: vEBT_VEBT] :
% 5.41/5.66 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.66 => ( vEBT_invar_vebt @ X6 @ N ) )
% 5.41/5.66 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.41/5.66 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.41/5.66 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.66 => ( ( M = N )
% 5.41/5.66 => ( ( Deg
% 5.41/5.66 = ( plus_plus_nat @ N @ M ) )
% 5.41/5.66 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.41/5.66 => ( ! [X6: vEBT_VEBT] :
% 5.41/5.66 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.66 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) )
% 5.41/5.66 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % invar_vebt.intros(2)
% 5.41/5.66 thf(fact_2735_zmult__zless__mono2,axiom,
% 5.41/5.66 ! [I: int,J: int,K: int] :
% 5.41/5.66 ( ( ord_less_int @ I @ J )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.66 => ( ord_less_int @ ( times_times_int @ K @ I ) @ ( times_times_int @ K @ J ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zmult_zless_mono2
% 5.41/5.66 thf(fact_2736_odd__nonzero,axiom,
% 5.41/5.66 ! [Z: int] :
% 5.41/5.66 ( ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z )
% 5.41/5.66 != zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % odd_nonzero
% 5.41/5.66 thf(fact_2737_int__induct,axiom,
% 5.41/5.66 ! [P: int > $o,K: int,I: int] :
% 5.41/5.66 ( ( P @ K )
% 5.41/5.66 => ( ! [I4: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ K @ I4 )
% 5.41/5.66 => ( ( P @ I4 )
% 5.41/5.66 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.41/5.66 => ( ! [I4: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ I4 @ K )
% 5.41/5.66 => ( ( P @ I4 )
% 5.41/5.66 => ( P @ ( minus_minus_int @ I4 @ one_one_int ) ) ) )
% 5.41/5.66 => ( P @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_induct
% 5.41/5.66 thf(fact_2738_int__ge__induct,axiom,
% 5.41/5.66 ! [K: int,I: int,P: int > $o] :
% 5.41/5.66 ( ( ord_less_eq_int @ K @ I )
% 5.41/5.66 => ( ( P @ K )
% 5.41/5.66 => ( ! [I4: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ K @ I4 )
% 5.41/5.66 => ( ( P @ I4 )
% 5.41/5.66 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.41/5.66 => ( P @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_ge_induct
% 5.41/5.66 thf(fact_2739_zless__add1__eq,axiom,
% 5.41/5.66 ! [W: int,Z: int] :
% 5.41/5.66 ( ( ord_less_int @ W @ ( plus_plus_int @ Z @ one_one_int ) )
% 5.41/5.66 = ( ( ord_less_int @ W @ Z )
% 5.41/5.66 | ( W = Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % zless_add1_eq
% 5.41/5.66 thf(fact_2740_int__gr__induct,axiom,
% 5.41/5.66 ! [K: int,I: int,P: int > $o] :
% 5.41/5.66 ( ( ord_less_int @ K @ I )
% 5.41/5.66 => ( ( P @ ( plus_plus_int @ K @ one_one_int ) )
% 5.41/5.66 => ( ! [I4: int] :
% 5.41/5.66 ( ( ord_less_int @ K @ I4 )
% 5.41/5.66 => ( ( P @ I4 )
% 5.41/5.66 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) ) ) )
% 5.41/5.66 => ( P @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_gr_induct
% 5.41/5.66 thf(fact_2741_option_Oexhaust__sel,axiom,
% 5.41/5.66 ! [Option: option_nat] :
% 5.41/5.66 ( ( Option != none_nat )
% 5.41/5.66 => ( Option
% 5.41/5.66 = ( some_nat @ ( the_nat @ Option ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.exhaust_sel
% 5.41/5.66 thf(fact_2742_option_Oexhaust__sel,axiom,
% 5.41/5.66 ! [Option: option4927543243414619207at_nat] :
% 5.41/5.66 ( ( Option != none_P5556105721700978146at_nat )
% 5.41/5.66 => ( Option
% 5.41/5.66 = ( some_P7363390416028606310at_nat @ ( the_Pr8591224930841456533at_nat @ Option ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.exhaust_sel
% 5.41/5.66 thf(fact_2743_option_Oexhaust__sel,axiom,
% 5.41/5.66 ! [Option: option_num] :
% 5.41/5.66 ( ( Option != none_num )
% 5.41/5.66 => ( Option
% 5.41/5.66 = ( some_num @ ( the_num @ Option ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % option.exhaust_sel
% 5.41/5.66 thf(fact_2744_int__one__le__iff__zero__less,axiom,
% 5.41/5.66 ! [Z: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ one_one_int @ Z )
% 5.41/5.66 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.66
% 5.41/5.66 % int_one_le_iff_zero_less
% 5.41/5.66 thf(fact_2745_pos__zmult__eq__1__iff,axiom,
% 5.41/5.66 ! [M: int,N: int] :
% 5.41/5.66 ( ( ord_less_int @ zero_zero_int @ M )
% 5.41/5.66 => ( ( ( times_times_int @ M @ N )
% 5.41/5.66 = one_one_int )
% 5.41/5.66 = ( ( M = one_one_int )
% 5.41/5.66 & ( N = one_one_int ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % pos_zmult_eq_1_iff
% 5.41/5.66 thf(fact_2746_odd__less__0__iff,axiom,
% 5.41/5.66 ! [Z: int] :
% 5.41/5.66 ( ( ord_less_int @ ( plus_plus_int @ ( plus_plus_int @ one_one_int @ Z ) @ Z ) @ zero_zero_int )
% 5.41/5.66 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % odd_less_0_iff
% 5.41/5.66 thf(fact_2747_zless__imp__add1__zle,axiom,
% 5.41/5.66 ! [W: int,Z: int] :
% 5.41/5.66 ( ( ord_less_int @ W @ Z )
% 5.41/5.66 => ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z ) ) ).
% 5.41/5.66
% 5.41/5.66 % zless_imp_add1_zle
% 5.41/5.66 thf(fact_2748_add1__zle__eq,axiom,
% 5.41/5.66 ! [W: int,Z: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ ( plus_plus_int @ W @ one_one_int ) @ Z )
% 5.41/5.66 = ( ord_less_int @ W @ Z ) ) ).
% 5.41/5.66
% 5.41/5.66 % add1_zle_eq
% 5.41/5.66 thf(fact_2749_le__imp__0__less,axiom,
% 5.41/5.66 ! [Z: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.66 => ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % le_imp_0_less
% 5.41/5.66 thf(fact_2750_nested__mint,axiom,
% 5.41/5.66 ! [Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,N: nat,Va: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ N )
% 5.41/5.66 => ( ( N
% 5.41/5.66 = ( suc @ ( suc @ Va ) ) )
% 5.41/5.66 => ( ~ ( ord_less_nat @ Ma @ Mi )
% 5.41/5.66 => ( ( Ma != Mi )
% 5.41/5.66 => ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( suc @ ( divide_divide_nat @ Va @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nested_mint
% 5.41/5.66 thf(fact_2751_aampt,axiom,
% 5.41/5.66 ( ( ( xa = ma )
% 5.41/5.66 => ( mi
% 5.41/5.66 = ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ mi
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.66 & ( ( xa != ma )
% 5.41/5.66 => ( mi = ma ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % aampt
% 5.41/5.66 thf(fact_2752_verit__le__mono__div__int,axiom,
% 5.41/5.66 ! [A2: int,B3: int,N: int] :
% 5.41/5.66 ( ( ord_less_int @ A2 @ B3 )
% 5.41/5.66 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.41/5.66 => ( ord_less_eq_int
% 5.41/5.66 @ ( plus_plus_int @ ( divide_divide_int @ A2 @ N )
% 5.41/5.66 @ ( if_int
% 5.41/5.66 @ ( ( modulo_modulo_int @ B3 @ N )
% 5.41/5.66 = zero_zero_int )
% 5.41/5.66 @ one_one_int
% 5.41/5.66 @ zero_zero_int ) )
% 5.41/5.66 @ ( divide_divide_int @ B3 @ N ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % verit_le_mono_div_int
% 5.41/5.66 thf(fact_2753_buildup__gives__valid,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( vEBT_invar_vebt @ ( vEBT_vebt_buildup @ N ) @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % buildup_gives_valid
% 5.41/5.66 thf(fact_2754_verit__le__mono__div,axiom,
% 5.41/5.66 ! [A2: nat,B3: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ A2 @ B3 )
% 5.41/5.66 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ord_less_eq_nat
% 5.41/5.66 @ ( plus_plus_nat @ ( divide_divide_nat @ A2 @ N )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( modulo_modulo_nat @ B3 @ N )
% 5.41/5.66 = zero_zero_nat )
% 5.41/5.66 @ one_one_nat
% 5.41/5.66 @ zero_zero_nat ) )
% 5.41/5.66 @ ( divide_divide_nat @ B3 @ N ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % verit_le_mono_div
% 5.41/5.66 thf(fact_2755_inrange,axiom,
% 5.41/5.66 ! [T: vEBT_VEBT,N: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.66 => ( ord_less_eq_set_nat @ ( vEBT_VEBT_set_vebt @ T ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % inrange
% 5.41/5.66 thf(fact_2756_mul__def,axiom,
% 5.41/5.66 ( vEBT_VEBT_mul
% 5.41/5.66 = ( vEBT_V4262088993061758097ft_nat @ times_times_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % mul_def
% 5.41/5.66 thf(fact_2757_add__def,axiom,
% 5.41/5.66 ( vEBT_VEBT_add
% 5.41/5.66 = ( vEBT_V4262088993061758097ft_nat @ plus_plus_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_def
% 5.41/5.66 thf(fact_2758_set__bit__0,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( bit_se7879613467334960850it_int @ zero_zero_nat @ A )
% 5.41/5.66 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % set_bit_0
% 5.41/5.66 thf(fact_2759_set__bit__0,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( bit_se7882103937844011126it_nat @ zero_zero_nat @ A )
% 5.41/5.66 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % set_bit_0
% 5.41/5.66 thf(fact_2760_even__odd__cases,axiom,
% 5.41/5.66 ! [X: nat] :
% 5.41/5.66 ( ! [N3: nat] :
% 5.41/5.66 ( X
% 5.41/5.66 != ( plus_plus_nat @ N3 @ N3 ) )
% 5.41/5.66 => ~ ! [N3: nat] :
% 5.41/5.66 ( X
% 5.41/5.66 != ( plus_plus_nat @ N3 @ ( suc @ N3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % even_odd_cases
% 5.41/5.66 thf(fact_2761_set__vebt_H__def,axiom,
% 5.41/5.66 ( vEBT_VEBT_set_vebt
% 5.41/5.66 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_vebt_member @ T2 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % set_vebt'_def
% 5.41/5.66 thf(fact_2762_deg__SUcn__Node,axiom,
% 5.41/5.66 ! [Tree: vEBT_VEBT,N: nat] :
% 5.41/5.66 ( ( vEBT_invar_vebt @ Tree @ ( suc @ ( suc @ N ) ) )
% 5.41/5.66 => ? [Info2: option4927543243414619207at_nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.66 ( Tree
% 5.41/5.66 = ( vEBT_Node @ Info2 @ ( suc @ ( suc @ N ) ) @ TreeList3 @ S3 ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % deg_SUcn_Node
% 5.41/5.66 thf(fact_2763_add__shift,axiom,
% 5.41/5.66 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.66 ( ( ( plus_plus_nat @ X @ Y )
% 5.41/5.66 = Z )
% 5.41/5.66 = ( ( vEBT_VEBT_add @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.41/5.66 = ( some_nat @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_shift
% 5.41/5.66 thf(fact_2764_mul__shift,axiom,
% 5.41/5.66 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.66 ( ( ( times_times_nat @ X @ Y )
% 5.41/5.66 = Z )
% 5.41/5.66 = ( ( vEBT_VEBT_mul @ ( some_nat @ X ) @ ( some_nat @ Y ) )
% 5.41/5.66 = ( some_nat @ Z ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mul_shift
% 5.41/5.66 thf(fact_2765_verit__eq__simplify_I8_J,axiom,
% 5.41/5.66 ! [X22: num,Y22: num] :
% 5.41/5.66 ( ( ( bit0 @ X22 )
% 5.41/5.66 = ( bit0 @ Y22 ) )
% 5.41/5.66 = ( X22 = Y22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % verit_eq_simplify(8)
% 5.41/5.66 thf(fact_2766_nat_Oinject,axiom,
% 5.41/5.66 ! [X22: nat,Y22: nat] :
% 5.41/5.66 ( ( ( suc @ X22 )
% 5.41/5.66 = ( suc @ Y22 ) )
% 5.41/5.66 = ( X22 = Y22 ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat.inject
% 5.41/5.66 thf(fact_2767_old_Onat_Oinject,axiom,
% 5.41/5.66 ! [Nat: nat,Nat2: nat] :
% 5.41/5.66 ( ( ( suc @ Nat )
% 5.41/5.66 = ( suc @ Nat2 ) )
% 5.41/5.66 = ( Nat = Nat2 ) ) ).
% 5.41/5.66
% 5.41/5.66 % old.nat.inject
% 5.41/5.66 thf(fact_2768_max__enat__simps_I2_J,axiom,
% 5.41/5.66 ! [Q2: extended_enat] :
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ Q2 @ zero_z5237406670263579293d_enat )
% 5.41/5.66 = Q2 ) ).
% 5.41/5.66
% 5.41/5.66 % max_enat_simps(2)
% 5.41/5.66 thf(fact_2769_max__enat__simps_I3_J,axiom,
% 5.41/5.66 ! [Q2: extended_enat] :
% 5.41/5.66 ( ( ord_ma741700101516333627d_enat @ zero_z5237406670263579293d_enat @ Q2 )
% 5.41/5.66 = Q2 ) ).
% 5.41/5.66
% 5.41/5.66 % max_enat_simps(3)
% 5.41/5.66 thf(fact_2770_Suc__less__eq,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.41/5.66 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_less_eq
% 5.41/5.66 thf(fact_2771_Suc__mono,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ M @ N )
% 5.41/5.66 => ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_mono
% 5.41/5.66 thf(fact_2772_lessI,axiom,
% 5.41/5.66 ! [N: nat] : ( ord_less_nat @ N @ ( suc @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % lessI
% 5.41/5.66 thf(fact_2773_atLeastAtMost__iff,axiom,
% 5.41/5.66 ! [I: set_nat,L2: set_nat,U: set_nat] :
% 5.41/5.66 ( ( member_set_nat @ I @ ( set_or4548717258645045905et_nat @ L2 @ U ) )
% 5.41/5.66 = ( ( ord_less_eq_set_nat @ L2 @ I )
% 5.41/5.66 & ( ord_less_eq_set_nat @ I @ U ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastAtMost_iff
% 5.41/5.66 thf(fact_2774_atLeastAtMost__iff,axiom,
% 5.41/5.66 ! [I: set_int,L2: set_int,U: set_int] :
% 5.41/5.66 ( ( member_set_int @ I @ ( set_or370866239135849197et_int @ L2 @ U ) )
% 5.41/5.66 = ( ( ord_less_eq_set_int @ L2 @ I )
% 5.41/5.66 & ( ord_less_eq_set_int @ I @ U ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastAtMost_iff
% 5.41/5.66 thf(fact_2775_atLeastAtMost__iff,axiom,
% 5.41/5.66 ! [I: rat,L2: rat,U: rat] :
% 5.41/5.66 ( ( member_rat @ I @ ( set_or633870826150836451st_rat @ L2 @ U ) )
% 5.41/5.66 = ( ( ord_less_eq_rat @ L2 @ I )
% 5.41/5.66 & ( ord_less_eq_rat @ I @ U ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastAtMost_iff
% 5.41/5.66 thf(fact_2776_atLeastAtMost__iff,axiom,
% 5.41/5.66 ! [I: num,L2: num,U: num] :
% 5.41/5.66 ( ( member_num @ I @ ( set_or7049704709247886629st_num @ L2 @ U ) )
% 5.41/5.66 = ( ( ord_less_eq_num @ L2 @ I )
% 5.41/5.66 & ( ord_less_eq_num @ I @ U ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastAtMost_iff
% 5.41/5.66 thf(fact_2777_atLeastAtMost__iff,axiom,
% 5.41/5.66 ! [I: nat,L2: nat,U: nat] :
% 5.41/5.66 ( ( member_nat @ I @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.41/5.66 = ( ( ord_less_eq_nat @ L2 @ I )
% 5.41/5.66 & ( ord_less_eq_nat @ I @ U ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastAtMost_iff
% 5.41/5.66 thf(fact_2778_atLeastAtMost__iff,axiom,
% 5.41/5.66 ! [I: int,L2: int,U: int] :
% 5.41/5.66 ( ( member_int @ I @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.41/5.66 = ( ( ord_less_eq_int @ L2 @ I )
% 5.41/5.66 & ( ord_less_eq_int @ I @ U ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastAtMost_iff
% 5.41/5.66 thf(fact_2779_atLeastAtMost__iff,axiom,
% 5.41/5.66 ! [I: real,L2: real,U: real] :
% 5.41/5.66 ( ( member_real @ I @ ( set_or1222579329274155063t_real @ L2 @ U ) )
% 5.41/5.66 = ( ( ord_less_eq_real @ L2 @ I )
% 5.41/5.66 & ( ord_less_eq_real @ I @ U ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastAtMost_iff
% 5.41/5.66 thf(fact_2780_Icc__eq__Icc,axiom,
% 5.41/5.66 ! [L2: set_int,H2: set_int,L3: set_int,H3: set_int] :
% 5.41/5.66 ( ( ( set_or370866239135849197et_int @ L2 @ H2 )
% 5.41/5.66 = ( set_or370866239135849197et_int @ L3 @ H3 ) )
% 5.41/5.66 = ( ( ( L2 = L3 )
% 5.41/5.66 & ( H2 = H3 ) )
% 5.41/5.66 | ( ~ ( ord_less_eq_set_int @ L2 @ H2 )
% 5.41/5.66 & ~ ( ord_less_eq_set_int @ L3 @ H3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Icc_eq_Icc
% 5.41/5.66 thf(fact_2781_Icc__eq__Icc,axiom,
% 5.41/5.66 ! [L2: rat,H2: rat,L3: rat,H3: rat] :
% 5.41/5.66 ( ( ( set_or633870826150836451st_rat @ L2 @ H2 )
% 5.41/5.66 = ( set_or633870826150836451st_rat @ L3 @ H3 ) )
% 5.41/5.66 = ( ( ( L2 = L3 )
% 5.41/5.66 & ( H2 = H3 ) )
% 5.41/5.66 | ( ~ ( ord_less_eq_rat @ L2 @ H2 )
% 5.41/5.66 & ~ ( ord_less_eq_rat @ L3 @ H3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Icc_eq_Icc
% 5.41/5.66 thf(fact_2782_Icc__eq__Icc,axiom,
% 5.41/5.66 ! [L2: num,H2: num,L3: num,H3: num] :
% 5.41/5.66 ( ( ( set_or7049704709247886629st_num @ L2 @ H2 )
% 5.41/5.66 = ( set_or7049704709247886629st_num @ L3 @ H3 ) )
% 5.41/5.66 = ( ( ( L2 = L3 )
% 5.41/5.66 & ( H2 = H3 ) )
% 5.41/5.66 | ( ~ ( ord_less_eq_num @ L2 @ H2 )
% 5.41/5.66 & ~ ( ord_less_eq_num @ L3 @ H3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Icc_eq_Icc
% 5.41/5.66 thf(fact_2783_Icc__eq__Icc,axiom,
% 5.41/5.66 ! [L2: nat,H2: nat,L3: nat,H3: nat] :
% 5.41/5.66 ( ( ( set_or1269000886237332187st_nat @ L2 @ H2 )
% 5.41/5.66 = ( set_or1269000886237332187st_nat @ L3 @ H3 ) )
% 5.41/5.66 = ( ( ( L2 = L3 )
% 5.41/5.66 & ( H2 = H3 ) )
% 5.41/5.66 | ( ~ ( ord_less_eq_nat @ L2 @ H2 )
% 5.41/5.66 & ~ ( ord_less_eq_nat @ L3 @ H3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Icc_eq_Icc
% 5.41/5.66 thf(fact_2784_Icc__eq__Icc,axiom,
% 5.41/5.66 ! [L2: int,H2: int,L3: int,H3: int] :
% 5.41/5.66 ( ( ( set_or1266510415728281911st_int @ L2 @ H2 )
% 5.41/5.66 = ( set_or1266510415728281911st_int @ L3 @ H3 ) )
% 5.41/5.66 = ( ( ( L2 = L3 )
% 5.41/5.66 & ( H2 = H3 ) )
% 5.41/5.66 | ( ~ ( ord_less_eq_int @ L2 @ H2 )
% 5.41/5.66 & ~ ( ord_less_eq_int @ L3 @ H3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Icc_eq_Icc
% 5.41/5.66 thf(fact_2785_Icc__eq__Icc,axiom,
% 5.41/5.66 ! [L2: real,H2: real,L3: real,H3: real] :
% 5.41/5.66 ( ( ( set_or1222579329274155063t_real @ L2 @ H2 )
% 5.41/5.66 = ( set_or1222579329274155063t_real @ L3 @ H3 ) )
% 5.41/5.66 = ( ( ( L2 = L3 )
% 5.41/5.66 & ( H2 = H3 ) )
% 5.41/5.66 | ( ~ ( ord_less_eq_real @ L2 @ H2 )
% 5.41/5.66 & ~ ( ord_less_eq_real @ L3 @ H3 ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Icc_eq_Icc
% 5.41/5.66 thf(fact_2786_Suc__le__mono,axiom,
% 5.41/5.66 ! [N: nat,M: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( suc @ M ) )
% 5.41/5.66 = ( ord_less_eq_nat @ N @ M ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_le_mono
% 5.41/5.66 thf(fact_2787_add__Suc__right,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ M @ ( suc @ N ) )
% 5.41/5.66 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_Suc_right
% 5.41/5.66 thf(fact_2788_diff__Suc__Suc,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( minus_minus_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.41/5.66 = ( minus_minus_nat @ M @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_Suc_Suc
% 5.41/5.66 thf(fact_2789_Suc__diff__diff,axiom,
% 5.41/5.66 ! [M: nat,N: nat,K: nat] :
% 5.41/5.66 ( ( minus_minus_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( suc @ K ) )
% 5.41/5.66 = ( minus_minus_nat @ ( minus_minus_nat @ M @ N ) @ K ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_diff_diff
% 5.41/5.66 thf(fact_2790_set__bit__nonnegative__int__iff,axiom,
% 5.41/5.66 ! [N: nat,K: int] :
% 5.41/5.66 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se7879613467334960850it_int @ N @ K ) )
% 5.41/5.66 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.66
% 5.41/5.66 % set_bit_nonnegative_int_iff
% 5.41/5.66 thf(fact_2791_set__bit__negative__int__iff,axiom,
% 5.41/5.66 ! [N: nat,K: int] :
% 5.41/5.66 ( ( ord_less_int @ ( bit_se7879613467334960850it_int @ N @ K ) @ zero_zero_int )
% 5.41/5.66 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.66
% 5.41/5.66 % set_bit_negative_int_iff
% 5.41/5.66 thf(fact_2792_max__Suc__Suc,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_max_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.41/5.66 = ( suc @ ( ord_max_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % max_Suc_Suc
% 5.41/5.66 thf(fact_2793_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_rat @ zero_zero_rat @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_rat ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_2794_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_2795_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_real @ zero_zero_real @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_real ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_2796_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_int @ zero_zero_int @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_int ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_2797_power__0__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_complex @ zero_zero_complex @ ( suc @ N ) )
% 5.41/5.66 = zero_zero_complex ) ).
% 5.41/5.66
% 5.41/5.66 % power_0_Suc
% 5.41/5.66 thf(fact_2798_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: nat] :
% 5.41/5.66 ( ( power_power_nat @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_2799_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: real] :
% 5.41/5.66 ( ( power_power_real @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_2800_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: int] :
% 5.41/5.66 ( ( power_power_int @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_2801_power__Suc0__right,axiom,
% 5.41/5.66 ! [A: complex] :
% 5.41/5.66 ( ( power_power_complex @ A @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = A ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc0_right
% 5.41/5.66 thf(fact_2802_zero__less__Suc,axiom,
% 5.41/5.66 ! [N: nat] : ( ord_less_nat @ zero_zero_nat @ ( suc @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % zero_less_Suc
% 5.41/5.66 thf(fact_2803_less__Suc0,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( N = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % less_Suc0
% 5.41/5.66 thf(fact_2804_atLeastatMost__subset__iff,axiom,
% 5.41/5.66 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.41/5.66 ( ( ord_le4403425263959731960et_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.41/5.66 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.41/5.66 | ( ( ord_less_eq_set_int @ C @ A )
% 5.41/5.66 & ( ord_less_eq_set_int @ B @ D ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastatMost_subset_iff
% 5.41/5.66 thf(fact_2805_atLeastatMost__subset__iff,axiom,
% 5.41/5.66 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.66 ( ( ord_less_eq_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.41/5.66 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.41/5.66 | ( ( ord_less_eq_rat @ C @ A )
% 5.41/5.66 & ( ord_less_eq_rat @ B @ D ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastatMost_subset_iff
% 5.41/5.66 thf(fact_2806_atLeastatMost__subset__iff,axiom,
% 5.41/5.66 ! [A: num,B: num,C: num,D: num] :
% 5.41/5.66 ( ( ord_less_eq_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.41/5.66 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.41/5.66 | ( ( ord_less_eq_num @ C @ A )
% 5.41/5.66 & ( ord_less_eq_num @ B @ D ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastatMost_subset_iff
% 5.41/5.66 thf(fact_2807_atLeastatMost__subset__iff,axiom,
% 5.41/5.66 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.66 ( ( ord_less_eq_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.41/5.66 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.41/5.66 | ( ( ord_less_eq_nat @ C @ A )
% 5.41/5.66 & ( ord_less_eq_nat @ B @ D ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastatMost_subset_iff
% 5.41/5.66 thf(fact_2808_atLeastatMost__subset__iff,axiom,
% 5.41/5.66 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.66 ( ( ord_less_eq_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.41/5.66 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.41/5.66 | ( ( ord_less_eq_int @ C @ A )
% 5.41/5.66 & ( ord_less_eq_int @ B @ D ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastatMost_subset_iff
% 5.41/5.66 thf(fact_2809_atLeastatMost__subset__iff,axiom,
% 5.41/5.66 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.66 ( ( ord_less_eq_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.41/5.66 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.41/5.66 | ( ( ord_less_eq_real @ C @ A )
% 5.41/5.66 & ( ord_less_eq_real @ B @ D ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % atLeastatMost_subset_iff
% 5.41/5.66 thf(fact_2810_one__eq__mult__iff,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( suc @ zero_zero_nat )
% 5.41/5.66 = ( times_times_nat @ M @ N ) )
% 5.41/5.66 = ( ( M
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_eq_mult_iff
% 5.41/5.66 thf(fact_2811_mult__eq__1__iff,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ( times_times_nat @ M @ N )
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( ( M
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 & ( N
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_eq_1_iff
% 5.41/5.66 thf(fact_2812_div__by__Suc__0,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = M ) ).
% 5.41/5.66
% 5.41/5.66 % div_by_Suc_0
% 5.41/5.66 thf(fact_2813_power__Suc__0,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( power_power_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % power_Suc_0
% 5.41/5.66 thf(fact_2814_nat__power__eq__Suc__0__iff,axiom,
% 5.41/5.66 ! [X: nat,M: nat] :
% 5.41/5.66 ( ( ( power_power_nat @ X @ M )
% 5.41/5.66 = ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( ( M = zero_zero_nat )
% 5.41/5.66 | ( X
% 5.41/5.66 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % nat_power_eq_Suc_0_iff
% 5.41/5.66 thf(fact_2815_mult__Suc__right,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( times_times_nat @ M @ ( suc @ N ) )
% 5.41/5.66 = ( plus_plus_nat @ M @ ( times_times_nat @ M @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mult_Suc_right
% 5.41/5.66 thf(fact_2816_diff__Suc__1,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( minus_minus_nat @ ( suc @ N ) @ one_one_nat )
% 5.41/5.66 = N ) ).
% 5.41/5.66
% 5.41/5.66 % diff_Suc_1
% 5.41/5.66 thf(fact_2817_mod__by__Suc__0,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.41/5.66 = zero_zero_nat ) ).
% 5.41/5.66
% 5.41/5.66 % mod_by_Suc_0
% 5.41/5.66 thf(fact_2818_Suc__pred,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.41/5.66 = N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_pred
% 5.41/5.66 thf(fact_2819_one__le__mult__iff,axiom,
% 5.41/5.66 ! [M: nat,N: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) )
% 5.41/5.66 = ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.41/5.66 & ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % one_le_mult_iff
% 5.41/5.66 thf(fact_2820_diff__Suc__diff__eq2,axiom,
% 5.41/5.66 ! [K: nat,J: nat,I: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.66 => ( ( minus_minus_nat @ ( suc @ ( minus_minus_nat @ J @ K ) ) @ I )
% 5.41/5.66 = ( minus_minus_nat @ ( suc @ J ) @ ( plus_plus_nat @ K @ I ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_Suc_diff_eq2
% 5.41/5.66 thf(fact_2821_diff__Suc__diff__eq1,axiom,
% 5.41/5.66 ! [K: nat,J: nat,I: nat] :
% 5.41/5.66 ( ( ord_less_eq_nat @ K @ J )
% 5.41/5.66 => ( ( minus_minus_nat @ I @ ( suc @ ( minus_minus_nat @ J @ K ) ) )
% 5.41/5.66 = ( minus_minus_nat @ ( plus_plus_nat @ I @ K ) @ ( suc @ J ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % diff_Suc_diff_eq1
% 5.41/5.66 thf(fact_2822_Suc__numeral,axiom,
% 5.41/5.66 ! [N: num] :
% 5.41/5.66 ( ( suc @ ( numeral_numeral_nat @ N ) )
% 5.41/5.66 = ( numeral_numeral_nat @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_numeral
% 5.41/5.66 thf(fact_2823_Suc__mod__mult__self1,axiom,
% 5.41/5.66 ! [M: nat,K: nat,N: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ K @ N ) ) ) @ N )
% 5.41/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_mod_mult_self1
% 5.41/5.66 thf(fact_2824_Suc__mod__mult__self2,axiom,
% 5.41/5.66 ! [M: nat,N: nat,K: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ M @ ( times_times_nat @ N @ K ) ) ) @ N )
% 5.41/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_mod_mult_self2
% 5.41/5.66 thf(fact_2825_Suc__mod__mult__self3,axiom,
% 5.41/5.66 ! [K: nat,N: nat,M: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ K @ N ) @ M ) ) @ N )
% 5.41/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_mod_mult_self3
% 5.41/5.66 thf(fact_2826_Suc__mod__mult__self4,axiom,
% 5.41/5.66 ! [N: nat,K: nat,M: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( suc @ ( plus_plus_nat @ ( times_times_nat @ N @ K ) @ M ) ) @ N )
% 5.41/5.66 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_mod_mult_self4
% 5.41/5.66 thf(fact_2827_add__2__eq__Suc_H,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( suc @ ( suc @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_2_eq_Suc'
% 5.41/5.66 thf(fact_2828_add__2__eq__Suc,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.66 = ( suc @ ( suc @ N ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % add_2_eq_Suc
% 5.41/5.66 thf(fact_2829_div2__Suc__Suc,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( divide_divide_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( suc @ ( divide_divide_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % div2_Suc_Suc
% 5.41/5.66 thf(fact_2830_Suc__1,axiom,
% 5.41/5.66 ( ( suc @ one_one_nat )
% 5.41/5.66 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_1
% 5.41/5.66 thf(fact_2831_mod2__Suc__Suc,axiom,
% 5.41/5.66 ! [M: nat] :
% 5.41/5.66 ( ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % mod2_Suc_Suc
% 5.41/5.66 thf(fact_2832_Suc__diff__1,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.66 => ( ( suc @ ( minus_minus_nat @ N @ one_one_nat ) )
% 5.41/5.66 = N ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_diff_1
% 5.41/5.66 thf(fact_2833_Suc__times__numeral__mod__eq,axiom,
% 5.41/5.66 ! [K: num,N: nat] :
% 5.41/5.66 ( ( ( numeral_numeral_nat @ K )
% 5.41/5.66 != one_one_nat )
% 5.41/5.66 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ K ) @ N ) ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.66 = one_one_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % Suc_times_numeral_mod_eq
% 5.41/5.66 thf(fact_2834_not__mod2__eq__Suc__0__eq__0,axiom,
% 5.41/5.66 ! [N: nat] :
% 5.41/5.66 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 != ( suc @ zero_zero_nat ) )
% 5.41/5.66 = ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.66 = zero_zero_nat ) ) ).
% 5.41/5.66
% 5.41/5.66 % not_mod2_eq_Suc_0_eq_0
% 5.41/5.66 thf(fact_2835_del__x__not__mia,axiom,
% 5.41/5.66 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ( ord_less_nat @ Mi @ X )
% 5.41/5.66 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 @ ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ Mi
% 5.41/5.66 @ ( if_nat @ ( X = Ma )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ Mi
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_not_mia
% 5.41/5.66 thf(fact_2836_del__x__not__mi__new__node__nil,axiom,
% 5.41/5.66 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Sn: vEBT_VEBT,Summary: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.41/5.66 ( ( ( ord_less_nat @ Mi @ X )
% 5.41/5.66 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( Newnode
% 5.41/5.66 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( Sn
% 5.41/5.66 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 => ( ( Newlist
% 5.41/5.66 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ Mi
% 5.41/5.66 @ ( if_nat @ ( X = Ma )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ Mi
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ Newlist
% 5.41/5.66 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_not_mi_new_node_nil
% 5.41/5.66 thf(fact_2837_del__x__not__mi,axiom,
% 5.41/5.66 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,H2: nat,L2: nat,Newnode: vEBT_VEBT,TreeList2: list_VEBT_VEBT,Newlist: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ( ord_less_nat @ Mi @ X )
% 5.41/5.66 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( Newnode
% 5.41/5.66 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 => ( ( Newlist
% 5.41/5.66 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ Mi
% 5.41/5.66 @ ( if_nat @ ( X = Ma )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ Mi
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ Newlist
% 5.41/5.66 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.41/5.66 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ ( if_nat @ ( X = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_not_mi
% 5.41/5.66 thf(fact_2838_del__x__mia,axiom,
% 5.41/5.66 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ( X = Mi )
% 5.41/5.66 & ( ord_less_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.66 = Ma )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.66 = Ma )
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ Summary ) )
% 5.41/5.66 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_mia
% 5.41/5.66 thf(fact_2839_del__x__mi__lets__in__minNull,axiom,
% 5.41/5.66 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT,Sn: vEBT_VEBT] :
% 5.41/5.66 ( ( ( X = Mi )
% 5.41/5.66 & ( ord_less_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( Xn
% 5.41/5.66 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( Newnode
% 5.41/5.66 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 => ( ( Newlist
% 5.41/5.66 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.41/5.66 => ( ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( Sn
% 5.41/5.66 = ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ Xn
% 5.41/5.66 @ ( if_nat @ ( Xn = Ma )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ Sn )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ Xn
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ Sn ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ Newlist
% 5.41/5.66 @ Sn ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_mi_lets_in_minNull
% 5.41/5.66 thf(fact_2840_del__x__mi__lets__in,axiom,
% 5.41/5.66 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat,Newnode: vEBT_VEBT,Newlist: list_VEBT_VEBT] :
% 5.41/5.66 ( ( ( X = Mi )
% 5.41/5.66 & ( ord_less_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( Xn
% 5.41/5.66 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( Newnode
% 5.41/5.66 = ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 => ( ( Newlist
% 5.41/5.66 = ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ Newnode ) )
% 5.41/5.66 => ( ( ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ Xn
% 5.41/5.66 @ ( if_nat @ ( Xn = Ma )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ Xn
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ Newlist
% 5.41/5.66 @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) )
% 5.41/5.66 & ( ~ ( vEBT_VEBT_minNull @ Newnode )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ Newlist @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ Newlist @ Summary ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_mi_lets_in
% 5.41/5.66 thf(fact_2841_del__x__mi,axiom,
% 5.41/5.66 ! [X: nat,Mi: nat,Ma: nat,Deg: nat,Xn: nat,H2: nat,Summary: vEBT_VEBT,TreeList2: list_VEBT_VEBT,L2: nat] :
% 5.41/5.66 ( ( ( X = Mi )
% 5.41/5.66 & ( ord_less_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = H2 )
% 5.41/5.66 => ( ( Xn
% 5.41/5.66 = ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) )
% 5.41/5.66 => ( ( ( vEBT_VEBT_low @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.66 = L2 )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xn @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 @ ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ Xn
% 5.41/5.66 @ ( if_nat @ ( Xn = Ma )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ Xn
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ H2 ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) )
% 5.41/5.66 @ ( vEBT_vebt_delete @ Summary @ H2 ) )
% 5.41/5.66 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xn @ ( if_nat @ ( Xn = Ma ) @ ( plus_plus_nat @ ( times_times_nat @ H2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ H2 ) ) ) ) @ Ma ) ) ) @ Deg @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ H2 @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ H2 ) @ L2 ) ) @ Summary ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_x_mi
% 5.41/5.66 thf(fact_2842_del__in__range,axiom,
% 5.41/5.66 ! [Mi: nat,X: nat,Ma: nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ( ord_less_eq_nat @ Mi @ X )
% 5.41/5.66 & ( ord_less_eq_nat @ X @ Ma ) )
% 5.41/5.66 => ( ( Mi != Ma )
% 5.41/5.66 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( ( X = Mi )
% 5.41/5.66 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.66 = Ma ) )
% 5.41/5.66 & ( ( X != Mi )
% 5.41/5.66 => ( X = Ma ) ) )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 = none_nat )
% 5.41/5.66 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ ( vEBT_Node
% 5.41/5.66 @ ( some_P7363390416028606310at_nat
% 5.41/5.66 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.41/5.66 @ ( if_nat
% 5.41/5.66 @ ( ( ( X = Mi )
% 5.41/5.66 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.66 = Ma ) )
% 5.41/5.66 & ( ( X != Mi )
% 5.41/5.66 => ( X = Ma ) ) )
% 5.41/5.66 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.66 @ Ma ) ) )
% 5.41/5.66 @ Deg
% 5.41/5.66 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 @ Summary ) )
% 5.41/5.66 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) ) ) ) ) ) ).
% 5.41/5.66
% 5.41/5.66 % del_in_range
% 5.41/5.66 thf(fact_2843_pred__less__length__list,axiom,
% 5.41/5.66 ! [Deg: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Mi: nat,Summary: vEBT_VEBT] :
% 5.41/5.66 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.66 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.41/5.66 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.66 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.66 = ( if_option_nat
% 5.41/5.66 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.66 != none_nat )
% 5.41/5.66 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.66 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pred_less_length_list
% 5.41/5.67 thf(fact_2844_pred__lesseq__max,axiom,
% 5.41/5.67 ! [Deg: nat,X: nat,Ma: nat,Mi: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.67 => ( ( ord_less_eq_nat @ X @ Ma )
% 5.41/5.67 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 != none_nat )
% 5.41/5.67 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ none_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pred_lesseq_max
% 5.41/5.67 thf(fact_2845_succ__greatereq__min,axiom,
% 5.41/5.67 ! [Deg: nat,Mi: nat,X: nat,Ma: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.67 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.41/5.67 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 != none_nat )
% 5.41/5.67 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ none_nat
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ none_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % succ_greatereq_min
% 5.41/5.67 thf(fact_2846_succ__less__length__list,axiom,
% 5.41/5.67 ! [Deg: nat,Mi: nat,X: nat,TreeList2: list_VEBT_VEBT,Ma: nat,Summary: vEBT_VEBT] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg )
% 5.41/5.67 => ( ( ord_less_eq_nat @ Mi @ X )
% 5.41/5.67 => ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( if_option_nat
% 5.41/5.67 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 != none_nat )
% 5.41/5.67 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ none_nat
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % succ_less_length_list
% 5.41/5.67 thf(fact_2847_dsimp,axiom,
% 5.41/5.67 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ mi @ ma ) ) @ deg @ treeList @ summary ) @ xa )
% 5.41/5.67 = ( vEBT_Node
% 5.41/5.67 @ ( some_P7363390416028606310at_nat
% 5.41/5.67 @ ( product_Pair_nat_nat @ mi
% 5.41/5.67 @ ( if_nat @ ( xa = ma )
% 5.41/5.67 @ ( if_nat
% 5.41/5.67 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ mi
% 5.41/5.67 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ ma ) ) )
% 5.41/5.67 @ deg
% 5.41/5.67 @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) )
% 5.41/5.67 @ ( vEBT_vebt_delete @ summary @ ( vEBT_VEBT_high @ xa @ na ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % dsimp
% 5.41/5.67 thf(fact_2848_mult__commute__abs,axiom,
% 5.41/5.67 ! [C: real] :
% 5.41/5.67 ( ( ^ [X3: real] : ( times_times_real @ X3 @ C ) )
% 5.41/5.67 = ( times_times_real @ C ) ) ).
% 5.41/5.67
% 5.41/5.67 % mult_commute_abs
% 5.41/5.67 thf(fact_2849_mult__commute__abs,axiom,
% 5.41/5.67 ! [C: rat] :
% 5.41/5.67 ( ( ^ [X3: rat] : ( times_times_rat @ X3 @ C ) )
% 5.41/5.67 = ( times_times_rat @ C ) ) ).
% 5.41/5.67
% 5.41/5.67 % mult_commute_abs
% 5.41/5.67 thf(fact_2850_mult__commute__abs,axiom,
% 5.41/5.67 ! [C: nat] :
% 5.41/5.67 ( ( ^ [X3: nat] : ( times_times_nat @ X3 @ C ) )
% 5.41/5.67 = ( times_times_nat @ C ) ) ).
% 5.41/5.67
% 5.41/5.67 % mult_commute_abs
% 5.41/5.67 thf(fact_2851_mult__commute__abs,axiom,
% 5.41/5.67 ! [C: int] :
% 5.41/5.67 ( ( ^ [X3: int] : ( times_times_int @ X3 @ C ) )
% 5.41/5.67 = ( times_times_int @ C ) ) ).
% 5.41/5.67
% 5.41/5.67 % mult_commute_abs
% 5.41/5.67 thf(fact_2852_Suc__inject,axiom,
% 5.41/5.67 ! [X: nat,Y: nat] :
% 5.41/5.67 ( ( ( suc @ X )
% 5.41/5.67 = ( suc @ Y ) )
% 5.41/5.67 => ( X = Y ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_inject
% 5.41/5.67 thf(fact_2853_n__not__Suc__n,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( N
% 5.41/5.67 != ( suc @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % n_not_Suc_n
% 5.41/5.67 thf(fact_2854_max__def__raw,axiom,
% 5.41/5.67 ( ord_ma741700101516333627d_enat
% 5.41/5.67 = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % max_def_raw
% 5.41/5.67 thf(fact_2855_max__def__raw,axiom,
% 5.41/5.67 ( ord_max_Code_integer
% 5.41/5.67 = ( ^ [A3: code_integer,B2: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % max_def_raw
% 5.41/5.67 thf(fact_2856_max__def__raw,axiom,
% 5.41/5.67 ( ord_max_set_int
% 5.41/5.67 = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % max_def_raw
% 5.41/5.67 thf(fact_2857_max__def__raw,axiom,
% 5.41/5.67 ( ord_max_rat
% 5.41/5.67 = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % max_def_raw
% 5.41/5.67 thf(fact_2858_max__def__raw,axiom,
% 5.41/5.67 ( ord_max_num
% 5.41/5.67 = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % max_def_raw
% 5.41/5.67 thf(fact_2859_max__def__raw,axiom,
% 5.41/5.67 ( ord_max_nat
% 5.41/5.67 = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % max_def_raw
% 5.41/5.67 thf(fact_2860_max__def__raw,axiom,
% 5.41/5.67 ( ord_max_int
% 5.41/5.67 = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % max_def_raw
% 5.41/5.67 thf(fact_2861_lambda__zero,axiom,
% 5.41/5.67 ( ( ^ [H: complex] : zero_zero_complex )
% 5.41/5.67 = ( times_times_complex @ zero_zero_complex ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_zero
% 5.41/5.67 thf(fact_2862_lambda__zero,axiom,
% 5.41/5.67 ( ( ^ [H: real] : zero_zero_real )
% 5.41/5.67 = ( times_times_real @ zero_zero_real ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_zero
% 5.41/5.67 thf(fact_2863_lambda__zero,axiom,
% 5.41/5.67 ( ( ^ [H: rat] : zero_zero_rat )
% 5.41/5.67 = ( times_times_rat @ zero_zero_rat ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_zero
% 5.41/5.67 thf(fact_2864_lambda__zero,axiom,
% 5.41/5.67 ( ( ^ [H: nat] : zero_zero_nat )
% 5.41/5.67 = ( times_times_nat @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_zero
% 5.41/5.67 thf(fact_2865_lambda__zero,axiom,
% 5.41/5.67 ( ( ^ [H: int] : zero_zero_int )
% 5.41/5.67 = ( times_times_int @ zero_zero_int ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_zero
% 5.41/5.67 thf(fact_2866_lambda__one,axiom,
% 5.41/5.67 ( ( ^ [X3: complex] : X3 )
% 5.41/5.67 = ( times_times_complex @ one_one_complex ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_one
% 5.41/5.67 thf(fact_2867_lambda__one,axiom,
% 5.41/5.67 ( ( ^ [X3: real] : X3 )
% 5.41/5.67 = ( times_times_real @ one_one_real ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_one
% 5.41/5.67 thf(fact_2868_lambda__one,axiom,
% 5.41/5.67 ( ( ^ [X3: rat] : X3 )
% 5.41/5.67 = ( times_times_rat @ one_one_rat ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_one
% 5.41/5.67 thf(fact_2869_lambda__one,axiom,
% 5.41/5.67 ( ( ^ [X3: nat] : X3 )
% 5.41/5.67 = ( times_times_nat @ one_one_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_one
% 5.41/5.67 thf(fact_2870_lambda__one,axiom,
% 5.41/5.67 ( ( ^ [X3: int] : X3 )
% 5.41/5.67 = ( times_times_int @ one_one_int ) ) ).
% 5.41/5.67
% 5.41/5.67 % lambda_one
% 5.41/5.67 thf(fact_2871_vebt__buildup_Ocases,axiom,
% 5.41/5.67 ! [X: nat] :
% 5.41/5.67 ( ( X != zero_zero_nat )
% 5.41/5.67 => ( ( X
% 5.41/5.67 != ( suc @ zero_zero_nat ) )
% 5.41/5.67 => ~ ! [Va2: nat] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( suc @ ( suc @ Va2 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_buildup.cases
% 5.41/5.67 thf(fact_2872_not0__implies__Suc,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( N != zero_zero_nat )
% 5.41/5.67 => ? [M4: nat] :
% 5.41/5.67 ( N
% 5.41/5.67 = ( suc @ M4 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % not0_implies_Suc
% 5.41/5.67 thf(fact_2873_Zero__not__Suc,axiom,
% 5.41/5.67 ! [M: nat] :
% 5.41/5.67 ( zero_zero_nat
% 5.41/5.67 != ( suc @ M ) ) ).
% 5.41/5.67
% 5.41/5.67 % Zero_not_Suc
% 5.41/5.67 thf(fact_2874_Zero__neq__Suc,axiom,
% 5.41/5.67 ! [M: nat] :
% 5.41/5.67 ( zero_zero_nat
% 5.41/5.67 != ( suc @ M ) ) ).
% 5.41/5.67
% 5.41/5.67 % Zero_neq_Suc
% 5.41/5.67 thf(fact_2875_Suc__neq__Zero,axiom,
% 5.41/5.67 ! [M: nat] :
% 5.41/5.67 ( ( suc @ M )
% 5.41/5.67 != zero_zero_nat ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_neq_Zero
% 5.41/5.67 thf(fact_2876_zero__induct,axiom,
% 5.41/5.67 ! [P: nat > $o,K: nat] :
% 5.41/5.67 ( ( P @ K )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( P @ ( suc @ N3 ) )
% 5.41/5.67 => ( P @ N3 ) )
% 5.41/5.67 => ( P @ zero_zero_nat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_induct
% 5.41/5.67 thf(fact_2877_diff__induct,axiom,
% 5.41/5.67 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.41/5.67 ( ! [X6: nat] : ( P @ X6 @ zero_zero_nat )
% 5.41/5.67 => ( ! [Y5: nat] : ( P @ zero_zero_nat @ ( suc @ Y5 ) )
% 5.41/5.67 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.67 ( ( P @ X6 @ Y5 )
% 5.41/5.67 => ( P @ ( suc @ X6 ) @ ( suc @ Y5 ) ) )
% 5.41/5.67 => ( P @ M @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % diff_induct
% 5.41/5.67 thf(fact_2878_nat__induct,axiom,
% 5.41/5.67 ! [P: nat > $o,N: nat] :
% 5.41/5.67 ( ( P @ zero_zero_nat )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( P @ N3 )
% 5.41/5.67 => ( P @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( P @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat_induct
% 5.41/5.67 thf(fact_2879_old_Onat_Oexhaust,axiom,
% 5.41/5.67 ! [Y: nat] :
% 5.41/5.67 ( ( Y != zero_zero_nat )
% 5.41/5.67 => ~ ! [Nat3: nat] :
% 5.41/5.67 ( Y
% 5.41/5.67 != ( suc @ Nat3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % old.nat.exhaust
% 5.41/5.67 thf(fact_2880_nat_OdiscI,axiom,
% 5.41/5.67 ! [Nat: nat,X22: nat] :
% 5.41/5.67 ( ( Nat
% 5.41/5.67 = ( suc @ X22 ) )
% 5.41/5.67 => ( Nat != zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat.discI
% 5.41/5.67 thf(fact_2881_old_Onat_Odistinct_I1_J,axiom,
% 5.41/5.67 ! [Nat2: nat] :
% 5.41/5.67 ( zero_zero_nat
% 5.41/5.67 != ( suc @ Nat2 ) ) ).
% 5.41/5.67
% 5.41/5.67 % old.nat.distinct(1)
% 5.41/5.67 thf(fact_2882_old_Onat_Odistinct_I2_J,axiom,
% 5.41/5.67 ! [Nat2: nat] :
% 5.41/5.67 ( ( suc @ Nat2 )
% 5.41/5.67 != zero_zero_nat ) ).
% 5.41/5.67
% 5.41/5.67 % old.nat.distinct(2)
% 5.41/5.67 thf(fact_2883_nat_Odistinct_I1_J,axiom,
% 5.41/5.67 ! [X22: nat] :
% 5.41/5.67 ( zero_zero_nat
% 5.41/5.67 != ( suc @ X22 ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat.distinct(1)
% 5.41/5.67 thf(fact_2884_not__less__less__Suc__eq,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ~ ( ord_less_nat @ N @ M )
% 5.41/5.67 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.41/5.67 = ( N = M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % not_less_less_Suc_eq
% 5.41/5.67 thf(fact_2885_strict__inc__induct,axiom,
% 5.41/5.67 ! [I: nat,J: nat,P: nat > $o] :
% 5.41/5.67 ( ( ord_less_nat @ I @ J )
% 5.41/5.67 => ( ! [I4: nat] :
% 5.41/5.67 ( ( J
% 5.41/5.67 = ( suc @ I4 ) )
% 5.41/5.67 => ( P @ I4 ) )
% 5.41/5.67 => ( ! [I4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I4 @ J )
% 5.41/5.67 => ( ( P @ ( suc @ I4 ) )
% 5.41/5.67 => ( P @ I4 ) ) )
% 5.41/5.67 => ( P @ I ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % strict_inc_induct
% 5.41/5.67 thf(fact_2886_less__Suc__induct,axiom,
% 5.41/5.67 ! [I: nat,J: nat,P: nat > nat > $o] :
% 5.41/5.67 ( ( ord_less_nat @ I @ J )
% 5.41/5.67 => ( ! [I4: nat] : ( P @ I4 @ ( suc @ I4 ) )
% 5.41/5.67 => ( ! [I4: nat,J2: nat,K3: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I4 @ J2 )
% 5.41/5.67 => ( ( ord_less_nat @ J2 @ K3 )
% 5.41/5.67 => ( ( P @ I4 @ J2 )
% 5.41/5.67 => ( ( P @ J2 @ K3 )
% 5.41/5.67 => ( P @ I4 @ K3 ) ) ) ) )
% 5.41/5.67 => ( P @ I @ J ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_Suc_induct
% 5.41/5.67 thf(fact_2887_less__trans__Suc,axiom,
% 5.41/5.67 ! [I: nat,J: nat,K: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I @ J )
% 5.41/5.67 => ( ( ord_less_nat @ J @ K )
% 5.41/5.67 => ( ord_less_nat @ ( suc @ I ) @ K ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_trans_Suc
% 5.41/5.67 thf(fact_2888_Suc__less__SucD,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ M ) @ ( suc @ N ) )
% 5.41/5.67 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_less_SucD
% 5.41/5.67 thf(fact_2889_less__antisym,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ~ ( ord_less_nat @ N @ M )
% 5.41/5.67 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.41/5.67 => ( M = N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_antisym
% 5.41/5.67 thf(fact_2890_Suc__less__eq2,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.67 = ( ? [M6: nat] :
% 5.41/5.67 ( ( M
% 5.41/5.67 = ( suc @ M6 ) )
% 5.41/5.67 & ( ord_less_nat @ N @ M6 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_less_eq2
% 5.41/5.67 thf(fact_2891_All__less__Suc,axiom,
% 5.41/5.67 ! [N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ! [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 5.41/5.67 => ( P @ I5 ) ) )
% 5.41/5.67 = ( ( P @ N )
% 5.41/5.67 & ! [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ N )
% 5.41/5.67 => ( P @ I5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % All_less_Suc
% 5.41/5.67 thf(fact_2892_not__less__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ~ ( ord_less_nat @ M @ N ) )
% 5.41/5.67 = ( ord_less_nat @ N @ ( suc @ M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % not_less_eq
% 5.41/5.67 thf(fact_2893_less__Suc__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.41/5.67 = ( ( ord_less_nat @ M @ N )
% 5.41/5.67 | ( M = N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_Suc_eq
% 5.41/5.67 thf(fact_2894_Ex__less__Suc,axiom,
% 5.41/5.67 ! [N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ? [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 5.41/5.67 & ( P @ I5 ) ) )
% 5.41/5.67 = ( ( P @ N )
% 5.41/5.67 | ? [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ N )
% 5.41/5.67 & ( P @ I5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Ex_less_Suc
% 5.41/5.67 thf(fact_2895_less__SucI,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ N )
% 5.41/5.67 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_SucI
% 5.41/5.67 thf(fact_2896_less__SucE,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.41/5.67 => ( ~ ( ord_less_nat @ M @ N )
% 5.41/5.67 => ( M = N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_SucE
% 5.41/5.67 thf(fact_2897_Suc__lessI,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ N )
% 5.41/5.67 => ( ( ( suc @ M )
% 5.41/5.67 != N )
% 5.41/5.67 => ( ord_less_nat @ ( suc @ M ) @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_lessI
% 5.41/5.67 thf(fact_2898_Suc__lessE,axiom,
% 5.41/5.67 ! [I: nat,K: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ I ) @ K )
% 5.41/5.67 => ~ ! [J2: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I @ J2 )
% 5.41/5.67 => ( K
% 5.41/5.67 != ( suc @ J2 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_lessE
% 5.41/5.67 thf(fact_2899_Suc__lessD,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ M ) @ N )
% 5.41/5.67 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_lessD
% 5.41/5.67 thf(fact_2900_Nat_OlessE,axiom,
% 5.41/5.67 ! [I: nat,K: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I @ K )
% 5.41/5.67 => ( ( K
% 5.41/5.67 != ( suc @ I ) )
% 5.41/5.67 => ~ ! [J2: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I @ J2 )
% 5.41/5.67 => ( K
% 5.41/5.67 != ( suc @ J2 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Nat.lessE
% 5.41/5.67 thf(fact_2901_set__vebt__def,axiom,
% 5.41/5.67 ( vEBT_set_vebt
% 5.41/5.67 = ( ^ [T2: vEBT_VEBT] : ( collect_nat @ ( vEBT_V8194947554948674370ptions @ T2 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % set_vebt_def
% 5.41/5.67 thf(fact_2902_transitive__stepwise__le,axiom,
% 5.41/5.67 ! [M: nat,N: nat,R4: nat > nat > $o] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.67 => ( ! [X6: nat] : ( R4 @ X6 @ X6 )
% 5.41/5.67 => ( ! [X6: nat,Y5: nat,Z5: nat] :
% 5.41/5.67 ( ( R4 @ X6 @ Y5 )
% 5.41/5.67 => ( ( R4 @ Y5 @ Z5 )
% 5.41/5.67 => ( R4 @ X6 @ Z5 ) ) )
% 5.41/5.67 => ( ! [N3: nat] : ( R4 @ N3 @ ( suc @ N3 ) )
% 5.41/5.67 => ( R4 @ M @ N ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % transitive_stepwise_le
% 5.41/5.67 thf(fact_2903_nat__induct__at__least,axiom,
% 5.41/5.67 ! [M: nat,N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.67 => ( ( P @ M )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ N3 )
% 5.41/5.67 => ( ( P @ N3 )
% 5.41/5.67 => ( P @ ( suc @ N3 ) ) ) )
% 5.41/5.67 => ( P @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat_induct_at_least
% 5.41/5.67 thf(fact_2904_full__nat__induct,axiom,
% 5.41/5.67 ! [P: nat > $o,N: nat] :
% 5.41/5.67 ( ! [N3: nat] :
% 5.41/5.67 ( ! [M2: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( suc @ M2 ) @ N3 )
% 5.41/5.67 => ( P @ M2 ) )
% 5.41/5.67 => ( P @ N3 ) )
% 5.41/5.67 => ( P @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % full_nat_induct
% 5.41/5.67 thf(fact_2905_not__less__eq__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ~ ( ord_less_eq_nat @ M @ N ) )
% 5.41/5.67 = ( ord_less_eq_nat @ ( suc @ N ) @ M ) ) ).
% 5.41/5.67
% 5.41/5.67 % not_less_eq_eq
% 5.41/5.67 thf(fact_2906_Suc__n__not__le__n,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ~ ( ord_less_eq_nat @ ( suc @ N ) @ N ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_n_not_le_n
% 5.41/5.67 thf(fact_2907_le__Suc__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.67 = ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.67 | ( M
% 5.41/5.67 = ( suc @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % le_Suc_eq
% 5.41/5.67 thf(fact_2908_Suc__le__D,axiom,
% 5.41/5.67 ! [N: nat,M7: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( suc @ N ) @ M7 )
% 5.41/5.67 => ? [M4: nat] :
% 5.41/5.67 ( M7
% 5.41/5.67 = ( suc @ M4 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_le_D
% 5.41/5.67 thf(fact_2909_le__SucI,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.67 => ( ord_less_eq_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % le_SucI
% 5.41/5.67 thf(fact_2910_le__SucE,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.67 => ( ~ ( ord_less_eq_nat @ M @ N )
% 5.41/5.67 => ( M
% 5.41/5.67 = ( suc @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % le_SucE
% 5.41/5.67 thf(fact_2911_Suc__leD,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.41/5.67 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_leD
% 5.41/5.67 thf(fact_2912_add__Suc__shift,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = ( plus_plus_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % add_Suc_shift
% 5.41/5.67 thf(fact_2913_add__Suc,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( plus_plus_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = ( suc @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % add_Suc
% 5.41/5.67 thf(fact_2914_nat__arith_Osuc1,axiom,
% 5.41/5.67 ! [A2: nat,K: nat,A: nat] :
% 5.41/5.67 ( ( A2
% 5.41/5.67 = ( plus_plus_nat @ K @ A ) )
% 5.41/5.67 => ( ( suc @ A2 )
% 5.41/5.67 = ( plus_plus_nat @ K @ ( suc @ A ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat_arith.suc1
% 5.41/5.67 thf(fact_2915_zero__induct__lemma,axiom,
% 5.41/5.67 ! [P: nat > $o,K: nat,I: nat] :
% 5.41/5.67 ( ( P @ K )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( P @ ( suc @ N3 ) )
% 5.41/5.67 => ( P @ N3 ) )
% 5.41/5.67 => ( P @ ( minus_minus_nat @ K @ I ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zero_induct_lemma
% 5.41/5.67 thf(fact_2916_Suc__mult__cancel1,axiom,
% 5.41/5.67 ! [K: nat,M: nat,N: nat] :
% 5.41/5.67 ( ( ( times_times_nat @ ( suc @ K ) @ M )
% 5.41/5.67 = ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.41/5.67 = ( M = N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_mult_cancel1
% 5.41/5.67 thf(fact_2917_numeral__code_I2_J,axiom,
% 5.41/5.67 ! [N: num] :
% 5.41/5.67 ( ( numera6690914467698888265omplex @ ( bit0 @ N ) )
% 5.41/5.67 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % numeral_code(2)
% 5.41/5.67 thf(fact_2918_numeral__code_I2_J,axiom,
% 5.41/5.67 ! [N: num] :
% 5.41/5.67 ( ( numeral_numeral_real @ ( bit0 @ N ) )
% 5.41/5.67 = ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % numeral_code(2)
% 5.41/5.67 thf(fact_2919_numeral__code_I2_J,axiom,
% 5.41/5.67 ! [N: num] :
% 5.41/5.67 ( ( numeral_numeral_rat @ ( bit0 @ N ) )
% 5.41/5.67 = ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % numeral_code(2)
% 5.41/5.67 thf(fact_2920_numeral__code_I2_J,axiom,
% 5.41/5.67 ! [N: num] :
% 5.41/5.67 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.41/5.67 = ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % numeral_code(2)
% 5.41/5.67 thf(fact_2921_numeral__code_I2_J,axiom,
% 5.41/5.67 ! [N: num] :
% 5.41/5.67 ( ( numeral_numeral_int @ ( bit0 @ N ) )
% 5.41/5.67 = ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % numeral_code(2)
% 5.41/5.67 thf(fact_2922_mod__Suc__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( modulo_modulo_nat @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) @ N )
% 5.41/5.67 = ( modulo_modulo_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % mod_Suc_eq
% 5.41/5.67 thf(fact_2923_mod__Suc__Suc__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) @ N )
% 5.41/5.67 = ( modulo_modulo_nat @ ( suc @ ( suc @ M ) ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % mod_Suc_Suc_eq
% 5.41/5.67 thf(fact_2924_set__bit__greater__eq,axiom,
% 5.41/5.67 ! [K: int,N: nat] : ( ord_less_eq_int @ K @ ( bit_se7879613467334960850it_int @ N @ K ) ) ).
% 5.41/5.67
% 5.41/5.67 % set_bit_greater_eq
% 5.41/5.67 thf(fact_2925_power__numeral__even,axiom,
% 5.41/5.67 ! [Z: complex,W: num] :
% 5.41/5.67 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.41/5.67 = ( times_times_complex @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_numeral_even
% 5.41/5.67 thf(fact_2926_power__numeral__even,axiom,
% 5.41/5.67 ! [Z: real,W: num] :
% 5.41/5.67 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.41/5.67 = ( times_times_real @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_numeral_even
% 5.41/5.67 thf(fact_2927_power__numeral__even,axiom,
% 5.41/5.67 ! [Z: rat,W: num] :
% 5.41/5.67 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.41/5.67 = ( times_times_rat @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_numeral_even
% 5.41/5.67 thf(fact_2928_power__numeral__even,axiom,
% 5.41/5.67 ! [Z: nat,W: num] :
% 5.41/5.67 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.41/5.67 = ( times_times_nat @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_numeral_even
% 5.41/5.67 thf(fact_2929_power__numeral__even,axiom,
% 5.41/5.67 ! [Z: int,W: num] :
% 5.41/5.67 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit0 @ W ) ) )
% 5.41/5.67 = ( times_times_int @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_numeral_even
% 5.41/5.67 thf(fact_2930_atLeastatMost__psubset__iff,axiom,
% 5.41/5.67 ! [A: set_int,B: set_int,C: set_int,D: set_int] :
% 5.41/5.67 ( ( ord_less_set_set_int @ ( set_or370866239135849197et_int @ A @ B ) @ ( set_or370866239135849197et_int @ C @ D ) )
% 5.41/5.67 = ( ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.41/5.67 | ( ( ord_less_eq_set_int @ C @ A )
% 5.41/5.67 & ( ord_less_eq_set_int @ B @ D )
% 5.41/5.67 & ( ( ord_less_set_int @ C @ A )
% 5.41/5.67 | ( ord_less_set_int @ B @ D ) ) ) )
% 5.41/5.67 & ( ord_less_eq_set_int @ C @ D ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % atLeastatMost_psubset_iff
% 5.41/5.67 thf(fact_2931_atLeastatMost__psubset__iff,axiom,
% 5.41/5.67 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.67 ( ( ord_less_set_rat @ ( set_or633870826150836451st_rat @ A @ B ) @ ( set_or633870826150836451st_rat @ C @ D ) )
% 5.41/5.67 = ( ( ~ ( ord_less_eq_rat @ A @ B )
% 5.41/5.67 | ( ( ord_less_eq_rat @ C @ A )
% 5.41/5.67 & ( ord_less_eq_rat @ B @ D )
% 5.41/5.67 & ( ( ord_less_rat @ C @ A )
% 5.41/5.67 | ( ord_less_rat @ B @ D ) ) ) )
% 5.41/5.67 & ( ord_less_eq_rat @ C @ D ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % atLeastatMost_psubset_iff
% 5.41/5.67 thf(fact_2932_atLeastatMost__psubset__iff,axiom,
% 5.41/5.67 ! [A: num,B: num,C: num,D: num] :
% 5.41/5.67 ( ( ord_less_set_num @ ( set_or7049704709247886629st_num @ A @ B ) @ ( set_or7049704709247886629st_num @ C @ D ) )
% 5.41/5.67 = ( ( ~ ( ord_less_eq_num @ A @ B )
% 5.41/5.67 | ( ( ord_less_eq_num @ C @ A )
% 5.41/5.67 & ( ord_less_eq_num @ B @ D )
% 5.41/5.67 & ( ( ord_less_num @ C @ A )
% 5.41/5.67 | ( ord_less_num @ B @ D ) ) ) )
% 5.41/5.67 & ( ord_less_eq_num @ C @ D ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % atLeastatMost_psubset_iff
% 5.41/5.67 thf(fact_2933_atLeastatMost__psubset__iff,axiom,
% 5.41/5.67 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.67 ( ( ord_less_set_nat @ ( set_or1269000886237332187st_nat @ A @ B ) @ ( set_or1269000886237332187st_nat @ C @ D ) )
% 5.41/5.67 = ( ( ~ ( ord_less_eq_nat @ A @ B )
% 5.41/5.67 | ( ( ord_less_eq_nat @ C @ A )
% 5.41/5.67 & ( ord_less_eq_nat @ B @ D )
% 5.41/5.67 & ( ( ord_less_nat @ C @ A )
% 5.41/5.67 | ( ord_less_nat @ B @ D ) ) ) )
% 5.41/5.67 & ( ord_less_eq_nat @ C @ D ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % atLeastatMost_psubset_iff
% 5.41/5.67 thf(fact_2934_atLeastatMost__psubset__iff,axiom,
% 5.41/5.67 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.67 ( ( ord_less_set_int @ ( set_or1266510415728281911st_int @ A @ B ) @ ( set_or1266510415728281911st_int @ C @ D ) )
% 5.41/5.67 = ( ( ~ ( ord_less_eq_int @ A @ B )
% 5.41/5.67 | ( ( ord_less_eq_int @ C @ A )
% 5.41/5.67 & ( ord_less_eq_int @ B @ D )
% 5.41/5.67 & ( ( ord_less_int @ C @ A )
% 5.41/5.67 | ( ord_less_int @ B @ D ) ) ) )
% 5.41/5.67 & ( ord_less_eq_int @ C @ D ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % atLeastatMost_psubset_iff
% 5.41/5.67 thf(fact_2935_atLeastatMost__psubset__iff,axiom,
% 5.41/5.67 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.67 ( ( ord_less_set_real @ ( set_or1222579329274155063t_real @ A @ B ) @ ( set_or1222579329274155063t_real @ C @ D ) )
% 5.41/5.67 = ( ( ~ ( ord_less_eq_real @ A @ B )
% 5.41/5.67 | ( ( ord_less_eq_real @ C @ A )
% 5.41/5.67 & ( ord_less_eq_real @ B @ D )
% 5.41/5.67 & ( ( ord_less_real @ C @ A )
% 5.41/5.67 | ( ord_less_real @ B @ D ) ) ) )
% 5.41/5.67 & ( ord_less_eq_real @ C @ D ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % atLeastatMost_psubset_iff
% 5.41/5.67 thf(fact_2936_ex__nat__less,axiom,
% 5.41/5.67 ! [N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ? [M3: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M3 @ N )
% 5.41/5.67 & ( P @ M3 ) ) )
% 5.41/5.67 = ( ? [X3: nat] :
% 5.41/5.67 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.67 & ( P @ X3 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % ex_nat_less
% 5.41/5.67 thf(fact_2937_all__nat__less,axiom,
% 5.41/5.67 ! [N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ! [M3: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M3 @ N )
% 5.41/5.67 => ( P @ M3 ) ) )
% 5.41/5.67 = ( ! [X3: nat] :
% 5.41/5.67 ( ( member_nat @ X3 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.67 => ( P @ X3 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % all_nat_less
% 5.41/5.67 thf(fact_2938_lift__Suc__mono__less__iff,axiom,
% 5.41/5.67 ! [F: nat > real,N: nat,M: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_real @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less_iff
% 5.41/5.67 thf(fact_2939_lift__Suc__mono__less__iff,axiom,
% 5.41/5.67 ! [F: nat > rat,N: nat,M: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_rat @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less_iff
% 5.41/5.67 thf(fact_2940_lift__Suc__mono__less__iff,axiom,
% 5.41/5.67 ! [F: nat > num,N: nat,M: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_num @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less_iff
% 5.41/5.67 thf(fact_2941_lift__Suc__mono__less__iff,axiom,
% 5.41/5.67 ! [F: nat > nat,N: nat,M: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_nat @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less_iff
% 5.41/5.67 thf(fact_2942_lift__Suc__mono__less__iff,axiom,
% 5.41/5.67 ! [F: nat > int,N: nat,M: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_int @ ( F @ N ) @ ( F @ M ) )
% 5.41/5.67 = ( ord_less_nat @ N @ M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less_iff
% 5.41/5.67 thf(fact_2943_lift__Suc__mono__less,axiom,
% 5.41/5.67 ! [F: nat > real,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_real @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less
% 5.41/5.67 thf(fact_2944_lift__Suc__mono__less,axiom,
% 5.41/5.67 ! [F: nat > rat,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less
% 5.41/5.67 thf(fact_2945_lift__Suc__mono__less,axiom,
% 5.41/5.67 ! [F: nat > num,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less
% 5.41/5.67 thf(fact_2946_lift__Suc__mono__less,axiom,
% 5.41/5.67 ! [F: nat > nat,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less
% 5.41/5.67 thf(fact_2947_lift__Suc__mono__less,axiom,
% 5.41/5.67 ! [F: nat > int,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_less
% 5.41/5.67 thf(fact_2948_power__Suc,axiom,
% 5.41/5.67 ! [A: complex,N: nat] :
% 5.41/5.67 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_complex @ A @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc
% 5.41/5.67 thf(fact_2949_power__Suc,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_real @ A @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc
% 5.41/5.67 thf(fact_2950_power__Suc,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_rat @ A @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc
% 5.41/5.67 thf(fact_2951_power__Suc,axiom,
% 5.41/5.67 ! [A: nat,N: nat] :
% 5.41/5.67 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_nat @ A @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc
% 5.41/5.67 thf(fact_2952_power__Suc,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_int @ A @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc
% 5.41/5.67 thf(fact_2953_power__Suc2,axiom,
% 5.41/5.67 ! [A: complex,N: nat] :
% 5.41/5.67 ( ( power_power_complex @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_complex @ ( power_power_complex @ A @ N ) @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc2
% 5.41/5.67 thf(fact_2954_power__Suc2,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( power_power_real @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_real @ ( power_power_real @ A @ N ) @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc2
% 5.41/5.67 thf(fact_2955_power__Suc2,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_rat @ ( power_power_rat @ A @ N ) @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc2
% 5.41/5.67 thf(fact_2956_power__Suc2,axiom,
% 5.41/5.67 ! [A: nat,N: nat] :
% 5.41/5.67 ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_nat @ ( power_power_nat @ A @ N ) @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc2
% 5.41/5.67 thf(fact_2957_power__Suc2,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( power_power_int @ A @ ( suc @ N ) )
% 5.41/5.67 = ( times_times_int @ ( power_power_int @ A @ N ) @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc2
% 5.41/5.67 thf(fact_2958_lift__Suc__antimono__le,axiom,
% 5.41/5.67 ! [F: nat > set_int,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_set_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_antimono_le
% 5.41/5.67 thf(fact_2959_lift__Suc__antimono__le,axiom,
% 5.41/5.67 ! [F: nat > rat,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_rat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_antimono_le
% 5.41/5.67 thf(fact_2960_lift__Suc__antimono__le,axiom,
% 5.41/5.67 ! [F: nat > num,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_num @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_antimono_le
% 5.41/5.67 thf(fact_2961_lift__Suc__antimono__le,axiom,
% 5.41/5.67 ! [F: nat > nat,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_nat @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_antimono_le
% 5.41/5.67 thf(fact_2962_lift__Suc__antimono__le,axiom,
% 5.41/5.67 ! [F: nat > int,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ ( suc @ N3 ) ) @ ( F @ N3 ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_int @ ( F @ N5 ) @ ( F @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_antimono_le
% 5.41/5.67 thf(fact_2963_lift__Suc__mono__le,axiom,
% 5.41/5.67 ! [F: nat > set_int,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_set_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_set_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_le
% 5.41/5.67 thf(fact_2964_lift__Suc__mono__le,axiom,
% 5.41/5.67 ! [F: nat > rat,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_rat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_rat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_le
% 5.41/5.67 thf(fact_2965_lift__Suc__mono__le,axiom,
% 5.41/5.67 ! [F: nat > num,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_num @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_num @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_le
% 5.41/5.67 thf(fact_2966_lift__Suc__mono__le,axiom,
% 5.41/5.67 ! [F: nat > nat,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_nat @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_nat @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_le
% 5.41/5.67 thf(fact_2967_lift__Suc__mono__le,axiom,
% 5.41/5.67 ! [F: nat > int,N: nat,N5: nat] :
% 5.41/5.67 ( ! [N3: nat] : ( ord_less_eq_int @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ N5 )
% 5.41/5.67 => ( ord_less_eq_int @ ( F @ N ) @ ( F @ N5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % lift_Suc_mono_le
% 5.41/5.67 thf(fact_2968_less__Suc__eq__0__disj,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.41/5.67 = ( ( M = zero_zero_nat )
% 5.41/5.67 | ? [J3: nat] :
% 5.41/5.67 ( ( M
% 5.41/5.67 = ( suc @ J3 ) )
% 5.41/5.67 & ( ord_less_nat @ J3 @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_Suc_eq_0_disj
% 5.41/5.67 thf(fact_2969_gr0__implies__Suc,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ? [M4: nat] :
% 5.41/5.67 ( N
% 5.41/5.67 = ( suc @ M4 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % gr0_implies_Suc
% 5.41/5.67 thf(fact_2970_All__less__Suc2,axiom,
% 5.41/5.67 ! [N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ! [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 5.41/5.67 => ( P @ I5 ) ) )
% 5.41/5.67 = ( ( P @ zero_zero_nat )
% 5.41/5.67 & ! [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ N )
% 5.41/5.67 => ( P @ ( suc @ I5 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % All_less_Suc2
% 5.41/5.67 thf(fact_2971_gr0__conv__Suc,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 = ( ? [M3: nat] :
% 5.41/5.67 ( N
% 5.41/5.67 = ( suc @ M3 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % gr0_conv_Suc
% 5.41/5.67 thf(fact_2972_Ex__less__Suc2,axiom,
% 5.41/5.67 ! [N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ? [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ ( suc @ N ) )
% 5.41/5.67 & ( P @ I5 ) ) )
% 5.41/5.67 = ( ( P @ zero_zero_nat )
% 5.41/5.67 | ? [I5: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I5 @ N )
% 5.41/5.67 & ( P @ ( suc @ I5 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Ex_less_Suc2
% 5.41/5.67 thf(fact_2973_Suc__leI,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ N )
% 5.41/5.67 => ( ord_less_eq_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_leI
% 5.41/5.67 thf(fact_2974_Suc__le__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_le_eq
% 5.41/5.67 thf(fact_2975_dec__induct,axiom,
% 5.41/5.67 ! [I: nat,J: nat,P: nat > $o] :
% 5.41/5.67 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.67 => ( ( P @ I )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ I @ N3 )
% 5.41/5.67 => ( ( ord_less_nat @ N3 @ J )
% 5.41/5.67 => ( ( P @ N3 )
% 5.41/5.67 => ( P @ ( suc @ N3 ) ) ) ) )
% 5.41/5.67 => ( P @ J ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % dec_induct
% 5.41/5.67 thf(fact_2976_inc__induct,axiom,
% 5.41/5.67 ! [I: nat,J: nat,P: nat > $o] :
% 5.41/5.67 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.67 => ( ( P @ J )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ I @ N3 )
% 5.41/5.67 => ( ( ord_less_nat @ N3 @ J )
% 5.41/5.67 => ( ( P @ ( suc @ N3 ) )
% 5.41/5.67 => ( P @ N3 ) ) ) )
% 5.41/5.67 => ( P @ I ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % inc_induct
% 5.41/5.67 thf(fact_2977_Suc__le__lessD,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.41/5.67 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_le_lessD
% 5.41/5.67 thf(fact_2978_le__less__Suc__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.67 => ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.41/5.67 = ( N = M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % le_less_Suc_eq
% 5.41/5.67 thf(fact_2979_less__Suc__eq__le,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ ( suc @ N ) )
% 5.41/5.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_Suc_eq_le
% 5.41/5.67 thf(fact_2980_less__eq__Suc__le,axiom,
% 5.41/5.67 ( ord_less_nat
% 5.41/5.67 = ( ^ [N2: nat] : ( ord_less_eq_nat @ ( suc @ N2 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_eq_Suc_le
% 5.41/5.67 thf(fact_2981_le__imp__less__Suc,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.67 => ( ord_less_nat @ M @ ( suc @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % le_imp_less_Suc
% 5.41/5.67 thf(fact_2982_add__is__1,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ( plus_plus_nat @ M @ N )
% 5.41/5.67 = ( suc @ zero_zero_nat ) )
% 5.41/5.67 = ( ( ( M
% 5.41/5.67 = ( suc @ zero_zero_nat ) )
% 5.41/5.67 & ( N = zero_zero_nat ) )
% 5.41/5.67 | ( ( M = zero_zero_nat )
% 5.41/5.67 & ( N
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % add_is_1
% 5.41/5.67 thf(fact_2983_one__is__add,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ( suc @ zero_zero_nat )
% 5.41/5.67 = ( plus_plus_nat @ M @ N ) )
% 5.41/5.67 = ( ( ( M
% 5.41/5.67 = ( suc @ zero_zero_nat ) )
% 5.41/5.67 & ( N = zero_zero_nat ) )
% 5.41/5.67 | ( ( M = zero_zero_nat )
% 5.41/5.67 & ( N
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % one_is_add
% 5.41/5.67 thf(fact_2984_option_Osize_I4_J,axiom,
% 5.41/5.67 ! [X22: nat] :
% 5.41/5.67 ( ( size_size_option_nat @ ( some_nat @ X22 ) )
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % option.size(4)
% 5.41/5.67 thf(fact_2985_option_Osize_I4_J,axiom,
% 5.41/5.67 ! [X22: product_prod_nat_nat] :
% 5.41/5.67 ( ( size_s170228958280169651at_nat @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % option.size(4)
% 5.41/5.67 thf(fact_2986_option_Osize_I4_J,axiom,
% 5.41/5.67 ! [X22: num] :
% 5.41/5.67 ( ( size_size_option_num @ ( some_num @ X22 ) )
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % option.size(4)
% 5.41/5.67 thf(fact_2987_less__natE,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ N )
% 5.41/5.67 => ~ ! [Q3: nat] :
% 5.41/5.67 ( N
% 5.41/5.67 != ( suc @ ( plus_plus_nat @ M @ Q3 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_natE
% 5.41/5.67 thf(fact_2988_less__add__Suc1,axiom,
% 5.41/5.67 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ I @ M ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_add_Suc1
% 5.41/5.67 thf(fact_2989_less__add__Suc2,axiom,
% 5.41/5.67 ! [I: nat,M: nat] : ( ord_less_nat @ I @ ( suc @ ( plus_plus_nat @ M @ I ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_add_Suc2
% 5.41/5.67 thf(fact_2990_less__iff__Suc__add,axiom,
% 5.41/5.67 ( ord_less_nat
% 5.41/5.67 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.67 ? [K2: nat] :
% 5.41/5.67 ( N2
% 5.41/5.67 = ( suc @ ( plus_plus_nat @ M3 @ K2 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_iff_Suc_add
% 5.41/5.67 thf(fact_2991_less__imp__Suc__add,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ M @ N )
% 5.41/5.67 => ? [K3: nat] :
% 5.41/5.67 ( N
% 5.41/5.67 = ( suc @ ( plus_plus_nat @ M @ K3 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_imp_Suc_add
% 5.41/5.67 thf(fact_2992_option_Osize_I3_J,axiom,
% 5.41/5.67 ( ( size_size_option_nat @ none_nat )
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % option.size(3)
% 5.41/5.67 thf(fact_2993_option_Osize_I3_J,axiom,
% 5.41/5.67 ( ( size_s170228958280169651at_nat @ none_P5556105721700978146at_nat )
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % option.size(3)
% 5.41/5.67 thf(fact_2994_option_Osize_I3_J,axiom,
% 5.41/5.67 ( ( size_size_option_num @ none_num )
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % option.size(3)
% 5.41/5.67 thf(fact_2995_diff__less__Suc,axiom,
% 5.41/5.67 ! [M: nat,N: nat] : ( ord_less_nat @ ( minus_minus_nat @ M @ N ) @ ( suc @ M ) ) ).
% 5.41/5.67
% 5.41/5.67 % diff_less_Suc
% 5.41/5.67 thf(fact_2996_Suc__diff__Suc,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ N @ M )
% 5.41/5.67 => ( ( suc @ ( minus_minus_nat @ M @ ( suc @ N ) ) )
% 5.41/5.67 = ( minus_minus_nat @ M @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_diff_Suc
% 5.41/5.67 thf(fact_2997_Suc__mult__less__cancel1,axiom,
% 5.41/5.67 ! [K: nat,M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.41/5.67 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_mult_less_cancel1
% 5.41/5.67 thf(fact_2998_Suc__diff__le,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.67 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = ( suc @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_diff_le
% 5.41/5.67 thf(fact_2999_Suc__mult__le__cancel1,axiom,
% 5.41/5.67 ! [K: nat,M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( times_times_nat @ ( suc @ K ) @ M ) @ ( times_times_nat @ ( suc @ K ) @ N ) )
% 5.41/5.67 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_mult_le_cancel1
% 5.41/5.67 thf(fact_3000_One__nat__def,axiom,
% 5.41/5.67 ( one_one_nat
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % One_nat_def
% 5.41/5.67 thf(fact_3001_Suc__div__le__mono,axiom,
% 5.41/5.67 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( divide_divide_nat @ M @ N ) @ ( divide_divide_nat @ ( suc @ M ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_div_le_mono
% 5.41/5.67 thf(fact_3002_mult__Suc,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( times_times_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = ( plus_plus_nat @ N @ ( times_times_nat @ M @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % mult_Suc
% 5.41/5.67 thf(fact_3003_Suc__eq__plus1,axiom,
% 5.41/5.67 ( suc
% 5.41/5.67 = ( ^ [N2: nat] : ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_eq_plus1
% 5.41/5.67 thf(fact_3004_plus__1__eq__Suc,axiom,
% 5.41/5.67 ( ( plus_plus_nat @ one_one_nat )
% 5.41/5.67 = suc ) ).
% 5.41/5.67
% 5.41/5.67 % plus_1_eq_Suc
% 5.41/5.67 thf(fact_3005_Suc__eq__plus1__left,axiom,
% 5.41/5.67 ( suc
% 5.41/5.67 = ( plus_plus_nat @ one_one_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_eq_plus1_left
% 5.41/5.67 thf(fact_3006_diff__Suc__eq__diff__pred,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.41/5.67 = ( minus_minus_nat @ ( minus_minus_nat @ M @ one_one_nat ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % diff_Suc_eq_diff_pred
% 5.41/5.67 thf(fact_3007_mod__Suc,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.41/5.67 = N )
% 5.41/5.67 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = zero_zero_nat ) )
% 5.41/5.67 & ( ( ( suc @ ( modulo_modulo_nat @ M @ N ) )
% 5.41/5.67 != N )
% 5.41/5.67 => ( ( modulo_modulo_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = ( suc @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % mod_Suc
% 5.41/5.67 thf(fact_3008_mod__induct,axiom,
% 5.41/5.67 ! [P: nat > $o,N: nat,P5: nat,M: nat] :
% 5.41/5.67 ( ( P @ N )
% 5.41/5.67 => ( ( ord_less_nat @ N @ P5 )
% 5.41/5.67 => ( ( ord_less_nat @ M @ P5 )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( ord_less_nat @ N3 @ P5 )
% 5.41/5.67 => ( ( P @ N3 )
% 5.41/5.67 => ( P @ ( modulo_modulo_nat @ ( suc @ N3 ) @ P5 ) ) ) )
% 5.41/5.67 => ( P @ M ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % mod_induct
% 5.41/5.67 thf(fact_3009_mod__Suc__le__divisor,axiom,
% 5.41/5.67 ! [M: nat,N: nat] : ( ord_less_eq_nat @ ( modulo_modulo_nat @ M @ ( suc @ N ) ) @ N ) ).
% 5.41/5.67
% 5.41/5.67 % mod_Suc_le_divisor
% 5.41/5.67 thf(fact_3010_power__inject__base,axiom,
% 5.41/5.67 ! [A: real,N: nat,B: real] :
% 5.41/5.67 ( ( ( power_power_real @ A @ ( suc @ N ) )
% 5.41/5.67 = ( power_power_real @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.67 => ( A = B ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_inject_base
% 5.41/5.67 thf(fact_3011_power__inject__base,axiom,
% 5.41/5.67 ! [A: rat,N: nat,B: rat] :
% 5.41/5.67 ( ( ( power_power_rat @ A @ ( suc @ N ) )
% 5.41/5.67 = ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.67 => ( A = B ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_inject_base
% 5.41/5.67 thf(fact_3012_power__inject__base,axiom,
% 5.41/5.67 ! [A: nat,N: nat,B: nat] :
% 5.41/5.67 ( ( ( power_power_nat @ A @ ( suc @ N ) )
% 5.41/5.67 = ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.67 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.67 => ( A = B ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_inject_base
% 5.41/5.67 thf(fact_3013_power__inject__base,axiom,
% 5.41/5.67 ! [A: int,N: nat,B: int] :
% 5.41/5.67 ( ( ( power_power_int @ A @ ( suc @ N ) )
% 5.41/5.67 = ( power_power_int @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.67 => ( A = B ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_inject_base
% 5.41/5.67 thf(fact_3014_power__le__imp__le__base,axiom,
% 5.41/5.67 ! [A: real,N: nat,B: real] :
% 5.41/5.67 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ ( power_power_real @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.67 => ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_le_imp_le_base
% 5.41/5.67 thf(fact_3015_power__le__imp__le__base,axiom,
% 5.41/5.67 ! [A: rat,N: nat,B: rat] :
% 5.41/5.67 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ ( power_power_rat @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.67 => ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_le_imp_le_base
% 5.41/5.67 thf(fact_3016_power__le__imp__le__base,axiom,
% 5.41/5.67 ! [A: nat,N: nat,B: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ ( power_power_nat @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ zero_zero_nat @ B )
% 5.41/5.67 => ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_le_imp_le_base
% 5.41/5.67 thf(fact_3017_power__le__imp__le__base,axiom,
% 5.41/5.67 ! [A: int,N: nat,B: int] :
% 5.41/5.67 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ ( power_power_int @ B @ ( suc @ N ) ) )
% 5.41/5.67 => ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.67 => ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_le_imp_le_base
% 5.41/5.67 thf(fact_3018_power__gt1,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.67 => ( ord_less_real @ one_one_real @ ( power_power_real @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_gt1
% 5.41/5.67 thf(fact_3019_power__gt1,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( ord_less_rat @ one_one_rat @ A )
% 5.41/5.67 => ( ord_less_rat @ one_one_rat @ ( power_power_rat @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_gt1
% 5.41/5.67 thf(fact_3020_power__gt1,axiom,
% 5.41/5.67 ! [A: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ one_one_nat @ A )
% 5.41/5.67 => ( ord_less_nat @ one_one_nat @ ( power_power_nat @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_gt1
% 5.41/5.67 thf(fact_3021_power__gt1,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( ord_less_int @ one_one_int @ A )
% 5.41/5.67 => ( ord_less_int @ one_one_int @ ( power_power_int @ A @ ( suc @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_gt1
% 5.41/5.67 thf(fact_3022_numeral__1__eq__Suc__0,axiom,
% 5.41/5.67 ( ( numeral_numeral_nat @ one )
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % numeral_1_eq_Suc_0
% 5.41/5.67 thf(fact_3023_ex__least__nat__less,axiom,
% 5.41/5.67 ! [P: nat > $o,N: nat] :
% 5.41/5.67 ( ( P @ N )
% 5.41/5.67 => ( ~ ( P @ zero_zero_nat )
% 5.41/5.67 => ? [K3: nat] :
% 5.41/5.67 ( ( ord_less_nat @ K3 @ N )
% 5.41/5.67 & ! [I2: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ I2 @ K3 )
% 5.41/5.67 => ~ ( P @ I2 ) )
% 5.41/5.67 & ( P @ ( suc @ K3 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % ex_least_nat_less
% 5.41/5.67 thf(fact_3024_verit__la__disequality,axiom,
% 5.41/5.67 ! [A: rat,B: rat] :
% 5.41/5.67 ( ( A = B )
% 5.41/5.67 | ~ ( ord_less_eq_rat @ A @ B )
% 5.41/5.67 | ~ ( ord_less_eq_rat @ B @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_la_disequality
% 5.41/5.67 thf(fact_3025_verit__la__disequality,axiom,
% 5.41/5.67 ! [A: num,B: num] :
% 5.41/5.67 ( ( A = B )
% 5.41/5.67 | ~ ( ord_less_eq_num @ A @ B )
% 5.41/5.67 | ~ ( ord_less_eq_num @ B @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_la_disequality
% 5.41/5.67 thf(fact_3026_verit__la__disequality,axiom,
% 5.41/5.67 ! [A: nat,B: nat] :
% 5.41/5.67 ( ( A = B )
% 5.41/5.67 | ~ ( ord_less_eq_nat @ A @ B )
% 5.41/5.67 | ~ ( ord_less_eq_nat @ B @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_la_disequality
% 5.41/5.67 thf(fact_3027_verit__la__disequality,axiom,
% 5.41/5.67 ! [A: int,B: int] :
% 5.41/5.67 ( ( A = B )
% 5.41/5.67 | ~ ( ord_less_eq_int @ A @ B )
% 5.41/5.67 | ~ ( ord_less_eq_int @ B @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_la_disequality
% 5.41/5.67 thf(fact_3028_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.67 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(2)
% 5.41/5.67 thf(fact_3029_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.67 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(2)
% 5.41/5.67 thf(fact_3030_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.67 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(2)
% 5.41/5.67 thf(fact_3031_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.67 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(2)
% 5.41/5.67 thf(fact_3032_verit__comp__simplify1_I2_J,axiom,
% 5.41/5.67 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(2)
% 5.41/5.67 thf(fact_3033_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.67 ! [A: real] :
% 5.41/5.67 ~ ( ord_less_real @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(1)
% 5.41/5.67 thf(fact_3034_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.67 ! [A: rat] :
% 5.41/5.67 ~ ( ord_less_rat @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(1)
% 5.41/5.67 thf(fact_3035_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.67 ! [A: num] :
% 5.41/5.67 ~ ( ord_less_num @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(1)
% 5.41/5.67 thf(fact_3036_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.67 ! [A: nat] :
% 5.41/5.67 ~ ( ord_less_nat @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(1)
% 5.41/5.67 thf(fact_3037_verit__comp__simplify1_I1_J,axiom,
% 5.41/5.67 ! [A: int] :
% 5.41/5.67 ~ ( ord_less_int @ A @ A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(1)
% 5.41/5.67 thf(fact_3038_diff__Suc__less,axiom,
% 5.41/5.67 ! [N: nat,I: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ord_less_nat @ ( minus_minus_nat @ N @ ( suc @ I ) ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % diff_Suc_less
% 5.41/5.67 thf(fact_3039_n__less__n__mult__m,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.41/5.67 => ( ord_less_nat @ N @ ( times_times_nat @ N @ M ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % n_less_n_mult_m
% 5.41/5.67 thf(fact_3040_n__less__m__mult__n,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.41/5.67 => ( ord_less_nat @ N @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % n_less_m_mult_n
% 5.41/5.67 thf(fact_3041_one__less__mult,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.67 => ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.41/5.67 => ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( times_times_nat @ M @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % one_less_mult
% 5.41/5.67 thf(fact_3042_nat__induct__non__zero,axiom,
% 5.41/5.67 ! [N: nat,P: nat > $o] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ( P @ one_one_nat )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.41/5.67 => ( ( P @ N3 )
% 5.41/5.67 => ( P @ ( suc @ N3 ) ) ) )
% 5.41/5.67 => ( P @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat_induct_non_zero
% 5.41/5.67 thf(fact_3043_power__gt__expt,axiom,
% 5.41/5.67 ! [N: nat,K: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.67 => ( ord_less_nat @ K @ ( power_power_nat @ N @ K ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_gt_expt
% 5.41/5.67 thf(fact_3044_realpow__pos__nth2,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.67 => ? [R2: real] :
% 5.41/5.67 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.41/5.67 & ( ( power_power_real @ R2 @ ( suc @ N ) )
% 5.41/5.67 = A ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % realpow_pos_nth2
% 5.41/5.67 thf(fact_3045_nat__one__le__power,axiom,
% 5.41/5.67 ! [I: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ I )
% 5.41/5.67 => ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( power_power_nat @ I @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat_one_le_power
% 5.41/5.67 thf(fact_3046_verit__la__generic,axiom,
% 5.41/5.67 ! [A: int,X: int] :
% 5.41/5.67 ( ( ord_less_eq_int @ A @ X )
% 5.41/5.67 | ( A = X )
% 5.41/5.67 | ( ord_less_eq_int @ X @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_la_generic
% 5.41/5.67 thf(fact_3047_power__Suc__le__self,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.67 => ( ( ord_less_eq_real @ A @ one_one_real )
% 5.41/5.67 => ( ord_less_eq_real @ ( power_power_real @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_le_self
% 5.41/5.67 thf(fact_3048_power__Suc__le__self,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.67 => ( ( ord_less_eq_rat @ A @ one_one_rat )
% 5.41/5.67 => ( ord_less_eq_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_le_self
% 5.41/5.67 thf(fact_3049_power__Suc__le__self,axiom,
% 5.41/5.67 ! [A: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ zero_zero_nat @ A )
% 5.41/5.67 => ( ( ord_less_eq_nat @ A @ one_one_nat )
% 5.41/5.67 => ( ord_less_eq_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_le_self
% 5.41/5.67 thf(fact_3050_power__Suc__le__self,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.67 => ( ( ord_less_eq_int @ A @ one_one_int )
% 5.41/5.67 => ( ord_less_eq_int @ ( power_power_int @ A @ ( suc @ N ) ) @ A ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_le_self
% 5.41/5.67 thf(fact_3051_power__Suc__less__one,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.67 => ( ( ord_less_real @ A @ one_one_real )
% 5.41/5.67 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ N ) ) @ one_one_real ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_less_one
% 5.41/5.67 thf(fact_3052_power__Suc__less__one,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.67 => ( ( ord_less_rat @ A @ one_one_rat )
% 5.41/5.67 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ N ) ) @ one_one_rat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_less_one
% 5.41/5.67 thf(fact_3053_power__Suc__less__one,axiom,
% 5.41/5.67 ! [A: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ A )
% 5.41/5.67 => ( ( ord_less_nat @ A @ one_one_nat )
% 5.41/5.67 => ( ord_less_nat @ ( power_power_nat @ A @ ( suc @ N ) ) @ one_one_nat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_less_one
% 5.41/5.67 thf(fact_3054_power__Suc__less__one,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.67 => ( ( ord_less_int @ A @ one_one_int )
% 5.41/5.67 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ N ) ) @ one_one_int ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_Suc_less_one
% 5.41/5.67 thf(fact_3055_numeral__2__eq__2,axiom,
% 5.41/5.67 ( ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.41/5.67 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % numeral_2_eq_2
% 5.41/5.67 thf(fact_3056_double__not__eq__Suc__double,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.41/5.67 != ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % double_not_eq_Suc_double
% 5.41/5.67 thf(fact_3057_Suc__double__not__eq__double,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.67 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_double_not_eq_double
% 5.41/5.67 thf(fact_3058_div__if,axiom,
% 5.41/5.67 ( divide_divide_nat
% 5.41/5.67 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.67 ( if_nat
% 5.41/5.67 @ ( ( ord_less_nat @ M3 @ N2 )
% 5.41/5.67 | ( N2 = zero_zero_nat ) )
% 5.41/5.67 @ zero_zero_nat
% 5.41/5.67 @ ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % div_if
% 5.41/5.67 thf(fact_3059_div__geq,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ~ ( ord_less_nat @ M @ N )
% 5.41/5.67 => ( ( divide_divide_nat @ M @ N )
% 5.41/5.67 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % div_geq
% 5.41/5.67 thf(fact_3060_Suc__diff__eq__diff__pred,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ( minus_minus_nat @ ( suc @ M ) @ N )
% 5.41/5.67 = ( minus_minus_nat @ M @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_diff_eq_diff_pred
% 5.41/5.67 thf(fact_3061_Suc__pred_H,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( N
% 5.41/5.67 = ( suc @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_pred'
% 5.41/5.67 thf(fact_3062_div__nat__eqI,axiom,
% 5.41/5.67 ! [N: nat,Q2: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q2 ) @ M )
% 5.41/5.67 => ( ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q2 ) ) )
% 5.41/5.67 => ( ( divide_divide_nat @ M @ N )
% 5.41/5.67 = Q2 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % div_nat_eqI
% 5.41/5.67 thf(fact_3063_add__eq__if,axiom,
% 5.41/5.67 ( plus_plus_nat
% 5.41/5.67 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( suc @ ( plus_plus_nat @ ( minus_minus_nat @ M3 @ one_one_nat ) @ N2 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % add_eq_if
% 5.41/5.67 thf(fact_3064_Suc__nat__number__of__add,axiom,
% 5.41/5.67 ! [V: num,N: nat] :
% 5.41/5.67 ( ( suc @ ( plus_plus_nat @ ( numeral_numeral_nat @ V ) @ N ) )
% 5.41/5.67 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( plus_plus_num @ V @ one ) ) @ N ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_nat_number_of_add
% 5.41/5.67 thf(fact_3065_set__bit__Suc,axiom,
% 5.41/5.67 ! [N: nat,A: code_integer] :
% 5.41/5.67 ( ( bit_se2793503036327961859nteger @ ( suc @ N ) @ A )
% 5.41/5.67 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % set_bit_Suc
% 5.41/5.67 thf(fact_3066_set__bit__Suc,axiom,
% 5.41/5.67 ! [N: nat,A: int] :
% 5.41/5.67 ( ( bit_se7879613467334960850it_int @ ( suc @ N ) @ A )
% 5.41/5.67 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % set_bit_Suc
% 5.41/5.67 thf(fact_3067_set__bit__Suc,axiom,
% 5.41/5.67 ! [N: nat,A: nat] :
% 5.41/5.67 ( ( bit_se7882103937844011126it_nat @ ( suc @ N ) @ A )
% 5.41/5.67 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % set_bit_Suc
% 5.41/5.67 thf(fact_3068_num_Osize_I5_J,axiom,
% 5.41/5.67 ! [X22: num] :
% 5.41/5.67 ( ( size_size_num @ ( bit0 @ X22 ) )
% 5.41/5.67 = ( plus_plus_nat @ ( size_size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % num.size(5)
% 5.41/5.67 thf(fact_3069_less__2__cases__iff,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 = ( ( N = zero_zero_nat )
% 5.41/5.67 | ( N
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_2_cases_iff
% 5.41/5.67 thf(fact_3070_less__2__cases,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.67 => ( ( N = zero_zero_nat )
% 5.41/5.67 | ( N
% 5.41/5.67 = ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % less_2_cases
% 5.41/5.67 thf(fact_3071_le__div__geq,axiom,
% 5.41/5.67 ! [N: nat,M: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.67 => ( ( divide_divide_nat @ M @ N )
% 5.41/5.67 = ( suc @ ( divide_divide_nat @ ( minus_minus_nat @ M @ N ) @ N ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % le_div_geq
% 5.41/5.67 thf(fact_3072_split__div_H,axiom,
% 5.41/5.67 ! [P: nat > $o,M: nat,N: nat] :
% 5.41/5.67 ( ( P @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.67 = ( ( ( N = zero_zero_nat )
% 5.41/5.67 & ( P @ zero_zero_nat ) )
% 5.41/5.67 | ? [Q5: nat] :
% 5.41/5.67 ( ( ord_less_eq_nat @ ( times_times_nat @ N @ Q5 ) @ M )
% 5.41/5.67 & ( ord_less_nat @ M @ ( times_times_nat @ N @ ( suc @ Q5 ) ) )
% 5.41/5.67 & ( P @ Q5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % split_div'
% 5.41/5.67 thf(fact_3073_Suc__times__mod__eq,axiom,
% 5.41/5.67 ! [M: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ M )
% 5.41/5.67 => ( ( modulo_modulo_nat @ ( suc @ ( times_times_nat @ M @ N ) ) @ M )
% 5.41/5.67 = one_one_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_times_mod_eq
% 5.41/5.67 thf(fact_3074_power__odd__eq,axiom,
% 5.41/5.67 ! [A: complex,N: nat] :
% 5.41/5.67 ( ( power_power_complex @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.67 = ( times_times_complex @ A @ ( power_power_complex @ ( power_power_complex @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_odd_eq
% 5.41/5.67 thf(fact_3075_power__odd__eq,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.67 = ( times_times_real @ A @ ( power_power_real @ ( power_power_real @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_odd_eq
% 5.41/5.67 thf(fact_3076_power__odd__eq,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.67 = ( times_times_rat @ A @ ( power_power_rat @ ( power_power_rat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_odd_eq
% 5.41/5.67 thf(fact_3077_power__odd__eq,axiom,
% 5.41/5.67 ! [A: nat,N: nat] :
% 5.41/5.67 ( ( power_power_nat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.67 = ( times_times_nat @ A @ ( power_power_nat @ ( power_power_nat @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_odd_eq
% 5.41/5.67 thf(fact_3078_power__odd__eq,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.67 = ( times_times_int @ A @ ( power_power_int @ ( power_power_int @ A @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % power_odd_eq
% 5.41/5.67 thf(fact_3079_nat__bit__induct,axiom,
% 5.41/5.67 ! [P: nat > $o,N: nat] :
% 5.41/5.67 ( ( P @ zero_zero_nat )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( P @ N3 )
% 5.41/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.41/5.67 => ( P @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.41/5.67 => ( ! [N3: nat] :
% 5.41/5.67 ( ( P @ N3 )
% 5.41/5.67 => ( P @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 ) ) ) )
% 5.41/5.67 => ( P @ N ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % nat_bit_induct
% 5.41/5.67 thf(fact_3080_Suc__n__div__2__gt__zero,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % Suc_n_div_2_gt_zero
% 5.41/5.67 thf(fact_3081_div__2__gt__zero,axiom,
% 5.41/5.67 ! [N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.67 => ( ord_less_nat @ zero_zero_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % div_2_gt_zero
% 5.41/5.67 thf(fact_3082_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.67 ! [B4: real,A4: real] :
% 5.41/5.67 ( ( ~ ( ord_less_eq_real @ B4 @ A4 ) )
% 5.41/5.67 = ( ord_less_real @ A4 @ B4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(3)
% 5.41/5.67 thf(fact_3083_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.67 ! [B4: rat,A4: rat] :
% 5.41/5.67 ( ( ~ ( ord_less_eq_rat @ B4 @ A4 ) )
% 5.41/5.67 = ( ord_less_rat @ A4 @ B4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(3)
% 5.41/5.67 thf(fact_3084_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.67 ! [B4: num,A4: num] :
% 5.41/5.67 ( ( ~ ( ord_less_eq_num @ B4 @ A4 ) )
% 5.41/5.67 = ( ord_less_num @ A4 @ B4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(3)
% 5.41/5.67 thf(fact_3085_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.67 ! [B4: nat,A4: nat] :
% 5.41/5.67 ( ( ~ ( ord_less_eq_nat @ B4 @ A4 ) )
% 5.41/5.67 = ( ord_less_nat @ A4 @ B4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(3)
% 5.41/5.67 thf(fact_3086_verit__comp__simplify1_I3_J,axiom,
% 5.41/5.67 ! [B4: int,A4: int] :
% 5.41/5.67 ( ( ~ ( ord_less_eq_int @ B4 @ A4 ) )
% 5.41/5.67 = ( ord_less_int @ A4 @ B4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_comp_simplify1(3)
% 5.41/5.67 thf(fact_3087_verit__sum__simplify,axiom,
% 5.41/5.67 ! [A: complex] :
% 5.41/5.67 ( ( plus_plus_complex @ A @ zero_zero_complex )
% 5.41/5.67 = A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_sum_simplify
% 5.41/5.67 thf(fact_3088_verit__sum__simplify,axiom,
% 5.41/5.67 ! [A: real] :
% 5.41/5.67 ( ( plus_plus_real @ A @ zero_zero_real )
% 5.41/5.67 = A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_sum_simplify
% 5.41/5.67 thf(fact_3089_verit__sum__simplify,axiom,
% 5.41/5.67 ! [A: rat] :
% 5.41/5.67 ( ( plus_plus_rat @ A @ zero_zero_rat )
% 5.41/5.67 = A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_sum_simplify
% 5.41/5.67 thf(fact_3090_verit__sum__simplify,axiom,
% 5.41/5.67 ! [A: nat] :
% 5.41/5.67 ( ( plus_plus_nat @ A @ zero_zero_nat )
% 5.41/5.67 = A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_sum_simplify
% 5.41/5.67 thf(fact_3091_verit__sum__simplify,axiom,
% 5.41/5.67 ! [A: int] :
% 5.41/5.67 ( ( plus_plus_int @ A @ zero_zero_int )
% 5.41/5.67 = A ) ).
% 5.41/5.67
% 5.41/5.67 % verit_sum_simplify
% 5.41/5.67 thf(fact_3092_verit__eq__simplify_I10_J,axiom,
% 5.41/5.67 ! [X22: num] :
% 5.41/5.67 ( one
% 5.41/5.67 != ( bit0 @ X22 ) ) ).
% 5.41/5.67
% 5.41/5.67 % verit_eq_simplify(10)
% 5.41/5.67 thf(fact_3093_odd__0__le__power__imp__0__le,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.41/5.67 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_0_le_power_imp_0_le
% 5.41/5.67 thf(fact_3094_odd__0__le__power__imp__0__le,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.41/5.67 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_0_le_power_imp_0_le
% 5.41/5.67 thf(fact_3095_odd__0__le__power__imp__0__le,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.41/5.67 => ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_0_le_power_imp_0_le
% 5.41/5.67 thf(fact_3096_odd__power__less__zero,axiom,
% 5.41/5.67 ! [A: real,N: nat] :
% 5.41/5.67 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.67 => ( ord_less_real @ ( power_power_real @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_real ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_power_less_zero
% 5.41/5.67 thf(fact_3097_odd__power__less__zero,axiom,
% 5.41/5.67 ! [A: rat,N: nat] :
% 5.41/5.67 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.67 => ( ord_less_rat @ ( power_power_rat @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_rat ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_power_less_zero
% 5.41/5.67 thf(fact_3098_odd__power__less__zero,axiom,
% 5.41/5.67 ! [A: int,N: nat] :
% 5.41/5.67 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.67 => ( ord_less_int @ ( power_power_int @ A @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ zero_zero_int ) ) ).
% 5.41/5.67
% 5.41/5.67 % odd_power_less_zero
% 5.41/5.67 thf(fact_3099_int__power__div__base,axiom,
% 5.41/5.67 ! [M: nat,K: int] :
% 5.41/5.67 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.67 => ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.67 => ( ( divide_divide_int @ ( power_power_int @ K @ M ) @ K )
% 5.41/5.67 = ( power_power_int @ K @ ( minus_minus_nat @ M @ ( suc @ zero_zero_nat ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % int_power_div_base
% 5.41/5.67 thf(fact_3100_invar__vebt_Ointros_I3_J,axiom,
% 5.41/5.67 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat] :
% 5.41/5.67 ( ! [X6: vEBT_VEBT] :
% 5.41/5.67 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.67 => ( vEBT_invar_vebt @ X6 @ N ) )
% 5.41/5.67 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.41/5.67 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.41/5.67 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.67 => ( ( M
% 5.41/5.67 = ( suc @ N ) )
% 5.41/5.67 => ( ( Deg
% 5.41/5.67 = ( plus_plus_nat @ N @ M ) )
% 5.41/5.67 => ( ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X_1 )
% 5.41/5.67 => ( ! [X6: vEBT_VEBT] :
% 5.41/5.67 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.67 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) )
% 5.41/5.67 => ( vEBT_invar_vebt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % invar_vebt.intros(3)
% 5.41/5.67 thf(fact_3101_div__less__mono,axiom,
% 5.41/5.67 ! [A2: nat,B3: nat,N: nat] :
% 5.41/5.67 ( ( ord_less_nat @ A2 @ B3 )
% 5.41/5.67 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.67 => ( ( ( modulo_modulo_nat @ A2 @ N )
% 5.41/5.67 = zero_zero_nat )
% 5.41/5.67 => ( ( ( modulo_modulo_nat @ B3 @ N )
% 5.41/5.67 = zero_zero_nat )
% 5.41/5.67 => ( ord_less_nat @ ( divide_divide_nat @ A2 @ N ) @ ( divide_divide_nat @ B3 @ N ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % div_less_mono
% 5.41/5.67 thf(fact_3102_div__mod__decomp,axiom,
% 5.41/5.67 ! [A2: nat,N: nat] :
% 5.41/5.67 ( A2
% 5.41/5.67 = ( plus_plus_nat @ ( times_times_nat @ ( divide_divide_nat @ A2 @ N ) @ N ) @ ( modulo_modulo_nat @ A2 @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % div_mod_decomp
% 5.41/5.67 thf(fact_3103_zdiv__mono__strict,axiom,
% 5.41/5.67 ! [A2: int,B3: int,N: int] :
% 5.41/5.67 ( ( ord_less_int @ A2 @ B3 )
% 5.41/5.67 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.41/5.67 => ( ( ( modulo_modulo_int @ A2 @ N )
% 5.41/5.67 = zero_zero_int )
% 5.41/5.67 => ( ( ( modulo_modulo_int @ B3 @ N )
% 5.41/5.67 = zero_zero_int )
% 5.41/5.67 => ( ord_less_int @ ( divide_divide_int @ A2 @ N ) @ ( divide_divide_int @ B3 @ N ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % zdiv_mono_strict
% 5.41/5.67 thf(fact_3104_div__mod__decomp__int,axiom,
% 5.41/5.67 ! [A2: int,N: int] :
% 5.41/5.67 ( A2
% 5.41/5.67 = ( plus_plus_int @ ( times_times_int @ ( divide_divide_int @ A2 @ N ) @ N ) @ ( modulo_modulo_int @ A2 @ N ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % div_mod_decomp_int
% 5.41/5.67 thf(fact_3105_invar__vebt_Ointros_I5_J,axiom,
% 5.41/5.67 ! [TreeList2: list_VEBT_VEBT,N: nat,Summary: vEBT_VEBT,M: nat,Deg: nat,Mi: nat,Ma: nat] :
% 5.41/5.67 ( ! [X6: vEBT_VEBT] :
% 5.41/5.67 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.67 => ( vEBT_invar_vebt @ X6 @ N ) )
% 5.41/5.67 => ( ( vEBT_invar_vebt @ Summary @ M )
% 5.41/5.67 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.41/5.67 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.67 => ( ( M
% 5.41/5.67 = ( suc @ N ) )
% 5.41/5.67 => ( ( Deg
% 5.41/5.67 = ( plus_plus_nat @ N @ M ) )
% 5.41/5.67 => ( ! [I4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.67 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ X2 ) )
% 5.41/5.67 = ( vEBT_V8194947554948674370ptions @ Summary @ I4 ) ) )
% 5.41/5.67 => ( ( ( Mi = Ma )
% 5.41/5.67 => ! [X6: vEBT_VEBT] :
% 5.41/5.67 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.67 => ~ ? [X_1: nat] : ( vEBT_V8194947554948674370ptions @ X6 @ X_1 ) ) )
% 5.41/5.67 => ( ( ord_less_eq_nat @ Mi @ Ma )
% 5.41/5.67 => ( ( ord_less_nat @ Ma @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.41/5.67 => ( ( ( Mi != Ma )
% 5.41/5.67 => ! [I4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ I4 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) )
% 5.41/5.67 => ( ( ( ( vEBT_VEBT_high @ Ma @ N )
% 5.41/5.67 = I4 )
% 5.41/5.67 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ Ma @ N ) ) )
% 5.41/5.67 & ! [X6: nat] :
% 5.41/5.67 ( ( ( ( vEBT_VEBT_high @ X6 @ N )
% 5.41/5.67 = I4 )
% 5.41/5.67 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I4 ) @ ( vEBT_VEBT_low @ X6 @ N ) ) )
% 5.41/5.67 => ( ( ord_less_nat @ Mi @ X6 )
% 5.41/5.67 & ( ord_less_eq_nat @ X6 @ Ma ) ) ) ) ) )
% 5.41/5.67 => ( vEBT_invar_vebt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Deg @ TreeList2 @ Summary ) @ Deg ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % invar_vebt.intros(5)
% 5.41/5.67 thf(fact_3106_vebt__delete_Osimps_I7_J,axiom,
% 5.41/5.67 ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.67 ( ( ( ( ord_less_nat @ X @ Mi )
% 5.41/5.67 | ( ord_less_nat @ Ma @ X ) )
% 5.41/5.67 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 5.41/5.67 & ( ~ ( ( ord_less_nat @ X @ Mi )
% 5.41/5.67 | ( ord_less_nat @ Ma @ X ) )
% 5.41/5.67 => ( ( ( ( X = Mi )
% 5.41/5.67 & ( X = Ma ) )
% 5.41/5.67 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) )
% 5.41/5.67 & ( ~ ( ( X = Mi )
% 5.41/5.67 & ( X = Ma ) )
% 5.41/5.67 => ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_Node
% 5.41/5.67 @ ( some_P7363390416028606310at_nat
% 5.41/5.67 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.41/5.67 @ ( if_nat
% 5.41/5.67 @ ( ( ( X = Mi )
% 5.41/5.67 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.67 = Ma ) )
% 5.41/5.67 & ( ( X != Mi )
% 5.41/5.67 => ( X = Ma ) ) )
% 5.41/5.67 @ ( if_nat
% 5.41/5.67 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.41/5.67 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ Ma ) ) )
% 5.41/5.67 @ ( suc @ ( suc @ Va ) )
% 5.41/5.67 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_vebt_delete @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_Node
% 5.41/5.67 @ ( some_P7363390416028606310at_nat
% 5.41/5.67 @ ( product_Pair_nat_nat @ ( if_nat @ ( X = Mi ) @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ Mi )
% 5.41/5.67 @ ( if_nat
% 5.41/5.67 @ ( ( ( X = Mi )
% 5.41/5.67 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) )
% 5.41/5.67 = Ma ) )
% 5.41/5.67 & ( ( X != Mi )
% 5.41/5.67 => ( X = Ma ) ) )
% 5.41/5.67 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ Ma ) ) )
% 5.41/5.67 @ ( suc @ ( suc @ Va ) )
% 5.41/5.67 @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( X = Mi ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_mint @ Summary ) ) ) ) ) ) @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ Summary ) )
% 5.41/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.simps(7)
% 5.41/5.67 thf(fact_3107_vebt__pred_Osimps_I7_J,axiom,
% 5.41/5.67 ! [Ma: nat,X: nat,Mi: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.67 ( ( ( ord_less_nat @ Ma @ X )
% 5.41/5.67 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( some_nat @ Ma ) ) )
% 5.41/5.67 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.41/5.67 => ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 != none_nat )
% 5.41/5.67 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ ( if_option_nat @ ( ord_less_nat @ Mi @ X ) @ ( some_nat @ Mi ) @ none_nat )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_pred @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ none_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_pred.simps(7)
% 5.41/5.67 thf(fact_3108_vebt__succ_Osimps_I6_J,axiom,
% 5.41/5.67 ! [X: nat,Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT] :
% 5.41/5.67 ( ( ( ord_less_nat @ X @ Mi )
% 5.41/5.67 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( some_nat @ Mi ) ) )
% 5.41/5.67 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.41/5.67 => ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 != none_nat )
% 5.41/5.67 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ none_nat
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList2 @ ( the_nat @ ( vEBT_vebt_succ @ Summary @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ none_nat ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_succ.simps(6)
% 5.41/5.67 thf(fact_3109_vebt__insert_Osimps_I5_J,axiom,
% 5.41/5.67 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_insert @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( if_VEBT_VEBT
% 5.41/5.67 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 & ~ ( ( X = Mi )
% 5.41/5.67 | ( X = Ma ) ) )
% 5.41/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ X @ Mi ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ Ma ) ) ) @ ( suc @ ( suc @ Va ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ X @ Mi ) @ Mi @ X ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary ) )
% 5.41/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_insert.simps(5)
% 5.41/5.67 thf(fact_3110_vebt__member_Osimps_I5_J,axiom,
% 5.41/5.67 ! [Mi: nat,Ma: nat,Va: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ ( suc @ Va ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( ( X != Mi )
% 5.41/5.67 => ( ( X != Ma )
% 5.41/5.67 => ( ~ ( ord_less_nat @ X @ Mi )
% 5.41/5.67 & ( ~ ( ord_less_nat @ X @ Mi )
% 5.41/5.67 => ( ~ ( ord_less_nat @ Ma @ X )
% 5.41/5.67 & ( ~ ( ord_less_nat @ Ma @ X )
% 5.41/5.67 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.67 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_member.simps(5)
% 5.41/5.67 thf(fact_3111_vebt__insert_Osimps_I4_J,axiom,
% 5.41/5.67 ! [V: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_insert @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) @ X )
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ X @ X ) ) @ ( suc @ ( suc @ V ) ) @ TreeList2 @ Summary ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_insert.simps(4)
% 5.41/5.67 thf(fact_3112_vebt__pred_Osimps_I6_J,axiom,
% 5.41/5.67 ! [V: product_prod_nat_nat,Vh: list_VEBT_VEBT,Vi: vEBT_VEBT,Vj: nat] :
% 5.41/5.67 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vh @ Vi ) @ Vj )
% 5.41/5.67 = none_nat ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_pred.simps(6)
% 5.41/5.67 thf(fact_3113_vebt__succ_Osimps_I5_J,axiom,
% 5.41/5.67 ! [V: product_prod_nat_nat,Vg: list_VEBT_VEBT,Vh: vEBT_VEBT,Vi: nat] :
% 5.41/5.67 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vg @ Vh ) @ Vi )
% 5.41/5.67 = none_nat ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_succ.simps(5)
% 5.41/5.67 thf(fact_3114_vebt__delete_Osimps_I6_J,axiom,
% 5.41/5.67 ! [Mi: nat,Ma: nat,Tr: list_VEBT_VEBT,Sm: vEBT_VEBT,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) @ X )
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ zero_zero_nat ) @ Tr @ Sm ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.simps(6)
% 5.41/5.67 thf(fact_3115_vebt__insert_Osimps_I2_J,axiom,
% 5.41/5.67 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) @ X )
% 5.41/5.67 = ( vEBT_Node @ Info @ zero_zero_nat @ Ts @ S ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_insert.simps(2)
% 5.41/5.67 thf(fact_3116_vebt__delete_Osimps_I4_J,axiom,
% 5.41/5.67 ! [Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Uu: nat] :
% 5.41/5.67 ( ( vEBT_vebt_delete @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) @ Uu )
% 5.41/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg @ TreeList2 @ Summary ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.simps(4)
% 5.41/5.67 thf(fact_3117_VEBT__internal_OminNull_Osimps_I5_J,axiom,
% 5.41/5.67 ! [Uz: product_prod_nat_nat,Va: nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT] :
% 5.41/5.67 ~ ( vEBT_VEBT_minNull @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz ) @ Va @ Vb @ Vc ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.minNull.simps(5)
% 5.41/5.67 thf(fact_3118_vebt__member_Osimps_I2_J,axiom,
% 5.41/5.67 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,X: nat] :
% 5.41/5.67 ~ ( vEBT_vebt_member @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) @ X ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_member.simps(2)
% 5.41/5.67 thf(fact_3119_VEBT__internal_OminNull_Osimps_I4_J,axiom,
% 5.41/5.67 ! [Uw: nat,Ux: list_VEBT_VEBT,Uy: vEBT_VEBT] : ( vEBT_VEBT_minNull @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw @ Ux @ Uy ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.minNull.simps(4)
% 5.41/5.67 thf(fact_3120_is__pred__in__set__def,axiom,
% 5.41/5.67 ( vEBT_is_pred_in_set
% 5.41/5.67 = ( ^ [Xs2: set_nat,X3: nat,Y3: nat] :
% 5.41/5.67 ( ( member_nat @ Y3 @ Xs2 )
% 5.41/5.67 & ( ord_less_nat @ Y3 @ X3 )
% 5.41/5.67 & ! [Z3: nat] :
% 5.41/5.67 ( ( member_nat @ Z3 @ Xs2 )
% 5.41/5.67 => ( ( ord_less_nat @ Z3 @ X3 )
% 5.41/5.67 => ( ord_less_eq_nat @ Z3 @ Y3 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % is_pred_in_set_def
% 5.41/5.67 thf(fact_3121_is__succ__in__set__def,axiom,
% 5.41/5.67 ( vEBT_is_succ_in_set
% 5.41/5.67 = ( ^ [Xs2: set_nat,X3: nat,Y3: nat] :
% 5.41/5.67 ( ( member_nat @ Y3 @ Xs2 )
% 5.41/5.67 & ( ord_less_nat @ X3 @ Y3 )
% 5.41/5.67 & ! [Z3: nat] :
% 5.41/5.67 ( ( member_nat @ Z3 @ Xs2 )
% 5.41/5.67 => ( ( ord_less_nat @ X3 @ Z3 )
% 5.41/5.67 => ( ord_less_eq_nat @ Y3 @ Z3 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % is_succ_in_set_def
% 5.41/5.67 thf(fact_3122_vebt__insert_Osimps_I3_J,axiom,
% 5.41/5.67 ! [Info: option4927543243414619207at_nat,Ts: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_insert @ ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) @ X )
% 5.41/5.67 = ( vEBT_Node @ Info @ ( suc @ zero_zero_nat ) @ Ts @ S ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_insert.simps(3)
% 5.41/5.67 thf(fact_3123_vebt__member_Osimps_I3_J,axiom,
% 5.41/5.67 ! [V: product_prod_nat_nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,X: nat] :
% 5.41/5.67 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Uy @ Uz ) @ X ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_member.simps(3)
% 5.41/5.67 thf(fact_3124_vebt__succ_Osimps_I3_J,axiom,
% 5.41/5.67 ! [Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT,Va: nat] :
% 5.41/5.67 ( ( vEBT_vebt_succ @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux @ Uy @ Uz ) @ Va )
% 5.41/5.67 = none_nat ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_succ.simps(3)
% 5.41/5.67 thf(fact_3125_vebt__pred_Osimps_I4_J,axiom,
% 5.41/5.67 ! [Uy: nat,Uz: list_VEBT_VEBT,Va: vEBT_VEBT,Vb: nat] :
% 5.41/5.67 ( ( vEBT_vebt_pred @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy @ Uz @ Va ) @ Vb )
% 5.41/5.67 = none_nat ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_pred.simps(4)
% 5.41/5.67 thf(fact_3126_vebt__member_Osimps_I4_J,axiom,
% 5.41/5.67 ! [V: product_prod_nat_nat,Vb: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.41/5.67 ~ ( vEBT_vebt_member @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ ( suc @ zero_zero_nat ) @ Vb @ Vc ) @ X ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_member.simps(4)
% 5.41/5.67 thf(fact_3127_vebt__delete_Osimps_I5_J,axiom,
% 5.41/5.67 ! [Mi: nat,Ma: nat,TrLst: list_VEBT_VEBT,Smry: vEBT_VEBT,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_delete @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) @ X )
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ TrLst @ Smry ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.simps(5)
% 5.41/5.67 thf(fact_3128_vebt__succ_Osimps_I4_J,axiom,
% 5.41/5.67 ! [V: product_prod_nat_nat,Vc: list_VEBT_VEBT,Vd: vEBT_VEBT,Ve: nat] :
% 5.41/5.67 ( ( vEBT_vebt_succ @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vc @ Vd ) @ Ve )
% 5.41/5.67 = none_nat ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_succ.simps(4)
% 5.41/5.67 thf(fact_3129_vebt__pred_Osimps_I5_J,axiom,
% 5.41/5.67 ! [V: product_prod_nat_nat,Vd: list_VEBT_VEBT,Ve: vEBT_VEBT,Vf: nat] :
% 5.41/5.67 ( ( vEBT_vebt_pred @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V ) @ zero_zero_nat @ Vd @ Ve ) @ Vf )
% 5.41/5.67 = none_nat ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_pred.simps(5)
% 5.41/5.67 thf(fact_3130_vebt__pred_Oelims,axiom,
% 5.41/5.67 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.41/5.67 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.41/5.67 = Y )
% 5.41/5.67 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.67 => ( ( Xa2 = zero_zero_nat )
% 5.41/5.67 => ( Y != none_nat ) ) )
% 5.41/5.67 => ( ! [A5: $o] :
% 5.41/5.67 ( ? [Uw2: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 5.41/5.67 => ( ( Xa2
% 5.41/5.67 = ( suc @ zero_zero_nat ) )
% 5.41/5.67 => ~ ( ( A5
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.67 & ( ~ A5
% 5.41/5.67 => ( Y = none_nat ) ) ) ) )
% 5.41/5.67 => ( ! [A5: $o,B5: $o] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.67 => ( ? [Va2: nat] :
% 5.41/5.67 ( Xa2
% 5.41/5.67 = ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.67 => ~ ( ( B5
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.67 & ( ~ B5
% 5.41/5.67 => ( ( A5
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.67 & ( ~ A5
% 5.41/5.67 => ( Y = none_nat ) ) ) ) ) ) )
% 5.41/5.67 => ( ( ? [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.41/5.67 => ( Y != none_nat ) )
% 5.41/5.67 => ( ( ? [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.41/5.67 => ( Y != none_nat ) )
% 5.41/5.67 => ( ( ? [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.41/5.67 => ( Y != none_nat ) )
% 5.41/5.67 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.67 => ~ ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( some_nat @ Ma2 ) ) )
% 5.41/5.67 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 != none_nat )
% 5.41/5.67 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_pred.elims
% 5.41/5.67 thf(fact_3131_vebt__succ_Oelims,axiom,
% 5.41/5.67 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.41/5.67 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.41/5.67 = Y )
% 5.41/5.67 => ( ! [Uu2: $o,B5: $o] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 5.41/5.67 => ( ( Xa2 = zero_zero_nat )
% 5.41/5.67 => ~ ( ( B5
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.67 & ( ~ B5
% 5.41/5.67 => ( Y = none_nat ) ) ) ) )
% 5.41/5.67 => ( ( ? [Uv2: $o,Uw2: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.41/5.67 => ( ? [N3: nat] :
% 5.41/5.67 ( Xa2
% 5.41/5.67 = ( suc @ N3 ) )
% 5.41/5.67 => ( Y != none_nat ) ) )
% 5.41/5.67 => ( ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.41/5.67 => ( Y != none_nat ) )
% 5.41/5.67 => ( ( ? [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.41/5.67 => ( Y != none_nat ) )
% 5.41/5.67 => ( ( ? [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.41/5.67 => ( Y != none_nat ) )
% 5.41/5.67 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.67 => ~ ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( some_nat @ Mi2 ) ) )
% 5.41/5.67 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 != none_nat )
% 5.41/5.67 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( if_option_nat
% 5.41/5.67 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ none_nat
% 5.41/5.67 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ none_nat ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_succ.elims
% 5.41/5.67 thf(fact_3132_vebt__delete_Oelims,axiom,
% 5.41/5.67 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.41/5.67 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.41/5.67 = Y )
% 5.41/5.67 => ( ! [A5: $o,B5: $o] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.67 => ( ( Xa2 = zero_zero_nat )
% 5.41/5.67 => ( Y
% 5.41/5.67 != ( vEBT_Leaf @ $false @ B5 ) ) ) )
% 5.41/5.67 => ( ! [A5: $o] :
% 5.41/5.67 ( ? [B5: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.67 => ( ( Xa2
% 5.41/5.67 = ( suc @ zero_zero_nat ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 != ( vEBT_Leaf @ A5 @ $false ) ) ) )
% 5.41/5.67 => ( ! [A5: $o,B5: $o] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.67 => ( ? [N3: nat] :
% 5.41/5.67 ( Xa2
% 5.41/5.67 = ( suc @ ( suc @ N3 ) ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 != ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.41/5.67 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) ) )
% 5.41/5.67 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) ) )
% 5.41/5.67 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) ) )
% 5.41/5.67 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.67 ( ( X
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.67 => ~ ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.67 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.41/5.67 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.67 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.41/5.67 => ( ( ( ( Xa2 = Mi2 )
% 5.41/5.67 & ( Xa2 = Ma2 ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.41/5.67 & ( ~ ( ( Xa2 = Mi2 )
% 5.41/5.67 & ( Xa2 = Ma2 ) )
% 5.41/5.67 => ( Y
% 5.41/5.67 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.67 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_Node
% 5.41/5.67 @ ( some_P7363390416028606310at_nat
% 5.41/5.67 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.41/5.67 @ ( if_nat
% 5.41/5.67 @ ( ( ( Xa2 = Mi2 )
% 5.41/5.67 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.41/5.67 = Ma2 ) )
% 5.41/5.67 & ( ( Xa2 != Mi2 )
% 5.41/5.67 => ( Xa2 = Ma2 ) ) )
% 5.41/5.67 @ ( if_nat
% 5.41/5.67 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 = none_nat )
% 5.41/5.67 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.41/5.67 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.67 @ Ma2 ) ) )
% 5.41/5.67 @ ( suc @ ( suc @ Va2 ) )
% 5.41/5.67 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ ( vEBT_Node
% 5.41/5.67 @ ( some_P7363390416028606310at_nat
% 5.41/5.67 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.41/5.67 @ ( if_nat
% 5.41/5.67 @ ( ( ( Xa2 = Mi2 )
% 5.41/5.67 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.41/5.67 = Ma2 ) )
% 5.41/5.67 & ( ( Xa2 != Mi2 )
% 5.41/5.67 => ( Xa2 = Ma2 ) ) )
% 5.41/5.67 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.67 @ Ma2 ) ) )
% 5.41/5.67 @ ( suc @ ( suc @ Va2 ) )
% 5.41/5.67 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.67 @ Summary2 ) )
% 5.41/5.67 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.elims
% 5.41/5.67 thf(fact_3133_cppi,axiom,
% 5.41/5.67 ! [D4: int,P: int > $o,P6: int > $o,A2: set_int] :
% 5.41/5.67 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.67 => ( ? [Z4: int] :
% 5.41/5.67 ! [X6: int] :
% 5.41/5.67 ( ( ord_less_int @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ! [X6: int] :
% 5.41/5.67 ( ! [Xa: int] :
% 5.41/5.67 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 => ! [Xb: int] :
% 5.41/5.67 ( ( member_int @ Xb @ A2 )
% 5.41/5.67 => ( X6
% 5.41/5.67 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 5.41/5.67 => ( ! [X6: int,K3: int] :
% 5.41/5.67 ( ( P6 @ X6 )
% 5.41/5.67 = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.41/5.67 => ( ( ? [X2: int] : ( P @ X2 ) )
% 5.41/5.67 = ( ? [X3: int] :
% 5.41/5.67 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 & ( P6 @ X3 ) )
% 5.41/5.67 | ? [X3: int] :
% 5.41/5.67 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 & ? [Y3: int] :
% 5.41/5.67 ( ( member_int @ Y3 @ A2 )
% 5.41/5.67 & ( P @ ( minus_minus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % cppi
% 5.41/5.67 thf(fact_3134_cpmi,axiom,
% 5.41/5.67 ! [D4: int,P: int > $o,P6: int > $o,B3: set_int] :
% 5.41/5.67 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.67 => ( ? [Z4: int] :
% 5.41/5.67 ! [X6: int] :
% 5.41/5.67 ( ( ord_less_int @ X6 @ Z4 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ! [X6: int] :
% 5.41/5.67 ( ! [Xa: int] :
% 5.41/5.67 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 => ! [Xb: int] :
% 5.41/5.67 ( ( member_int @ Xb @ B3 )
% 5.41/5.67 => ( X6
% 5.41/5.67 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 5.41/5.67 => ( ! [X6: int,K3: int] :
% 5.41/5.67 ( ( P6 @ X6 )
% 5.41/5.67 = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.41/5.67 => ( ( ? [X2: int] : ( P @ X2 ) )
% 5.41/5.67 = ( ? [X3: int] :
% 5.41/5.67 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 & ( P6 @ X3 ) )
% 5.41/5.67 | ? [X3: int] :
% 5.41/5.67 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 & ? [Y3: int] :
% 5.41/5.67 ( ( member_int @ Y3 @ B3 )
% 5.41/5.67 & ( P @ ( plus_plus_int @ Y3 @ X3 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % cpmi
% 5.41/5.67 thf(fact_3135_bset_I6_J,axiom,
% 5.41/5.67 ! [D4: int,B3: set_int,T: int] :
% 5.41/5.67 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.67 => ! [X4: int] :
% 5.41/5.67 ( ! [Xa3: int] :
% 5.41/5.67 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 => ! [Xb2: int] :
% 5.41/5.67 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.67 => ( X4
% 5.41/5.67 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.67 => ( ( ord_less_eq_int @ X4 @ T )
% 5.41/5.67 => ( ord_less_eq_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % bset(6)
% 5.41/5.67 thf(fact_3136_bset_I8_J,axiom,
% 5.41/5.67 ! [D4: int,T: int,B3: set_int] :
% 5.41/5.67 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.67 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.41/5.67 => ! [X4: int] :
% 5.41/5.67 ( ! [Xa3: int] :
% 5.41/5.67 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.67 => ! [Xb2: int] :
% 5.41/5.67 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.67 => ( X4
% 5.41/5.67 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.67 => ( ( ord_less_eq_int @ T @ X4 )
% 5.41/5.67 => ( ord_less_eq_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % bset(8)
% 5.41/5.67 thf(fact_3137_Leaf__0__not,axiom,
% 5.41/5.67 ! [A: $o,B: $o] :
% 5.41/5.67 ~ ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat ) ).
% 5.41/5.67
% 5.41/5.67 % Leaf_0_not
% 5.41/5.67 thf(fact_3138_deg__1__Leafy,axiom,
% 5.41/5.67 ! [T: vEBT_VEBT,N: nat] :
% 5.41/5.67 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.67 => ( ( N = one_one_nat )
% 5.41/5.67 => ? [A5: $o,B5: $o] :
% 5.41/5.67 ( T
% 5.41/5.67 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % deg_1_Leafy
% 5.41/5.67 thf(fact_3139_deg__1__Leaf,axiom,
% 5.41/5.67 ! [T: vEBT_VEBT] :
% 5.41/5.67 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.41/5.67 => ? [A5: $o,B5: $o] :
% 5.41/5.67 ( T
% 5.41/5.67 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % deg_1_Leaf
% 5.41/5.67 thf(fact_3140_deg1Leaf,axiom,
% 5.41/5.67 ! [T: vEBT_VEBT] :
% 5.41/5.67 ( ( vEBT_invar_vebt @ T @ one_one_nat )
% 5.41/5.67 = ( ? [A3: $o,B2: $o] :
% 5.41/5.67 ( T
% 5.41/5.67 = ( vEBT_Leaf @ A3 @ B2 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % deg1Leaf
% 5.41/5.67 thf(fact_3141_VEBT_Osize_I4_J,axiom,
% 5.41/5.67 ! [X21: $o,X222: $o] :
% 5.41/5.67 ( ( size_size_VEBT_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.41/5.67 = zero_zero_nat ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT.size(4)
% 5.41/5.67 thf(fact_3142_VEBT_Oexhaust,axiom,
% 5.41/5.67 ! [Y: vEBT_VEBT] :
% 5.41/5.67 ( ! [X112: option4927543243414619207at_nat,X122: nat,X132: list_VEBT_VEBT,X142: vEBT_VEBT] :
% 5.41/5.67 ( Y
% 5.41/5.67 != ( vEBT_Node @ X112 @ X122 @ X132 @ X142 ) )
% 5.41/5.67 => ~ ! [X212: $o,X223: $o] :
% 5.41/5.67 ( Y
% 5.41/5.67 != ( vEBT_Leaf @ X212 @ X223 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT.exhaust
% 5.41/5.67 thf(fact_3143_VEBT_Odistinct_I1_J,axiom,
% 5.41/5.67 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT,X21: $o,X222: $o] :
% 5.41/5.67 ( ( vEBT_Node @ X11 @ X12 @ X13 @ X14 )
% 5.41/5.67 != ( vEBT_Leaf @ X21 @ X222 ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT.distinct(1)
% 5.41/5.67 thf(fact_3144_VEBT__internal_Ovalid_H_Ocases,axiom,
% 5.41/5.67 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.67 ( ! [Uu2: $o,Uv2: $o,D3: nat] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ D3 ) )
% 5.41/5.67 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Deg3: nat] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Deg3 ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.valid'.cases
% 5.41/5.67 thf(fact_3145_VEBT__internal_OminNull_Osimps_I1_J,axiom,
% 5.41/5.67 vEBT_VEBT_minNull @ ( vEBT_Leaf @ $false @ $false ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.minNull.simps(1)
% 5.41/5.67 thf(fact_3146_VEBT__internal_OminNull_Osimps_I2_J,axiom,
% 5.41/5.67 ! [Uv: $o] :
% 5.41/5.67 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ $true @ Uv ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.minNull.simps(2)
% 5.41/5.67 thf(fact_3147_VEBT__internal_OminNull_Osimps_I3_J,axiom,
% 5.41/5.67 ! [Uu: $o] :
% 5.41/5.67 ~ ( vEBT_VEBT_minNull @ ( vEBT_Leaf @ Uu @ $true ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.minNull.simps(3)
% 5.41/5.67 thf(fact_3148_vebt__delete_Osimps_I3_J,axiom,
% 5.41/5.67 ! [A: $o,B: $o,N: nat] :
% 5.41/5.67 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ N ) ) )
% 5.41/5.67 = ( vEBT_Leaf @ A @ B ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.simps(3)
% 5.41/5.67 thf(fact_3149_vebt__delete_Osimps_I1_J,axiom,
% 5.41/5.67 ! [A: $o,B: $o] :
% 5.41/5.67 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ zero_zero_nat )
% 5.41/5.67 = ( vEBT_Leaf @ $false @ B ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.simps(1)
% 5.41/5.67 thf(fact_3150_vebt__buildup_Osimps_I1_J,axiom,
% 5.41/5.67 ( ( vEBT_vebt_buildup @ zero_zero_nat )
% 5.41/5.67 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_buildup.simps(1)
% 5.41/5.67 thf(fact_3151_VEBT__internal_Onaive__member_Ocases,axiom,
% 5.41/5.67 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.67 ( ! [A5: $o,B5: $o,X6: nat] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 5.41/5.67 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,Ux2: nat] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Ux2 ) )
% 5.41/5.67 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ X6 ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.naive_member.cases
% 5.41/5.67 thf(fact_3152_invar__vebt_Ointros_I1_J,axiom,
% 5.41/5.67 ! [A: $o,B: $o] : ( vEBT_invar_vebt @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) ) ).
% 5.41/5.67
% 5.41/5.67 % invar_vebt.intros(1)
% 5.41/5.67 thf(fact_3153_vebt__delete_Osimps_I2_J,axiom,
% 5.41/5.67 ! [A: $o,B: $o] :
% 5.41/5.67 ( ( vEBT_vebt_delete @ ( vEBT_Leaf @ A @ B ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.67 = ( vEBT_Leaf @ A @ $false ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_delete.simps(2)
% 5.41/5.67 thf(fact_3154_VEBT__internal_OminNull_Ocases,axiom,
% 5.41/5.67 ! [X: vEBT_VEBT] :
% 5.41/5.67 ( ( X
% 5.41/5.67 != ( vEBT_Leaf @ $false @ $false ) )
% 5.41/5.67 => ( ! [Uv2: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.41/5.67 => ( ! [Uu2: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.41/5.67 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.41/5.67 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.minNull.cases
% 5.41/5.67 thf(fact_3155_vebt__member_Osimps_I1_J,axiom,
% 5.41/5.67 ! [A: $o,B: $o,X: nat] :
% 5.41/5.67 ( ( vEBT_vebt_member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.41/5.67 = ( ( ( X = zero_zero_nat )
% 5.41/5.67 => A )
% 5.41/5.67 & ( ( X != zero_zero_nat )
% 5.41/5.67 => ( ( ( X = one_one_nat )
% 5.41/5.67 => B )
% 5.41/5.67 & ( X = one_one_nat ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_member.simps(1)
% 5.41/5.67 thf(fact_3156_vebt__buildup_Osimps_I2_J,axiom,
% 5.41/5.67 ( ( vEBT_vebt_buildup @ ( suc @ zero_zero_nat ) )
% 5.41/5.67 = ( vEBT_Leaf @ $false @ $false ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_buildup.simps(2)
% 5.41/5.67 thf(fact_3157_vebt__insert_Osimps_I1_J,axiom,
% 5.41/5.67 ! [X: nat,A: $o,B: $o] :
% 5.41/5.67 ( ( ( X = zero_zero_nat )
% 5.41/5.67 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.41/5.67 = ( vEBT_Leaf @ $true @ B ) ) )
% 5.41/5.67 & ( ( X != zero_zero_nat )
% 5.41/5.67 => ( ( ( X = one_one_nat )
% 5.41/5.67 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.41/5.67 = ( vEBT_Leaf @ A @ $true ) ) )
% 5.41/5.67 & ( ( X != one_one_nat )
% 5.41/5.67 => ( ( vEBT_vebt_insert @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.41/5.67 = ( vEBT_Leaf @ A @ B ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % vebt_insert.simps(1)
% 5.41/5.67 thf(fact_3158_VEBT__internal_OminNull_Oelims_I3_J,axiom,
% 5.41/5.67 ! [X: vEBT_VEBT] :
% 5.41/5.67 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.41/5.67 => ( ! [Uv2: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.41/5.67 => ( ! [Uu2: $o] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.41/5.67 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.67 ( X
% 5.41/5.67 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % VEBT_internal.minNull.elims(3)
% 5.41/5.67 thf(fact_3159_pinf_I1_J,axiom,
% 5.41/5.67 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.41/5.67 ( ? [Z4: real] :
% 5.41/5.67 ! [X6: real] :
% 5.41/5.67 ( ( ord_less_real @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: real] :
% 5.41/5.67 ! [X6: real] :
% 5.41/5.67 ( ( ord_less_real @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: real] :
% 5.41/5.67 ! [X4: real] :
% 5.41/5.67 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 & ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(1)
% 5.41/5.67 thf(fact_3160_pinf_I1_J,axiom,
% 5.41/5.67 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.41/5.67 ( ? [Z4: rat] :
% 5.41/5.67 ! [X6: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: rat] :
% 5.41/5.67 ! [X6: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: rat] :
% 5.41/5.67 ! [X4: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 & ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(1)
% 5.41/5.67 thf(fact_3161_pinf_I1_J,axiom,
% 5.41/5.67 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.41/5.67 ( ? [Z4: num] :
% 5.41/5.67 ! [X6: num] :
% 5.41/5.67 ( ( ord_less_num @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: num] :
% 5.41/5.67 ! [X6: num] :
% 5.41/5.67 ( ( ord_less_num @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: num] :
% 5.41/5.67 ! [X4: num] :
% 5.41/5.67 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 & ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(1)
% 5.41/5.67 thf(fact_3162_pinf_I1_J,axiom,
% 5.41/5.67 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.41/5.67 ( ? [Z4: nat] :
% 5.41/5.67 ! [X6: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: nat] :
% 5.41/5.67 ! [X6: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: nat] :
% 5.41/5.67 ! [X4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 & ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(1)
% 5.41/5.67 thf(fact_3163_pinf_I1_J,axiom,
% 5.41/5.67 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.41/5.67 ( ? [Z4: int] :
% 5.41/5.67 ! [X6: int] :
% 5.41/5.67 ( ( ord_less_int @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: int] :
% 5.41/5.67 ! [X6: int] :
% 5.41/5.67 ( ( ord_less_int @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: int] :
% 5.41/5.67 ! [X4: int] :
% 5.41/5.67 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 & ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(1)
% 5.41/5.67 thf(fact_3164_pinf_I2_J,axiom,
% 5.41/5.67 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.41/5.67 ( ? [Z4: real] :
% 5.41/5.67 ! [X6: real] :
% 5.41/5.67 ( ( ord_less_real @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: real] :
% 5.41/5.67 ! [X6: real] :
% 5.41/5.67 ( ( ord_less_real @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: real] :
% 5.41/5.67 ! [X4: real] :
% 5.41/5.67 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 | ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(2)
% 5.41/5.67 thf(fact_3165_pinf_I2_J,axiom,
% 5.41/5.67 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.41/5.67 ( ? [Z4: rat] :
% 5.41/5.67 ! [X6: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: rat] :
% 5.41/5.67 ! [X6: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: rat] :
% 5.41/5.67 ! [X4: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 | ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(2)
% 5.41/5.67 thf(fact_3166_pinf_I2_J,axiom,
% 5.41/5.67 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.41/5.67 ( ? [Z4: num] :
% 5.41/5.67 ! [X6: num] :
% 5.41/5.67 ( ( ord_less_num @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: num] :
% 5.41/5.67 ! [X6: num] :
% 5.41/5.67 ( ( ord_less_num @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: num] :
% 5.41/5.67 ! [X4: num] :
% 5.41/5.67 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 | ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(2)
% 5.41/5.67 thf(fact_3167_pinf_I2_J,axiom,
% 5.41/5.67 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.41/5.67 ( ? [Z4: nat] :
% 5.41/5.67 ! [X6: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: nat] :
% 5.41/5.67 ! [X6: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: nat] :
% 5.41/5.67 ! [X4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 | ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(2)
% 5.41/5.67 thf(fact_3168_pinf_I2_J,axiom,
% 5.41/5.67 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.41/5.67 ( ? [Z4: int] :
% 5.41/5.67 ! [X6: int] :
% 5.41/5.67 ( ( ord_less_int @ Z4 @ X6 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: int] :
% 5.41/5.67 ! [X6: int] :
% 5.41/5.67 ( ( ord_less_int @ Z4 @ X6 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: int] :
% 5.41/5.67 ! [X4: int] :
% 5.41/5.67 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 | ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(2)
% 5.41/5.67 thf(fact_3169_pinf_I3_J,axiom,
% 5.41/5.67 ! [T: real] :
% 5.41/5.67 ? [Z5: real] :
% 5.41/5.67 ! [X4: real] :
% 5.41/5.67 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(3)
% 5.41/5.67 thf(fact_3170_pinf_I3_J,axiom,
% 5.41/5.67 ! [T: rat] :
% 5.41/5.67 ? [Z5: rat] :
% 5.41/5.67 ! [X4: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(3)
% 5.41/5.67 thf(fact_3171_pinf_I3_J,axiom,
% 5.41/5.67 ! [T: num] :
% 5.41/5.67 ? [Z5: num] :
% 5.41/5.67 ! [X4: num] :
% 5.41/5.67 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(3)
% 5.41/5.67 thf(fact_3172_pinf_I3_J,axiom,
% 5.41/5.67 ! [T: nat] :
% 5.41/5.67 ? [Z5: nat] :
% 5.41/5.67 ! [X4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(3)
% 5.41/5.67 thf(fact_3173_pinf_I3_J,axiom,
% 5.41/5.67 ! [T: int] :
% 5.41/5.67 ? [Z5: int] :
% 5.41/5.67 ! [X4: int] :
% 5.41/5.67 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(3)
% 5.41/5.67 thf(fact_3174_pinf_I4_J,axiom,
% 5.41/5.67 ! [T: real] :
% 5.41/5.67 ? [Z5: real] :
% 5.41/5.67 ! [X4: real] :
% 5.41/5.67 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(4)
% 5.41/5.67 thf(fact_3175_pinf_I4_J,axiom,
% 5.41/5.67 ! [T: rat] :
% 5.41/5.67 ? [Z5: rat] :
% 5.41/5.67 ! [X4: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(4)
% 5.41/5.67 thf(fact_3176_pinf_I4_J,axiom,
% 5.41/5.67 ! [T: num] :
% 5.41/5.67 ? [Z5: num] :
% 5.41/5.67 ! [X4: num] :
% 5.41/5.67 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(4)
% 5.41/5.67 thf(fact_3177_pinf_I4_J,axiom,
% 5.41/5.67 ! [T: nat] :
% 5.41/5.67 ? [Z5: nat] :
% 5.41/5.67 ! [X4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(4)
% 5.41/5.67 thf(fact_3178_pinf_I4_J,axiom,
% 5.41/5.67 ! [T: int] :
% 5.41/5.67 ? [Z5: int] :
% 5.41/5.67 ! [X4: int] :
% 5.41/5.67 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.67 => ( X4 != T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(4)
% 5.41/5.67 thf(fact_3179_pinf_I5_J,axiom,
% 5.41/5.67 ! [T: real] :
% 5.41/5.67 ? [Z5: real] :
% 5.41/5.67 ! [X4: real] :
% 5.41/5.67 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.67 => ~ ( ord_less_real @ X4 @ T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(5)
% 5.41/5.67 thf(fact_3180_pinf_I5_J,axiom,
% 5.41/5.67 ! [T: rat] :
% 5.41/5.67 ? [Z5: rat] :
% 5.41/5.67 ! [X4: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.67 => ~ ( ord_less_rat @ X4 @ T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(5)
% 5.41/5.67 thf(fact_3181_pinf_I5_J,axiom,
% 5.41/5.67 ! [T: num] :
% 5.41/5.67 ? [Z5: num] :
% 5.41/5.67 ! [X4: num] :
% 5.41/5.67 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.67 => ~ ( ord_less_num @ X4 @ T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(5)
% 5.41/5.67 thf(fact_3182_pinf_I5_J,axiom,
% 5.41/5.67 ! [T: nat] :
% 5.41/5.67 ? [Z5: nat] :
% 5.41/5.67 ! [X4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.67 => ~ ( ord_less_nat @ X4 @ T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(5)
% 5.41/5.67 thf(fact_3183_pinf_I5_J,axiom,
% 5.41/5.67 ! [T: int] :
% 5.41/5.67 ? [Z5: int] :
% 5.41/5.67 ! [X4: int] :
% 5.41/5.67 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.67 => ~ ( ord_less_int @ X4 @ T ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(5)
% 5.41/5.67 thf(fact_3184_pinf_I7_J,axiom,
% 5.41/5.67 ! [T: real] :
% 5.41/5.67 ? [Z5: real] :
% 5.41/5.67 ! [X4: real] :
% 5.41/5.67 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.67 => ( ord_less_real @ T @ X4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(7)
% 5.41/5.67 thf(fact_3185_pinf_I7_J,axiom,
% 5.41/5.67 ! [T: rat] :
% 5.41/5.67 ? [Z5: rat] :
% 5.41/5.67 ! [X4: rat] :
% 5.41/5.67 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.67 => ( ord_less_rat @ T @ X4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(7)
% 5.41/5.67 thf(fact_3186_pinf_I7_J,axiom,
% 5.41/5.67 ! [T: num] :
% 5.41/5.67 ? [Z5: num] :
% 5.41/5.67 ! [X4: num] :
% 5.41/5.67 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.67 => ( ord_less_num @ T @ X4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(7)
% 5.41/5.67 thf(fact_3187_pinf_I7_J,axiom,
% 5.41/5.67 ! [T: nat] :
% 5.41/5.67 ? [Z5: nat] :
% 5.41/5.67 ! [X4: nat] :
% 5.41/5.67 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.67 => ( ord_less_nat @ T @ X4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(7)
% 5.41/5.67 thf(fact_3188_pinf_I7_J,axiom,
% 5.41/5.67 ! [T: int] :
% 5.41/5.67 ? [Z5: int] :
% 5.41/5.67 ! [X4: int] :
% 5.41/5.67 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.67 => ( ord_less_int @ T @ X4 ) ) ).
% 5.41/5.67
% 5.41/5.67 % pinf(7)
% 5.41/5.67 thf(fact_3189_minf_I1_J,axiom,
% 5.41/5.67 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.41/5.67 ( ? [Z4: real] :
% 5.41/5.67 ! [X6: real] :
% 5.41/5.67 ( ( ord_less_real @ X6 @ Z4 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.67 = ( P6 @ X6 ) ) )
% 5.41/5.67 => ( ? [Z4: real] :
% 5.41/5.67 ! [X6: real] :
% 5.41/5.67 ( ( ord_less_real @ X6 @ Z4 )
% 5.41/5.67 => ( ( Q @ X6 )
% 5.41/5.67 = ( Q6 @ X6 ) ) )
% 5.41/5.67 => ? [Z5: real] :
% 5.41/5.67 ! [X4: real] :
% 5.41/5.67 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.67 => ( ( ( P @ X4 )
% 5.41/5.67 & ( Q @ X4 ) )
% 5.41/5.67 = ( ( P6 @ X4 )
% 5.41/5.67 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.67
% 5.41/5.67 % minf(1)
% 5.41/5.67 thf(fact_3190_minf_I1_J,axiom,
% 5.41/5.67 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.41/5.67 ( ? [Z4: rat] :
% 5.41/5.67 ! [X6: rat] :
% 5.41/5.67 ( ( ord_less_rat @ X6 @ Z4 )
% 5.41/5.67 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: rat] :
% 5.41/5.68 ! [X6: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(1)
% 5.41/5.68 thf(fact_3191_minf_I1_J,axiom,
% 5.41/5.68 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.41/5.68 ( ? [Z4: num] :
% 5.41/5.68 ! [X6: num] :
% 5.41/5.68 ( ( ord_less_num @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: num] :
% 5.41/5.68 ! [X6: num] :
% 5.41/5.68 ( ( ord_less_num @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(1)
% 5.41/5.68 thf(fact_3192_minf_I1_J,axiom,
% 5.41/5.68 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.41/5.68 ( ? [Z4: nat] :
% 5.41/5.68 ! [X6: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: nat] :
% 5.41/5.68 ! [X6: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(1)
% 5.41/5.68 thf(fact_3193_minf_I1_J,axiom,
% 5.41/5.68 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.41/5.68 ( ? [Z4: int] :
% 5.41/5.68 ! [X6: int] :
% 5.41/5.68 ( ( ord_less_int @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: int] :
% 5.41/5.68 ! [X6: int] :
% 5.41/5.68 ( ( ord_less_int @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 & ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(1)
% 5.41/5.68 thf(fact_3194_minf_I2_J,axiom,
% 5.41/5.68 ! [P: real > $o,P6: real > $o,Q: real > $o,Q6: real > $o] :
% 5.41/5.68 ( ? [Z4: real] :
% 5.41/5.68 ! [X6: real] :
% 5.41/5.68 ( ( ord_less_real @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: real] :
% 5.41/5.68 ! [X6: real] :
% 5.41/5.68 ( ( ord_less_real @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(2)
% 5.41/5.68 thf(fact_3195_minf_I2_J,axiom,
% 5.41/5.68 ! [P: rat > $o,P6: rat > $o,Q: rat > $o,Q6: rat > $o] :
% 5.41/5.68 ( ? [Z4: rat] :
% 5.41/5.68 ! [X6: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: rat] :
% 5.41/5.68 ! [X6: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(2)
% 5.41/5.68 thf(fact_3196_minf_I2_J,axiom,
% 5.41/5.68 ! [P: num > $o,P6: num > $o,Q: num > $o,Q6: num > $o] :
% 5.41/5.68 ( ? [Z4: num] :
% 5.41/5.68 ! [X6: num] :
% 5.41/5.68 ( ( ord_less_num @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: num] :
% 5.41/5.68 ! [X6: num] :
% 5.41/5.68 ( ( ord_less_num @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(2)
% 5.41/5.68 thf(fact_3197_minf_I2_J,axiom,
% 5.41/5.68 ! [P: nat > $o,P6: nat > $o,Q: nat > $o,Q6: nat > $o] :
% 5.41/5.68 ( ? [Z4: nat] :
% 5.41/5.68 ! [X6: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: nat] :
% 5.41/5.68 ! [X6: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(2)
% 5.41/5.68 thf(fact_3198_minf_I2_J,axiom,
% 5.41/5.68 ! [P: int > $o,P6: int > $o,Q: int > $o,Q6: int > $o] :
% 5.41/5.68 ( ? [Z4: int] :
% 5.41/5.68 ! [X6: int] :
% 5.41/5.68 ( ( ord_less_int @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [Z4: int] :
% 5.41/5.68 ! [X6: int] :
% 5.41/5.68 ( ( ord_less_int @ X6 @ Z4 )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 = ( Q6 @ X6 ) ) )
% 5.41/5.68 => ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P6 @ X4 )
% 5.41/5.68 | ( Q6 @ X4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(2)
% 5.41/5.68 thf(fact_3199_minf_I3_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(3)
% 5.41/5.68 thf(fact_3200_minf_I3_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(3)
% 5.41/5.68 thf(fact_3201_minf_I3_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(3)
% 5.41/5.68 thf(fact_3202_minf_I3_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(3)
% 5.41/5.68 thf(fact_3203_minf_I3_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(3)
% 5.41/5.68 thf(fact_3204_minf_I4_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(4)
% 5.41/5.68 thf(fact_3205_minf_I4_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(4)
% 5.41/5.68 thf(fact_3206_minf_I4_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(4)
% 5.41/5.68 thf(fact_3207_minf_I4_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(4)
% 5.41/5.68 thf(fact_3208_minf_I4_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ( X4 != T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(4)
% 5.41/5.68 thf(fact_3209_minf_I5_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_real @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(5)
% 5.41/5.68 thf(fact_3210_minf_I5_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_rat @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(5)
% 5.41/5.68 thf(fact_3211_minf_I5_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_num @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(5)
% 5.41/5.68 thf(fact_3212_minf_I5_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_nat @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(5)
% 5.41/5.68 thf(fact_3213_minf_I5_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_int @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(5)
% 5.41/5.68 thf(fact_3214_minf_I7_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_real @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(7)
% 5.41/5.68 thf(fact_3215_minf_I7_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_rat @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(7)
% 5.41/5.68 thf(fact_3216_minf_I7_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_num @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(7)
% 5.41/5.68 thf(fact_3217_minf_I7_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_nat @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(7)
% 5.41/5.68 thf(fact_3218_minf_I7_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_int @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(7)
% 5.41/5.68 thf(fact_3219_vebt__succ_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Uv: $o,Uw: $o,N: nat] :
% 5.41/5.68 ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uv @ Uw ) @ ( suc @ N ) )
% 5.41/5.68 = none_nat ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_succ.simps(2)
% 5.41/5.68 thf(fact_3220_vebt__pred_Osimps_I1_J,axiom,
% 5.41/5.68 ! [Uu: $o,Uv: $o] :
% 5.41/5.68 ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ Uu @ Uv ) @ zero_zero_nat )
% 5.41/5.68 = none_nat ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_pred.simps(1)
% 5.41/5.68 thf(fact_3221_VEBT__internal_OminNull_Oelims_I2_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT] :
% 5.41/5.68 ( ( vEBT_VEBT_minNull @ X )
% 5.41/5.68 => ( ( X
% 5.41/5.68 != ( vEBT_Leaf @ $false @ $false ) )
% 5.41/5.68 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.minNull.elims(2)
% 5.41/5.68 thf(fact_3222_VEBT__internal_OminNull_Oelims_I1_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Y: $o] :
% 5.41/5.68 ( ( ( vEBT_VEBT_minNull @ X )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ $false @ $false ) )
% 5.41/5.68 => ~ Y )
% 5.41/5.68 => ( ( ? [Uv2: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ( ( ? [Uu2: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ( ( ? [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.41/5.68 => ~ Y )
% 5.41/5.68 => ~ ( ? [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.41/5.68 => Y ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.minNull.elims(1)
% 5.41/5.68 thf(fact_3223_vebt__pred_Osimps_I2_J,axiom,
% 5.41/5.68 ! [A: $o,Uw: $o] :
% 5.41/5.68 ( ( A
% 5.41/5.68 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A
% 5.41/5.68 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ Uw ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.68 = none_nat ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_pred.simps(2)
% 5.41/5.68 thf(fact_3224_vebt__succ_Osimps_I1_J,axiom,
% 5.41/5.68 ! [B: $o,Uu: $o] :
% 5.41/5.68 ( ( B
% 5.41/5.68 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B
% 5.41/5.68 => ( ( vEBT_vebt_succ @ ( vEBT_Leaf @ Uu @ B ) @ zero_zero_nat )
% 5.41/5.68 = none_nat ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_succ.simps(1)
% 5.41/5.68 thf(fact_3225_VEBT__internal_Omembermima_Ocases,axiom,
% 5.41/5.68 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.68 ( ! [Uu2: $o,Uv2: $o,Uw2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Uw2 ) )
% 5.41/5.68 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT,Uz2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Uz2 ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ X6 ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ X6 ) )
% 5.41/5.68 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ X6 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.cases
% 5.41/5.68 thf(fact_3226_vebt__pred_Ocases,axiom,
% 5.41/5.68 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.68 ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) )
% 5.41/5.68 => ( ! [A5: $o,Uw2: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) )
% 5.41/5.68 => ( ! [A5: $o,B5: $o,Va2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) )
% 5.41/5.68 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT,Vb2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Vb2 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT,Vf2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Vf2 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT,Vj2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Vj2 ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_pred.cases
% 5.41/5.68 thf(fact_3227_vebt__succ_Ocases,axiom,
% 5.41/5.68 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.68 ( ! [Uu2: $o,B5: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) )
% 5.41/5.68 => ( ! [Uv2: $o,Uw2: $o,N3: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) )
% 5.41/5.68 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,Va3: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Va3 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT,Ve2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Ve2 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT,Vi2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Vi2 ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_succ.cases
% 5.41/5.68 thf(fact_3228_vebt__delete_Ocases,axiom,
% 5.41/5.68 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.68 ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) )
% 5.41/5.68 => ( ! [A5: $o,B5: $o,N3: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N3 ) ) ) )
% 5.41/5.68 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,Uu2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Uu2 ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ X6 ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ X6 ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_delete.cases
% 5.41/5.68 thf(fact_3229_vebt__insert_Ocases,axiom,
% 5.41/5.68 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.68 ( ! [A5: $o,B5: $o,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 5.41/5.68 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ X6 ) )
% 5.41/5.68 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ X6 ) )
% 5.41/5.68 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_insert.cases
% 5.41/5.68 thf(fact_3230_vebt__member_Ocases,axiom,
% 5.41/5.68 ! [X: produc9072475918466114483BT_nat] :
% 5.41/5.68 ( ! [A5: $o,B5: $o,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ X6 ) )
% 5.41/5.68 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ X6 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ X6 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ X6 ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT,X6: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ X6 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_member.cases
% 5.41/5.68 thf(fact_3231_vebt__pred_Osimps_I3_J,axiom,
% 5.41/5.68 ! [B: $o,A: $o,Va: nat] :
% 5.41/5.68 ( ( B
% 5.41/5.68 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B
% 5.41/5.68 => ( ( A
% 5.41/5.68 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A
% 5.41/5.68 => ( ( vEBT_vebt_pred @ ( vEBT_Leaf @ A @ B ) @ ( suc @ ( suc @ Va ) ) )
% 5.41/5.68 = none_nat ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_pred.simps(3)
% 5.41/5.68 thf(fact_3232_pinf_I6_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.68 => ~ ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(6)
% 5.41/5.68 thf(fact_3233_pinf_I6_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.68 => ~ ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(6)
% 5.41/5.68 thf(fact_3234_pinf_I6_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.68 => ~ ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(6)
% 5.41/5.68 thf(fact_3235_pinf_I6_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.68 => ~ ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(6)
% 5.41/5.68 thf(fact_3236_pinf_I6_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.68 => ~ ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(6)
% 5.41/5.68 thf(fact_3237_pinf_I8_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.68 => ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(8)
% 5.41/5.68 thf(fact_3238_pinf_I8_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.68 => ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(8)
% 5.41/5.68 thf(fact_3239_pinf_I8_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ Z5 @ X4 )
% 5.41/5.68 => ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(8)
% 5.41/5.68 thf(fact_3240_pinf_I8_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.68 => ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(8)
% 5.41/5.68 thf(fact_3241_pinf_I8_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.68 => ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % pinf(8)
% 5.41/5.68 thf(fact_3242_minf_I6_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_eq_real @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(6)
% 5.41/5.68 thf(fact_3243_minf_I6_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_eq_rat @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(6)
% 5.41/5.68 thf(fact_3244_minf_I6_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_eq_num @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(6)
% 5.41/5.68 thf(fact_3245_minf_I6_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_eq_nat @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(6)
% 5.41/5.68 thf(fact_3246_minf_I6_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ( ord_less_eq_int @ X4 @ T ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(6)
% 5.41/5.68 thf(fact_3247_minf_I8_J,axiom,
% 5.41/5.68 ! [T: real] :
% 5.41/5.68 ? [Z5: real] :
% 5.41/5.68 ! [X4: real] :
% 5.41/5.68 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_eq_real @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(8)
% 5.41/5.68 thf(fact_3248_minf_I8_J,axiom,
% 5.41/5.68 ! [T: rat] :
% 5.41/5.68 ? [Z5: rat] :
% 5.41/5.68 ! [X4: rat] :
% 5.41/5.68 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_eq_rat @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(8)
% 5.41/5.68 thf(fact_3249_minf_I8_J,axiom,
% 5.41/5.68 ! [T: num] :
% 5.41/5.68 ? [Z5: num] :
% 5.41/5.68 ! [X4: num] :
% 5.41/5.68 ( ( ord_less_num @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_eq_num @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(8)
% 5.41/5.68 thf(fact_3250_minf_I8_J,axiom,
% 5.41/5.68 ! [T: nat] :
% 5.41/5.68 ? [Z5: nat] :
% 5.41/5.68 ! [X4: nat] :
% 5.41/5.68 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_eq_nat @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(8)
% 5.41/5.68 thf(fact_3251_minf_I8_J,axiom,
% 5.41/5.68 ! [T: int] :
% 5.41/5.68 ? [Z5: int] :
% 5.41/5.68 ! [X4: int] :
% 5.41/5.68 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.68 => ~ ( ord_less_eq_int @ T @ X4 ) ) ).
% 5.41/5.68
% 5.41/5.68 % minf(8)
% 5.41/5.68 thf(fact_3252_inf__period_I1_J,axiom,
% 5.41/5.68 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.41/5.68 ( ! [X6: real,K3: real] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 = ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: real,K3: real] :
% 5.41/5.68 ( ( Q @ X6 )
% 5.41/5.68 = ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: real,K4: real] :
% 5.41/5.68 ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.41/5.68 & ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % inf_period(1)
% 5.41/5.68 thf(fact_3253_inf__period_I1_J,axiom,
% 5.41/5.68 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.41/5.68 ( ! [X6: rat,K3: rat] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 = ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: rat,K3: rat] :
% 5.41/5.68 ( ( Q @ X6 )
% 5.41/5.68 = ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: rat,K4: rat] :
% 5.41/5.68 ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.41/5.68 & ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % inf_period(1)
% 5.41/5.68 thf(fact_3254_inf__period_I1_J,axiom,
% 5.41/5.68 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.41/5.68 ( ! [X6: int,K3: int] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: int,K3: int] :
% 5.41/5.68 ( ( Q @ X6 )
% 5.41/5.68 = ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: int,K4: int] :
% 5.41/5.68 ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.41/5.68 & ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % inf_period(1)
% 5.41/5.68 thf(fact_3255_inf__period_I2_J,axiom,
% 5.41/5.68 ! [P: real > $o,D4: real,Q: real > $o] :
% 5.41/5.68 ( ! [X6: real,K3: real] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 = ( P @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: real,K3: real] :
% 5.41/5.68 ( ( Q @ X6 )
% 5.41/5.68 = ( Q @ ( minus_minus_real @ X6 @ ( times_times_real @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: real,K4: real] :
% 5.41/5.68 ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) )
% 5.41/5.68 | ( Q @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % inf_period(2)
% 5.41/5.68 thf(fact_3256_inf__period_I2_J,axiom,
% 5.41/5.68 ! [P: rat > $o,D4: rat,Q: rat > $o] :
% 5.41/5.68 ( ! [X6: rat,K3: rat] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 = ( P @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: rat,K3: rat] :
% 5.41/5.68 ( ( Q @ X6 )
% 5.41/5.68 = ( Q @ ( minus_minus_rat @ X6 @ ( times_times_rat @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: rat,K4: rat] :
% 5.41/5.68 ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) )
% 5.41/5.68 | ( Q @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % inf_period(2)
% 5.41/5.68 thf(fact_3257_inf__period_I2_J,axiom,
% 5.41/5.68 ! [P: int > $o,D4: int,Q: int > $o] :
% 5.41/5.68 ( ! [X6: int,K3: int] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: int,K3: int] :
% 5.41/5.68 ( ( Q @ X6 )
% 5.41/5.68 = ( Q @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: int,K4: int] :
% 5.41/5.68 ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 = ( ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) )
% 5.41/5.68 | ( Q @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % inf_period(2)
% 5.41/5.68 thf(fact_3258_conj__le__cong,axiom,
% 5.41/5.68 ! [X: int,X5: int,P: $o,P6: $o] :
% 5.41/5.68 ( ( X = X5 )
% 5.41/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.41/5.68 => ( P = P6 ) )
% 5.41/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.68 & P )
% 5.41/5.68 = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.41/5.68 & P6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % conj_le_cong
% 5.41/5.68 thf(fact_3259_imp__le__cong,axiom,
% 5.41/5.68 ! [X: int,X5: int,P: $o,P6: $o] :
% 5.41/5.68 ( ( X = X5 )
% 5.41/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.41/5.68 => ( P = P6 ) )
% 5.41/5.68 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.68 => P )
% 5.41/5.68 = ( ( ord_less_eq_int @ zero_zero_int @ X5 )
% 5.41/5.68 => P6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % imp_le_cong
% 5.41/5.68 thf(fact_3260_bset_I1_J,axiom,
% 5.41/5.68 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.41/5.68 ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ B3 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ B3 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 => ( Q @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 5.41/5.68 & ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % bset(1)
% 5.41/5.68 thf(fact_3261_bset_I2_J,axiom,
% 5.41/5.68 ! [D4: int,B3: set_int,P: int > $o,Q: int > $o] :
% 5.41/5.68 ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ B3 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 => ( P @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ B3 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( plus_plus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 => ( Q @ ( minus_minus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 => ( ( P @ ( minus_minus_int @ X4 @ D4 ) )
% 5.41/5.68 | ( Q @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % bset(2)
% 5.41/5.68 thf(fact_3262_aset_I1_J,axiom,
% 5.41/5.68 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.41/5.68 ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ A2 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ A2 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 => ( Q @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 & ( Q @ X4 ) )
% 5.41/5.68 => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 5.41/5.68 & ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(1)
% 5.41/5.68 thf(fact_3263_aset_I2_J,axiom,
% 5.41/5.68 ! [D4: int,A2: set_int,P: int > $o,Q: int > $o] :
% 5.41/5.68 ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ A2 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 => ( P @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ( ! [X6: int] :
% 5.41/5.68 ( ! [Xa: int] :
% 5.41/5.68 ( ( member_int @ Xa @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb: int] :
% 5.41/5.68 ( ( member_int @ Xb @ A2 )
% 5.41/5.68 => ( X6
% 5.41/5.68 != ( minus_minus_int @ Xb @ Xa ) ) ) )
% 5.41/5.68 => ( ( Q @ X6 )
% 5.41/5.68 => ( Q @ ( plus_plus_int @ X6 @ D4 ) ) ) )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ( P @ X4 )
% 5.41/5.68 | ( Q @ X4 ) )
% 5.41/5.68 => ( ( P @ ( plus_plus_int @ X4 @ D4 ) )
% 5.41/5.68 | ( Q @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(2)
% 5.41/5.68 thf(fact_3264_plusinfinity,axiom,
% 5.41/5.68 ! [D: int,P6: int > $o,P: int > $o] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D )
% 5.41/5.68 => ( ! [X6: int,K3: int] :
% 5.41/5.68 ( ( P6 @ X6 )
% 5.41/5.68 = ( P6 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.41/5.68 => ( ? [Z4: int] :
% 5.41/5.68 ! [X6: int] :
% 5.41/5.68 ( ( ord_less_int @ Z4 @ X6 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P6 @ X6 ) ) )
% 5.41/5.68 => ( ? [X_12: int] : ( P6 @ X_12 )
% 5.41/5.68 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % plusinfinity
% 5.41/5.68 thf(fact_3265_minusinfinity,axiom,
% 5.41/5.68 ! [D: int,P1: int > $o,P: int > $o] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D )
% 5.41/5.68 => ( ! [X6: int,K3: int] :
% 5.41/5.68 ( ( P1 @ X6 )
% 5.41/5.68 = ( P1 @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.41/5.68 => ( ? [Z4: int] :
% 5.41/5.68 ! [X6: int] :
% 5.41/5.68 ( ( ord_less_int @ X6 @ Z4 )
% 5.41/5.68 => ( ( P @ X6 )
% 5.41/5.68 = ( P1 @ X6 ) ) )
% 5.41/5.68 => ( ? [X_12: int] : ( P1 @ X_12 )
% 5.41/5.68 => ? [X_1: int] : ( P @ X_1 ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % minusinfinity
% 5.41/5.68 thf(fact_3266_vebt__member_Oelims_I2_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.68 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => A5 )
% 5.41/5.68 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.68 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.68 => B5 )
% 5.41/5.68 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Summary2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ~ ( ( Xa2 != Mi2 )
% 5.41/5.68 => ( ( Xa2 != Ma2 )
% 5.41/5.68 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_member.elims(2)
% 5.41/5.68 thf(fact_3267_vebt__member_Oelims_I3_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.68 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => A5 )
% 5.41/5.68 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.68 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.68 => B5 )
% 5.41/5.68 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.41/5.68 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Summary2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( ( Xa2 != Mi2 )
% 5.41/5.68 => ( ( Xa2 != Ma2 )
% 5.41/5.68 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_member.elims(3)
% 5.41/5.68 thf(fact_3268_vebt__member_Oelims_I1_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.68 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => A5 )
% 5.41/5.68 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.68 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.68 => B5 )
% 5.41/5.68 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.41/5.68 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ( ( ? [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ( ( ? [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Summary2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( ~ ( ( Xa2 != Mi2 )
% 5.41/5.68 => ( ( Xa2 != Ma2 )
% 5.41/5.68 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_member.elims(1)
% 5.41/5.68 thf(fact_3269_incr__mult__lemma,axiom,
% 5.41/5.68 ! [D: int,P: int > $o,K: int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D )
% 5.41/5.68 => ( ! [X6: int] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 => ( P @ ( plus_plus_int @ X6 @ D ) ) )
% 5.41/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ( P @ X4 )
% 5.41/5.68 => ( P @ ( plus_plus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % incr_mult_lemma
% 5.41/5.68 thf(fact_3270_decr__mult__lemma,axiom,
% 5.41/5.68 ! [D: int,P: int > $o,K: int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D )
% 5.41/5.68 => ( ! [X6: int] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 => ( P @ ( minus_minus_int @ X6 @ D ) ) )
% 5.41/5.68 => ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ( P @ X4 )
% 5.41/5.68 => ( P @ ( minus_minus_int @ X4 @ ( times_times_int @ K @ D ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % decr_mult_lemma
% 5.41/5.68 thf(fact_3271_periodic__finite__ex,axiom,
% 5.41/5.68 ! [D: int,P: int > $o] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D )
% 5.41/5.68 => ( ! [X6: int,K3: int] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 = ( P @ ( minus_minus_int @ X6 @ ( times_times_int @ K3 @ D ) ) ) )
% 5.41/5.68 => ( ( ? [X2: int] : ( P @ X2 ) )
% 5.41/5.68 = ( ? [X3: int] :
% 5.41/5.68 ( ( member_int @ X3 @ ( set_or1266510415728281911st_int @ one_one_int @ D ) )
% 5.41/5.68 & ( P @ X3 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % periodic_finite_ex
% 5.41/5.68 thf(fact_3272_aset_I7_J,axiom,
% 5.41/5.68 ! [D4: int,A2: set_int,T: int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ord_less_int @ T @ X4 )
% 5.41/5.68 => ( ord_less_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(7)
% 5.41/5.68 thf(fact_3273_aset_I5_J,axiom,
% 5.41/5.68 ! [D4: int,T: int,A2: set_int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ( ( member_int @ T @ A2 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ord_less_int @ X4 @ T )
% 5.41/5.68 => ( ord_less_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(5)
% 5.41/5.68 thf(fact_3274_aset_I4_J,axiom,
% 5.41/5.68 ! [D4: int,T: int,A2: set_int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ( ( member_int @ T @ A2 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( X4 != T )
% 5.41/5.68 => ( ( plus_plus_int @ X4 @ D4 )
% 5.41/5.68 != T ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(4)
% 5.41/5.68 thf(fact_3275_aset_I3_J,axiom,
% 5.41/5.68 ! [D4: int,T: int,A2: set_int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( X4 = T )
% 5.41/5.68 => ( ( plus_plus_int @ X4 @ D4 )
% 5.41/5.68 = T ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(3)
% 5.41/5.68 thf(fact_3276_bset_I7_J,axiom,
% 5.41/5.68 ! [D4: int,T: int,B3: set_int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ( ( member_int @ T @ B3 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ord_less_int @ T @ X4 )
% 5.41/5.68 => ( ord_less_int @ T @ ( minus_minus_int @ X4 @ D4 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % bset(7)
% 5.41/5.68 thf(fact_3277_bset_I5_J,axiom,
% 5.41/5.68 ! [D4: int,B3: set_int,T: int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ord_less_int @ X4 @ T )
% 5.41/5.68 => ( ord_less_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % bset(5)
% 5.41/5.68 thf(fact_3278_bset_I4_J,axiom,
% 5.41/5.68 ! [D4: int,T: int,B3: set_int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ( ( member_int @ T @ B3 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( X4 != T )
% 5.41/5.68 => ( ( minus_minus_int @ X4 @ D4 )
% 5.41/5.68 != T ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % bset(4)
% 5.41/5.68 thf(fact_3279_bset_I3_J,axiom,
% 5.41/5.68 ! [D4: int,T: int,B3: set_int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ( ( member_int @ ( minus_minus_int @ T @ one_one_int ) @ B3 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( X4 = T )
% 5.41/5.68 => ( ( minus_minus_int @ X4 @ D4 )
% 5.41/5.68 = T ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % bset(3)
% 5.41/5.68 thf(fact_3280_invar__vebt_Osimps,axiom,
% 5.41/5.68 ( vEBT_invar_vebt
% 5.41/5.68 = ( ^ [A1: vEBT_VEBT,A22: nat] :
% 5.41/5.68 ( ( ? [A3: $o,B2: $o] :
% 5.41/5.68 ( A1
% 5.41/5.68 = ( vEBT_Leaf @ A3 @ B2 ) )
% 5.41/5.68 & ( A22
% 5.41/5.68 = ( suc @ zero_zero_nat ) ) )
% 5.41/5.68 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.41/5.68 ( ( A1
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.41/5.68 & ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.41/5.68 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.41/5.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.41/5.68 & ( A22
% 5.41/5.68 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.41/5.68 & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 5.41/5.68 & ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.68 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT] :
% 5.41/5.68 ( ( A1
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ A22 @ TreeList @ Summary3 ) )
% 5.41/5.68 & ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.41/5.68 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.41/5.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.41/5.68 & ( A22
% 5.41/5.68 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.41/5.68 & ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary3 @ X2 )
% 5.41/5.68 & ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.68 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.41/5.68 ( ( A1
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.41/5.68 & ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.41/5.68 & ( vEBT_invar_vebt @ Summary3 @ N2 )
% 5.41/5.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.41/5.68 & ( A22
% 5.41/5.68 = ( plus_plus_nat @ N2 @ N2 ) )
% 5.41/5.68 & ! [I5: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.41/5.68 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X2 ) )
% 5.41/5.68 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 5.41/5.68 & ( ( Mi3 = Ma3 )
% 5.41/5.68 => ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.68 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.41/5.68 & ( ( Mi3 != Ma3 )
% 5.41/5.68 => ! [I5: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) )
% 5.41/5.68 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.41/5.68 = I5 )
% 5.41/5.68 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.41/5.68 & ! [X3: nat] :
% 5.41/5.68 ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 5.41/5.68 = I5 )
% 5.41/5.68 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 5.41/5.68 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.68 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) )
% 5.41/5.68 | ? [TreeList: list_VEBT_VEBT,N2: nat,Summary3: vEBT_VEBT,Mi3: nat,Ma3: nat] :
% 5.41/5.68 ( ( A1
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi3 @ Ma3 ) ) @ A22 @ TreeList @ Summary3 ) )
% 5.41/5.68 & ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X3 @ N2 ) )
% 5.41/5.68 & ( vEBT_invar_vebt @ Summary3 @ ( suc @ N2 ) )
% 5.41/5.68 & ( ( size_s6755466524823107622T_VEBT @ TreeList )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.41/5.68 & ( A22
% 5.41/5.68 = ( plus_plus_nat @ N2 @ ( suc @ N2 ) ) )
% 5.41/5.68 & ! [I5: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.41/5.68 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ X2 ) )
% 5.41/5.68 = ( vEBT_V8194947554948674370ptions @ Summary3 @ I5 ) ) )
% 5.41/5.68 & ( ( Mi3 = Ma3 )
% 5.41/5.68 => ! [X3: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList ) )
% 5.41/5.68 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.68 & ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.68 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A22 ) )
% 5.41/5.68 & ( ( Mi3 != Ma3 )
% 5.41/5.68 => ! [I5: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) )
% 5.41/5.68 => ( ( ( ( vEBT_VEBT_high @ Ma3 @ N2 )
% 5.41/5.68 = I5 )
% 5.41/5.68 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ Ma3 @ N2 ) ) )
% 5.41/5.68 & ! [X3: nat] :
% 5.41/5.68 ( ( ( ( vEBT_VEBT_high @ X3 @ N2 )
% 5.41/5.68 = I5 )
% 5.41/5.68 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList @ I5 ) @ ( vEBT_VEBT_low @ X3 @ N2 ) ) )
% 5.41/5.68 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.68 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % invar_vebt.simps
% 5.41/5.68 thf(fact_3281_invar__vebt_Ocases,axiom,
% 5.41/5.68 ! [A12: vEBT_VEBT,A23: nat] :
% 5.41/5.68 ( ( vEBT_invar_vebt @ A12 @ A23 )
% 5.41/5.68 => ( ( ? [A5: $o,B5: $o] :
% 5.41/5.68 ( A12
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ( A23
% 5.41/5.68 != ( suc @ zero_zero_nat ) ) )
% 5.41/5.68 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.41/5.68 ( ( A12
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( ( A23 = Deg2 )
% 5.41/5.68 => ( ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.41/5.68 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.41/5.68 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( M4 = N3 )
% 5.41/5.68 => ( ( Deg2
% 5.41/5.68 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.41/5.68 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.41/5.68 => ~ ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.41/5.68 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat] :
% 5.41/5.68 ( ( A12
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( ( A23 = Deg2 )
% 5.41/5.68 => ( ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.41/5.68 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.41/5.68 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( M4
% 5.41/5.68 = ( suc @ N3 ) )
% 5.41/5.68 => ( ( Deg2
% 5.41/5.68 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.41/5.68 => ( ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X_12 )
% 5.41/5.68 => ~ ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) ) ) ) ) ) ) ) )
% 5.41/5.68 => ( ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.41/5.68 ( ( A12
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( ( A23 = Deg2 )
% 5.41/5.68 => ( ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.41/5.68 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.41/5.68 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( M4 = N3 )
% 5.41/5.68 => ( ( Deg2
% 5.41/5.68 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.41/5.68 => ( ! [I2: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X2 ) )
% 5.41/5.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.41/5.68 => ( ( ( Mi2 = Ma2 )
% 5.41/5.68 => ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.41/5.68 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.41/5.68 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.68 => ~ ( ( Mi2 != Ma2 )
% 5.41/5.68 => ! [I2: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.41/5.68 = I2 )
% 5.41/5.68 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.41/5.68 & ! [X4: nat] :
% 5.41/5.68 ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 5.41/5.68 = I2 )
% 5.41/5.68 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 5.41/5.68 => ( ( ord_less_nat @ Mi2 @ X4 )
% 5.41/5.68 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.68 => ~ ! [TreeList3: list_VEBT_VEBT,N3: nat,Summary2: vEBT_VEBT,M4: nat,Deg2: nat,Mi2: nat,Ma2: nat] :
% 5.41/5.68 ( ( A12
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( ( A23 = Deg2 )
% 5.41/5.68 => ( ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_invar_vebt @ X4 @ N3 ) )
% 5.41/5.68 => ( ( vEBT_invar_vebt @ Summary2 @ M4 )
% 5.41/5.68 => ( ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.68 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( M4
% 5.41/5.68 = ( suc @ N3 ) )
% 5.41/5.68 => ( ( Deg2
% 5.41/5.68 = ( plus_plus_nat @ N3 @ M4 ) )
% 5.41/5.68 => ( ! [I2: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ X2 ) )
% 5.41/5.68 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I2 ) ) )
% 5.41/5.68 => ( ( ( Mi2 = Ma2 )
% 5.41/5.68 => ! [X4: vEBT_VEBT] :
% 5.41/5.68 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.68 => ~ ? [X_12: nat] : ( vEBT_V8194947554948674370ptions @ X4 @ X_12 ) ) )
% 5.41/5.68 => ( ( ord_less_eq_nat @ Mi2 @ Ma2 )
% 5.41/5.68 => ( ( ord_less_nat @ Ma2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.68 => ~ ( ( Mi2 != Ma2 )
% 5.41/5.68 => ! [I2: nat] :
% 5.41/5.68 ( ( ord_less_nat @ I2 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M4 ) )
% 5.41/5.68 => ( ( ( ( vEBT_VEBT_high @ Ma2 @ N3 )
% 5.41/5.68 = I2 )
% 5.41/5.68 => ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ Ma2 @ N3 ) ) )
% 5.41/5.68 & ! [X4: nat] :
% 5.41/5.68 ( ( ( ( vEBT_VEBT_high @ X4 @ N3 )
% 5.41/5.68 = I2 )
% 5.41/5.68 & ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I2 ) @ ( vEBT_VEBT_low @ X4 @ N3 ) ) )
% 5.41/5.68 => ( ( ord_less_nat @ Mi2 @ X4 )
% 5.41/5.68 & ( ord_less_eq_nat @ X4 @ Ma2 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % invar_vebt.cases
% 5.41/5.68 thf(fact_3282_vebt__insert_Oelims,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.41/5.68 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.41/5.68 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.68 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.41/5.68 & ( ( Xa2 != one_one_nat )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) ) )
% 5.41/5.68 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) ) )
% 5.41/5.68 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) ) )
% 5.41/5.68 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( if_VEBT_VEBT
% 5.41/5.68 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 & ~ ( ( Xa2 = Mi2 )
% 5.41/5.68 | ( Xa2 = Ma2 ) ) )
% 5.41/5.68 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.41/5.68 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_insert.elims
% 5.41/5.68 thf(fact_3283_aset_I8_J,axiom,
% 5.41/5.68 ! [D4: int,A2: set_int,T: int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ord_less_eq_int @ T @ X4 )
% 5.41/5.68 => ( ord_less_eq_int @ T @ ( plus_plus_int @ X4 @ D4 ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(8)
% 5.41/5.68 thf(fact_3284_aset_I6_J,axiom,
% 5.41/5.68 ! [D4: int,T: int,A2: set_int] :
% 5.41/5.68 ( ( ord_less_int @ zero_zero_int @ D4 )
% 5.41/5.68 => ( ( member_int @ ( plus_plus_int @ T @ one_one_int ) @ A2 )
% 5.41/5.68 => ! [X4: int] :
% 5.41/5.68 ( ! [Xa3: int] :
% 5.41/5.68 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.68 => ! [Xb2: int] :
% 5.41/5.68 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.68 => ( X4
% 5.41/5.68 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.68 => ( ( ord_less_eq_int @ X4 @ T )
% 5.41/5.68 => ( ord_less_eq_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % aset(6)
% 5.41/5.68 thf(fact_3285_vebt__mint_Oelims,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.41/5.68 ( ( ( vEBT_vebt_mint @ X )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ~ ( ( A5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A5
% 5.41/5.68 => ( ( B5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B5
% 5.41/5.68 => ( Y = none_nat ) ) ) ) ) )
% 5.41/5.68 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.68 => ( Y != none_nat ) )
% 5.41/5.68 => ~ ! [Mi2: nat] :
% 5.41/5.68 ( ? [Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( some_nat @ Mi2 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_mint.elims
% 5.41/5.68 thf(fact_3286_vebt__maxt_Oelims,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.41/5.68 ( ( ( vEBT_vebt_maxt @ X )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ~ ( ( B5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B5
% 5.41/5.68 => ( ( A5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A5
% 5.41/5.68 => ( Y = none_nat ) ) ) ) ) )
% 5.41/5.68 => ( ( ? [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.68 => ( Y != none_nat ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat] :
% 5.41/5.68 ( ? [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( some_nat @ Ma2 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_maxt.elims
% 5.41/5.68 thf(fact_3287_vebt__mint_Osimps_I1_J,axiom,
% 5.41/5.68 ! [A: $o,B: $o] :
% 5.41/5.68 ( ( A
% 5.41/5.68 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A
% 5.41/5.68 => ( ( B
% 5.41/5.68 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B
% 5.41/5.68 => ( ( vEBT_vebt_mint @ ( vEBT_Leaf @ A @ B ) )
% 5.41/5.68 = none_nat ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_mint.simps(1)
% 5.41/5.68 thf(fact_3288_vebt__maxt_Osimps_I1_J,axiom,
% 5.41/5.68 ! [B: $o,A: $o] :
% 5.41/5.68 ( ( B
% 5.41/5.68 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B
% 5.41/5.68 => ( ( A
% 5.41/5.68 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A
% 5.41/5.68 => ( ( vEBT_vebt_maxt @ ( vEBT_Leaf @ A @ B ) )
% 5.41/5.68 = none_nat ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_maxt.simps(1)
% 5.41/5.68 thf(fact_3289_VEBT__internal_Omembermima_Oelims_I1_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.68 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ( ( ? [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat] :
% 5.41/5.68 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( ~ ( ( Xa2 = Mi2 )
% 5.41/5.68 | ( Xa2 = Ma2 ) ) ) ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Vc2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( ~ ( ( Xa2 = Mi2 )
% 5.41/5.68 | ( Xa2 = Ma2 )
% 5.41/5.68 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) )
% 5.41/5.68 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Vd2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.elims(1)
% 5.41/5.68 thf(fact_3290_VEBT__internal_Omembermima_Oelims_I3_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.68 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.41/5.68 => ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.68 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat] :
% 5.41/5.68 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.41/5.68 => ( ( Xa2 = Mi2 )
% 5.41/5.68 | ( Xa2 = Ma2 ) ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Vc2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.41/5.68 => ( ( Xa2 = Mi2 )
% 5.41/5.68 | ( Xa2 = Ma2 )
% 5.41/5.68 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.41/5.68 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Vd2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.41/5.68 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.elims(3)
% 5.41/5.68 thf(fact_3291_VEBT__internal_Onaive__member_Oelims_I1_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.68 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( ~ ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => A5 )
% 5.41/5.68 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.68 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.68 => B5 )
% 5.41/5.68 & ( Xa2 = one_one_nat ) ) ) ) ) ) )
% 5.41/5.68 => ( ( ? [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.41/5.68 => Y )
% 5.41/5.68 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [S3: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.naive_member.elims(1)
% 5.41/5.68 thf(fact_3292_VEBT__internal_Onaive__member_Oelims_I2_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.68 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => A5 )
% 5.41/5.68 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.68 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.68 => B5 )
% 5.41/5.68 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.41/5.68 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [S3: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.41/5.68 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.naive_member.elims(2)
% 5.41/5.68 thf(fact_3293_buildup__nothing__in__min__max,axiom,
% 5.41/5.68 ! [N: nat,X: nat] :
% 5.41/5.68 ~ ( vEBT_VEBT_membermima @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.41/5.68
% 5.41/5.68 % buildup_nothing_in_min_max
% 5.41/5.68 thf(fact_3294_buildup__nothing__in__leaf,axiom,
% 5.41/5.68 ! [N: nat,X: nat] :
% 5.41/5.68 ~ ( vEBT_V5719532721284313246member @ ( vEBT_vebt_buildup @ N ) @ X ) ).
% 5.41/5.68
% 5.41/5.68 % buildup_nothing_in_leaf
% 5.41/5.68 thf(fact_3295_both__member__options__def,axiom,
% 5.41/5.68 ( vEBT_V8194947554948674370ptions
% 5.41/5.68 = ( ^ [T2: vEBT_VEBT,X3: nat] :
% 5.41/5.68 ( ( vEBT_V5719532721284313246member @ T2 @ X3 )
% 5.41/5.68 | ( vEBT_VEBT_membermima @ T2 @ X3 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % both_member_options_def
% 5.41/5.68 thf(fact_3296_member__valid__both__member__options,axiom,
% 5.41/5.68 ! [Tree: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.68 ( ( vEBT_invar_vebt @ Tree @ N )
% 5.41/5.68 => ( ( vEBT_vebt_member @ Tree @ X )
% 5.41/5.68 => ( ( vEBT_V5719532721284313246member @ Tree @ X )
% 5.41/5.68 | ( vEBT_VEBT_membermima @ Tree @ X ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % member_valid_both_member_options
% 5.41/5.68 thf(fact_3297_VEBT__internal_Onaive__member_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Uu: option4927543243414619207at_nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT,Ux: nat] :
% 5.41/5.68 ~ ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uu @ zero_zero_nat @ Uv @ Uw ) @ Ux ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.naive_member.simps(2)
% 5.41/5.68 thf(fact_3298_VEBT__internal_Omembermima_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Ux: list_VEBT_VEBT,Uy: vEBT_VEBT,Uz: nat] :
% 5.41/5.68 ~ ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux @ Uy ) @ Uz ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.simps(2)
% 5.41/5.68 thf(fact_3299_VEBT__internal_Onaive__member_Osimps_I1_J,axiom,
% 5.41/5.68 ! [A: $o,B: $o,X: nat] :
% 5.41/5.68 ( ( vEBT_V5719532721284313246member @ ( vEBT_Leaf @ A @ B ) @ X )
% 5.41/5.68 = ( ( ( X = zero_zero_nat )
% 5.41/5.68 => A )
% 5.41/5.68 & ( ( X != zero_zero_nat )
% 5.41/5.68 => ( ( ( X = one_one_nat )
% 5.41/5.68 => B )
% 5.41/5.68 & ( X = one_one_nat ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.naive_member.simps(1)
% 5.41/5.68 thf(fact_3300_VEBT__internal_Omembermima_Osimps_I3_J,axiom,
% 5.41/5.68 ! [Mi: nat,Ma: nat,Va: list_VEBT_VEBT,Vb: vEBT_VEBT,X: nat] :
% 5.41/5.68 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ zero_zero_nat @ Va @ Vb ) @ X )
% 5.41/5.68 = ( ( X = Mi )
% 5.41/5.68 | ( X = Ma ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.simps(3)
% 5.41/5.68 thf(fact_3301_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.41/5.68 ! [X: produc8306885398267862888on_nat] :
% 5.41/5.68 ( ! [Uu2: nat > nat > nat,Uv2: option_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc8929957630744042906on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.41/5.68 => ( ! [Uw2: nat > nat > nat,V2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc8929957630744042906on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.41/5.68 => ~ ! [F2: nat > nat > nat,A5: nat,B5: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc8929957630744042906on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ A5 ) @ ( some_nat @ B5 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.cases
% 5.41/5.68 thf(fact_3302_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.41/5.68 ! [X: produc5542196010084753463at_nat] :
% 5.41/5.68 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv2: option4927543243414619207at_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc2899441246263362727at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.41/5.68 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V2: product_prod_nat_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc2899441246263362727at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.41/5.68 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A5: product_prod_nat_nat,B5: product_prod_nat_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc2899441246263362727at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ A5 ) @ ( some_P7363390416028606310at_nat @ B5 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.cases
% 5.41/5.68 thf(fact_3303_VEBT__internal_Ooption__shift_Ocases,axiom,
% 5.41/5.68 ! [X: produc1193250871479095198on_num] :
% 5.41/5.68 ( ! [Uu2: num > num > num,Uv2: option_num] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc5778274026573060048on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.41/5.68 => ( ! [Uw2: num > num > num,V2: num] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc5778274026573060048on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.41/5.68 => ~ ! [F2: num > num > num,A5: num,B5: num] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc5778274026573060048on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ A5 ) @ ( some_num @ B5 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.cases
% 5.41/5.68 thf(fact_3304_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.41/5.68 ! [X: produc2233624965454879586on_nat] :
% 5.41/5.68 ( ! [Uu2: nat > nat > $o,Uv2: option_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc4035269172776083154on_nat @ Uu2 @ ( produc5098337634421038937on_nat @ none_nat @ Uv2 ) ) )
% 5.41/5.68 => ( ! [Uw2: nat > nat > $o,V2: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc4035269172776083154on_nat @ Uw2 @ ( produc5098337634421038937on_nat @ ( some_nat @ V2 ) @ none_nat ) ) )
% 5.41/5.68 => ~ ! [F2: nat > nat > $o,X6: nat,Y5: nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc4035269172776083154on_nat @ F2 @ ( produc5098337634421038937on_nat @ ( some_nat @ X6 ) @ ( some_nat @ Y5 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_comp_shift.cases
% 5.41/5.68 thf(fact_3305_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.41/5.68 ! [X: produc5491161045314408544at_nat] :
% 5.41/5.68 ( ! [Uu2: product_prod_nat_nat > product_prod_nat_nat > $o,Uv2: option4927543243414619207at_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc3994169339658061776at_nat @ Uu2 @ ( produc488173922507101015at_nat @ none_P5556105721700978146at_nat @ Uv2 ) ) )
% 5.41/5.68 => ( ! [Uw2: product_prod_nat_nat > product_prod_nat_nat > $o,V2: product_prod_nat_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc3994169339658061776at_nat @ Uw2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ V2 ) @ none_P5556105721700978146at_nat ) ) )
% 5.41/5.68 => ~ ! [F2: product_prod_nat_nat > product_prod_nat_nat > $o,X6: product_prod_nat_nat,Y5: product_prod_nat_nat] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc3994169339658061776at_nat @ F2 @ ( produc488173922507101015at_nat @ ( some_P7363390416028606310at_nat @ X6 ) @ ( some_P7363390416028606310at_nat @ Y5 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_comp_shift.cases
% 5.41/5.68 thf(fact_3306_VEBT__internal_Ooption__comp__shift_Ocases,axiom,
% 5.41/5.68 ! [X: produc7036089656553540234on_num] :
% 5.41/5.68 ( ! [Uu2: num > num > $o,Uv2: option_num] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc3576312749637752826on_num @ Uu2 @ ( produc8585076106096196333on_num @ none_num @ Uv2 ) ) )
% 5.41/5.68 => ( ! [Uw2: num > num > $o,V2: num] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc3576312749637752826on_num @ Uw2 @ ( produc8585076106096196333on_num @ ( some_num @ V2 ) @ none_num ) ) )
% 5.41/5.68 => ~ ! [F2: num > num > $o,X6: num,Y5: num] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( produc3576312749637752826on_num @ F2 @ ( produc8585076106096196333on_num @ ( some_num @ X6 ) @ ( some_num @ Y5 ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_comp_shift.cases
% 5.41/5.68 thf(fact_3307_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.41/5.68 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,A: product_prod_nat_nat,B: product_prod_nat_nat] :
% 5.41/5.68 ( ( vEBT_V1502963449132264192at_nat @ F @ ( some_P7363390416028606310at_nat @ A ) @ ( some_P7363390416028606310at_nat @ B ) )
% 5.41/5.68 = ( some_P7363390416028606310at_nat @ ( F @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(3)
% 5.41/5.68 thf(fact_3308_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.41/5.68 ! [F: num > num > num,A: num,B: num] :
% 5.41/5.68 ( ( vEBT_V819420779217536731ft_num @ F @ ( some_num @ A ) @ ( some_num @ B ) )
% 5.41/5.68 = ( some_num @ ( F @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(3)
% 5.41/5.68 thf(fact_3309_VEBT__internal_Ooption__shift_Osimps_I3_J,axiom,
% 5.41/5.68 ! [F: nat > nat > nat,A: nat,B: nat] :
% 5.41/5.68 ( ( vEBT_V4262088993061758097ft_nat @ F @ ( some_nat @ A ) @ ( some_nat @ B ) )
% 5.41/5.68 = ( some_nat @ ( F @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(3)
% 5.41/5.68 thf(fact_3310_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.41/5.68 ! [Uu: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Uv: option4927543243414619207at_nat] :
% 5.41/5.68 ( ( vEBT_V1502963449132264192at_nat @ Uu @ none_P5556105721700978146at_nat @ Uv )
% 5.41/5.68 = none_P5556105721700978146at_nat ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(1)
% 5.41/5.68 thf(fact_3311_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.41/5.68 ! [Uu: num > num > num,Uv: option_num] :
% 5.41/5.68 ( ( vEBT_V819420779217536731ft_num @ Uu @ none_num @ Uv )
% 5.41/5.68 = none_num ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(1)
% 5.41/5.68 thf(fact_3312_VEBT__internal_Ooption__shift_Osimps_I1_J,axiom,
% 5.41/5.68 ! [Uu: nat > nat > nat,Uv: option_nat] :
% 5.41/5.68 ( ( vEBT_V4262088993061758097ft_nat @ Uu @ none_nat @ Uv )
% 5.41/5.68 = none_nat ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(1)
% 5.41/5.68 thf(fact_3313_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Uw: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,V: product_prod_nat_nat] :
% 5.41/5.68 ( ( vEBT_V1502963449132264192at_nat @ Uw @ ( some_P7363390416028606310at_nat @ V ) @ none_P5556105721700978146at_nat )
% 5.41/5.68 = none_P5556105721700978146at_nat ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(2)
% 5.41/5.68 thf(fact_3314_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Uw: num > num > num,V: num] :
% 5.41/5.68 ( ( vEBT_V819420779217536731ft_num @ Uw @ ( some_num @ V ) @ none_num )
% 5.41/5.68 = none_num ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(2)
% 5.41/5.68 thf(fact_3315_VEBT__internal_Ooption__shift_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Uw: nat > nat > nat,V: nat] :
% 5.41/5.68 ( ( vEBT_V4262088993061758097ft_nat @ Uw @ ( some_nat @ V ) @ none_nat )
% 5.41/5.68 = none_nat ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.simps(2)
% 5.41/5.68 thf(fact_3316_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.41/5.68 ! [X: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat,Xa2: option4927543243414619207at_nat,Xb3: option4927543243414619207at_nat,Y: option4927543243414619207at_nat] :
% 5.41/5.68 ( ( ( vEBT_V1502963449132264192at_nat @ X @ Xa2 @ Xb3 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ( ( Xa2 = none_P5556105721700978146at_nat )
% 5.41/5.68 => ( Y != none_P5556105721700978146at_nat ) )
% 5.41/5.68 => ( ( ? [V2: product_prod_nat_nat] :
% 5.41/5.68 ( Xa2
% 5.41/5.68 = ( some_P7363390416028606310at_nat @ V2 ) )
% 5.41/5.68 => ( ( Xb3 = none_P5556105721700978146at_nat )
% 5.41/5.68 => ( Y != none_P5556105721700978146at_nat ) ) )
% 5.41/5.68 => ~ ! [A5: product_prod_nat_nat] :
% 5.41/5.68 ( ( Xa2
% 5.41/5.68 = ( some_P7363390416028606310at_nat @ A5 ) )
% 5.41/5.68 => ! [B5: product_prod_nat_nat] :
% 5.41/5.68 ( ( Xb3
% 5.41/5.68 = ( some_P7363390416028606310at_nat @ B5 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( some_P7363390416028606310at_nat @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.elims
% 5.41/5.68 thf(fact_3317_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.41/5.68 ! [X: num > num > num,Xa2: option_num,Xb3: option_num,Y: option_num] :
% 5.41/5.68 ( ( ( vEBT_V819420779217536731ft_num @ X @ Xa2 @ Xb3 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ( ( Xa2 = none_num )
% 5.41/5.68 => ( Y != none_num ) )
% 5.41/5.68 => ( ( ? [V2: num] :
% 5.41/5.68 ( Xa2
% 5.41/5.68 = ( some_num @ V2 ) )
% 5.41/5.68 => ( ( Xb3 = none_num )
% 5.41/5.68 => ( Y != none_num ) ) )
% 5.41/5.68 => ~ ! [A5: num] :
% 5.41/5.68 ( ( Xa2
% 5.41/5.68 = ( some_num @ A5 ) )
% 5.41/5.68 => ! [B5: num] :
% 5.41/5.68 ( ( Xb3
% 5.41/5.68 = ( some_num @ B5 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( some_num @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.elims
% 5.41/5.68 thf(fact_3318_VEBT__internal_Ooption__shift_Oelims,axiom,
% 5.41/5.68 ! [X: nat > nat > nat,Xa2: option_nat,Xb3: option_nat,Y: option_nat] :
% 5.41/5.68 ( ( ( vEBT_V4262088993061758097ft_nat @ X @ Xa2 @ Xb3 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ( ( Xa2 = none_nat )
% 5.41/5.68 => ( Y != none_nat ) )
% 5.41/5.68 => ( ( ? [V2: nat] :
% 5.41/5.68 ( Xa2
% 5.41/5.68 = ( some_nat @ V2 ) )
% 5.41/5.68 => ( ( Xb3 = none_nat )
% 5.41/5.68 => ( Y != none_nat ) ) )
% 5.41/5.68 => ~ ! [A5: nat] :
% 5.41/5.68 ( ( Xa2
% 5.41/5.68 = ( some_nat @ A5 ) )
% 5.41/5.68 => ! [B5: nat] :
% 5.41/5.68 ( ( Xb3
% 5.41/5.68 = ( some_nat @ B5 ) )
% 5.41/5.68 => ( Y
% 5.41/5.68 != ( some_nat @ ( X @ A5 @ B5 ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.option_shift.elims
% 5.41/5.68 thf(fact_3319_vebt__maxt_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.41/5.68 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.41/5.68 = none_nat ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_maxt.simps(2)
% 5.41/5.68 thf(fact_3320_vebt__mint_Osimps_I2_J,axiom,
% 5.41/5.68 ! [Uu: nat,Uv: list_VEBT_VEBT,Uw: vEBT_VEBT] :
% 5.41/5.68 ( ( vEBT_vebt_mint @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu @ Uv @ Uw ) )
% 5.41/5.68 = none_nat ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_mint.simps(2)
% 5.41/5.68 thf(fact_3321_VEBT__internal_Omembermima_Osimps_I5_J,axiom,
% 5.41/5.68 ! [V: nat,TreeList2: list_VEBT_VEBT,Vd: vEBT_VEBT,X: nat] :
% 5.41/5.68 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V ) @ TreeList2 @ Vd ) @ X )
% 5.41/5.68 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.simps(5)
% 5.41/5.68 thf(fact_3322_VEBT__internal_Onaive__member_Osimps_I3_J,axiom,
% 5.41/5.68 ! [Uy: option4927543243414619207at_nat,V: nat,TreeList2: list_VEBT_VEBT,S: vEBT_VEBT,X: nat] :
% 5.41/5.68 ( ( vEBT_V5719532721284313246member @ ( vEBT_Node @ Uy @ ( suc @ V ) @ TreeList2 @ S ) @ X )
% 5.41/5.68 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.68 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.naive_member.simps(3)
% 5.41/5.68 thf(fact_3323_VEBT__internal_Omembermima_Osimps_I4_J,axiom,
% 5.41/5.68 ! [Mi: nat,Ma: nat,V: nat,TreeList2: list_VEBT_VEBT,Vc: vEBT_VEBT,X: nat] :
% 5.41/5.68 ( ( vEBT_VEBT_membermima @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ ( suc @ V ) @ TreeList2 @ Vc ) @ X )
% 5.41/5.68 = ( ( X = Mi )
% 5.41/5.68 | ( X = Ma )
% 5.41/5.68 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList2 @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ X @ ( divide_divide_nat @ ( suc @ V ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList2 ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.simps(4)
% 5.41/5.68 thf(fact_3324_vebt__mint_Ocases,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT] :
% 5.41/5.68 ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_mint.cases
% 5.41/5.68 thf(fact_3325_vebt__maxt_Osimps_I3_J,axiom,
% 5.41/5.68 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.41/5.68 ( ( vEBT_vebt_maxt @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.41/5.68 = ( some_nat @ Ma ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_maxt.simps(3)
% 5.41/5.68 thf(fact_3326_vebt__mint_Osimps_I3_J,axiom,
% 5.41/5.68 ! [Mi: nat,Ma: nat,Ux: nat,Uy: list_VEBT_VEBT,Uz: vEBT_VEBT] :
% 5.41/5.68 ( ( vEBT_vebt_mint @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi @ Ma ) ) @ Ux @ Uy @ Uz ) )
% 5.41/5.68 = ( some_nat @ Mi ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_mint.simps(3)
% 5.41/5.68 thf(fact_3327_VEBT__internal_Omembermima_Oelims_I2_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.68 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat] :
% 5.41/5.68 ( ? [Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.41/5.68 => ~ ( ( Xa2 = Mi2 )
% 5.41/5.68 | ( Xa2 = Ma2 ) ) )
% 5.41/5.68 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Vc2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.41/5.68 => ~ ( ( Xa2 = Mi2 )
% 5.41/5.68 | ( Xa2 = Ma2 )
% 5.41/5.68 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.41/5.68 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [Vd2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.41/5.68 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.membermima.elims(2)
% 5.41/5.68 thf(fact_3328_VEBT__internal_Onaive__member_Oelims_I3_J,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.68 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => A5 )
% 5.41/5.68 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.68 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.68 => B5 )
% 5.41/5.68 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.41/5.68 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 != ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.41/5.68 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT] :
% 5.41/5.68 ( ? [S3: vEBT_VEBT] :
% 5.41/5.68 ( X
% 5.41/5.68 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.41/5.68 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % VEBT_internal.naive_member.elims(3)
% 5.41/5.68 thf(fact_3329_succ__empty,axiom,
% 5.41/5.68 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.68 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.68 => ( ( ( vEBT_vebt_succ @ T @ X )
% 5.41/5.68 = none_nat )
% 5.41/5.68 = ( ( collect_nat
% 5.41/5.68 @ ^ [Y3: nat] :
% 5.41/5.68 ( ( vEBT_vebt_member @ T @ Y3 )
% 5.41/5.68 & ( ord_less_nat @ X @ Y3 ) ) )
% 5.41/5.68 = bot_bot_set_nat ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % succ_empty
% 5.41/5.68 thf(fact_3330_pred__empty,axiom,
% 5.41/5.68 ! [T: vEBT_VEBT,N: nat,X: nat] :
% 5.41/5.68 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.68 => ( ( ( vEBT_vebt_pred @ T @ X )
% 5.41/5.68 = none_nat )
% 5.41/5.68 = ( ( collect_nat
% 5.41/5.68 @ ^ [Y3: nat] :
% 5.41/5.68 ( ( vEBT_vebt_member @ T @ Y3 )
% 5.41/5.68 & ( ord_less_nat @ Y3 @ X ) ) )
% 5.41/5.68 = bot_bot_set_nat ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % pred_empty
% 5.41/5.68 thf(fact_3331_vebt__succ_Opelims,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.41/5.68 ( ( ( vEBT_vebt_succ @ X @ Xa2 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.68 => ( ! [Uu2: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ Uu2 @ B5 ) )
% 5.41/5.68 => ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => ( ( ( B5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B5
% 5.41/5.68 => ( Y = none_nat ) ) )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 5.41/5.68 => ( ! [Uv2: $o,Uw2: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ Uv2 @ Uw2 ) )
% 5.41/5.68 => ! [N3: nat] :
% 5.41/5.68 ( ( Xa2
% 5.41/5.68 = ( suc @ N3 ) )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uv2 @ Uw2 ) @ ( suc @ N3 ) ) ) ) ) )
% 5.41/5.68 => ( ! [Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Ux2 @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vc2: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vc2 @ Vd2 ) @ Xa2 ) ) ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vg2: list_VEBT_VEBT,Vh2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vg2 @ Vh2 ) @ Xa2 ) ) ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ Mi2 ) ) )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 @ ( if_option_nat
% 5.41/5.68 @ ( ( ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 != none_nat )
% 5.41/5.68 & ( vEBT_VEBT_less @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.68 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_succ @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 @ ( if_option_nat
% 5.41/5.68 @ ( ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.68 = none_nat )
% 5.41/5.68 @ none_nat
% 5.41/5.68 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_succ @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.68 @ none_nat ) ) ) )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_succ_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_succ.pelims
% 5.41/5.68 thf(fact_3332_psubsetI,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.68 => ( ( A2 != B3 )
% 5.41/5.68 => ( ord_less_set_int @ A2 @ B3 ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % psubsetI
% 5.41/5.68 thf(fact_3333_vebt__pred_Opelims,axiom,
% 5.41/5.68 ! [X: vEBT_VEBT,Xa2: nat,Y: option_nat] :
% 5.41/5.68 ( ( ( vEBT_vebt_pred @ X @ Xa2 )
% 5.41/5.68 = Y )
% 5.41/5.68 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.68 => ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.68 => ( ( Xa2 = zero_zero_nat )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ zero_zero_nat ) ) ) ) )
% 5.41/5.68 => ( ! [A5: $o,Uw2: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ Uw2 ) )
% 5.41/5.68 => ( ( Xa2
% 5.41/5.68 = ( suc @ zero_zero_nat ) )
% 5.41/5.68 => ( ( ( A5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A5
% 5.41/5.68 => ( Y = none_nat ) ) )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ Uw2 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.41/5.68 => ( ! [A5: $o,B5: $o] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.68 => ! [Va2: nat] :
% 5.41/5.68 ( ( Xa2
% 5.41/5.68 = ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.68 => ( ( ( B5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.68 & ( ~ B5
% 5.41/5.68 => ( ( A5
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.68 & ( ~ A5
% 5.41/5.68 => ( Y = none_nat ) ) ) ) )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) )
% 5.41/5.68 => ( ! [Uy2: nat,Uz2: list_VEBT_VEBT,Va3: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uy2 @ Uz2 @ Va3 ) @ Xa2 ) ) ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vd2: list_VEBT_VEBT,Ve2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Vd2 @ Ve2 ) @ Xa2 ) ) ) )
% 5.41/5.68 => ( ! [V2: product_prod_nat_nat,Vh2: list_VEBT_VEBT,Vi2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) )
% 5.41/5.68 => ( ( Y = none_nat )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vh2 @ Vi2 ) @ Xa2 ) ) ) )
% 5.41/5.68 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.68 ( ( X
% 5.41/5.68 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.68 => ( ( ( ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( some_nat @ Ma2 ) ) )
% 5.41/5.68 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.68 => ( Y
% 5.41/5.68 = ( if_option_nat @ ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.68 @ ( if_option_nat
% 5.41/5.68 @ ( ( ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 != none_nat )
% 5.41/5.68 & ( vEBT_VEBT_greater @ ( some_nat @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.68 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( some_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_pred @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.68 @ ( if_option_nat
% 5.41/5.68 @ ( ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.68 = none_nat )
% 5.41/5.68 @ ( if_option_nat @ ( ord_less_nat @ Mi2 @ Xa2 ) @ ( some_nat @ Mi2 ) @ none_nat )
% 5.41/5.68 @ ( vEBT_VEBT_add @ ( vEBT_VEBT_mul @ ( some_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_pred @ Summary2 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.68 @ none_nat ) ) ) )
% 5.41/5.68 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_pred_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % vebt_pred.pelims
% 5.41/5.68 thf(fact_3334_max_Oabsorb3,axiom,
% 5.41/5.68 ! [B: extended_enat,A: extended_enat] :
% 5.41/5.68 ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.41/5.68 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb3
% 5.41/5.68 thf(fact_3335_max_Oabsorb3,axiom,
% 5.41/5.68 ! [B: code_integer,A: code_integer] :
% 5.41/5.68 ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.41/5.68 => ( ( ord_max_Code_integer @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb3
% 5.41/5.68 thf(fact_3336_max_Oabsorb3,axiom,
% 5.41/5.68 ! [B: real,A: real] :
% 5.41/5.68 ( ( ord_less_real @ B @ A )
% 5.41/5.68 => ( ( ord_max_real @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb3
% 5.41/5.68 thf(fact_3337_max_Oabsorb3,axiom,
% 5.41/5.68 ! [B: rat,A: rat] :
% 5.41/5.68 ( ( ord_less_rat @ B @ A )
% 5.41/5.68 => ( ( ord_max_rat @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb3
% 5.41/5.68 thf(fact_3338_max_Oabsorb3,axiom,
% 5.41/5.68 ! [B: num,A: num] :
% 5.41/5.68 ( ( ord_less_num @ B @ A )
% 5.41/5.68 => ( ( ord_max_num @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb3
% 5.41/5.68 thf(fact_3339_max_Oabsorb3,axiom,
% 5.41/5.68 ! [B: nat,A: nat] :
% 5.41/5.68 ( ( ord_less_nat @ B @ A )
% 5.41/5.68 => ( ( ord_max_nat @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb3
% 5.41/5.68 thf(fact_3340_max_Oabsorb3,axiom,
% 5.41/5.68 ! [B: int,A: int] :
% 5.41/5.68 ( ( ord_less_int @ B @ A )
% 5.41/5.68 => ( ( ord_max_int @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb3
% 5.41/5.68 thf(fact_3341_max_Oabsorb4,axiom,
% 5.41/5.68 ! [A: extended_enat,B: extended_enat] :
% 5.41/5.68 ( ( ord_le72135733267957522d_enat @ A @ B )
% 5.41/5.68 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb4
% 5.41/5.68 thf(fact_3342_max_Oabsorb4,axiom,
% 5.41/5.68 ! [A: code_integer,B: code_integer] :
% 5.41/5.68 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.41/5.68 => ( ( ord_max_Code_integer @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb4
% 5.41/5.68 thf(fact_3343_max_Oabsorb4,axiom,
% 5.41/5.68 ! [A: real,B: real] :
% 5.41/5.68 ( ( ord_less_real @ A @ B )
% 5.41/5.68 => ( ( ord_max_real @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb4
% 5.41/5.68 thf(fact_3344_max_Oabsorb4,axiom,
% 5.41/5.68 ! [A: rat,B: rat] :
% 5.41/5.68 ( ( ord_less_rat @ A @ B )
% 5.41/5.68 => ( ( ord_max_rat @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb4
% 5.41/5.68 thf(fact_3345_max_Oabsorb4,axiom,
% 5.41/5.68 ! [A: num,B: num] :
% 5.41/5.68 ( ( ord_less_num @ A @ B )
% 5.41/5.68 => ( ( ord_max_num @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb4
% 5.41/5.68 thf(fact_3346_max_Oabsorb4,axiom,
% 5.41/5.68 ! [A: nat,B: nat] :
% 5.41/5.68 ( ( ord_less_nat @ A @ B )
% 5.41/5.68 => ( ( ord_max_nat @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb4
% 5.41/5.68 thf(fact_3347_max_Oabsorb4,axiom,
% 5.41/5.68 ! [A: int,B: int] :
% 5.41/5.68 ( ( ord_less_int @ A @ B )
% 5.41/5.68 => ( ( ord_max_int @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb4
% 5.41/5.68 thf(fact_3348_max__less__iff__conj,axiom,
% 5.41/5.68 ! [X: extended_enat,Y: extended_enat,Z: extended_enat] :
% 5.41/5.68 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ X @ Y ) @ Z )
% 5.41/5.68 = ( ( ord_le72135733267957522d_enat @ X @ Z )
% 5.41/5.68 & ( ord_le72135733267957522d_enat @ Y @ Z ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max_less_iff_conj
% 5.41/5.68 thf(fact_3349_max__less__iff__conj,axiom,
% 5.41/5.68 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.41/5.68 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ X @ Y ) @ Z )
% 5.41/5.68 = ( ( ord_le6747313008572928689nteger @ X @ Z )
% 5.41/5.68 & ( ord_le6747313008572928689nteger @ Y @ Z ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max_less_iff_conj
% 5.41/5.68 thf(fact_3350_max__less__iff__conj,axiom,
% 5.41/5.68 ! [X: real,Y: real,Z: real] :
% 5.41/5.68 ( ( ord_less_real @ ( ord_max_real @ X @ Y ) @ Z )
% 5.41/5.68 = ( ( ord_less_real @ X @ Z )
% 5.41/5.68 & ( ord_less_real @ Y @ Z ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max_less_iff_conj
% 5.41/5.68 thf(fact_3351_max__less__iff__conj,axiom,
% 5.41/5.68 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.68 ( ( ord_less_rat @ ( ord_max_rat @ X @ Y ) @ Z )
% 5.41/5.68 = ( ( ord_less_rat @ X @ Z )
% 5.41/5.68 & ( ord_less_rat @ Y @ Z ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max_less_iff_conj
% 5.41/5.68 thf(fact_3352_max__less__iff__conj,axiom,
% 5.41/5.68 ! [X: num,Y: num,Z: num] :
% 5.41/5.68 ( ( ord_less_num @ ( ord_max_num @ X @ Y ) @ Z )
% 5.41/5.68 = ( ( ord_less_num @ X @ Z )
% 5.41/5.68 & ( ord_less_num @ Y @ Z ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max_less_iff_conj
% 5.41/5.68 thf(fact_3353_max__less__iff__conj,axiom,
% 5.41/5.68 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.68 ( ( ord_less_nat @ ( ord_max_nat @ X @ Y ) @ Z )
% 5.41/5.68 = ( ( ord_less_nat @ X @ Z )
% 5.41/5.68 & ( ord_less_nat @ Y @ Z ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max_less_iff_conj
% 5.41/5.68 thf(fact_3354_max__less__iff__conj,axiom,
% 5.41/5.68 ! [X: int,Y: int,Z: int] :
% 5.41/5.68 ( ( ord_less_int @ ( ord_max_int @ X @ Y ) @ Z )
% 5.41/5.68 = ( ( ord_less_int @ X @ Z )
% 5.41/5.68 & ( ord_less_int @ Y @ Z ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max_less_iff_conj
% 5.41/5.68 thf(fact_3355_buildup__gives__empty,axiom,
% 5.41/5.68 ! [N: nat] :
% 5.41/5.68 ( ( vEBT_VEBT_set_vebt @ ( vEBT_vebt_buildup @ N ) )
% 5.41/5.68 = bot_bot_set_nat ) ).
% 5.41/5.68
% 5.41/5.68 % buildup_gives_empty
% 5.41/5.68 thf(fact_3356_Diff__empty,axiom,
% 5.41/5.68 ! [A2: set_int] :
% 5.41/5.68 ( ( minus_minus_set_int @ A2 @ bot_bot_set_int )
% 5.41/5.68 = A2 ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_empty
% 5.41/5.68 thf(fact_3357_Diff__empty,axiom,
% 5.41/5.68 ! [A2: set_real] :
% 5.41/5.68 ( ( minus_minus_set_real @ A2 @ bot_bot_set_real )
% 5.41/5.68 = A2 ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_empty
% 5.41/5.68 thf(fact_3358_Diff__empty,axiom,
% 5.41/5.68 ! [A2: set_nat] :
% 5.41/5.68 ( ( minus_minus_set_nat @ A2 @ bot_bot_set_nat )
% 5.41/5.68 = A2 ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_empty
% 5.41/5.68 thf(fact_3359_empty__Diff,axiom,
% 5.41/5.68 ! [A2: set_int] :
% 5.41/5.68 ( ( minus_minus_set_int @ bot_bot_set_int @ A2 )
% 5.41/5.68 = bot_bot_set_int ) ).
% 5.41/5.68
% 5.41/5.68 % empty_Diff
% 5.41/5.68 thf(fact_3360_empty__Diff,axiom,
% 5.41/5.68 ! [A2: set_real] :
% 5.41/5.68 ( ( minus_minus_set_real @ bot_bot_set_real @ A2 )
% 5.41/5.68 = bot_bot_set_real ) ).
% 5.41/5.68
% 5.41/5.68 % empty_Diff
% 5.41/5.68 thf(fact_3361_empty__Diff,axiom,
% 5.41/5.68 ! [A2: set_nat] :
% 5.41/5.68 ( ( minus_minus_set_nat @ bot_bot_set_nat @ A2 )
% 5.41/5.68 = bot_bot_set_nat ) ).
% 5.41/5.68
% 5.41/5.68 % empty_Diff
% 5.41/5.68 thf(fact_3362_Diff__cancel,axiom,
% 5.41/5.68 ! [A2: set_int] :
% 5.41/5.68 ( ( minus_minus_set_int @ A2 @ A2 )
% 5.41/5.68 = bot_bot_set_int ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_cancel
% 5.41/5.68 thf(fact_3363_Diff__cancel,axiom,
% 5.41/5.68 ! [A2: set_real] :
% 5.41/5.68 ( ( minus_minus_set_real @ A2 @ A2 )
% 5.41/5.68 = bot_bot_set_real ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_cancel
% 5.41/5.68 thf(fact_3364_Diff__cancel,axiom,
% 5.41/5.68 ! [A2: set_nat] :
% 5.41/5.68 ( ( minus_minus_set_nat @ A2 @ A2 )
% 5.41/5.68 = bot_bot_set_nat ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_cancel
% 5.41/5.68 thf(fact_3365_subset__antisym,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.68 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.68 => ( A2 = B3 ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_antisym
% 5.41/5.68 thf(fact_3366_subsetI,axiom,
% 5.41/5.68 ! [A2: set_complex,B3: set_complex] :
% 5.41/5.68 ( ! [X6: complex] :
% 5.41/5.68 ( ( member_complex @ X6 @ A2 )
% 5.41/5.68 => ( member_complex @ X6 @ B3 ) )
% 5.41/5.68 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % subsetI
% 5.41/5.68 thf(fact_3367_subsetI,axiom,
% 5.41/5.68 ! [A2: set_real,B3: set_real] :
% 5.41/5.68 ( ! [X6: real] :
% 5.41/5.68 ( ( member_real @ X6 @ A2 )
% 5.41/5.68 => ( member_real @ X6 @ B3 ) )
% 5.41/5.68 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % subsetI
% 5.41/5.68 thf(fact_3368_subsetI,axiom,
% 5.41/5.68 ! [A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.68 ( ! [X6: set_nat] :
% 5.41/5.68 ( ( member_set_nat @ X6 @ A2 )
% 5.41/5.68 => ( member_set_nat @ X6 @ B3 ) )
% 5.41/5.68 => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % subsetI
% 5.41/5.68 thf(fact_3369_subsetI,axiom,
% 5.41/5.68 ! [A2: set_nat,B3: set_nat] :
% 5.41/5.68 ( ! [X6: nat] :
% 5.41/5.68 ( ( member_nat @ X6 @ A2 )
% 5.41/5.68 => ( member_nat @ X6 @ B3 ) )
% 5.41/5.68 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % subsetI
% 5.41/5.68 thf(fact_3370_subsetI,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int] :
% 5.41/5.68 ( ! [X6: int] :
% 5.41/5.68 ( ( member_int @ X6 @ A2 )
% 5.41/5.68 => ( member_int @ X6 @ B3 ) )
% 5.41/5.68 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % subsetI
% 5.41/5.68 thf(fact_3371_maxt__corr__help__empty,axiom,
% 5.41/5.68 ! [T: vEBT_VEBT,N: nat] :
% 5.41/5.68 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.68 => ( ( ( vEBT_vebt_maxt @ T )
% 5.41/5.68 = none_nat )
% 5.41/5.68 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.41/5.68 = bot_bot_set_nat ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % maxt_corr_help_empty
% 5.41/5.68 thf(fact_3372_mint__corr__help__empty,axiom,
% 5.41/5.68 ! [T: vEBT_VEBT,N: nat] :
% 5.41/5.68 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.68 => ( ( ( vEBT_vebt_mint @ T )
% 5.41/5.68 = none_nat )
% 5.41/5.68 => ( ( vEBT_VEBT_set_vebt @ T )
% 5.41/5.68 = bot_bot_set_nat ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % mint_corr_help_empty
% 5.41/5.68 thf(fact_3373_Diff__eq__empty__iff,axiom,
% 5.41/5.68 ! [A2: set_real,B3: set_real] :
% 5.41/5.68 ( ( ( minus_minus_set_real @ A2 @ B3 )
% 5.41/5.68 = bot_bot_set_real )
% 5.41/5.68 = ( ord_less_eq_set_real @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_eq_empty_iff
% 5.41/5.68 thf(fact_3374_Diff__eq__empty__iff,axiom,
% 5.41/5.68 ! [A2: set_nat,B3: set_nat] :
% 5.41/5.68 ( ( ( minus_minus_set_nat @ A2 @ B3 )
% 5.41/5.68 = bot_bot_set_nat )
% 5.41/5.68 = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_eq_empty_iff
% 5.41/5.68 thf(fact_3375_Diff__eq__empty__iff,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int] :
% 5.41/5.68 ( ( ( minus_minus_set_int @ A2 @ B3 )
% 5.41/5.68 = bot_bot_set_int )
% 5.41/5.68 = ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_eq_empty_iff
% 5.41/5.68 thf(fact_3376_empty__subsetI,axiom,
% 5.41/5.68 ! [A2: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A2 ) ).
% 5.41/5.68
% 5.41/5.68 % empty_subsetI
% 5.41/5.68 thf(fact_3377_empty__subsetI,axiom,
% 5.41/5.68 ! [A2: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A2 ) ).
% 5.41/5.68
% 5.41/5.68 % empty_subsetI
% 5.41/5.68 thf(fact_3378_empty__subsetI,axiom,
% 5.41/5.68 ! [A2: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A2 ) ).
% 5.41/5.68
% 5.41/5.68 % empty_subsetI
% 5.41/5.68 thf(fact_3379_subset__empty,axiom,
% 5.41/5.68 ! [A2: set_nat] :
% 5.41/5.68 ( ( ord_less_eq_set_nat @ A2 @ bot_bot_set_nat )
% 5.41/5.68 = ( A2 = bot_bot_set_nat ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_empty
% 5.41/5.68 thf(fact_3380_subset__empty,axiom,
% 5.41/5.68 ! [A2: set_real] :
% 5.41/5.68 ( ( ord_less_eq_set_real @ A2 @ bot_bot_set_real )
% 5.41/5.68 = ( A2 = bot_bot_set_real ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_empty
% 5.41/5.68 thf(fact_3381_subset__empty,axiom,
% 5.41/5.68 ! [A2: set_int] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ A2 @ bot_bot_set_int )
% 5.41/5.68 = ( A2 = bot_bot_set_int ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_empty
% 5.41/5.68 thf(fact_3382_max_Obounded__iff,axiom,
% 5.41/5.68 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.41/5.68 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.41/5.68 = ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.41/5.68 & ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.bounded_iff
% 5.41/5.68 thf(fact_3383_max_Obounded__iff,axiom,
% 5.41/5.68 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.41/5.68 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.41/5.68 = ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.41/5.68 & ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.bounded_iff
% 5.41/5.68 thf(fact_3384_max_Obounded__iff,axiom,
% 5.41/5.68 ! [B: rat,C: rat,A: rat] :
% 5.41/5.68 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.41/5.68 = ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.68 & ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.bounded_iff
% 5.41/5.68 thf(fact_3385_max_Obounded__iff,axiom,
% 5.41/5.68 ! [B: num,C: num,A: num] :
% 5.41/5.68 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.41/5.68 = ( ( ord_less_eq_num @ B @ A )
% 5.41/5.68 & ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.bounded_iff
% 5.41/5.68 thf(fact_3386_max_Obounded__iff,axiom,
% 5.41/5.68 ! [B: nat,C: nat,A: nat] :
% 5.41/5.68 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.41/5.68 = ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.68 & ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.bounded_iff
% 5.41/5.68 thf(fact_3387_max_Obounded__iff,axiom,
% 5.41/5.68 ! [B: int,C: int,A: int] :
% 5.41/5.68 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.41/5.68 = ( ( ord_less_eq_int @ B @ A )
% 5.41/5.68 & ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.bounded_iff
% 5.41/5.68 thf(fact_3388_max_Oabsorb2,axiom,
% 5.41/5.68 ! [A: extended_enat,B: extended_enat] :
% 5.41/5.68 ( ( ord_le2932123472753598470d_enat @ A @ B )
% 5.41/5.68 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb2
% 5.41/5.68 thf(fact_3389_max_Oabsorb2,axiom,
% 5.41/5.68 ! [A: code_integer,B: code_integer] :
% 5.41/5.68 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.41/5.68 => ( ( ord_max_Code_integer @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb2
% 5.41/5.68 thf(fact_3390_max_Oabsorb2,axiom,
% 5.41/5.68 ! [A: rat,B: rat] :
% 5.41/5.68 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.68 => ( ( ord_max_rat @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb2
% 5.41/5.68 thf(fact_3391_max_Oabsorb2,axiom,
% 5.41/5.68 ! [A: num,B: num] :
% 5.41/5.68 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.68 => ( ( ord_max_num @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb2
% 5.41/5.68 thf(fact_3392_max_Oabsorb2,axiom,
% 5.41/5.68 ! [A: nat,B: nat] :
% 5.41/5.68 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.68 => ( ( ord_max_nat @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb2
% 5.41/5.68 thf(fact_3393_max_Oabsorb2,axiom,
% 5.41/5.68 ! [A: int,B: int] :
% 5.41/5.68 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.68 => ( ( ord_max_int @ A @ B )
% 5.41/5.68 = B ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb2
% 5.41/5.68 thf(fact_3394_max_Oabsorb1,axiom,
% 5.41/5.68 ! [B: extended_enat,A: extended_enat] :
% 5.41/5.68 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.41/5.68 => ( ( ord_ma741700101516333627d_enat @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb1
% 5.41/5.68 thf(fact_3395_max_Oabsorb1,axiom,
% 5.41/5.68 ! [B: code_integer,A: code_integer] :
% 5.41/5.68 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.41/5.68 => ( ( ord_max_Code_integer @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb1
% 5.41/5.68 thf(fact_3396_max_Oabsorb1,axiom,
% 5.41/5.68 ! [B: rat,A: rat] :
% 5.41/5.68 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.68 => ( ( ord_max_rat @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb1
% 5.41/5.68 thf(fact_3397_max_Oabsorb1,axiom,
% 5.41/5.68 ! [B: num,A: num] :
% 5.41/5.68 ( ( ord_less_eq_num @ B @ A )
% 5.41/5.68 => ( ( ord_max_num @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb1
% 5.41/5.68 thf(fact_3398_max_Oabsorb1,axiom,
% 5.41/5.68 ! [B: nat,A: nat] :
% 5.41/5.68 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.68 => ( ( ord_max_nat @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb1
% 5.41/5.68 thf(fact_3399_max_Oabsorb1,axiom,
% 5.41/5.68 ! [B: int,A: int] :
% 5.41/5.68 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.68 => ( ( ord_max_int @ A @ B )
% 5.41/5.68 = A ) ) ).
% 5.41/5.68
% 5.41/5.68 % max.absorb1
% 5.41/5.68 thf(fact_3400_atLeastatMost__empty__iff2,axiom,
% 5.41/5.68 ! [A: set_int,B: set_int] :
% 5.41/5.68 ( ( bot_bot_set_set_int
% 5.41/5.68 = ( set_or370866239135849197et_int @ A @ B ) )
% 5.41/5.68 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff2
% 5.41/5.68 thf(fact_3401_atLeastatMost__empty__iff2,axiom,
% 5.41/5.68 ! [A: rat,B: rat] :
% 5.41/5.68 ( ( bot_bot_set_rat
% 5.41/5.68 = ( set_or633870826150836451st_rat @ A @ B ) )
% 5.41/5.68 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff2
% 5.41/5.68 thf(fact_3402_atLeastatMost__empty__iff2,axiom,
% 5.41/5.68 ! [A: num,B: num] :
% 5.41/5.68 ( ( bot_bot_set_num
% 5.41/5.68 = ( set_or7049704709247886629st_num @ A @ B ) )
% 5.41/5.68 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff2
% 5.41/5.68 thf(fact_3403_atLeastatMost__empty__iff2,axiom,
% 5.41/5.68 ! [A: nat,B: nat] :
% 5.41/5.68 ( ( bot_bot_set_nat
% 5.41/5.68 = ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.41/5.68 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff2
% 5.41/5.68 thf(fact_3404_atLeastatMost__empty__iff2,axiom,
% 5.41/5.68 ! [A: int,B: int] :
% 5.41/5.68 ( ( bot_bot_set_int
% 5.41/5.68 = ( set_or1266510415728281911st_int @ A @ B ) )
% 5.41/5.68 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff2
% 5.41/5.68 thf(fact_3405_atLeastatMost__empty__iff2,axiom,
% 5.41/5.68 ! [A: real,B: real] :
% 5.41/5.68 ( ( bot_bot_set_real
% 5.41/5.68 = ( set_or1222579329274155063t_real @ A @ B ) )
% 5.41/5.68 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff2
% 5.41/5.68 thf(fact_3406_atLeastatMost__empty__iff,axiom,
% 5.41/5.68 ! [A: set_int,B: set_int] :
% 5.41/5.68 ( ( ( set_or370866239135849197et_int @ A @ B )
% 5.41/5.68 = bot_bot_set_set_int )
% 5.41/5.68 = ( ~ ( ord_less_eq_set_int @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff
% 5.41/5.68 thf(fact_3407_atLeastatMost__empty__iff,axiom,
% 5.41/5.68 ! [A: rat,B: rat] :
% 5.41/5.68 ( ( ( set_or633870826150836451st_rat @ A @ B )
% 5.41/5.68 = bot_bot_set_rat )
% 5.41/5.68 = ( ~ ( ord_less_eq_rat @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff
% 5.41/5.68 thf(fact_3408_atLeastatMost__empty__iff,axiom,
% 5.41/5.68 ! [A: num,B: num] :
% 5.41/5.68 ( ( ( set_or7049704709247886629st_num @ A @ B )
% 5.41/5.68 = bot_bot_set_num )
% 5.41/5.68 = ( ~ ( ord_less_eq_num @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff
% 5.41/5.68 thf(fact_3409_atLeastatMost__empty__iff,axiom,
% 5.41/5.68 ! [A: nat,B: nat] :
% 5.41/5.68 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.41/5.68 = bot_bot_set_nat )
% 5.41/5.68 = ( ~ ( ord_less_eq_nat @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff
% 5.41/5.68 thf(fact_3410_atLeastatMost__empty__iff,axiom,
% 5.41/5.68 ! [A: int,B: int] :
% 5.41/5.68 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.41/5.68 = bot_bot_set_int )
% 5.41/5.68 = ( ~ ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff
% 5.41/5.68 thf(fact_3411_atLeastatMost__empty__iff,axiom,
% 5.41/5.68 ! [A: real,B: real] :
% 5.41/5.68 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.41/5.68 = bot_bot_set_real )
% 5.41/5.68 = ( ~ ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty_iff
% 5.41/5.68 thf(fact_3412_atLeastatMost__empty,axiom,
% 5.41/5.68 ! [B: rat,A: rat] :
% 5.41/5.68 ( ( ord_less_rat @ B @ A )
% 5.41/5.68 => ( ( set_or633870826150836451st_rat @ A @ B )
% 5.41/5.68 = bot_bot_set_rat ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty
% 5.41/5.68 thf(fact_3413_atLeastatMost__empty,axiom,
% 5.41/5.68 ! [B: num,A: num] :
% 5.41/5.68 ( ( ord_less_num @ B @ A )
% 5.41/5.68 => ( ( set_or7049704709247886629st_num @ A @ B )
% 5.41/5.68 = bot_bot_set_num ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty
% 5.41/5.68 thf(fact_3414_atLeastatMost__empty,axiom,
% 5.41/5.68 ! [B: nat,A: nat] :
% 5.41/5.68 ( ( ord_less_nat @ B @ A )
% 5.41/5.68 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.41/5.68 = bot_bot_set_nat ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty
% 5.41/5.68 thf(fact_3415_atLeastatMost__empty,axiom,
% 5.41/5.68 ! [B: int,A: int] :
% 5.41/5.68 ( ( ord_less_int @ B @ A )
% 5.41/5.68 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.41/5.68 = bot_bot_set_int ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty
% 5.41/5.68 thf(fact_3416_atLeastatMost__empty,axiom,
% 5.41/5.68 ! [B: real,A: real] :
% 5.41/5.68 ( ( ord_less_real @ B @ A )
% 5.41/5.68 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.41/5.68 = bot_bot_set_real ) ) ).
% 5.41/5.68
% 5.41/5.68 % atLeastatMost_empty
% 5.41/5.68 thf(fact_3417_double__diff,axiom,
% 5.41/5.68 ! [A2: set_nat,B3: set_nat,C4: set_nat] :
% 5.41/5.68 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.68 => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 5.41/5.68 => ( ( minus_minus_set_nat @ B3 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.41/5.68 = A2 ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % double_diff
% 5.41/5.68 thf(fact_3418_double__diff,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.68 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.41/5.68 => ( ( minus_minus_set_int @ B3 @ ( minus_minus_set_int @ C4 @ A2 ) )
% 5.41/5.68 = A2 ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % double_diff
% 5.41/5.68 thf(fact_3419_Diff__subset,axiom,
% 5.41/5.68 ! [A2: set_nat,B3: set_nat] : ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ A2 ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_subset
% 5.41/5.68 thf(fact_3420_Diff__subset,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int] : ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ A2 ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_subset
% 5.41/5.68 thf(fact_3421_Diff__mono,axiom,
% 5.41/5.68 ! [A2: set_nat,C4: set_nat,D4: set_nat,B3: set_nat] :
% 5.41/5.68 ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.41/5.68 => ( ( ord_less_eq_set_nat @ D4 @ B3 )
% 5.41/5.68 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( minus_minus_set_nat @ C4 @ D4 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_mono
% 5.41/5.68 thf(fact_3422_Diff__mono,axiom,
% 5.41/5.68 ! [A2: set_int,C4: set_int,D4: set_int,B3: set_int] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ A2 @ C4 )
% 5.41/5.68 => ( ( ord_less_eq_set_int @ D4 @ B3 )
% 5.41/5.68 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( minus_minus_set_int @ C4 @ D4 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Diff_mono
% 5.41/5.68 thf(fact_3423_Collect__mono__iff,axiom,
% 5.41/5.68 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.41/5.68 ( ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) )
% 5.41/5.68 = ( ! [X3: product_prod_int_int] :
% 5.41/5.68 ( ( P @ X3 )
% 5.41/5.68 => ( Q @ X3 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono_iff
% 5.41/5.68 thf(fact_3424_Collect__mono__iff,axiom,
% 5.41/5.68 ! [P: complex > $o,Q: complex > $o] :
% 5.41/5.68 ( ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) )
% 5.41/5.68 = ( ! [X3: complex] :
% 5.41/5.68 ( ( P @ X3 )
% 5.41/5.68 => ( Q @ X3 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono_iff
% 5.41/5.68 thf(fact_3425_Collect__mono__iff,axiom,
% 5.41/5.68 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.41/5.68 ( ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) )
% 5.41/5.68 = ( ! [X3: set_nat] :
% 5.41/5.68 ( ( P @ X3 )
% 5.41/5.68 => ( Q @ X3 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono_iff
% 5.41/5.68 thf(fact_3426_Collect__mono__iff,axiom,
% 5.41/5.68 ! [P: nat > $o,Q: nat > $o] :
% 5.41/5.68 ( ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) )
% 5.41/5.68 = ( ! [X3: nat] :
% 5.41/5.68 ( ( P @ X3 )
% 5.41/5.68 => ( Q @ X3 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono_iff
% 5.41/5.68 thf(fact_3427_Collect__mono__iff,axiom,
% 5.41/5.68 ! [P: int > $o,Q: int > $o] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) )
% 5.41/5.68 = ( ! [X3: int] :
% 5.41/5.68 ( ( P @ X3 )
% 5.41/5.68 => ( Q @ X3 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono_iff
% 5.41/5.68 thf(fact_3428_set__eq__subset,axiom,
% 5.41/5.68 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 5.41/5.68 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.41/5.68 & ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % set_eq_subset
% 5.41/5.68 thf(fact_3429_subset__trans,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.41/5.68 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.68 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.41/5.68 => ( ord_less_eq_set_int @ A2 @ C4 ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_trans
% 5.41/5.68 thf(fact_3430_Collect__mono,axiom,
% 5.41/5.68 ! [P: product_prod_int_int > $o,Q: product_prod_int_int > $o] :
% 5.41/5.68 ( ! [X6: product_prod_int_int] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 => ( Q @ X6 ) )
% 5.41/5.68 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ P ) @ ( collec213857154873943460nt_int @ Q ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono
% 5.41/5.68 thf(fact_3431_Collect__mono,axiom,
% 5.41/5.68 ! [P: complex > $o,Q: complex > $o] :
% 5.41/5.68 ( ! [X6: complex] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 => ( Q @ X6 ) )
% 5.41/5.68 => ( ord_le211207098394363844omplex @ ( collect_complex @ P ) @ ( collect_complex @ Q ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono
% 5.41/5.68 thf(fact_3432_Collect__mono,axiom,
% 5.41/5.68 ! [P: set_nat > $o,Q: set_nat > $o] :
% 5.41/5.68 ( ! [X6: set_nat] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 => ( Q @ X6 ) )
% 5.41/5.68 => ( ord_le6893508408891458716et_nat @ ( collect_set_nat @ P ) @ ( collect_set_nat @ Q ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono
% 5.41/5.68 thf(fact_3433_Collect__mono,axiom,
% 5.41/5.68 ! [P: nat > $o,Q: nat > $o] :
% 5.41/5.68 ( ! [X6: nat] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 => ( Q @ X6 ) )
% 5.41/5.68 => ( ord_less_eq_set_nat @ ( collect_nat @ P ) @ ( collect_nat @ Q ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono
% 5.41/5.68 thf(fact_3434_Collect__mono,axiom,
% 5.41/5.68 ! [P: int > $o,Q: int > $o] :
% 5.41/5.68 ( ! [X6: int] :
% 5.41/5.68 ( ( P @ X6 )
% 5.41/5.68 => ( Q @ X6 ) )
% 5.41/5.68 => ( ord_less_eq_set_int @ ( collect_int @ P ) @ ( collect_int @ Q ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % Collect_mono
% 5.41/5.68 thf(fact_3435_subset__refl,axiom,
% 5.41/5.68 ! [A2: set_int] : ( ord_less_eq_set_int @ A2 @ A2 ) ).
% 5.41/5.68
% 5.41/5.68 % subset_refl
% 5.41/5.68 thf(fact_3436_subset__iff,axiom,
% 5.41/5.68 ( ord_le211207098394363844omplex
% 5.41/5.68 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.41/5.68 ! [T2: complex] :
% 5.41/5.68 ( ( member_complex @ T2 @ A6 )
% 5.41/5.68 => ( member_complex @ T2 @ B6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_iff
% 5.41/5.68 thf(fact_3437_subset__iff,axiom,
% 5.41/5.68 ( ord_less_eq_set_real
% 5.41/5.68 = ( ^ [A6: set_real,B6: set_real] :
% 5.41/5.68 ! [T2: real] :
% 5.41/5.68 ( ( member_real @ T2 @ A6 )
% 5.41/5.68 => ( member_real @ T2 @ B6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_iff
% 5.41/5.68 thf(fact_3438_subset__iff,axiom,
% 5.41/5.68 ( ord_le6893508408891458716et_nat
% 5.41/5.68 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.41/5.68 ! [T2: set_nat] :
% 5.41/5.68 ( ( member_set_nat @ T2 @ A6 )
% 5.41/5.68 => ( member_set_nat @ T2 @ B6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_iff
% 5.41/5.68 thf(fact_3439_subset__iff,axiom,
% 5.41/5.68 ( ord_less_eq_set_nat
% 5.41/5.68 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.41/5.68 ! [T2: nat] :
% 5.41/5.68 ( ( member_nat @ T2 @ A6 )
% 5.41/5.68 => ( member_nat @ T2 @ B6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_iff
% 5.41/5.68 thf(fact_3440_subset__iff,axiom,
% 5.41/5.68 ( ord_less_eq_set_int
% 5.41/5.68 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.68 ! [T2: int] :
% 5.41/5.68 ( ( member_int @ T2 @ A6 )
% 5.41/5.68 => ( member_int @ T2 @ B6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_iff
% 5.41/5.68 thf(fact_3441_equalityD2,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int] :
% 5.41/5.68 ( ( A2 = B3 )
% 5.41/5.68 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.41/5.68
% 5.41/5.68 % equalityD2
% 5.41/5.68 thf(fact_3442_equalityD1,axiom,
% 5.41/5.68 ! [A2: set_int,B3: set_int] :
% 5.41/5.68 ( ( A2 = B3 )
% 5.41/5.68 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.41/5.68
% 5.41/5.68 % equalityD1
% 5.41/5.68 thf(fact_3443_subset__eq,axiom,
% 5.41/5.68 ( ord_le211207098394363844omplex
% 5.41/5.68 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.41/5.68 ! [X3: complex] :
% 5.41/5.68 ( ( member_complex @ X3 @ A6 )
% 5.41/5.68 => ( member_complex @ X3 @ B6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_eq
% 5.41/5.68 thf(fact_3444_subset__eq,axiom,
% 5.41/5.68 ( ord_less_eq_set_real
% 5.41/5.68 = ( ^ [A6: set_real,B6: set_real] :
% 5.41/5.68 ! [X3: real] :
% 5.41/5.68 ( ( member_real @ X3 @ A6 )
% 5.41/5.68 => ( member_real @ X3 @ B6 ) ) ) ) ).
% 5.41/5.68
% 5.41/5.68 % subset_eq
% 5.41/5.68 thf(fact_3445_subset__eq,axiom,
% 5.41/5.68 ( ord_le6893508408891458716et_nat
% 5.41/5.68 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.41/5.68 ! [X3: set_nat] :
% 5.41/5.69 ( ( member_set_nat @ X3 @ A6 )
% 5.41/5.69 => ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subset_eq
% 5.41/5.69 thf(fact_3446_subset__eq,axiom,
% 5.41/5.69 ( ord_less_eq_set_nat
% 5.41/5.69 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.41/5.69 ! [X3: nat] :
% 5.41/5.69 ( ( member_nat @ X3 @ A6 )
% 5.41/5.69 => ( member_nat @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subset_eq
% 5.41/5.69 thf(fact_3447_subset__eq,axiom,
% 5.41/5.69 ( ord_less_eq_set_int
% 5.41/5.69 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.69 ! [X3: int] :
% 5.41/5.69 ( ( member_int @ X3 @ A6 )
% 5.41/5.69 => ( member_int @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subset_eq
% 5.41/5.69 thf(fact_3448_equalityE,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( A2 = B3 )
% 5.41/5.69 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.69 => ~ ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % equalityE
% 5.41/5.69 thf(fact_3449_subsetD,axiom,
% 5.41/5.69 ! [A2: set_complex,B3: set_complex,C: complex] :
% 5.41/5.69 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.69 => ( ( member_complex @ C @ A2 )
% 5.41/5.69 => ( member_complex @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subsetD
% 5.41/5.69 thf(fact_3450_subsetD,axiom,
% 5.41/5.69 ! [A2: set_real,B3: set_real,C: real] :
% 5.41/5.69 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.69 => ( ( member_real @ C @ A2 )
% 5.41/5.69 => ( member_real @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subsetD
% 5.41/5.69 thf(fact_3451_subsetD,axiom,
% 5.41/5.69 ! [A2: set_set_nat,B3: set_set_nat,C: set_nat] :
% 5.41/5.69 ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 5.41/5.69 => ( ( member_set_nat @ C @ A2 )
% 5.41/5.69 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subsetD
% 5.41/5.69 thf(fact_3452_subsetD,axiom,
% 5.41/5.69 ! [A2: set_nat,B3: set_nat,C: nat] :
% 5.41/5.69 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.69 => ( ( member_nat @ C @ A2 )
% 5.41/5.69 => ( member_nat @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subsetD
% 5.41/5.69 thf(fact_3453_subsetD,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int,C: int] :
% 5.41/5.69 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.69 => ( ( member_int @ C @ A2 )
% 5.41/5.69 => ( member_int @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subsetD
% 5.41/5.69 thf(fact_3454_in__mono,axiom,
% 5.41/5.69 ! [A2: set_complex,B3: set_complex,X: complex] :
% 5.41/5.69 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.69 => ( ( member_complex @ X @ A2 )
% 5.41/5.69 => ( member_complex @ X @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % in_mono
% 5.41/5.69 thf(fact_3455_in__mono,axiom,
% 5.41/5.69 ! [A2: set_real,B3: set_real,X: real] :
% 5.41/5.69 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.69 => ( ( member_real @ X @ A2 )
% 5.41/5.69 => ( member_real @ X @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % in_mono
% 5.41/5.69 thf(fact_3456_in__mono,axiom,
% 5.41/5.69 ! [A2: set_set_nat,B3: set_set_nat,X: set_nat] :
% 5.41/5.69 ( ( ord_le6893508408891458716et_nat @ A2 @ B3 )
% 5.41/5.69 => ( ( member_set_nat @ X @ A2 )
% 5.41/5.69 => ( member_set_nat @ X @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % in_mono
% 5.41/5.69 thf(fact_3457_in__mono,axiom,
% 5.41/5.69 ! [A2: set_nat,B3: set_nat,X: nat] :
% 5.41/5.69 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.69 => ( ( member_nat @ X @ A2 )
% 5.41/5.69 => ( member_nat @ X @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % in_mono
% 5.41/5.69 thf(fact_3458_in__mono,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int,X: int] :
% 5.41/5.69 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.69 => ( ( member_int @ X @ A2 )
% 5.41/5.69 => ( member_int @ X @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % in_mono
% 5.41/5.69 thf(fact_3459_psubset__imp__ex__mem,axiom,
% 5.41/5.69 ! [A2: set_complex,B3: set_complex] :
% 5.41/5.69 ( ( ord_less_set_complex @ A2 @ B3 )
% 5.41/5.69 => ? [B5: complex] : ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_imp_ex_mem
% 5.41/5.69 thf(fact_3460_psubset__imp__ex__mem,axiom,
% 5.41/5.69 ! [A2: set_real,B3: set_real] :
% 5.41/5.69 ( ( ord_less_set_real @ A2 @ B3 )
% 5.41/5.69 => ? [B5: real] : ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_imp_ex_mem
% 5.41/5.69 thf(fact_3461_psubset__imp__ex__mem,axiom,
% 5.41/5.69 ! [A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.69 ( ( ord_less_set_set_nat @ A2 @ B3 )
% 5.41/5.69 => ? [B5: set_nat] : ( member_set_nat @ B5 @ ( minus_2163939370556025621et_nat @ B3 @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_imp_ex_mem
% 5.41/5.69 thf(fact_3462_psubset__imp__ex__mem,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( ord_less_set_int @ A2 @ B3 )
% 5.41/5.69 => ? [B5: int] : ( member_int @ B5 @ ( minus_minus_set_int @ B3 @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_imp_ex_mem
% 5.41/5.69 thf(fact_3463_psubset__imp__ex__mem,axiom,
% 5.41/5.69 ! [A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( ord_less_set_nat @ A2 @ B3 )
% 5.41/5.69 => ? [B5: nat] : ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_imp_ex_mem
% 5.41/5.69 thf(fact_3464_Collect__subset,axiom,
% 5.41/5.69 ! [A2: set_real,P: real > $o] :
% 5.41/5.69 ( ord_less_eq_set_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [X3: real] :
% 5.41/5.69 ( ( member_real @ X3 @ A2 )
% 5.41/5.69 & ( P @ X3 ) ) )
% 5.41/5.69 @ A2 ) ).
% 5.41/5.69
% 5.41/5.69 % Collect_subset
% 5.41/5.69 thf(fact_3465_Collect__subset,axiom,
% 5.41/5.69 ! [A2: set_Pr958786334691620121nt_int,P: product_prod_int_int > $o] :
% 5.41/5.69 ( ord_le2843351958646193337nt_int
% 5.41/5.69 @ ( collec213857154873943460nt_int
% 5.41/5.69 @ ^ [X3: product_prod_int_int] :
% 5.41/5.69 ( ( member5262025264175285858nt_int @ X3 @ A2 )
% 5.41/5.69 & ( P @ X3 ) ) )
% 5.41/5.69 @ A2 ) ).
% 5.41/5.69
% 5.41/5.69 % Collect_subset
% 5.41/5.69 thf(fact_3466_Collect__subset,axiom,
% 5.41/5.69 ! [A2: set_complex,P: complex > $o] :
% 5.41/5.69 ( ord_le211207098394363844omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [X3: complex] :
% 5.41/5.69 ( ( member_complex @ X3 @ A2 )
% 5.41/5.69 & ( P @ X3 ) ) )
% 5.41/5.69 @ A2 ) ).
% 5.41/5.69
% 5.41/5.69 % Collect_subset
% 5.41/5.69 thf(fact_3467_Collect__subset,axiom,
% 5.41/5.69 ! [A2: set_set_nat,P: set_nat > $o] :
% 5.41/5.69 ( ord_le6893508408891458716et_nat
% 5.41/5.69 @ ( collect_set_nat
% 5.41/5.69 @ ^ [X3: set_nat] :
% 5.41/5.69 ( ( member_set_nat @ X3 @ A2 )
% 5.41/5.69 & ( P @ X3 ) ) )
% 5.41/5.69 @ A2 ) ).
% 5.41/5.69
% 5.41/5.69 % Collect_subset
% 5.41/5.69 thf(fact_3468_Collect__subset,axiom,
% 5.41/5.69 ! [A2: set_nat,P: nat > $o] :
% 5.41/5.69 ( ord_less_eq_set_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [X3: nat] :
% 5.41/5.69 ( ( member_nat @ X3 @ A2 )
% 5.41/5.69 & ( P @ X3 ) ) )
% 5.41/5.69 @ A2 ) ).
% 5.41/5.69
% 5.41/5.69 % Collect_subset
% 5.41/5.69 thf(fact_3469_Collect__subset,axiom,
% 5.41/5.69 ! [A2: set_int,P: int > $o] :
% 5.41/5.69 ( ord_less_eq_set_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [X3: int] :
% 5.41/5.69 ( ( member_int @ X3 @ A2 )
% 5.41/5.69 & ( P @ X3 ) ) )
% 5.41/5.69 @ A2 ) ).
% 5.41/5.69
% 5.41/5.69 % Collect_subset
% 5.41/5.69 thf(fact_3470_less__eq__set__def,axiom,
% 5.41/5.69 ( ord_le211207098394363844omplex
% 5.41/5.69 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.41/5.69 ( ord_le4573692005234683329plex_o
% 5.41/5.69 @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: complex] : ( member_complex @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_eq_set_def
% 5.41/5.69 thf(fact_3471_less__eq__set__def,axiom,
% 5.41/5.69 ( ord_less_eq_set_real
% 5.41/5.69 = ( ^ [A6: set_real,B6: set_real] :
% 5.41/5.69 ( ord_less_eq_real_o
% 5.41/5.69 @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: real] : ( member_real @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_eq_set_def
% 5.41/5.69 thf(fact_3472_less__eq__set__def,axiom,
% 5.41/5.69 ( ord_le6893508408891458716et_nat
% 5.41/5.69 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.41/5.69 ( ord_le3964352015994296041_nat_o
% 5.41/5.69 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_eq_set_def
% 5.41/5.69 thf(fact_3473_less__eq__set__def,axiom,
% 5.41/5.69 ( ord_less_eq_set_nat
% 5.41/5.69 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.41/5.69 ( ord_less_eq_nat_o
% 5.41/5.69 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_eq_set_def
% 5.41/5.69 thf(fact_3474_less__eq__set__def,axiom,
% 5.41/5.69 ( ord_less_eq_set_int
% 5.41/5.69 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.69 ( ord_less_eq_int_o
% 5.41/5.69 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_eq_set_def
% 5.41/5.69 thf(fact_3475_max_Omono,axiom,
% 5.41/5.69 ! [C: extended_enat,A: extended_enat,D: extended_enat,B: extended_enat] :
% 5.41/5.69 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.41/5.69 => ( ( ord_le2932123472753598470d_enat @ D @ B )
% 5.41/5.69 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ C @ D ) @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.mono
% 5.41/5.69 thf(fact_3476_max_Omono,axiom,
% 5.41/5.69 ! [C: code_integer,A: code_integer,D: code_integer,B: code_integer] :
% 5.41/5.69 ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.41/5.69 => ( ( ord_le3102999989581377725nteger @ D @ B )
% 5.41/5.69 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ C @ D ) @ ( ord_max_Code_integer @ A @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.mono
% 5.41/5.69 thf(fact_3477_max_Omono,axiom,
% 5.41/5.69 ! [C: rat,A: rat,D: rat,B: rat] :
% 5.41/5.69 ( ( ord_less_eq_rat @ C @ A )
% 5.41/5.69 => ( ( ord_less_eq_rat @ D @ B )
% 5.41/5.69 => ( ord_less_eq_rat @ ( ord_max_rat @ C @ D ) @ ( ord_max_rat @ A @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.mono
% 5.41/5.69 thf(fact_3478_max_Omono,axiom,
% 5.41/5.69 ! [C: num,A: num,D: num,B: num] :
% 5.41/5.69 ( ( ord_less_eq_num @ C @ A )
% 5.41/5.69 => ( ( ord_less_eq_num @ D @ B )
% 5.41/5.69 => ( ord_less_eq_num @ ( ord_max_num @ C @ D ) @ ( ord_max_num @ A @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.mono
% 5.41/5.69 thf(fact_3479_max_Omono,axiom,
% 5.41/5.69 ! [C: nat,A: nat,D: nat,B: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ C @ A )
% 5.41/5.69 => ( ( ord_less_eq_nat @ D @ B )
% 5.41/5.69 => ( ord_less_eq_nat @ ( ord_max_nat @ C @ D ) @ ( ord_max_nat @ A @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.mono
% 5.41/5.69 thf(fact_3480_max_Omono,axiom,
% 5.41/5.69 ! [C: int,A: int,D: int,B: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ C @ A )
% 5.41/5.69 => ( ( ord_less_eq_int @ D @ B )
% 5.41/5.69 => ( ord_less_eq_int @ ( ord_max_int @ C @ D ) @ ( ord_max_int @ A @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.mono
% 5.41/5.69 thf(fact_3481_max_OorderE,axiom,
% 5.41/5.69 ! [B: extended_enat,A: extended_enat] :
% 5.41/5.69 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.41/5.69 => ( A
% 5.41/5.69 = ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderE
% 5.41/5.69 thf(fact_3482_max_OorderE,axiom,
% 5.41/5.69 ! [B: code_integer,A: code_integer] :
% 5.41/5.69 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.41/5.69 => ( A
% 5.41/5.69 = ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderE
% 5.41/5.69 thf(fact_3483_max_OorderE,axiom,
% 5.41/5.69 ! [B: rat,A: rat] :
% 5.41/5.69 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.69 => ( A
% 5.41/5.69 = ( ord_max_rat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderE
% 5.41/5.69 thf(fact_3484_max_OorderE,axiom,
% 5.41/5.69 ! [B: num,A: num] :
% 5.41/5.69 ( ( ord_less_eq_num @ B @ A )
% 5.41/5.69 => ( A
% 5.41/5.69 = ( ord_max_num @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderE
% 5.41/5.69 thf(fact_3485_max_OorderE,axiom,
% 5.41/5.69 ! [B: nat,A: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.69 => ( A
% 5.41/5.69 = ( ord_max_nat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderE
% 5.41/5.69 thf(fact_3486_max_OorderE,axiom,
% 5.41/5.69 ! [B: int,A: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.69 => ( A
% 5.41/5.69 = ( ord_max_int @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderE
% 5.41/5.69 thf(fact_3487_max_OorderI,axiom,
% 5.41/5.69 ! [A: extended_enat,B: extended_enat] :
% 5.41/5.69 ( ( A
% 5.41/5.69 = ( ord_ma741700101516333627d_enat @ A @ B ) )
% 5.41/5.69 => ( ord_le2932123472753598470d_enat @ B @ A ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderI
% 5.41/5.69 thf(fact_3488_max_OorderI,axiom,
% 5.41/5.69 ! [A: code_integer,B: code_integer] :
% 5.41/5.69 ( ( A
% 5.41/5.69 = ( ord_max_Code_integer @ A @ B ) )
% 5.41/5.69 => ( ord_le3102999989581377725nteger @ B @ A ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderI
% 5.41/5.69 thf(fact_3489_max_OorderI,axiom,
% 5.41/5.69 ! [A: rat,B: rat] :
% 5.41/5.69 ( ( A
% 5.41/5.69 = ( ord_max_rat @ A @ B ) )
% 5.41/5.69 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderI
% 5.41/5.69 thf(fact_3490_max_OorderI,axiom,
% 5.41/5.69 ! [A: num,B: num] :
% 5.41/5.69 ( ( A
% 5.41/5.69 = ( ord_max_num @ A @ B ) )
% 5.41/5.69 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderI
% 5.41/5.69 thf(fact_3491_max_OorderI,axiom,
% 5.41/5.69 ! [A: nat,B: nat] :
% 5.41/5.69 ( ( A
% 5.41/5.69 = ( ord_max_nat @ A @ B ) )
% 5.41/5.69 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderI
% 5.41/5.69 thf(fact_3492_max_OorderI,axiom,
% 5.41/5.69 ! [A: int,B: int] :
% 5.41/5.69 ( ( A
% 5.41/5.69 = ( ord_max_int @ A @ B ) )
% 5.41/5.69 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.orderI
% 5.41/5.69 thf(fact_3493_max_OboundedE,axiom,
% 5.41/5.69 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.41/5.69 ( ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.41/5.69 => ~ ( ord_le2932123472753598470d_enat @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedE
% 5.41/5.69 thf(fact_3494_max_OboundedE,axiom,
% 5.41/5.69 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.41/5.69 ( ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.41/5.69 => ~ ( ord_le3102999989581377725nteger @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedE
% 5.41/5.69 thf(fact_3495_max_OboundedE,axiom,
% 5.41/5.69 ! [B: rat,C: rat,A: rat] :
% 5.41/5.69 ( ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.69 => ~ ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedE
% 5.41/5.69 thf(fact_3496_max_OboundedE,axiom,
% 5.41/5.69 ! [B: num,C: num,A: num] :
% 5.41/5.69 ( ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_eq_num @ B @ A )
% 5.41/5.69 => ~ ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedE
% 5.41/5.69 thf(fact_3497_max_OboundedE,axiom,
% 5.41/5.69 ! [B: nat,C: nat,A: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.69 => ~ ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedE
% 5.41/5.69 thf(fact_3498_max_OboundedE,axiom,
% 5.41/5.69 ! [B: int,C: int,A: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_eq_int @ B @ A )
% 5.41/5.69 => ~ ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedE
% 5.41/5.69 thf(fact_3499_max_OboundedI,axiom,
% 5.41/5.69 ! [B: extended_enat,A: extended_enat,C: extended_enat] :
% 5.41/5.69 ( ( ord_le2932123472753598470d_enat @ B @ A )
% 5.41/5.69 => ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.41/5.69 => ( ord_le2932123472753598470d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedI
% 5.41/5.69 thf(fact_3500_max_OboundedI,axiom,
% 5.41/5.69 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.69 ( ( ord_le3102999989581377725nteger @ B @ A )
% 5.41/5.69 => ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.41/5.69 => ( ord_le3102999989581377725nteger @ ( ord_max_Code_integer @ B @ C ) @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedI
% 5.41/5.69 thf(fact_3501_max_OboundedI,axiom,
% 5.41/5.69 ! [B: rat,A: rat,C: rat] :
% 5.41/5.69 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.69 => ( ( ord_less_eq_rat @ C @ A )
% 5.41/5.69 => ( ord_less_eq_rat @ ( ord_max_rat @ B @ C ) @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedI
% 5.41/5.69 thf(fact_3502_max_OboundedI,axiom,
% 5.41/5.69 ! [B: num,A: num,C: num] :
% 5.41/5.69 ( ( ord_less_eq_num @ B @ A )
% 5.41/5.69 => ( ( ord_less_eq_num @ C @ A )
% 5.41/5.69 => ( ord_less_eq_num @ ( ord_max_num @ B @ C ) @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedI
% 5.41/5.69 thf(fact_3503_max_OboundedI,axiom,
% 5.41/5.69 ! [B: nat,A: nat,C: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.69 => ( ( ord_less_eq_nat @ C @ A )
% 5.41/5.69 => ( ord_less_eq_nat @ ( ord_max_nat @ B @ C ) @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedI
% 5.41/5.69 thf(fact_3504_max_OboundedI,axiom,
% 5.41/5.69 ! [B: int,A: int,C: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.69 => ( ( ord_less_eq_int @ C @ A )
% 5.41/5.69 => ( ord_less_eq_int @ ( ord_max_int @ B @ C ) @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.boundedI
% 5.41/5.69 thf(fact_3505_max_Oorder__iff,axiom,
% 5.41/5.69 ( ord_le2932123472753598470d_enat
% 5.41/5.69 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.41/5.69 ( A3
% 5.41/5.69 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.order_iff
% 5.41/5.69 thf(fact_3506_max_Oorder__iff,axiom,
% 5.41/5.69 ( ord_le3102999989581377725nteger
% 5.41/5.69 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.41/5.69 ( A3
% 5.41/5.69 = ( ord_max_Code_integer @ A3 @ B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.order_iff
% 5.41/5.69 thf(fact_3507_max_Oorder__iff,axiom,
% 5.41/5.69 ( ord_less_eq_rat
% 5.41/5.69 = ( ^ [B2: rat,A3: rat] :
% 5.41/5.69 ( A3
% 5.41/5.69 = ( ord_max_rat @ A3 @ B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.order_iff
% 5.41/5.69 thf(fact_3508_max_Oorder__iff,axiom,
% 5.41/5.69 ( ord_less_eq_num
% 5.41/5.69 = ( ^ [B2: num,A3: num] :
% 5.41/5.69 ( A3
% 5.41/5.69 = ( ord_max_num @ A3 @ B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.order_iff
% 5.41/5.69 thf(fact_3509_max_Oorder__iff,axiom,
% 5.41/5.69 ( ord_less_eq_nat
% 5.41/5.69 = ( ^ [B2: nat,A3: nat] :
% 5.41/5.69 ( A3
% 5.41/5.69 = ( ord_max_nat @ A3 @ B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.order_iff
% 5.41/5.69 thf(fact_3510_max_Oorder__iff,axiom,
% 5.41/5.69 ( ord_less_eq_int
% 5.41/5.69 = ( ^ [B2: int,A3: int] :
% 5.41/5.69 ( A3
% 5.41/5.69 = ( ord_max_int @ A3 @ B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.order_iff
% 5.41/5.69 thf(fact_3511_max_Ocobounded1,axiom,
% 5.41/5.69 ! [A: extended_enat,B: extended_enat] : ( ord_le2932123472753598470d_enat @ A @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded1
% 5.41/5.69 thf(fact_3512_max_Ocobounded1,axiom,
% 5.41/5.69 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( ord_max_Code_integer @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded1
% 5.41/5.69 thf(fact_3513_max_Ocobounded1,axiom,
% 5.41/5.69 ! [A: rat,B: rat] : ( ord_less_eq_rat @ A @ ( ord_max_rat @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded1
% 5.41/5.69 thf(fact_3514_max_Ocobounded1,axiom,
% 5.41/5.69 ! [A: num,B: num] : ( ord_less_eq_num @ A @ ( ord_max_num @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded1
% 5.41/5.69 thf(fact_3515_max_Ocobounded1,axiom,
% 5.41/5.69 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( ord_max_nat @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded1
% 5.41/5.69 thf(fact_3516_max_Ocobounded1,axiom,
% 5.41/5.69 ! [A: int,B: int] : ( ord_less_eq_int @ A @ ( ord_max_int @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded1
% 5.41/5.69 thf(fact_3517_max_Ocobounded2,axiom,
% 5.41/5.69 ! [B: extended_enat,A: extended_enat] : ( ord_le2932123472753598470d_enat @ B @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded2
% 5.41/5.69 thf(fact_3518_max_Ocobounded2,axiom,
% 5.41/5.69 ! [B: code_integer,A: code_integer] : ( ord_le3102999989581377725nteger @ B @ ( ord_max_Code_integer @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded2
% 5.41/5.69 thf(fact_3519_max_Ocobounded2,axiom,
% 5.41/5.69 ! [B: rat,A: rat] : ( ord_less_eq_rat @ B @ ( ord_max_rat @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded2
% 5.41/5.69 thf(fact_3520_max_Ocobounded2,axiom,
% 5.41/5.69 ! [B: num,A: num] : ( ord_less_eq_num @ B @ ( ord_max_num @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded2
% 5.41/5.69 thf(fact_3521_max_Ocobounded2,axiom,
% 5.41/5.69 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( ord_max_nat @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded2
% 5.41/5.69 thf(fact_3522_max_Ocobounded2,axiom,
% 5.41/5.69 ! [B: int,A: int] : ( ord_less_eq_int @ B @ ( ord_max_int @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.cobounded2
% 5.41/5.69 thf(fact_3523_le__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.41/5.69 ( ( ord_le2932123472753598470d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.41/5.69 = ( ( ord_le2932123472753598470d_enat @ Z @ X )
% 5.41/5.69 | ( ord_le2932123472753598470d_enat @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % le_max_iff_disj
% 5.41/5.69 thf(fact_3524_le__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.41/5.69 ( ( ord_le3102999989581377725nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 5.41/5.69 = ( ( ord_le3102999989581377725nteger @ Z @ X )
% 5.41/5.69 | ( ord_le3102999989581377725nteger @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % le_max_iff_disj
% 5.41/5.69 thf(fact_3525_le__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.69 ( ( ord_less_eq_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_eq_rat @ Z @ X )
% 5.41/5.69 | ( ord_less_eq_rat @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % le_max_iff_disj
% 5.41/5.69 thf(fact_3526_le__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: num,X: num,Y: num] :
% 5.41/5.69 ( ( ord_less_eq_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_eq_num @ Z @ X )
% 5.41/5.69 | ( ord_less_eq_num @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % le_max_iff_disj
% 5.41/5.69 thf(fact_3527_le__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: nat,X: nat,Y: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_eq_nat @ Z @ X )
% 5.41/5.69 | ( ord_less_eq_nat @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % le_max_iff_disj
% 5.41/5.69 thf(fact_3528_le__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: int,X: int,Y: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_eq_int @ Z @ X )
% 5.41/5.69 | ( ord_less_eq_int @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % le_max_iff_disj
% 5.41/5.69 thf(fact_3529_max_Oabsorb__iff1,axiom,
% 5.41/5.69 ( ord_le2932123472753598470d_enat
% 5.41/5.69 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.41/5.69 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.41/5.69 = A3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff1
% 5.41/5.69 thf(fact_3530_max_Oabsorb__iff1,axiom,
% 5.41/5.69 ( ord_le3102999989581377725nteger
% 5.41/5.69 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.41/5.69 ( ( ord_max_Code_integer @ A3 @ B2 )
% 5.41/5.69 = A3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff1
% 5.41/5.69 thf(fact_3531_max_Oabsorb__iff1,axiom,
% 5.41/5.69 ( ord_less_eq_rat
% 5.41/5.69 = ( ^ [B2: rat,A3: rat] :
% 5.41/5.69 ( ( ord_max_rat @ A3 @ B2 )
% 5.41/5.69 = A3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff1
% 5.41/5.69 thf(fact_3532_max_Oabsorb__iff1,axiom,
% 5.41/5.69 ( ord_less_eq_num
% 5.41/5.69 = ( ^ [B2: num,A3: num] :
% 5.41/5.69 ( ( ord_max_num @ A3 @ B2 )
% 5.41/5.69 = A3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff1
% 5.41/5.69 thf(fact_3533_max_Oabsorb__iff1,axiom,
% 5.41/5.69 ( ord_less_eq_nat
% 5.41/5.69 = ( ^ [B2: nat,A3: nat] :
% 5.41/5.69 ( ( ord_max_nat @ A3 @ B2 )
% 5.41/5.69 = A3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff1
% 5.41/5.69 thf(fact_3534_max_Oabsorb__iff1,axiom,
% 5.41/5.69 ( ord_less_eq_int
% 5.41/5.69 = ( ^ [B2: int,A3: int] :
% 5.41/5.69 ( ( ord_max_int @ A3 @ B2 )
% 5.41/5.69 = A3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff1
% 5.41/5.69 thf(fact_3535_max_Oabsorb__iff2,axiom,
% 5.41/5.69 ( ord_le2932123472753598470d_enat
% 5.41/5.69 = ( ^ [A3: extended_enat,B2: extended_enat] :
% 5.41/5.69 ( ( ord_ma741700101516333627d_enat @ A3 @ B2 )
% 5.41/5.69 = B2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff2
% 5.41/5.69 thf(fact_3536_max_Oabsorb__iff2,axiom,
% 5.41/5.69 ( ord_le3102999989581377725nteger
% 5.41/5.69 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.41/5.69 ( ( ord_max_Code_integer @ A3 @ B2 )
% 5.41/5.69 = B2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff2
% 5.41/5.69 thf(fact_3537_max_Oabsorb__iff2,axiom,
% 5.41/5.69 ( ord_less_eq_rat
% 5.41/5.69 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.69 ( ( ord_max_rat @ A3 @ B2 )
% 5.41/5.69 = B2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff2
% 5.41/5.69 thf(fact_3538_max_Oabsorb__iff2,axiom,
% 5.41/5.69 ( ord_less_eq_num
% 5.41/5.69 = ( ^ [A3: num,B2: num] :
% 5.41/5.69 ( ( ord_max_num @ A3 @ B2 )
% 5.41/5.69 = B2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff2
% 5.41/5.69 thf(fact_3539_max_Oabsorb__iff2,axiom,
% 5.41/5.69 ( ord_less_eq_nat
% 5.41/5.69 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.69 ( ( ord_max_nat @ A3 @ B2 )
% 5.41/5.69 = B2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff2
% 5.41/5.69 thf(fact_3540_max_Oabsorb__iff2,axiom,
% 5.41/5.69 ( ord_less_eq_int
% 5.41/5.69 = ( ^ [A3: int,B2: int] :
% 5.41/5.69 ( ( ord_max_int @ A3 @ B2 )
% 5.41/5.69 = B2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.absorb_iff2
% 5.41/5.69 thf(fact_3541_max_OcoboundedI1,axiom,
% 5.41/5.69 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.41/5.69 ( ( ord_le2932123472753598470d_enat @ C @ A )
% 5.41/5.69 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI1
% 5.41/5.69 thf(fact_3542_max_OcoboundedI1,axiom,
% 5.41/5.69 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.69 ( ( ord_le3102999989581377725nteger @ C @ A )
% 5.41/5.69 => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI1
% 5.41/5.69 thf(fact_3543_max_OcoboundedI1,axiom,
% 5.41/5.69 ! [C: rat,A: rat,B: rat] :
% 5.41/5.69 ( ( ord_less_eq_rat @ C @ A )
% 5.41/5.69 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI1
% 5.41/5.69 thf(fact_3544_max_OcoboundedI1,axiom,
% 5.41/5.69 ! [C: num,A: num,B: num] :
% 5.41/5.69 ( ( ord_less_eq_num @ C @ A )
% 5.41/5.69 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI1
% 5.41/5.69 thf(fact_3545_max_OcoboundedI1,axiom,
% 5.41/5.69 ! [C: nat,A: nat,B: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ C @ A )
% 5.41/5.69 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI1
% 5.41/5.69 thf(fact_3546_max_OcoboundedI1,axiom,
% 5.41/5.69 ! [C: int,A: int,B: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ C @ A )
% 5.41/5.69 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI1
% 5.41/5.69 thf(fact_3547_max_OcoboundedI2,axiom,
% 5.41/5.69 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.41/5.69 ( ( ord_le2932123472753598470d_enat @ C @ B )
% 5.41/5.69 => ( ord_le2932123472753598470d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI2
% 5.41/5.69 thf(fact_3548_max_OcoboundedI2,axiom,
% 5.41/5.69 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.69 ( ( ord_le3102999989581377725nteger @ C @ B )
% 5.41/5.69 => ( ord_le3102999989581377725nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI2
% 5.41/5.69 thf(fact_3549_max_OcoboundedI2,axiom,
% 5.41/5.69 ! [C: rat,B: rat,A: rat] :
% 5.41/5.69 ( ( ord_less_eq_rat @ C @ B )
% 5.41/5.69 => ( ord_less_eq_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI2
% 5.41/5.69 thf(fact_3550_max_OcoboundedI2,axiom,
% 5.41/5.69 ! [C: num,B: num,A: num] :
% 5.41/5.69 ( ( ord_less_eq_num @ C @ B )
% 5.41/5.69 => ( ord_less_eq_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI2
% 5.41/5.69 thf(fact_3551_max_OcoboundedI2,axiom,
% 5.41/5.69 ! [C: nat,B: nat,A: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ C @ B )
% 5.41/5.69 => ( ord_less_eq_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI2
% 5.41/5.69 thf(fact_3552_max_OcoboundedI2,axiom,
% 5.41/5.69 ! [C: int,B: int,A: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ C @ B )
% 5.41/5.69 => ( ord_less_eq_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.coboundedI2
% 5.41/5.69 thf(fact_3553_less__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: extended_enat,X: extended_enat,Y: extended_enat] :
% 5.41/5.69 ( ( ord_le72135733267957522d_enat @ Z @ ( ord_ma741700101516333627d_enat @ X @ Y ) )
% 5.41/5.69 = ( ( ord_le72135733267957522d_enat @ Z @ X )
% 5.41/5.69 | ( ord_le72135733267957522d_enat @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_max_iff_disj
% 5.41/5.69 thf(fact_3554_less__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: code_integer,X: code_integer,Y: code_integer] :
% 5.41/5.69 ( ( ord_le6747313008572928689nteger @ Z @ ( ord_max_Code_integer @ X @ Y ) )
% 5.41/5.69 = ( ( ord_le6747313008572928689nteger @ Z @ X )
% 5.41/5.69 | ( ord_le6747313008572928689nteger @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_max_iff_disj
% 5.41/5.69 thf(fact_3555_less__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: real,X: real,Y: real] :
% 5.41/5.69 ( ( ord_less_real @ Z @ ( ord_max_real @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_real @ Z @ X )
% 5.41/5.69 | ( ord_less_real @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_max_iff_disj
% 5.41/5.69 thf(fact_3556_less__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.69 ( ( ord_less_rat @ Z @ ( ord_max_rat @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_rat @ Z @ X )
% 5.41/5.69 | ( ord_less_rat @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_max_iff_disj
% 5.41/5.69 thf(fact_3557_less__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: num,X: num,Y: num] :
% 5.41/5.69 ( ( ord_less_num @ Z @ ( ord_max_num @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_num @ Z @ X )
% 5.41/5.69 | ( ord_less_num @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_max_iff_disj
% 5.41/5.69 thf(fact_3558_less__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: nat,X: nat,Y: nat] :
% 5.41/5.69 ( ( ord_less_nat @ Z @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_nat @ Z @ X )
% 5.41/5.69 | ( ord_less_nat @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_max_iff_disj
% 5.41/5.69 thf(fact_3559_less__max__iff__disj,axiom,
% 5.41/5.69 ! [Z: int,X: int,Y: int] :
% 5.41/5.69 ( ( ord_less_int @ Z @ ( ord_max_int @ X @ Y ) )
% 5.41/5.69 = ( ( ord_less_int @ Z @ X )
% 5.41/5.69 | ( ord_less_int @ Z @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % less_max_iff_disj
% 5.41/5.69 thf(fact_3560_max_Ostrict__boundedE,axiom,
% 5.41/5.69 ! [B: extended_enat,C: extended_enat,A: extended_enat] :
% 5.41/5.69 ( ( ord_le72135733267957522d_enat @ ( ord_ma741700101516333627d_enat @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_le72135733267957522d_enat @ B @ A )
% 5.41/5.69 => ~ ( ord_le72135733267957522d_enat @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_boundedE
% 5.41/5.69 thf(fact_3561_max_Ostrict__boundedE,axiom,
% 5.41/5.69 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.41/5.69 ( ( ord_le6747313008572928689nteger @ ( ord_max_Code_integer @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_le6747313008572928689nteger @ B @ A )
% 5.41/5.69 => ~ ( ord_le6747313008572928689nteger @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_boundedE
% 5.41/5.69 thf(fact_3562_max_Ostrict__boundedE,axiom,
% 5.41/5.69 ! [B: real,C: real,A: real] :
% 5.41/5.69 ( ( ord_less_real @ ( ord_max_real @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_real @ B @ A )
% 5.41/5.69 => ~ ( ord_less_real @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_boundedE
% 5.41/5.69 thf(fact_3563_max_Ostrict__boundedE,axiom,
% 5.41/5.69 ! [B: rat,C: rat,A: rat] :
% 5.41/5.69 ( ( ord_less_rat @ ( ord_max_rat @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_rat @ B @ A )
% 5.41/5.69 => ~ ( ord_less_rat @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_boundedE
% 5.41/5.69 thf(fact_3564_max_Ostrict__boundedE,axiom,
% 5.41/5.69 ! [B: num,C: num,A: num] :
% 5.41/5.69 ( ( ord_less_num @ ( ord_max_num @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_num @ B @ A )
% 5.41/5.69 => ~ ( ord_less_num @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_boundedE
% 5.41/5.69 thf(fact_3565_max_Ostrict__boundedE,axiom,
% 5.41/5.69 ! [B: nat,C: nat,A: nat] :
% 5.41/5.69 ( ( ord_less_nat @ ( ord_max_nat @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_nat @ B @ A )
% 5.41/5.69 => ~ ( ord_less_nat @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_boundedE
% 5.41/5.69 thf(fact_3566_max_Ostrict__boundedE,axiom,
% 5.41/5.69 ! [B: int,C: int,A: int] :
% 5.41/5.69 ( ( ord_less_int @ ( ord_max_int @ B @ C ) @ A )
% 5.41/5.69 => ~ ( ( ord_less_int @ B @ A )
% 5.41/5.69 => ~ ( ord_less_int @ C @ A ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_boundedE
% 5.41/5.69 thf(fact_3567_max_Ostrict__order__iff,axiom,
% 5.41/5.69 ( ord_le72135733267957522d_enat
% 5.41/5.69 = ( ^ [B2: extended_enat,A3: extended_enat] :
% 5.41/5.69 ( ( A3
% 5.41/5.69 = ( ord_ma741700101516333627d_enat @ A3 @ B2 ) )
% 5.41/5.69 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_order_iff
% 5.41/5.69 thf(fact_3568_max_Ostrict__order__iff,axiom,
% 5.41/5.69 ( ord_le6747313008572928689nteger
% 5.41/5.69 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.41/5.69 ( ( A3
% 5.41/5.69 = ( ord_max_Code_integer @ A3 @ B2 ) )
% 5.41/5.69 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_order_iff
% 5.41/5.69 thf(fact_3569_max_Ostrict__order__iff,axiom,
% 5.41/5.69 ( ord_less_real
% 5.41/5.69 = ( ^ [B2: real,A3: real] :
% 5.41/5.69 ( ( A3
% 5.41/5.69 = ( ord_max_real @ A3 @ B2 ) )
% 5.41/5.69 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_order_iff
% 5.41/5.69 thf(fact_3570_max_Ostrict__order__iff,axiom,
% 5.41/5.69 ( ord_less_rat
% 5.41/5.69 = ( ^ [B2: rat,A3: rat] :
% 5.41/5.69 ( ( A3
% 5.41/5.69 = ( ord_max_rat @ A3 @ B2 ) )
% 5.41/5.69 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_order_iff
% 5.41/5.69 thf(fact_3571_max_Ostrict__order__iff,axiom,
% 5.41/5.69 ( ord_less_num
% 5.41/5.69 = ( ^ [B2: num,A3: num] :
% 5.41/5.69 ( ( A3
% 5.41/5.69 = ( ord_max_num @ A3 @ B2 ) )
% 5.41/5.69 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_order_iff
% 5.41/5.69 thf(fact_3572_max_Ostrict__order__iff,axiom,
% 5.41/5.69 ( ord_less_nat
% 5.41/5.69 = ( ^ [B2: nat,A3: nat] :
% 5.41/5.69 ( ( A3
% 5.41/5.69 = ( ord_max_nat @ A3 @ B2 ) )
% 5.41/5.69 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_order_iff
% 5.41/5.69 thf(fact_3573_max_Ostrict__order__iff,axiom,
% 5.41/5.69 ( ord_less_int
% 5.41/5.69 = ( ^ [B2: int,A3: int] :
% 5.41/5.69 ( ( A3
% 5.41/5.69 = ( ord_max_int @ A3 @ B2 ) )
% 5.41/5.69 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_order_iff
% 5.41/5.69 thf(fact_3574_max_Ostrict__coboundedI1,axiom,
% 5.41/5.69 ! [C: extended_enat,A: extended_enat,B: extended_enat] :
% 5.41/5.69 ( ( ord_le72135733267957522d_enat @ C @ A )
% 5.41/5.69 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI1
% 5.41/5.69 thf(fact_3575_max_Ostrict__coboundedI1,axiom,
% 5.41/5.69 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.69 ( ( ord_le6747313008572928689nteger @ C @ A )
% 5.41/5.69 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI1
% 5.41/5.69 thf(fact_3576_max_Ostrict__coboundedI1,axiom,
% 5.41/5.69 ! [C: real,A: real,B: real] :
% 5.41/5.69 ( ( ord_less_real @ C @ A )
% 5.41/5.69 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI1
% 5.41/5.69 thf(fact_3577_max_Ostrict__coboundedI1,axiom,
% 5.41/5.69 ! [C: rat,A: rat,B: rat] :
% 5.41/5.69 ( ( ord_less_rat @ C @ A )
% 5.41/5.69 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI1
% 5.41/5.69 thf(fact_3578_max_Ostrict__coboundedI1,axiom,
% 5.41/5.69 ! [C: num,A: num,B: num] :
% 5.41/5.69 ( ( ord_less_num @ C @ A )
% 5.41/5.69 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI1
% 5.41/5.69 thf(fact_3579_max_Ostrict__coboundedI1,axiom,
% 5.41/5.69 ! [C: nat,A: nat,B: nat] :
% 5.41/5.69 ( ( ord_less_nat @ C @ A )
% 5.41/5.69 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI1
% 5.41/5.69 thf(fact_3580_max_Ostrict__coboundedI1,axiom,
% 5.41/5.69 ! [C: int,A: int,B: int] :
% 5.41/5.69 ( ( ord_less_int @ C @ A )
% 5.41/5.69 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI1
% 5.41/5.69 thf(fact_3581_max_Ostrict__coboundedI2,axiom,
% 5.41/5.69 ! [C: extended_enat,B: extended_enat,A: extended_enat] :
% 5.41/5.69 ( ( ord_le72135733267957522d_enat @ C @ B )
% 5.41/5.69 => ( ord_le72135733267957522d_enat @ C @ ( ord_ma741700101516333627d_enat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI2
% 5.41/5.69 thf(fact_3582_max_Ostrict__coboundedI2,axiom,
% 5.41/5.69 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.69 ( ( ord_le6747313008572928689nteger @ C @ B )
% 5.41/5.69 => ( ord_le6747313008572928689nteger @ C @ ( ord_max_Code_integer @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI2
% 5.41/5.69 thf(fact_3583_max_Ostrict__coboundedI2,axiom,
% 5.41/5.69 ! [C: real,B: real,A: real] :
% 5.41/5.69 ( ( ord_less_real @ C @ B )
% 5.41/5.69 => ( ord_less_real @ C @ ( ord_max_real @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI2
% 5.41/5.69 thf(fact_3584_max_Ostrict__coboundedI2,axiom,
% 5.41/5.69 ! [C: rat,B: rat,A: rat] :
% 5.41/5.69 ( ( ord_less_rat @ C @ B )
% 5.41/5.69 => ( ord_less_rat @ C @ ( ord_max_rat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI2
% 5.41/5.69 thf(fact_3585_max_Ostrict__coboundedI2,axiom,
% 5.41/5.69 ! [C: num,B: num,A: num] :
% 5.41/5.69 ( ( ord_less_num @ C @ B )
% 5.41/5.69 => ( ord_less_num @ C @ ( ord_max_num @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI2
% 5.41/5.69 thf(fact_3586_max_Ostrict__coboundedI2,axiom,
% 5.41/5.69 ! [C: nat,B: nat,A: nat] :
% 5.41/5.69 ( ( ord_less_nat @ C @ B )
% 5.41/5.69 => ( ord_less_nat @ C @ ( ord_max_nat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI2
% 5.41/5.69 thf(fact_3587_max_Ostrict__coboundedI2,axiom,
% 5.41/5.69 ! [C: int,B: int,A: int] :
% 5.41/5.69 ( ( ord_less_int @ C @ B )
% 5.41/5.69 => ( ord_less_int @ C @ ( ord_max_int @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % max.strict_coboundedI2
% 5.41/5.69 thf(fact_3588_psubsetE,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( ord_less_set_int @ A2 @ B3 )
% 5.41/5.69 => ~ ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.69 => ( ord_less_eq_set_int @ B3 @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubsetE
% 5.41/5.69 thf(fact_3589_psubset__eq,axiom,
% 5.41/5.69 ( ord_less_set_int
% 5.41/5.69 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.69 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.41/5.69 & ( A6 != B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_eq
% 5.41/5.69 thf(fact_3590_psubset__imp__subset,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( ord_less_set_int @ A2 @ B3 )
% 5.41/5.69 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_imp_subset
% 5.41/5.69 thf(fact_3591_psubset__subset__trans,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.41/5.69 ( ( ord_less_set_int @ A2 @ B3 )
% 5.41/5.69 => ( ( ord_less_eq_set_int @ B3 @ C4 )
% 5.41/5.69 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % psubset_subset_trans
% 5.41/5.69 thf(fact_3592_subset__not__subset__eq,axiom,
% 5.41/5.69 ( ord_less_set_int
% 5.41/5.69 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.69 ( ( ord_less_eq_set_int @ A6 @ B6 )
% 5.41/5.69 & ~ ( ord_less_eq_set_int @ B6 @ A6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subset_not_subset_eq
% 5.41/5.69 thf(fact_3593_subset__psubset__trans,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int,C4: set_int] :
% 5.41/5.69 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.69 => ( ( ord_less_set_int @ B3 @ C4 )
% 5.41/5.69 => ( ord_less_set_int @ A2 @ C4 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subset_psubset_trans
% 5.41/5.69 thf(fact_3594_subset__iff__psubset__eq,axiom,
% 5.41/5.69 ( ord_less_eq_set_int
% 5.41/5.69 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.69 ( ( ord_less_set_int @ A6 @ B6 )
% 5.41/5.69 | ( A6 = B6 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % subset_iff_psubset_eq
% 5.41/5.69 thf(fact_3595_vebt__delete_Opelims,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.41/5.69 ( ( ( vEBT_vebt_delete @ X @ Xa2 )
% 5.41/5.69 = Y )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Leaf @ $false @ B5 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ zero_zero_nat ) ) ) ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( Xa2
% 5.41/5.69 = ( suc @ zero_zero_nat ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ $false ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ zero_zero_nat ) ) ) ) ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ! [N3: nat] :
% 5.41/5.69 ( ( Xa2
% 5.41/5.69 = ( suc @ ( suc @ N3 ) ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ ( suc @ ( suc @ N3 ) ) ) ) ) ) )
% 5.41/5.69 => ( ! [Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,TrLst2: list_VEBT_VEBT,Smry2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ TrLst2 @ Smry2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,Tr2: list_VEBT_VEBT,Sm2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ zero_zero_nat ) @ Tr2 @ Sm2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ( ( ( ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.41/5.69 => ( Y
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.41/5.69 & ( ~ ( ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 | ( ord_less_nat @ Ma2 @ Xa2 ) )
% 5.41/5.69 => ( ( ( ( Xa2 = Mi2 )
% 5.41/5.69 & ( Xa2 = Ma2 ) )
% 5.41/5.69 => ( Y
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.41/5.69 & ( ~ ( ( Xa2 = Mi2 )
% 5.41/5.69 & ( Xa2 = Ma2 ) )
% 5.41/5.69 => ( Y
% 5.41/5.69 = ( if_VEBT_VEBT @ ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 @ ( vEBT_Node
% 5.41/5.69 @ ( some_P7363390416028606310at_nat
% 5.41/5.69 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.41/5.69 @ ( if_nat
% 5.41/5.69 @ ( ( ( Xa2 = Mi2 )
% 5.41/5.69 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.41/5.69 = Ma2 ) )
% 5.41/5.69 & ( ( Xa2 != Mi2 )
% 5.41/5.69 => ( Xa2 = Ma2 ) ) )
% 5.41/5.69 @ ( if_nat
% 5.41/5.69 @ ( ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 = none_nat )
% 5.41/5.69 @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.41/5.69 @ ( plus_plus_nat @ ( times_times_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.69 @ Ma2 ) ) )
% 5.41/5.69 @ ( suc @ ( suc @ Va2 ) )
% 5.41/5.69 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 @ ( vEBT_vebt_delete @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 @ ( vEBT_Node
% 5.41/5.69 @ ( some_P7363390416028606310at_nat
% 5.41/5.69 @ ( product_Pair_nat_nat @ ( if_nat @ ( Xa2 = Mi2 ) @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ Mi2 )
% 5.41/5.69 @ ( if_nat
% 5.41/5.69 @ ( ( ( Xa2 = Mi2 )
% 5.41/5.69 => ( ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) )
% 5.41/5.69 = Ma2 ) )
% 5.41/5.69 & ( ( Xa2 != Mi2 )
% 5.41/5.69 => ( Xa2 = Ma2 ) ) )
% 5.41/5.69 @ ( plus_plus_nat @ ( times_times_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_maxt @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) )
% 5.41/5.69 @ Ma2 ) ) )
% 5.41/5.69 @ ( suc @ ( suc @ Va2 ) )
% 5.41/5.69 @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( Xa2 = Mi2 ) @ ( plus_plus_nat @ ( times_times_nat @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( the_nat @ ( vEBT_vebt_mint @ ( nth_VEBT_VEBT @ TreeList3 @ ( the_nat @ ( vEBT_vebt_mint @ Summary2 ) ) ) ) ) ) @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 @ Summary2 ) )
% 5.41/5.69 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) ) ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_delete_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % vebt_delete.pelims
% 5.41/5.69 thf(fact_3596_vebt__insert_Opelims,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat,Y: vEBT_VEBT] :
% 5.41/5.69 ( ( ( vEBT_vebt_insert @ X @ Xa2 )
% 5.41/5.69 = Y )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => ( Y
% 5.41/5.69 = ( vEBT_Leaf @ $true @ B5 ) ) )
% 5.41/5.69 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.69 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.69 => ( Y
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ $true ) ) )
% 5.41/5.69 & ( ( Xa2 != one_one_nat )
% 5.41/5.69 => ( Y
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) ) ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ zero_zero_nat @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Info2: option4927543243414619207at_nat,Ts2: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Info2 @ ( suc @ zero_zero_nat ) @ Ts2 @ S3 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [V2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Xa2 @ Xa2 ) ) @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ V2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( if_VEBT_VEBT
% 5.41/5.69 @ ( ( ord_less_nat @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 & ~ ( ( Xa2 = Mi2 )
% 5.41/5.69 | ( Xa2 = Ma2 ) ) )
% 5.41/5.69 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Xa2 @ Mi2 ) @ ( ord_max_nat @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ Ma2 ) ) ) @ ( suc @ ( suc @ Va2 ) ) @ ( list_u1324408373059187874T_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_insert @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( if_VEBT_VEBT @ ( vEBT_VEBT_minNull @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( vEBT_vebt_insert @ Summary2 @ ( vEBT_VEBT_high @ ( if_nat @ ( ord_less_nat @ Xa2 @ Mi2 ) @ Mi2 @ Xa2 ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ Summary2 ) )
% 5.41/5.69 @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_insert_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % vebt_insert.pelims
% 5.41/5.69 thf(fact_3597_vebt__member_Opelims_I3_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.69 ( ~ ( vEBT_vebt_member @ X @ Xa2 )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.41/5.69 => ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => A5 )
% 5.41/5.69 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.69 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.69 => B5 )
% 5.41/5.69 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.41/5.69 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.41/5.69 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) )
% 5.41/5.69 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) )
% 5.41/5.69 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.41/5.69 => ( ( Xa2 != Mi2 )
% 5.41/5.69 => ( ( Xa2 != Ma2 )
% 5.41/5.69 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.69 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.69 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % vebt_member.pelims(3)
% 5.41/5.69 thf(fact_3598_vebt__member_Opelims_I1_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.69 ( ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.41/5.69 = Y )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => A5 )
% 5.41/5.69 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.69 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.69 => B5 )
% 5.41/5.69 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.69 => ( ~ Y
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [V2: product_prod_nat_nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) )
% 5.41/5.69 => ( ~ Y
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ zero_zero_nat @ Uy2 @ Uz2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [V2: product_prod_nat_nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) )
% 5.41/5.69 => ( ~ Y
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ V2 ) @ ( suc @ zero_zero_nat ) @ Vb2 @ Vc2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( ( Xa2 != Mi2 )
% 5.41/5.69 => ( ( Xa2 != Ma2 )
% 5.41/5.69 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.69 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.69 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % vebt_member.pelims(1)
% 5.41/5.69 thf(fact_3599_VEBT__internal_Onaive__member_Opelims_I3_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.69 ( ~ ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.41/5.69 => ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => A5 )
% 5.41/5.69 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.69 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.69 => B5 )
% 5.41/5.69 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.41/5.69 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) )
% 5.41/5.69 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 5.41/5.69 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % VEBT_internal.naive_member.pelims(3)
% 5.41/5.69 thf(fact_3600_VEBT__internal_Onaive__member_Opelims_I2_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.69 ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.41/5.69 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => A5 )
% 5.41/5.69 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.69 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.69 => B5 )
% 5.41/5.69 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.41/5.69 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) )
% 5.41/5.69 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % VEBT_internal.naive_member.pelims(2)
% 5.41/5.69 thf(fact_3601_VEBT__internal_Onaive__member_Opelims_I1_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.69 ( ( ( vEBT_V5719532721284313246member @ X @ Xa2 )
% 5.41/5.69 = Y )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => A5 )
% 5.41/5.69 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.69 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.69 => B5 )
% 5.41/5.69 & ( Xa2 = one_one_nat ) ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Uu2: option4927543243414619207at_nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) )
% 5.41/5.69 => ( ~ Y
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uu2 @ zero_zero_nat @ Uv2 @ Uw2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ~ ! [Uy2: option4927543243414619207at_nat,V2: nat,TreeList3: list_VEBT_VEBT,S3: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_V5719532721284313246member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V5765760719290551771er_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Uy2 @ ( suc @ V2 ) @ TreeList3 @ S3 ) @ Xa2 ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % VEBT_internal.naive_member.pelims(1)
% 5.41/5.69 thf(fact_3602_vebt__member_Opelims_I2_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.69 ( ( vEBT_vebt_member @ X @ Xa2 )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [A5: $o,B5: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ A5 @ B5 ) @ Xa2 ) )
% 5.41/5.69 => ~ ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.69 => A5 )
% 5.41/5.69 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.69 => ( ( ( Xa2 = one_one_nat )
% 5.41/5.69 => B5 )
% 5.41/5.69 & ( Xa2 = one_one_nat ) ) ) ) ) )
% 5.41/5.69 => ~ ! [Mi2: nat,Ma2: nat,Va2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_vebt_member_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ ( suc @ Va2 ) ) @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.41/5.69 => ~ ( ( Xa2 != Mi2 )
% 5.41/5.69 => ( ( Xa2 != Ma2 )
% 5.41/5.69 => ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 & ( ~ ( ord_less_nat @ Xa2 @ Mi2 )
% 5.41/5.69 => ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.69 & ( ~ ( ord_less_nat @ Ma2 @ Xa2 )
% 5.41/5.69 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_vebt_member @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % vebt_member.pelims(2)
% 5.41/5.69 thf(fact_3603_DiffI,axiom,
% 5.41/5.69 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.69 ( ( member_complex @ C @ A2 )
% 5.41/5.69 => ( ~ ( member_complex @ C @ B3 )
% 5.41/5.69 => ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffI
% 5.41/5.69 thf(fact_3604_DiffI,axiom,
% 5.41/5.69 ! [C: real,A2: set_real,B3: set_real] :
% 5.41/5.69 ( ( member_real @ C @ A2 )
% 5.41/5.69 => ( ~ ( member_real @ C @ B3 )
% 5.41/5.69 => ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffI
% 5.41/5.69 thf(fact_3605_DiffI,axiom,
% 5.41/5.69 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.69 ( ( member_set_nat @ C @ A2 )
% 5.41/5.69 => ( ~ ( member_set_nat @ C @ B3 )
% 5.41/5.69 => ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffI
% 5.41/5.69 thf(fact_3606_DiffI,axiom,
% 5.41/5.69 ! [C: int,A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( member_int @ C @ A2 )
% 5.41/5.69 => ( ~ ( member_int @ C @ B3 )
% 5.41/5.69 => ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffI
% 5.41/5.69 thf(fact_3607_DiffI,axiom,
% 5.41/5.69 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( member_nat @ C @ A2 )
% 5.41/5.69 => ( ~ ( member_nat @ C @ B3 )
% 5.41/5.69 => ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffI
% 5.41/5.69 thf(fact_3608_Diff__iff,axiom,
% 5.41/5.69 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.69 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.69 = ( ( member_complex @ C @ A2 )
% 5.41/5.69 & ~ ( member_complex @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % Diff_iff
% 5.41/5.69 thf(fact_3609_Diff__iff,axiom,
% 5.41/5.69 ! [C: real,A2: set_real,B3: set_real] :
% 5.41/5.69 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.41/5.69 = ( ( member_real @ C @ A2 )
% 5.41/5.69 & ~ ( member_real @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % Diff_iff
% 5.41/5.69 thf(fact_3610_Diff__iff,axiom,
% 5.41/5.69 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.69 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.41/5.69 = ( ( member_set_nat @ C @ A2 )
% 5.41/5.69 & ~ ( member_set_nat @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % Diff_iff
% 5.41/5.69 thf(fact_3611_Diff__iff,axiom,
% 5.41/5.69 ! [C: int,A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.69 = ( ( member_int @ C @ A2 )
% 5.41/5.69 & ~ ( member_int @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % Diff_iff
% 5.41/5.69 thf(fact_3612_Diff__iff,axiom,
% 5.41/5.69 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.69 = ( ( member_nat @ C @ A2 )
% 5.41/5.69 & ~ ( member_nat @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % Diff_iff
% 5.41/5.69 thf(fact_3613_Diff__idemp,axiom,
% 5.41/5.69 ! [A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ B3 )
% 5.41/5.69 = ( minus_minus_set_nat @ A2 @ B3 ) ) ).
% 5.41/5.69
% 5.41/5.69 % Diff_idemp
% 5.41/5.69 thf(fact_3614_DiffE,axiom,
% 5.41/5.69 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.69 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( ( member_complex @ C @ A2 )
% 5.41/5.69 => ( member_complex @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffE
% 5.41/5.69 thf(fact_3615_DiffE,axiom,
% 5.41/5.69 ! [C: real,A2: set_real,B3: set_real] :
% 5.41/5.69 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( ( member_real @ C @ A2 )
% 5.41/5.69 => ( member_real @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffE
% 5.41/5.69 thf(fact_3616_DiffE,axiom,
% 5.41/5.69 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.69 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( ( member_set_nat @ C @ A2 )
% 5.41/5.69 => ( member_set_nat @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffE
% 5.41/5.69 thf(fact_3617_DiffE,axiom,
% 5.41/5.69 ! [C: int,A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( ( member_int @ C @ A2 )
% 5.41/5.69 => ( member_int @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffE
% 5.41/5.69 thf(fact_3618_DiffE,axiom,
% 5.41/5.69 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( ( member_nat @ C @ A2 )
% 5.41/5.69 => ( member_nat @ C @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffE
% 5.41/5.69 thf(fact_3619_DiffD1,axiom,
% 5.41/5.69 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.69 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.69 => ( member_complex @ C @ A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD1
% 5.41/5.69 thf(fact_3620_DiffD1,axiom,
% 5.41/5.69 ! [C: real,A2: set_real,B3: set_real] :
% 5.41/5.69 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.41/5.69 => ( member_real @ C @ A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD1
% 5.41/5.69 thf(fact_3621_DiffD1,axiom,
% 5.41/5.69 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.69 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.41/5.69 => ( member_set_nat @ C @ A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD1
% 5.41/5.69 thf(fact_3622_DiffD1,axiom,
% 5.41/5.69 ! [C: int,A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.69 => ( member_int @ C @ A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD1
% 5.41/5.69 thf(fact_3623_DiffD1,axiom,
% 5.41/5.69 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.69 => ( member_nat @ C @ A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD1
% 5.41/5.69 thf(fact_3624_DiffD2,axiom,
% 5.41/5.69 ! [C: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.69 ( ( member_complex @ C @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( member_complex @ C @ B3 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD2
% 5.41/5.69 thf(fact_3625_DiffD2,axiom,
% 5.41/5.69 ! [C: real,A2: set_real,B3: set_real] :
% 5.41/5.69 ( ( member_real @ C @ ( minus_minus_set_real @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( member_real @ C @ B3 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD2
% 5.41/5.69 thf(fact_3626_DiffD2,axiom,
% 5.41/5.69 ! [C: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.69 ( ( member_set_nat @ C @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( member_set_nat @ C @ B3 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD2
% 5.41/5.69 thf(fact_3627_DiffD2,axiom,
% 5.41/5.69 ! [C: int,A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( member_int @ C @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( member_int @ C @ B3 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD2
% 5.41/5.69 thf(fact_3628_DiffD2,axiom,
% 5.41/5.69 ! [C: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( member_nat @ C @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.69 => ~ ( member_nat @ C @ B3 ) ) ).
% 5.41/5.69
% 5.41/5.69 % DiffD2
% 5.41/5.69 thf(fact_3629_minus__set__def,axiom,
% 5.41/5.69 ( minus_minus_set_real
% 5.41/5.69 = ( ^ [A6: set_real,B6: set_real] :
% 5.41/5.69 ( collect_real
% 5.41/5.69 @ ( minus_minus_real_o
% 5.41/5.69 @ ^ [X3: real] : ( member_real @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: real] : ( member_real @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % minus_set_def
% 5.41/5.69 thf(fact_3630_minus__set__def,axiom,
% 5.41/5.69 ( minus_1052850069191792384nt_int
% 5.41/5.69 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.41/5.69 ( collec213857154873943460nt_int
% 5.41/5.69 @ ( minus_711738161318947805_int_o
% 5.41/5.69 @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: product_prod_int_int] : ( member5262025264175285858nt_int @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % minus_set_def
% 5.41/5.69 thf(fact_3631_minus__set__def,axiom,
% 5.41/5.69 ( minus_811609699411566653omplex
% 5.41/5.69 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.41/5.69 ( collect_complex
% 5.41/5.69 @ ( minus_8727706125548526216plex_o
% 5.41/5.69 @ ^ [X3: complex] : ( member_complex @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: complex] : ( member_complex @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % minus_set_def
% 5.41/5.69 thf(fact_3632_minus__set__def,axiom,
% 5.41/5.69 ( minus_2163939370556025621et_nat
% 5.41/5.69 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.41/5.69 ( collect_set_nat
% 5.41/5.69 @ ( minus_6910147592129066416_nat_o
% 5.41/5.69 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: set_nat] : ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % minus_set_def
% 5.41/5.69 thf(fact_3633_minus__set__def,axiom,
% 5.41/5.69 ( minus_minus_set_int
% 5.41/5.69 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.69 ( collect_int
% 5.41/5.69 @ ( minus_minus_int_o
% 5.41/5.69 @ ^ [X3: int] : ( member_int @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: int] : ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % minus_set_def
% 5.41/5.69 thf(fact_3634_minus__set__def,axiom,
% 5.41/5.69 ( minus_minus_set_nat
% 5.41/5.69 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.41/5.69 ( collect_nat
% 5.41/5.69 @ ( minus_minus_nat_o
% 5.41/5.69 @ ^ [X3: nat] : ( member_nat @ X3 @ A6 )
% 5.41/5.69 @ ^ [X3: nat] : ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % minus_set_def
% 5.41/5.69 thf(fact_3635_set__diff__eq,axiom,
% 5.41/5.69 ( minus_minus_set_real
% 5.41/5.69 = ( ^ [A6: set_real,B6: set_real] :
% 5.41/5.69 ( collect_real
% 5.41/5.69 @ ^ [X3: real] :
% 5.41/5.69 ( ( member_real @ X3 @ A6 )
% 5.41/5.69 & ~ ( member_real @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % set_diff_eq
% 5.41/5.69 thf(fact_3636_set__diff__eq,axiom,
% 5.41/5.69 ( minus_1052850069191792384nt_int
% 5.41/5.69 = ( ^ [A6: set_Pr958786334691620121nt_int,B6: set_Pr958786334691620121nt_int] :
% 5.41/5.69 ( collec213857154873943460nt_int
% 5.41/5.69 @ ^ [X3: product_prod_int_int] :
% 5.41/5.69 ( ( member5262025264175285858nt_int @ X3 @ A6 )
% 5.41/5.69 & ~ ( member5262025264175285858nt_int @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % set_diff_eq
% 5.41/5.69 thf(fact_3637_set__diff__eq,axiom,
% 5.41/5.69 ( minus_811609699411566653omplex
% 5.41/5.69 = ( ^ [A6: set_complex,B6: set_complex] :
% 5.41/5.69 ( collect_complex
% 5.41/5.69 @ ^ [X3: complex] :
% 5.41/5.69 ( ( member_complex @ X3 @ A6 )
% 5.41/5.69 & ~ ( member_complex @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % set_diff_eq
% 5.41/5.69 thf(fact_3638_set__diff__eq,axiom,
% 5.41/5.69 ( minus_2163939370556025621et_nat
% 5.41/5.69 = ( ^ [A6: set_set_nat,B6: set_set_nat] :
% 5.41/5.69 ( collect_set_nat
% 5.41/5.69 @ ^ [X3: set_nat] :
% 5.41/5.69 ( ( member_set_nat @ X3 @ A6 )
% 5.41/5.69 & ~ ( member_set_nat @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % set_diff_eq
% 5.41/5.69 thf(fact_3639_set__diff__eq,axiom,
% 5.41/5.69 ( minus_minus_set_int
% 5.41/5.69 = ( ^ [A6: set_int,B6: set_int] :
% 5.41/5.69 ( collect_int
% 5.41/5.69 @ ^ [X3: int] :
% 5.41/5.69 ( ( member_int @ X3 @ A6 )
% 5.41/5.69 & ~ ( member_int @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % set_diff_eq
% 5.41/5.69 thf(fact_3640_set__diff__eq,axiom,
% 5.41/5.69 ( minus_minus_set_nat
% 5.41/5.69 = ( ^ [A6: set_nat,B6: set_nat] :
% 5.41/5.69 ( collect_nat
% 5.41/5.69 @ ^ [X3: nat] :
% 5.41/5.69 ( ( member_nat @ X3 @ A6 )
% 5.41/5.69 & ~ ( member_nat @ X3 @ B6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % set_diff_eq
% 5.41/5.69 thf(fact_3641_VEBT__internal_Omembermima_Opelims_I1_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.69 ( ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.41/5.69 = Y )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.69 => ( ~ Y
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.41/5.69 => ( ~ Y
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( ( Xa2 = Mi2 )
% 5.41/5.69 | ( Xa2 = Ma2 ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( ( Xa2 = Mi2 )
% 5.41/5.69 | ( Xa2 = Ma2 )
% 5.41/5.69 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) ) ) )
% 5.41/5.69 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.41/5.69 => ( ( Y
% 5.41/5.69 = ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % VEBT_internal.membermima.pelims(1)
% 5.41/5.69 thf(fact_3642_VEBT__internal_Omembermima_Opelims_I3_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.69 ( ~ ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) )
% 5.41/5.69 => ( ! [Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) )
% 5.41/5.69 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ zero_zero_nat @ Ux2 @ Uy2 ) @ Xa2 ) ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.41/5.69 => ( ( Xa2 = Mi2 )
% 5.41/5.69 | ( Xa2 = Ma2 ) ) ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.41/5.69 => ( ( Xa2 = Mi2 )
% 5.41/5.69 | ( Xa2 = Ma2 )
% 5.41/5.69 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.41/5.69 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.41/5.69 => ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % VEBT_internal.membermima.pelims(3)
% 5.41/5.69 thf(fact_3643_VEBT__internal_Omembermima_Opelims_I2_J,axiom,
% 5.41/5.69 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.69 ( ( vEBT_VEBT_membermima @ X @ Xa2 )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,Va3: list_VEBT_VEBT,Vb2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ zero_zero_nat @ Va3 @ Vb2 ) @ Xa2 ) )
% 5.41/5.69 => ~ ( ( Xa2 = Mi2 )
% 5.41/5.69 | ( Xa2 = Ma2 ) ) ) )
% 5.41/5.69 => ( ! [Mi2: nat,Ma2: nat,V2: nat,TreeList3: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ ( suc @ V2 ) @ TreeList3 @ Vc2 ) @ Xa2 ) )
% 5.41/5.69 => ~ ( ( Xa2 = Mi2 )
% 5.41/5.69 | ( Xa2 = Ma2 )
% 5.41/5.69 | ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) )
% 5.41/5.69 => ~ ! [V2: nat,TreeList3: list_VEBT_VEBT,Vd2: vEBT_VEBT] :
% 5.41/5.69 ( ( X
% 5.41/5.69 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) )
% 5.41/5.69 => ( ( accp_P2887432264394892906BT_nat @ vEBT_V4351362008482014158ma_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ V2 ) @ TreeList3 @ Vd2 ) @ Xa2 ) )
% 5.41/5.69 => ~ ( ( ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) )
% 5.41/5.69 => ( vEBT_VEBT_membermima @ ( nth_VEBT_VEBT @ TreeList3 @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_VEBT_low @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.69 & ( ord_less_nat @ ( vEBT_VEBT_high @ Xa2 @ ( divide_divide_nat @ ( suc @ V2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( size_s6755466524823107622T_VEBT @ TreeList3 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % VEBT_internal.membermima.pelims(2)
% 5.41/5.69 thf(fact_3644_unset__bit__0,axiom,
% 5.41/5.69 ! [A: int] :
% 5.41/5.69 ( ( bit_se4203085406695923979it_int @ zero_zero_nat @ A )
% 5.41/5.69 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_0
% 5.41/5.69 thf(fact_3645_unset__bit__0,axiom,
% 5.41/5.69 ! [A: nat] :
% 5.41/5.69 ( ( bit_se4205575877204974255it_nat @ zero_zero_nat @ A )
% 5.41/5.69 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_0
% 5.41/5.69 thf(fact_3646_unset__bit__Suc,axiom,
% 5.41/5.69 ! [N: nat,A: code_integer] :
% 5.41/5.69 ( ( bit_se8260200283734997820nteger @ ( suc @ N ) @ A )
% 5.41/5.69 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_Suc
% 5.41/5.69 thf(fact_3647_unset__bit__Suc,axiom,
% 5.41/5.69 ! [N: nat,A: int] :
% 5.41/5.69 ( ( bit_se4203085406695923979it_int @ ( suc @ N ) @ A )
% 5.41/5.69 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_Suc
% 5.41/5.69 thf(fact_3648_unset__bit__Suc,axiom,
% 5.41/5.69 ! [N: nat,A: nat] :
% 5.41/5.69 ( ( bit_se4205575877204974255it_nat @ ( suc @ N ) @ A )
% 5.41/5.69 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_Suc
% 5.41/5.69 thf(fact_3649_flip__bit__Suc,axiom,
% 5.41/5.69 ! [N: nat,A: code_integer] :
% 5.41/5.69 ( ( bit_se1345352211410354436nteger @ ( suc @ N ) @ A )
% 5.41/5.69 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % flip_bit_Suc
% 5.41/5.69 thf(fact_3650_flip__bit__Suc,axiom,
% 5.41/5.69 ! [N: nat,A: int] :
% 5.41/5.69 ( ( bit_se2159334234014336723it_int @ ( suc @ N ) @ A )
% 5.41/5.69 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % flip_bit_Suc
% 5.41/5.69 thf(fact_3651_flip__bit__Suc,axiom,
% 5.41/5.69 ! [N: nat,A: nat] :
% 5.41/5.69 ( ( bit_se2161824704523386999it_nat @ ( suc @ N ) @ A )
% 5.41/5.69 = ( plus_plus_nat @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % flip_bit_Suc
% 5.41/5.69 thf(fact_3652_Bolzano,axiom,
% 5.41/5.69 ! [A: real,B: real,P: real > real > $o] :
% 5.41/5.69 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.69 => ( ! [A5: real,B5: real,C2: real] :
% 5.41/5.69 ( ( P @ A5 @ B5 )
% 5.41/5.69 => ( ( P @ B5 @ C2 )
% 5.41/5.69 => ( ( ord_less_eq_real @ A5 @ B5 )
% 5.41/5.69 => ( ( ord_less_eq_real @ B5 @ C2 )
% 5.41/5.69 => ( P @ A5 @ C2 ) ) ) ) )
% 5.41/5.69 => ( ! [X6: real] :
% 5.41/5.69 ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.69 => ( ( ord_less_eq_real @ X6 @ B )
% 5.41/5.69 => ? [D5: real] :
% 5.41/5.69 ( ( ord_less_real @ zero_zero_real @ D5 )
% 5.41/5.69 & ! [A5: real,B5: real] :
% 5.41/5.69 ( ( ( ord_less_eq_real @ A5 @ X6 )
% 5.41/5.69 & ( ord_less_eq_real @ X6 @ B5 )
% 5.41/5.69 & ( ord_less_real @ ( minus_minus_real @ B5 @ A5 ) @ D5 ) )
% 5.41/5.69 => ( P @ A5 @ B5 ) ) ) ) )
% 5.41/5.69 => ( P @ A @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % Bolzano
% 5.41/5.69 thf(fact_3653_unset__bit__nonnegative__int__iff,axiom,
% 5.41/5.69 ! [N: nat,K: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se4203085406695923979it_int @ N @ K ) )
% 5.41/5.69 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_nonnegative_int_iff
% 5.41/5.69 thf(fact_3654_flip__bit__nonnegative__int__iff,axiom,
% 5.41/5.69 ! [N: nat,K: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se2159334234014336723it_int @ N @ K ) )
% 5.41/5.69 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.69
% 5.41/5.69 % flip_bit_nonnegative_int_iff
% 5.41/5.69 thf(fact_3655_unset__bit__negative__int__iff,axiom,
% 5.41/5.69 ! [N: nat,K: int] :
% 5.41/5.69 ( ( ord_less_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ zero_zero_int )
% 5.41/5.69 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_negative_int_iff
% 5.41/5.69 thf(fact_3656_flip__bit__negative__int__iff,axiom,
% 5.41/5.69 ! [N: nat,K: int] :
% 5.41/5.69 ( ( ord_less_int @ ( bit_se2159334234014336723it_int @ N @ K ) @ zero_zero_int )
% 5.41/5.69 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.69
% 5.41/5.69 % flip_bit_negative_int_iff
% 5.41/5.69 thf(fact_3657_unset__bit__less__eq,axiom,
% 5.41/5.69 ! [N: nat,K: int] : ( ord_less_eq_int @ ( bit_se4203085406695923979it_int @ N @ K ) @ K ) ).
% 5.41/5.69
% 5.41/5.69 % unset_bit_less_eq
% 5.41/5.69 thf(fact_3658_mult__le__cancel__iff1,axiom,
% 5.41/5.69 ! [Z: real,X: real,Y: real] :
% 5.41/5.69 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.41/5.69 => ( ( ord_less_eq_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.41/5.69 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_le_cancel_iff1
% 5.41/5.69 thf(fact_3659_mult__le__cancel__iff1,axiom,
% 5.41/5.69 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.69 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.41/5.69 => ( ( ord_less_eq_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.41/5.69 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_le_cancel_iff1
% 5.41/5.69 thf(fact_3660_mult__le__cancel__iff1,axiom,
% 5.41/5.69 ! [Z: int,X: int,Y: int] :
% 5.41/5.69 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.69 => ( ( ord_less_eq_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.41/5.69 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_le_cancel_iff1
% 5.41/5.69 thf(fact_3661_mult__le__cancel__iff2,axiom,
% 5.41/5.69 ! [Z: real,X: real,Y: real] :
% 5.41/5.69 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.41/5.69 => ( ( ord_less_eq_real @ ( times_times_real @ Z @ X ) @ ( times_times_real @ Z @ Y ) )
% 5.41/5.69 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_le_cancel_iff2
% 5.41/5.69 thf(fact_3662_mult__le__cancel__iff2,axiom,
% 5.41/5.69 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.69 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.41/5.69 => ( ( ord_less_eq_rat @ ( times_times_rat @ Z @ X ) @ ( times_times_rat @ Z @ Y ) )
% 5.41/5.69 = ( ord_less_eq_rat @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_le_cancel_iff2
% 5.41/5.69 thf(fact_3663_mult__le__cancel__iff2,axiom,
% 5.41/5.69 ! [Z: int,X: int,Y: int] :
% 5.41/5.69 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.69 => ( ( ord_less_eq_int @ ( times_times_int @ Z @ X ) @ ( times_times_int @ Z @ Y ) )
% 5.41/5.69 = ( ord_less_eq_int @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_le_cancel_iff2
% 5.41/5.69 thf(fact_3664_divides__aux__eq,axiom,
% 5.41/5.69 ! [Q2: nat,R: nat] :
% 5.41/5.69 ( ( unique6322359934112328802ux_nat @ ( product_Pair_nat_nat @ Q2 @ R ) )
% 5.41/5.69 = ( R = zero_zero_nat ) ) ).
% 5.41/5.69
% 5.41/5.69 % divides_aux_eq
% 5.41/5.69 thf(fact_3665_divides__aux__eq,axiom,
% 5.41/5.69 ! [Q2: int,R: int] :
% 5.41/5.69 ( ( unique6319869463603278526ux_int @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 = ( R = zero_zero_int ) ) ).
% 5.41/5.69
% 5.41/5.69 % divides_aux_eq
% 5.41/5.69 thf(fact_3666_neg__eucl__rel__int__mult__2,axiom,
% 5.41/5.69 ! [B: int,A: int,Q2: int,R: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ B @ zero_zero_int )
% 5.41/5.69 => ( ( eucl_rel_int @ ( plus_plus_int @ A @ one_one_int ) @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( minus_minus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) @ one_one_int ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % neg_eucl_rel_int_mult_2
% 5.41/5.69 thf(fact_3667_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr4953567300277697838T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( produc537772716801021591T_VEBT @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3668_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr4606735188037164562VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( produc8721562602347293563VEBT_o @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3669_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr1791586995822124652BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( produc738532404422230701BT_nat @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3670_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_VEBT_VEBT,Ys: list_int] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr6837108013167703752BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( produc736041933913180425BT_int @ ( nth_VEBT_VEBT @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3671_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_o,Ys: list_VEBT_VEBT] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr6777367263587873994T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( produc2982872950893828659T_VEBT @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3672_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_o,Ys: list_o] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Product_prod_o_o @ ( product_o_o @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( product_Pair_o_o @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3673_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_o,Ys: list_nat] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr5826913651314560976_o_nat @ ( product_o_nat @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( product_Pair_o_nat @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_nat @ Ys ) ) ) @ ( nth_nat @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_nat @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3674_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_o,Ys: list_int] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr1649062631805364268_o_int @ ( product_o_int @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( product_Pair_o_int @ ( nth_o @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_int @ Ys ) ) ) @ ( nth_int @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_int @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3675_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_nat,Ys: list_VEBT_VEBT] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr744662078594809490T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( produc599794634098209291T_VEBT @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) @ ( nth_VEBT_VEBT @ Ys @ ( modulo_modulo_nat @ N @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3676_product__nth,axiom,
% 5.41/5.69 ! [N: nat,Xs: list_nat,Ys: list_o] :
% 5.41/5.69 ( ( ord_less_nat @ N @ ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) )
% 5.41/5.69 => ( ( nth_Pr112076138515278198_nat_o @ ( product_nat_o @ Xs @ Ys ) @ N )
% 5.41/5.69 = ( product_Pair_nat_o @ ( nth_nat @ Xs @ ( divide_divide_nat @ N @ ( size_size_list_o @ Ys ) ) ) @ ( nth_o @ Ys @ ( modulo_modulo_nat @ N @ ( size_size_list_o @ Ys ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % product_nth
% 5.41/5.69 thf(fact_3677_obtain__set__succ,axiom,
% 5.41/5.69 ! [X: nat,Z: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( ord_less_nat @ X @ Z )
% 5.41/5.69 => ( ( vEBT_VEBT_max_in_set @ A2 @ Z )
% 5.41/5.69 => ( ( finite_finite_nat @ B3 )
% 5.41/5.69 => ( ( A2 = B3 )
% 5.41/5.69 => ? [X_1: nat] : ( vEBT_is_succ_in_set @ A2 @ X @ X_1 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % obtain_set_succ
% 5.41/5.69 thf(fact_3678_obtain__set__pred,axiom,
% 5.41/5.69 ! [Z: nat,X: nat,A2: set_nat] :
% 5.41/5.69 ( ( ord_less_nat @ Z @ X )
% 5.41/5.69 => ( ( vEBT_VEBT_min_in_set @ A2 @ Z )
% 5.41/5.69 => ( ( finite_finite_nat @ A2 )
% 5.41/5.69 => ? [X_1: nat] : ( vEBT_is_pred_in_set @ A2 @ X @ X_1 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % obtain_set_pred
% 5.41/5.69 thf(fact_3679_set__vebt__finite,axiom,
% 5.41/5.69 ! [T: vEBT_VEBT,N: nat] :
% 5.41/5.69 ( ( vEBT_invar_vebt @ T @ N )
% 5.41/5.69 => ( finite_finite_nat @ ( vEBT_VEBT_set_vebt @ T ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % set_vebt_finite
% 5.41/5.69 thf(fact_3680_pred__none__empty,axiom,
% 5.41/5.69 ! [Xs: set_nat,A: nat] :
% 5.41/5.69 ( ~ ? [X_1: nat] : ( vEBT_is_pred_in_set @ Xs @ A @ X_1 )
% 5.41/5.69 => ( ( finite_finite_nat @ Xs )
% 5.41/5.69 => ~ ? [X4: nat] :
% 5.41/5.69 ( ( member_nat @ X4 @ Xs )
% 5.41/5.69 & ( ord_less_nat @ X4 @ A ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % pred_none_empty
% 5.41/5.69 thf(fact_3681_succ__none__empty,axiom,
% 5.41/5.69 ! [Xs: set_nat,A: nat] :
% 5.41/5.69 ( ~ ? [X_1: nat] : ( vEBT_is_succ_in_set @ Xs @ A @ X_1 )
% 5.41/5.69 => ( ( finite_finite_nat @ Xs )
% 5.41/5.69 => ~ ? [X4: nat] :
% 5.41/5.69 ( ( member_nat @ X4 @ Xs )
% 5.41/5.69 & ( ord_less_nat @ A @ X4 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % succ_none_empty
% 5.41/5.69 thf(fact_3682_List_Ofinite__set,axiom,
% 5.41/5.69 ! [Xs: list_VEBT_VEBT] : ( finite5795047828879050333T_VEBT @ ( set_VEBT_VEBT2 @ Xs ) ) ).
% 5.41/5.69
% 5.41/5.69 % List.finite_set
% 5.41/5.69 thf(fact_3683_List_Ofinite__set,axiom,
% 5.41/5.69 ! [Xs: list_nat] : ( finite_finite_nat @ ( set_nat2 @ Xs ) ) ).
% 5.41/5.69
% 5.41/5.69 % List.finite_set
% 5.41/5.69 thf(fact_3684_List_Ofinite__set,axiom,
% 5.41/5.69 ! [Xs: list_int] : ( finite_finite_int @ ( set_int2 @ Xs ) ) ).
% 5.41/5.69
% 5.41/5.69 % List.finite_set
% 5.41/5.69 thf(fact_3685_List_Ofinite__set,axiom,
% 5.41/5.69 ! [Xs: list_complex] : ( finite3207457112153483333omplex @ ( set_complex2 @ Xs ) ) ).
% 5.41/5.69
% 5.41/5.69 % List.finite_set
% 5.41/5.69 thf(fact_3686_finite__atLeastAtMost,axiom,
% 5.41/5.69 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_atLeastAtMost
% 5.41/5.69 thf(fact_3687_infinite__Icc__iff,axiom,
% 5.41/5.69 ! [A: rat,B: rat] :
% 5.41/5.69 ( ( ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) )
% 5.41/5.69 = ( ord_less_rat @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_Icc_iff
% 5.41/5.69 thf(fact_3688_infinite__Icc__iff,axiom,
% 5.41/5.69 ! [A: real,B: real] :
% 5.41/5.69 ( ( ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) )
% 5.41/5.69 = ( ord_less_real @ A @ B ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_Icc_iff
% 5.41/5.69 thf(fact_3689_length__product,axiom,
% 5.41/5.69 ! [Xs: list_VEBT_VEBT,Ys: list_VEBT_VEBT] :
% 5.41/5.69 ( ( size_s7466405169056248089T_VEBT @ ( produc4743750530478302277T_VEBT @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3690_length__product,axiom,
% 5.41/5.69 ! [Xs: list_VEBT_VEBT,Ys: list_o] :
% 5.41/5.69 ( ( size_s9168528473962070013VEBT_o @ ( product_VEBT_VEBT_o @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3691_length__product,axiom,
% 5.41/5.69 ! [Xs: list_VEBT_VEBT,Ys: list_nat] :
% 5.41/5.69 ( ( size_s6152045936467909847BT_nat @ ( produc7295137177222721919BT_nat @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3692_length__product,axiom,
% 5.41/5.69 ! [Xs: list_VEBT_VEBT,Ys: list_int] :
% 5.41/5.69 ( ( size_s3661962791536183091BT_int @ ( produc7292646706713671643BT_int @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_s6755466524823107622T_VEBT @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3693_length__product,axiom,
% 5.41/5.69 ! [Xs: list_o,Ys: list_VEBT_VEBT] :
% 5.41/5.69 ( ( size_s4313452262239582901T_VEBT @ ( product_o_VEBT_VEBT @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3694_length__product,axiom,
% 5.41/5.69 ! [Xs: list_o,Ys: list_o] :
% 5.41/5.69 ( ( size_s1515746228057227161od_o_o @ ( product_o_o @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3695_length__product,axiom,
% 5.41/5.69 ! [Xs: list_o,Ys: list_nat] :
% 5.41/5.69 ( ( size_s5443766701097040955_o_nat @ ( product_o_nat @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_nat @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3696_length__product,axiom,
% 5.41/5.69 ! [Xs: list_o,Ys: list_int] :
% 5.41/5.69 ( ( size_s2953683556165314199_o_int @ ( product_o_int @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_size_list_o @ Xs ) @ ( size_size_list_int @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3697_length__product,axiom,
% 5.41/5.69 ! [Xs: list_nat,Ys: list_VEBT_VEBT] :
% 5.41/5.69 ( ( size_s4762443039079500285T_VEBT @ ( produc7156399406898700509T_VEBT @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_s6755466524823107622T_VEBT @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3698_length__product,axiom,
% 5.41/5.69 ! [Xs: list_nat,Ys: list_o] :
% 5.41/5.69 ( ( size_s6491369823275344609_nat_o @ ( product_nat_o @ Xs @ Ys ) )
% 5.41/5.69 = ( times_times_nat @ ( size_size_list_nat @ Xs ) @ ( size_size_list_o @ Ys ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % length_product
% 5.41/5.69 thf(fact_3699_unique__remainder,axiom,
% 5.41/5.69 ! [A: int,B: int,Q2: int,R: int,Q4: int,R3: int] :
% 5.41/5.69 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 5.41/5.69 => ( R = R3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % unique_remainder
% 5.41/5.69 thf(fact_3700_unique__quotient,axiom,
% 5.41/5.69 ! [A: int,B: int,Q2: int,R: int,Q4: int,R3: int] :
% 5.41/5.69 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q4 @ R3 ) )
% 5.41/5.69 => ( Q2 = Q4 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % unique_quotient
% 5.41/5.69 thf(fact_3701_bounded__nat__set__is__finite,axiom,
% 5.41/5.69 ! [N4: set_nat,N: nat] :
% 5.41/5.69 ( ! [X6: nat] :
% 5.41/5.69 ( ( member_nat @ X6 @ N4 )
% 5.41/5.69 => ( ord_less_nat @ X6 @ N ) )
% 5.41/5.69 => ( finite_finite_nat @ N4 ) ) ).
% 5.41/5.69
% 5.41/5.69 % bounded_nat_set_is_finite
% 5.41/5.69 thf(fact_3702_finite__nat__set__iff__bounded,axiom,
% 5.41/5.69 ( finite_finite_nat
% 5.41/5.69 = ( ^ [N6: set_nat] :
% 5.41/5.69 ? [M3: nat] :
% 5.41/5.69 ! [X3: nat] :
% 5.41/5.69 ( ( member_nat @ X3 @ N6 )
% 5.41/5.69 => ( ord_less_nat @ X3 @ M3 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_nat_set_iff_bounded
% 5.41/5.69 thf(fact_3703_finite__nat__set__iff__bounded__le,axiom,
% 5.41/5.69 ( finite_finite_nat
% 5.41/5.69 = ( ^ [N6: set_nat] :
% 5.41/5.69 ? [M3: nat] :
% 5.41/5.69 ! [X3: nat] :
% 5.41/5.69 ( ( member_nat @ X3 @ N6 )
% 5.41/5.69 => ( ord_less_eq_nat @ X3 @ M3 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_nat_set_iff_bounded_le
% 5.41/5.69 thf(fact_3704_finite__list,axiom,
% 5.41/5.69 ! [A2: set_VEBT_VEBT] :
% 5.41/5.69 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.41/5.69 => ? [Xs3: list_VEBT_VEBT] :
% 5.41/5.69 ( ( set_VEBT_VEBT2 @ Xs3 )
% 5.41/5.69 = A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_list
% 5.41/5.69 thf(fact_3705_finite__list,axiom,
% 5.41/5.69 ! [A2: set_nat] :
% 5.41/5.69 ( ( finite_finite_nat @ A2 )
% 5.41/5.69 => ? [Xs3: list_nat] :
% 5.41/5.69 ( ( set_nat2 @ Xs3 )
% 5.41/5.69 = A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_list
% 5.41/5.69 thf(fact_3706_finite__list,axiom,
% 5.41/5.69 ! [A2: set_int] :
% 5.41/5.69 ( ( finite_finite_int @ A2 )
% 5.41/5.69 => ? [Xs3: list_int] :
% 5.41/5.69 ( ( set_int2 @ Xs3 )
% 5.41/5.69 = A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_list
% 5.41/5.69 thf(fact_3707_finite__list,axiom,
% 5.41/5.69 ! [A2: set_complex] :
% 5.41/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.69 => ? [Xs3: list_complex] :
% 5.41/5.69 ( ( set_complex2 @ Xs3 )
% 5.41/5.69 = A2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_list
% 5.41/5.69 thf(fact_3708_finite__M__bounded__by__nat,axiom,
% 5.41/5.69 ! [P: nat > $o,I: nat] :
% 5.41/5.69 ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [K2: nat] :
% 5.41/5.69 ( ( P @ K2 )
% 5.41/5.69 & ( ord_less_nat @ K2 @ I ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_M_bounded_by_nat
% 5.41/5.69 thf(fact_3709_finite__less__ub,axiom,
% 5.41/5.69 ! [F: nat > nat,U: nat] :
% 5.41/5.69 ( ! [N3: nat] : ( ord_less_eq_nat @ N3 @ ( F @ N3 ) )
% 5.41/5.69 => ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [N2: nat] : ( ord_less_eq_nat @ ( F @ N2 ) @ U ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_less_ub
% 5.41/5.69 thf(fact_3710_finite__lists__length__eq,axiom,
% 5.41/5.69 ! [A2: set_complex,N: nat] :
% 5.41/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.69 => ( finite8712137658972009173omplex
% 5.41/5.69 @ ( collect_list_complex
% 5.41/5.69 @ ^ [Xs2: list_complex] :
% 5.41/5.69 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ( size_s3451745648224563538omplex @ Xs2 )
% 5.41/5.69 = N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_eq
% 5.41/5.69 thf(fact_3711_finite__lists__length__eq,axiom,
% 5.41/5.69 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.41/5.69 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.41/5.69 => ( finite3004134309566078307T_VEBT
% 5.41/5.69 @ ( collec5608196760682091941T_VEBT
% 5.41/5.69 @ ^ [Xs2: list_VEBT_VEBT] :
% 5.41/5.69 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ( size_s6755466524823107622T_VEBT @ Xs2 )
% 5.41/5.69 = N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_eq
% 5.41/5.69 thf(fact_3712_finite__lists__length__eq,axiom,
% 5.41/5.69 ! [A2: set_o,N: nat] :
% 5.41/5.69 ( ( finite_finite_o @ A2 )
% 5.41/5.69 => ( finite_finite_list_o
% 5.41/5.69 @ ( collect_list_o
% 5.41/5.69 @ ^ [Xs2: list_o] :
% 5.41/5.69 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ( size_size_list_o @ Xs2 )
% 5.41/5.69 = N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_eq
% 5.41/5.69 thf(fact_3713_finite__lists__length__eq,axiom,
% 5.41/5.69 ! [A2: set_nat,N: nat] :
% 5.41/5.69 ( ( finite_finite_nat @ A2 )
% 5.41/5.69 => ( finite8100373058378681591st_nat
% 5.41/5.69 @ ( collect_list_nat
% 5.41/5.69 @ ^ [Xs2: list_nat] :
% 5.41/5.69 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ( size_size_list_nat @ Xs2 )
% 5.41/5.69 = N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_eq
% 5.41/5.69 thf(fact_3714_finite__lists__length__eq,axiom,
% 5.41/5.69 ! [A2: set_int,N: nat] :
% 5.41/5.69 ( ( finite_finite_int @ A2 )
% 5.41/5.69 => ( finite3922522038869484883st_int
% 5.41/5.69 @ ( collect_list_int
% 5.41/5.69 @ ^ [Xs2: list_int] :
% 5.41/5.69 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ( size_size_list_int @ Xs2 )
% 5.41/5.69 = N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_eq
% 5.41/5.69 thf(fact_3715_eucl__rel__int__by0,axiom,
% 5.41/5.69 ! [K: int] : ( eucl_rel_int @ K @ zero_zero_int @ ( product_Pair_int_int @ zero_zero_int @ K ) ) ).
% 5.41/5.69
% 5.41/5.69 % eucl_rel_int_by0
% 5.41/5.69 thf(fact_3716_div__int__unique,axiom,
% 5.41/5.69 ! [K: int,L2: int,Q2: int,R: int] :
% 5.41/5.69 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.69 = Q2 ) ) ).
% 5.41/5.69
% 5.41/5.69 % div_int_unique
% 5.41/5.69 thf(fact_3717_mod__int__unique,axiom,
% 5.41/5.69 ! [K: int,L2: int,Q2: int,R: int] :
% 5.41/5.69 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 => ( ( modulo_modulo_int @ K @ L2 )
% 5.41/5.69 = R ) ) ).
% 5.41/5.69
% 5.41/5.69 % mod_int_unique
% 5.41/5.69 thf(fact_3718_ex__min__if__finite,axiom,
% 5.41/5.69 ! [S2: set_real] :
% 5.41/5.69 ( ( finite_finite_real @ S2 )
% 5.41/5.69 => ( ( S2 != bot_bot_set_real )
% 5.41/5.69 => ? [X6: real] :
% 5.41/5.69 ( ( member_real @ X6 @ S2 )
% 5.41/5.69 & ~ ? [Xa: real] :
% 5.41/5.69 ( ( member_real @ Xa @ S2 )
% 5.41/5.69 & ( ord_less_real @ Xa @ X6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % ex_min_if_finite
% 5.41/5.69 thf(fact_3719_ex__min__if__finite,axiom,
% 5.41/5.69 ! [S2: set_rat] :
% 5.41/5.69 ( ( finite_finite_rat @ S2 )
% 5.41/5.69 => ( ( S2 != bot_bot_set_rat )
% 5.41/5.69 => ? [X6: rat] :
% 5.41/5.69 ( ( member_rat @ X6 @ S2 )
% 5.41/5.69 & ~ ? [Xa: rat] :
% 5.41/5.69 ( ( member_rat @ Xa @ S2 )
% 5.41/5.69 & ( ord_less_rat @ Xa @ X6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % ex_min_if_finite
% 5.41/5.69 thf(fact_3720_ex__min__if__finite,axiom,
% 5.41/5.69 ! [S2: set_num] :
% 5.41/5.69 ( ( finite_finite_num @ S2 )
% 5.41/5.69 => ( ( S2 != bot_bot_set_num )
% 5.41/5.69 => ? [X6: num] :
% 5.41/5.69 ( ( member_num @ X6 @ S2 )
% 5.41/5.69 & ~ ? [Xa: num] :
% 5.41/5.69 ( ( member_num @ Xa @ S2 )
% 5.41/5.69 & ( ord_less_num @ Xa @ X6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % ex_min_if_finite
% 5.41/5.69 thf(fact_3721_ex__min__if__finite,axiom,
% 5.41/5.69 ! [S2: set_nat] :
% 5.41/5.69 ( ( finite_finite_nat @ S2 )
% 5.41/5.69 => ( ( S2 != bot_bot_set_nat )
% 5.41/5.69 => ? [X6: nat] :
% 5.41/5.69 ( ( member_nat @ X6 @ S2 )
% 5.41/5.69 & ~ ? [Xa: nat] :
% 5.41/5.69 ( ( member_nat @ Xa @ S2 )
% 5.41/5.69 & ( ord_less_nat @ Xa @ X6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % ex_min_if_finite
% 5.41/5.69 thf(fact_3722_ex__min__if__finite,axiom,
% 5.41/5.69 ! [S2: set_int] :
% 5.41/5.69 ( ( finite_finite_int @ S2 )
% 5.41/5.69 => ( ( S2 != bot_bot_set_int )
% 5.41/5.69 => ? [X6: int] :
% 5.41/5.69 ( ( member_int @ X6 @ S2 )
% 5.41/5.69 & ~ ? [Xa: int] :
% 5.41/5.69 ( ( member_int @ Xa @ S2 )
% 5.41/5.69 & ( ord_less_int @ Xa @ X6 ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % ex_min_if_finite
% 5.41/5.69 thf(fact_3723_infinite__growing,axiom,
% 5.41/5.69 ! [X8: set_real] :
% 5.41/5.69 ( ( X8 != bot_bot_set_real )
% 5.41/5.69 => ( ! [X6: real] :
% 5.41/5.69 ( ( member_real @ X6 @ X8 )
% 5.41/5.69 => ? [Xa: real] :
% 5.41/5.69 ( ( member_real @ Xa @ X8 )
% 5.41/5.69 & ( ord_less_real @ X6 @ Xa ) ) )
% 5.41/5.69 => ~ ( finite_finite_real @ X8 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_growing
% 5.41/5.69 thf(fact_3724_infinite__growing,axiom,
% 5.41/5.69 ! [X8: set_rat] :
% 5.41/5.69 ( ( X8 != bot_bot_set_rat )
% 5.41/5.69 => ( ! [X6: rat] :
% 5.41/5.69 ( ( member_rat @ X6 @ X8 )
% 5.41/5.69 => ? [Xa: rat] :
% 5.41/5.69 ( ( member_rat @ Xa @ X8 )
% 5.41/5.69 & ( ord_less_rat @ X6 @ Xa ) ) )
% 5.41/5.69 => ~ ( finite_finite_rat @ X8 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_growing
% 5.41/5.69 thf(fact_3725_infinite__growing,axiom,
% 5.41/5.69 ! [X8: set_num] :
% 5.41/5.69 ( ( X8 != bot_bot_set_num )
% 5.41/5.69 => ( ! [X6: num] :
% 5.41/5.69 ( ( member_num @ X6 @ X8 )
% 5.41/5.69 => ? [Xa: num] :
% 5.41/5.69 ( ( member_num @ Xa @ X8 )
% 5.41/5.69 & ( ord_less_num @ X6 @ Xa ) ) )
% 5.41/5.69 => ~ ( finite_finite_num @ X8 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_growing
% 5.41/5.69 thf(fact_3726_infinite__growing,axiom,
% 5.41/5.69 ! [X8: set_nat] :
% 5.41/5.69 ( ( X8 != bot_bot_set_nat )
% 5.41/5.69 => ( ! [X6: nat] :
% 5.41/5.69 ( ( member_nat @ X6 @ X8 )
% 5.41/5.69 => ? [Xa: nat] :
% 5.41/5.69 ( ( member_nat @ Xa @ X8 )
% 5.41/5.69 & ( ord_less_nat @ X6 @ Xa ) ) )
% 5.41/5.69 => ~ ( finite_finite_nat @ X8 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_growing
% 5.41/5.69 thf(fact_3727_infinite__growing,axiom,
% 5.41/5.69 ! [X8: set_int] :
% 5.41/5.69 ( ( X8 != bot_bot_set_int )
% 5.41/5.69 => ( ! [X6: int] :
% 5.41/5.69 ( ( member_int @ X6 @ X8 )
% 5.41/5.69 => ? [Xa: int] :
% 5.41/5.69 ( ( member_int @ Xa @ X8 )
% 5.41/5.69 & ( ord_less_int @ X6 @ Xa ) ) )
% 5.41/5.69 => ~ ( finite_finite_int @ X8 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_growing
% 5.41/5.69 thf(fact_3728_infinite__Icc,axiom,
% 5.41/5.69 ! [A: rat,B: rat] :
% 5.41/5.69 ( ( ord_less_rat @ A @ B )
% 5.41/5.69 => ~ ( finite_finite_rat @ ( set_or633870826150836451st_rat @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_Icc
% 5.41/5.69 thf(fact_3729_infinite__Icc,axiom,
% 5.41/5.69 ! [A: real,B: real] :
% 5.41/5.69 ( ( ord_less_real @ A @ B )
% 5.41/5.69 => ~ ( finite_finite_real @ ( set_or1222579329274155063t_real @ A @ B ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % infinite_Icc
% 5.41/5.69 thf(fact_3730_finite__lists__length__le,axiom,
% 5.41/5.69 ! [A2: set_complex,N: nat] :
% 5.41/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.69 => ( finite8712137658972009173omplex
% 5.41/5.69 @ ( collect_list_complex
% 5.41/5.69 @ ^ [Xs2: list_complex] :
% 5.41/5.69 ( ( ord_le211207098394363844omplex @ ( set_complex2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ord_less_eq_nat @ ( size_s3451745648224563538omplex @ Xs2 ) @ N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_le
% 5.41/5.69 thf(fact_3731_finite__lists__length__le,axiom,
% 5.41/5.69 ! [A2: set_VEBT_VEBT,N: nat] :
% 5.41/5.69 ( ( finite5795047828879050333T_VEBT @ A2 )
% 5.41/5.69 => ( finite3004134309566078307T_VEBT
% 5.41/5.69 @ ( collec5608196760682091941T_VEBT
% 5.41/5.69 @ ^ [Xs2: list_VEBT_VEBT] :
% 5.41/5.69 ( ( ord_le4337996190870823476T_VEBT @ ( set_VEBT_VEBT2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ord_less_eq_nat @ ( size_s6755466524823107622T_VEBT @ Xs2 ) @ N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_le
% 5.41/5.69 thf(fact_3732_finite__lists__length__le,axiom,
% 5.41/5.69 ! [A2: set_o,N: nat] :
% 5.41/5.69 ( ( finite_finite_o @ A2 )
% 5.41/5.69 => ( finite_finite_list_o
% 5.41/5.69 @ ( collect_list_o
% 5.41/5.69 @ ^ [Xs2: list_o] :
% 5.41/5.69 ( ( ord_less_eq_set_o @ ( set_o2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ord_less_eq_nat @ ( size_size_list_o @ Xs2 ) @ N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_le
% 5.41/5.69 thf(fact_3733_finite__lists__length__le,axiom,
% 5.41/5.69 ! [A2: set_nat,N: nat] :
% 5.41/5.69 ( ( finite_finite_nat @ A2 )
% 5.41/5.69 => ( finite8100373058378681591st_nat
% 5.41/5.69 @ ( collect_list_nat
% 5.41/5.69 @ ^ [Xs2: list_nat] :
% 5.41/5.69 ( ( ord_less_eq_set_nat @ ( set_nat2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ord_less_eq_nat @ ( size_size_list_nat @ Xs2 ) @ N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_le
% 5.41/5.69 thf(fact_3734_finite__lists__length__le,axiom,
% 5.41/5.69 ! [A2: set_int,N: nat] :
% 5.41/5.69 ( ( finite_finite_int @ A2 )
% 5.41/5.69 => ( finite3922522038869484883st_int
% 5.41/5.69 @ ( collect_list_int
% 5.41/5.69 @ ^ [Xs2: list_int] :
% 5.41/5.69 ( ( ord_less_eq_set_int @ ( set_int2 @ Xs2 ) @ A2 )
% 5.41/5.69 & ( ord_less_eq_nat @ ( size_size_list_int @ Xs2 ) @ N ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_lists_length_le
% 5.41/5.69 thf(fact_3735_eucl__rel__int__dividesI,axiom,
% 5.41/5.69 ! [L2: int,K: int,Q2: int] :
% 5.41/5.69 ( ( L2 != zero_zero_int )
% 5.41/5.69 => ( ( K
% 5.41/5.69 = ( times_times_int @ Q2 @ L2 ) )
% 5.41/5.69 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ zero_zero_int ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % eucl_rel_int_dividesI
% 5.41/5.69 thf(fact_3736_eucl__rel__int,axiom,
% 5.41/5.69 ! [K: int,L2: int] : ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ ( divide_divide_int @ K @ L2 ) @ ( modulo_modulo_int @ K @ L2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % eucl_rel_int
% 5.41/5.69 thf(fact_3737_subset__eq__atLeast0__atMost__finite,axiom,
% 5.41/5.69 ! [N4: set_nat,N: nat] :
% 5.41/5.69 ( ( ord_less_eq_set_nat @ N4 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.69 => ( finite_finite_nat @ N4 ) ) ).
% 5.41/5.69
% 5.41/5.69 % subset_eq_atLeast0_atMost_finite
% 5.41/5.69 thf(fact_3738_eucl__rel__int__iff,axiom,
% 5.41/5.69 ! [K: int,L2: int,Q2: int,R: int] :
% 5.41/5.69 ( ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 = ( ( K
% 5.41/5.69 = ( plus_plus_int @ ( times_times_int @ L2 @ Q2 ) @ R ) )
% 5.41/5.69 & ( ( ord_less_int @ zero_zero_int @ L2 )
% 5.41/5.69 => ( ( ord_less_eq_int @ zero_zero_int @ R )
% 5.41/5.69 & ( ord_less_int @ R @ L2 ) ) )
% 5.41/5.69 & ( ~ ( ord_less_int @ zero_zero_int @ L2 )
% 5.41/5.69 => ( ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.41/5.69 => ( ( ord_less_int @ L2 @ R )
% 5.41/5.69 & ( ord_less_eq_int @ R @ zero_zero_int ) ) )
% 5.41/5.69 & ( ~ ( ord_less_int @ L2 @ zero_zero_int )
% 5.41/5.69 => ( Q2 = zero_zero_int ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % eucl_rel_int_iff
% 5.41/5.69 thf(fact_3739_mult__less__iff1,axiom,
% 5.41/5.69 ! [Z: real,X: real,Y: real] :
% 5.41/5.69 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.41/5.69 => ( ( ord_less_real @ ( times_times_real @ X @ Z ) @ ( times_times_real @ Y @ Z ) )
% 5.41/5.69 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_less_iff1
% 5.41/5.69 thf(fact_3740_mult__less__iff1,axiom,
% 5.41/5.69 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.69 ( ( ord_less_rat @ zero_zero_rat @ Z )
% 5.41/5.69 => ( ( ord_less_rat @ ( times_times_rat @ X @ Z ) @ ( times_times_rat @ Y @ Z ) )
% 5.41/5.69 = ( ord_less_rat @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_less_iff1
% 5.41/5.69 thf(fact_3741_mult__less__iff1,axiom,
% 5.41/5.69 ! [Z: int,X: int,Y: int] :
% 5.41/5.69 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.69 => ( ( ord_less_int @ ( times_times_int @ X @ Z ) @ ( times_times_int @ Y @ Z ) )
% 5.41/5.69 = ( ord_less_int @ X @ Y ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % mult_less_iff1
% 5.41/5.69 thf(fact_3742_pos__eucl__rel__int__mult__2,axiom,
% 5.41/5.69 ! [B: int,A: int,Q2: int,R: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.69 => ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.69 => ( eucl_rel_int @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) @ ( product_Pair_int_int @ Q2 @ ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % pos_eucl_rel_int_mult_2
% 5.41/5.69 thf(fact_3743_finite__Collect__le__nat,axiom,
% 5.41/5.69 ! [K: nat] :
% 5.41/5.69 ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [N2: nat] : ( ord_less_eq_nat @ N2 @ K ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Collect_le_nat
% 5.41/5.69 thf(fact_3744_finite__Collect__less__nat,axiom,
% 5.41/5.69 ! [K: nat] :
% 5.41/5.69 ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [N2: nat] : ( ord_less_nat @ N2 @ K ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Collect_less_nat
% 5.41/5.69 thf(fact_3745_finite__Collect__subsets,axiom,
% 5.41/5.69 ! [A2: set_nat] :
% 5.41/5.69 ( ( finite_finite_nat @ A2 )
% 5.41/5.69 => ( finite1152437895449049373et_nat
% 5.41/5.69 @ ( collect_set_nat
% 5.41/5.69 @ ^ [B6: set_nat] : ( ord_less_eq_set_nat @ B6 @ A2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Collect_subsets
% 5.41/5.69 thf(fact_3746_finite__Collect__subsets,axiom,
% 5.41/5.69 ! [A2: set_complex] :
% 5.41/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.69 => ( finite6551019134538273531omplex
% 5.41/5.69 @ ( collect_set_complex
% 5.41/5.69 @ ^ [B6: set_complex] : ( ord_le211207098394363844omplex @ B6 @ A2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Collect_subsets
% 5.41/5.69 thf(fact_3747_finite__Collect__subsets,axiom,
% 5.41/5.69 ! [A2: set_int] :
% 5.41/5.69 ( ( finite_finite_int @ A2 )
% 5.41/5.69 => ( finite6197958912794628473et_int
% 5.41/5.69 @ ( collect_set_int
% 5.41/5.69 @ ^ [B6: set_int] : ( ord_less_eq_set_int @ B6 @ A2 ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Collect_subsets
% 5.41/5.69 thf(fact_3748_finite__roots__unity,axiom,
% 5.41/5.69 ! [N: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.41/5.69 => ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [Z3: real] :
% 5.41/5.69 ( ( power_power_real @ Z3 @ N )
% 5.41/5.69 = one_one_real ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_roots_unity
% 5.41/5.69 thf(fact_3749_finite__roots__unity,axiom,
% 5.41/5.69 ! [N: nat] :
% 5.41/5.69 ( ( ord_less_eq_nat @ one_one_nat @ N )
% 5.41/5.69 => ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [Z3: complex] :
% 5.41/5.69 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.69 = one_one_complex ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_roots_unity
% 5.41/5.69 thf(fact_3750_finite__Diff2,axiom,
% 5.41/5.69 ! [B3: set_int,A2: set_int] :
% 5.41/5.69 ( ( finite_finite_int @ B3 )
% 5.41/5.69 => ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.69 = ( finite_finite_int @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Diff2
% 5.41/5.69 thf(fact_3751_finite__Diff2,axiom,
% 5.41/5.69 ! [B3: set_complex,A2: set_complex] :
% 5.41/5.69 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.69 => ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.69 = ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Diff2
% 5.41/5.69 thf(fact_3752_finite__Diff2,axiom,
% 5.41/5.69 ! [B3: set_nat,A2: set_nat] :
% 5.41/5.69 ( ( finite_finite_nat @ B3 )
% 5.41/5.69 => ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.69 = ( finite_finite_nat @ A2 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Diff2
% 5.41/5.69 thf(fact_3753_finite__Diff,axiom,
% 5.41/5.69 ! [A2: set_int,B3: set_int] :
% 5.41/5.69 ( ( finite_finite_int @ A2 )
% 5.41/5.69 => ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Diff
% 5.41/5.69 thf(fact_3754_finite__Diff,axiom,
% 5.41/5.69 ! [A2: set_complex,B3: set_complex] :
% 5.41/5.69 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.69 => ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Diff
% 5.41/5.69 thf(fact_3755_finite__Diff,axiom,
% 5.41/5.69 ! [A2: set_nat,B3: set_nat] :
% 5.41/5.69 ( ( finite_finite_nat @ A2 )
% 5.41/5.69 => ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_Diff
% 5.41/5.69 thf(fact_3756_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_real,X: real > complex,Y: real > complex] :
% 5.41/5.69 ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3757_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 5.41/5.69 ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3758_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_int,X: int > complex,Y: int > complex] :
% 5.41/5.69 ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3759_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 5.41/5.69 ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_complex ) ) ) )
% 5.41/5.69 => ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3760_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_real,X: real > real,Y: real > real] :
% 5.41/5.69 ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3761_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 5.41/5.69 ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3762_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_int,X: int > real,Y: int > real] :
% 5.41/5.69 ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3763_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 5.41/5.69 ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_real ) ) ) )
% 5.41/5.69 => ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3764_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_real,X: real > rat,Y: real > rat] :
% 5.41/5.69 ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_rat ) ) ) )
% 5.41/5.69 => ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_rat ) ) ) )
% 5.41/5.69 => ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_rat ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3765_prod_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 5.41/5.69 ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != one_one_rat ) ) ) )
% 5.41/5.69 => ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != one_one_rat ) ) ) )
% 5.41/5.69 => ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( times_times_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != one_one_rat ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % prod.finite_Collect_op
% 5.41/5.69 thf(fact_3766_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_real,X: real > complex,Y: real > complex] :
% 5.41/5.69 ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3767_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_nat,X: nat > complex,Y: nat > complex] :
% 5.41/5.69 ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3768_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_int,X: int > complex,Y: int > complex] :
% 5.41/5.69 ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3769_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_complex,X: complex > complex,Y: complex > complex] :
% 5.41/5.69 ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_complex ) ) ) )
% 5.41/5.69 => ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_complex @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_complex ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3770_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_real,X: real > real,Y: real > real] :
% 5.41/5.69 ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3771_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_nat,X: nat > real,Y: nat > real] :
% 5.41/5.69 ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3772_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_int,X: int > real,Y: int > real] :
% 5.41/5.69 ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( member_int @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3773_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_complex,X: complex > real,Y: complex > real] :
% 5.41/5.69 ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_real ) ) ) )
% 5.41/5.69 => ( finite3207457112153483333omplex
% 5.41/5.69 @ ( collect_complex
% 5.41/5.69 @ ^ [I5: complex] :
% 5.41/5.69 ( ( member_complex @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_real @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3774_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_real,X: real > rat,Y: real > rat] :
% 5.41/5.69 ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_rat ) ) ) )
% 5.41/5.69 => ( ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_rat ) ) ) )
% 5.41/5.69 => ( finite_finite_real
% 5.41/5.69 @ ( collect_real
% 5.41/5.69 @ ^ [I5: real] :
% 5.41/5.69 ( ( member_real @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3775_sum_Ofinite__Collect__op,axiom,
% 5.41/5.69 ! [I6: set_nat,X: nat > rat,Y: nat > rat] :
% 5.41/5.69 ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( X @ I5 )
% 5.41/5.69 != zero_zero_rat ) ) ) )
% 5.41/5.69 => ( ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( Y @ I5 )
% 5.41/5.69 != zero_zero_rat ) ) ) )
% 5.41/5.69 => ( finite_finite_nat
% 5.41/5.69 @ ( collect_nat
% 5.41/5.69 @ ^ [I5: nat] :
% 5.41/5.69 ( ( member_nat @ I5 @ I6 )
% 5.41/5.69 & ( ( plus_plus_rat @ ( X @ I5 ) @ ( Y @ I5 ) )
% 5.41/5.69 != zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % sum.finite_Collect_op
% 5.41/5.69 thf(fact_3776_finite__atLeastAtMost__int,axiom,
% 5.41/5.69 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_atLeastAtMost_int
% 5.41/5.69 thf(fact_3777_finite__interval__int1,axiom,
% 5.41/5.69 ! [A: int,B: int] :
% 5.41/5.69 ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( ord_less_eq_int @ A @ I5 )
% 5.41/5.69 & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 5.41/5.69
% 5.41/5.69 % finite_interval_int1
% 5.41/5.69 thf(fact_3778_finite__interval__int3,axiom,
% 5.41/5.69 ! [A: int,B: int] :
% 5.41/5.69 ( finite_finite_int
% 5.41/5.69 @ ( collect_int
% 5.41/5.69 @ ^ [I5: int] :
% 5.41/5.69 ( ( ord_less_int @ A @ I5 )
% 5.41/5.69 & ( ord_less_eq_int @ I5 @ B ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_interval_int3
% 5.41/5.70 thf(fact_3779_finite__interval__int2,axiom,
% 5.41/5.70 ! [A: int,B: int] :
% 5.41/5.70 ( finite_finite_int
% 5.41/5.70 @ ( collect_int
% 5.41/5.70 @ ^ [I5: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ A @ I5 )
% 5.41/5.70 & ( ord_less_int @ I5 @ B ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_interval_int2
% 5.41/5.70 thf(fact_3780_finite__maxlen,axiom,
% 5.41/5.70 ! [M5: set_list_VEBT_VEBT] :
% 5.41/5.70 ( ( finite3004134309566078307T_VEBT @ M5 )
% 5.41/5.70 => ? [N3: nat] :
% 5.41/5.70 ! [X4: list_VEBT_VEBT] :
% 5.41/5.70 ( ( member2936631157270082147T_VEBT @ X4 @ M5 )
% 5.41/5.70 => ( ord_less_nat @ ( size_s6755466524823107622T_VEBT @ X4 ) @ N3 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_maxlen
% 5.41/5.70 thf(fact_3781_finite__maxlen,axiom,
% 5.41/5.70 ! [M5: set_list_o] :
% 5.41/5.70 ( ( finite_finite_list_o @ M5 )
% 5.41/5.70 => ? [N3: nat] :
% 5.41/5.70 ! [X4: list_o] :
% 5.41/5.70 ( ( member_list_o @ X4 @ M5 )
% 5.41/5.70 => ( ord_less_nat @ ( size_size_list_o @ X4 ) @ N3 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_maxlen
% 5.41/5.70 thf(fact_3782_finite__maxlen,axiom,
% 5.41/5.70 ! [M5: set_list_nat] :
% 5.41/5.70 ( ( finite8100373058378681591st_nat @ M5 )
% 5.41/5.70 => ? [N3: nat] :
% 5.41/5.70 ! [X4: list_nat] :
% 5.41/5.70 ( ( member_list_nat @ X4 @ M5 )
% 5.41/5.70 => ( ord_less_nat @ ( size_size_list_nat @ X4 ) @ N3 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_maxlen
% 5.41/5.70 thf(fact_3783_finite__maxlen,axiom,
% 5.41/5.70 ! [M5: set_list_int] :
% 5.41/5.70 ( ( finite3922522038869484883st_int @ M5 )
% 5.41/5.70 => ? [N3: nat] :
% 5.41/5.70 ! [X4: list_int] :
% 5.41/5.70 ( ( member_list_int @ X4 @ M5 )
% 5.41/5.70 => ( ord_less_nat @ ( size_size_list_int @ X4 ) @ N3 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_maxlen
% 5.41/5.70 thf(fact_3784_finite__has__maximal2,axiom,
% 5.41/5.70 ! [A2: set_real,A: real] :
% 5.41/5.70 ( ( finite_finite_real @ A2 )
% 5.41/5.70 => ( ( member_real @ A @ A2 )
% 5.41/5.70 => ? [X6: real] :
% 5.41/5.70 ( ( member_real @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_real @ A @ X6 )
% 5.41/5.70 & ! [Xa: real] :
% 5.41/5.70 ( ( member_real @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_real @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal2
% 5.41/5.70 thf(fact_3785_finite__has__maximal2,axiom,
% 5.41/5.70 ! [A2: set_set_nat,A: set_nat] :
% 5.41/5.70 ( ( finite1152437895449049373et_nat @ A2 )
% 5.41/5.70 => ( ( member_set_nat @ A @ A2 )
% 5.41/5.70 => ? [X6: set_nat] :
% 5.41/5.70 ( ( member_set_nat @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_set_nat @ A @ X6 )
% 5.41/5.70 & ! [Xa: set_nat] :
% 5.41/5.70 ( ( member_set_nat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_set_nat @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal2
% 5.41/5.70 thf(fact_3786_finite__has__maximal2,axiom,
% 5.41/5.70 ! [A2: set_set_int,A: set_int] :
% 5.41/5.70 ( ( finite6197958912794628473et_int @ A2 )
% 5.41/5.70 => ( ( member_set_int @ A @ A2 )
% 5.41/5.70 => ? [X6: set_int] :
% 5.41/5.70 ( ( member_set_int @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_set_int @ A @ X6 )
% 5.41/5.70 & ! [Xa: set_int] :
% 5.41/5.70 ( ( member_set_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal2
% 5.41/5.70 thf(fact_3787_finite__has__maximal2,axiom,
% 5.41/5.70 ! [A2: set_rat,A: rat] :
% 5.41/5.70 ( ( finite_finite_rat @ A2 )
% 5.41/5.70 => ( ( member_rat @ A @ A2 )
% 5.41/5.70 => ? [X6: rat] :
% 5.41/5.70 ( ( member_rat @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_rat @ A @ X6 )
% 5.41/5.70 & ! [Xa: rat] :
% 5.41/5.70 ( ( member_rat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_rat @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal2
% 5.41/5.70 thf(fact_3788_finite__has__maximal2,axiom,
% 5.41/5.70 ! [A2: set_num,A: num] :
% 5.41/5.70 ( ( finite_finite_num @ A2 )
% 5.41/5.70 => ( ( member_num @ A @ A2 )
% 5.41/5.70 => ? [X6: num] :
% 5.41/5.70 ( ( member_num @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_num @ A @ X6 )
% 5.41/5.70 & ! [Xa: num] :
% 5.41/5.70 ( ( member_num @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_num @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal2
% 5.41/5.70 thf(fact_3789_finite__has__maximal2,axiom,
% 5.41/5.70 ! [A2: set_nat,A: nat] :
% 5.41/5.70 ( ( finite_finite_nat @ A2 )
% 5.41/5.70 => ( ( member_nat @ A @ A2 )
% 5.41/5.70 => ? [X6: nat] :
% 5.41/5.70 ( ( member_nat @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_nat @ A @ X6 )
% 5.41/5.70 & ! [Xa: nat] :
% 5.41/5.70 ( ( member_nat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_nat @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal2
% 5.41/5.70 thf(fact_3790_finite__has__maximal2,axiom,
% 5.41/5.70 ! [A2: set_int,A: int] :
% 5.41/5.70 ( ( finite_finite_int @ A2 )
% 5.41/5.70 => ( ( member_int @ A @ A2 )
% 5.41/5.70 => ? [X6: int] :
% 5.41/5.70 ( ( member_int @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_int @ A @ X6 )
% 5.41/5.70 & ! [Xa: int] :
% 5.41/5.70 ( ( member_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_int @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal2
% 5.41/5.70 thf(fact_3791_finite__has__minimal2,axiom,
% 5.41/5.70 ! [A2: set_real,A: real] :
% 5.41/5.70 ( ( finite_finite_real @ A2 )
% 5.41/5.70 => ( ( member_real @ A @ A2 )
% 5.41/5.70 => ? [X6: real] :
% 5.41/5.70 ( ( member_real @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_real @ X6 @ A )
% 5.41/5.70 & ! [Xa: real] :
% 5.41/5.70 ( ( member_real @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_real @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal2
% 5.41/5.70 thf(fact_3792_finite__has__minimal2,axiom,
% 5.41/5.70 ! [A2: set_set_nat,A: set_nat] :
% 5.41/5.70 ( ( finite1152437895449049373et_nat @ A2 )
% 5.41/5.70 => ( ( member_set_nat @ A @ A2 )
% 5.41/5.70 => ? [X6: set_nat] :
% 5.41/5.70 ( ( member_set_nat @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_set_nat @ X6 @ A )
% 5.41/5.70 & ! [Xa: set_nat] :
% 5.41/5.70 ( ( member_set_nat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_set_nat @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal2
% 5.41/5.70 thf(fact_3793_finite__has__minimal2,axiom,
% 5.41/5.70 ! [A2: set_set_int,A: set_int] :
% 5.41/5.70 ( ( finite6197958912794628473et_int @ A2 )
% 5.41/5.70 => ( ( member_set_int @ A @ A2 )
% 5.41/5.70 => ? [X6: set_int] :
% 5.41/5.70 ( ( member_set_int @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_set_int @ X6 @ A )
% 5.41/5.70 & ! [Xa: set_int] :
% 5.41/5.70 ( ( member_set_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal2
% 5.41/5.70 thf(fact_3794_finite__has__minimal2,axiom,
% 5.41/5.70 ! [A2: set_rat,A: rat] :
% 5.41/5.70 ( ( finite_finite_rat @ A2 )
% 5.41/5.70 => ( ( member_rat @ A @ A2 )
% 5.41/5.70 => ? [X6: rat] :
% 5.41/5.70 ( ( member_rat @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_rat @ X6 @ A )
% 5.41/5.70 & ! [Xa: rat] :
% 5.41/5.70 ( ( member_rat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_rat @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal2
% 5.41/5.70 thf(fact_3795_finite__has__minimal2,axiom,
% 5.41/5.70 ! [A2: set_num,A: num] :
% 5.41/5.70 ( ( finite_finite_num @ A2 )
% 5.41/5.70 => ( ( member_num @ A @ A2 )
% 5.41/5.70 => ? [X6: num] :
% 5.41/5.70 ( ( member_num @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_num @ X6 @ A )
% 5.41/5.70 & ! [Xa: num] :
% 5.41/5.70 ( ( member_num @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_num @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal2
% 5.41/5.70 thf(fact_3796_finite__has__minimal2,axiom,
% 5.41/5.70 ! [A2: set_nat,A: nat] :
% 5.41/5.70 ( ( finite_finite_nat @ A2 )
% 5.41/5.70 => ( ( member_nat @ A @ A2 )
% 5.41/5.70 => ? [X6: nat] :
% 5.41/5.70 ( ( member_nat @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_nat @ X6 @ A )
% 5.41/5.70 & ! [Xa: nat] :
% 5.41/5.70 ( ( member_nat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_nat @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal2
% 5.41/5.70 thf(fact_3797_finite__has__minimal2,axiom,
% 5.41/5.70 ! [A2: set_int,A: int] :
% 5.41/5.70 ( ( finite_finite_int @ A2 )
% 5.41/5.70 => ( ( member_int @ A @ A2 )
% 5.41/5.70 => ? [X6: int] :
% 5.41/5.70 ( ( member_int @ X6 @ A2 )
% 5.41/5.70 & ( ord_less_eq_int @ X6 @ A )
% 5.41/5.70 & ! [Xa: int] :
% 5.41/5.70 ( ( member_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_int @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal2
% 5.41/5.70 thf(fact_3798_finite__subset,axiom,
% 5.41/5.70 ! [A2: set_nat,B3: set_nat] :
% 5.41/5.70 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.70 => ( ( finite_finite_nat @ B3 )
% 5.41/5.70 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_subset
% 5.41/5.70 thf(fact_3799_finite__subset,axiom,
% 5.41/5.70 ! [A2: set_complex,B3: set_complex] :
% 5.41/5.70 ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.70 => ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.70 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_subset
% 5.41/5.70 thf(fact_3800_finite__subset,axiom,
% 5.41/5.70 ! [A2: set_int,B3: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.70 => ( ( finite_finite_int @ B3 )
% 5.41/5.70 => ( finite_finite_int @ A2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_subset
% 5.41/5.70 thf(fact_3801_infinite__super,axiom,
% 5.41/5.70 ! [S2: set_nat,T3: set_nat] :
% 5.41/5.70 ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.70 => ( ~ ( finite_finite_nat @ S2 )
% 5.41/5.70 => ~ ( finite_finite_nat @ T3 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % infinite_super
% 5.41/5.70 thf(fact_3802_infinite__super,axiom,
% 5.41/5.70 ! [S2: set_complex,T3: set_complex] :
% 5.41/5.70 ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.70 => ( ~ ( finite3207457112153483333omplex @ S2 )
% 5.41/5.70 => ~ ( finite3207457112153483333omplex @ T3 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % infinite_super
% 5.41/5.70 thf(fact_3803_infinite__super,axiom,
% 5.41/5.70 ! [S2: set_int,T3: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.41/5.70 => ( ~ ( finite_finite_int @ S2 )
% 5.41/5.70 => ~ ( finite_finite_int @ T3 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % infinite_super
% 5.41/5.70 thf(fact_3804_rev__finite__subset,axiom,
% 5.41/5.70 ! [B3: set_nat,A2: set_nat] :
% 5.41/5.70 ( ( finite_finite_nat @ B3 )
% 5.41/5.70 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.70 => ( finite_finite_nat @ A2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % rev_finite_subset
% 5.41/5.70 thf(fact_3805_rev__finite__subset,axiom,
% 5.41/5.70 ! [B3: set_complex,A2: set_complex] :
% 5.41/5.70 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.70 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.70 => ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % rev_finite_subset
% 5.41/5.70 thf(fact_3806_rev__finite__subset,axiom,
% 5.41/5.70 ! [B3: set_int,A2: set_int] :
% 5.41/5.70 ( ( finite_finite_int @ B3 )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.70 => ( finite_finite_int @ A2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % rev_finite_subset
% 5.41/5.70 thf(fact_3807_Diff__infinite__finite,axiom,
% 5.41/5.70 ! [T3: set_int,S2: set_int] :
% 5.41/5.70 ( ( finite_finite_int @ T3 )
% 5.41/5.70 => ( ~ ( finite_finite_int @ S2 )
% 5.41/5.70 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ T3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Diff_infinite_finite
% 5.41/5.70 thf(fact_3808_Diff__infinite__finite,axiom,
% 5.41/5.70 ! [T3: set_complex,S2: set_complex] :
% 5.41/5.70 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.70 => ( ~ ( finite3207457112153483333omplex @ S2 )
% 5.41/5.70 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ T3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Diff_infinite_finite
% 5.41/5.70 thf(fact_3809_Diff__infinite__finite,axiom,
% 5.41/5.70 ! [T3: set_nat,S2: set_nat] :
% 5.41/5.70 ( ( finite_finite_nat @ T3 )
% 5.41/5.70 => ( ~ ( finite_finite_nat @ S2 )
% 5.41/5.70 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ T3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Diff_infinite_finite
% 5.41/5.70 thf(fact_3810_finite__has__minimal,axiom,
% 5.41/5.70 ! [A2: set_real] :
% 5.41/5.70 ( ( finite_finite_real @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_real )
% 5.41/5.70 => ? [X6: real] :
% 5.41/5.70 ( ( member_real @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: real] :
% 5.41/5.70 ( ( member_real @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_real @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal
% 5.41/5.70 thf(fact_3811_finite__has__minimal,axiom,
% 5.41/5.70 ! [A2: set_set_int] :
% 5.41/5.70 ( ( finite6197958912794628473et_int @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_set_int )
% 5.41/5.70 => ? [X6: set_int] :
% 5.41/5.70 ( ( member_set_int @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: set_int] :
% 5.41/5.70 ( ( member_set_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal
% 5.41/5.70 thf(fact_3812_finite__has__minimal,axiom,
% 5.41/5.70 ! [A2: set_rat] :
% 5.41/5.70 ( ( finite_finite_rat @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_rat )
% 5.41/5.70 => ? [X6: rat] :
% 5.41/5.70 ( ( member_rat @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: rat] :
% 5.41/5.70 ( ( member_rat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_rat @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal
% 5.41/5.70 thf(fact_3813_finite__has__minimal,axiom,
% 5.41/5.70 ! [A2: set_num] :
% 5.41/5.70 ( ( finite_finite_num @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_num )
% 5.41/5.70 => ? [X6: num] :
% 5.41/5.70 ( ( member_num @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: num] :
% 5.41/5.70 ( ( member_num @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_num @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal
% 5.41/5.70 thf(fact_3814_finite__has__minimal,axiom,
% 5.41/5.70 ! [A2: set_nat] :
% 5.41/5.70 ( ( finite_finite_nat @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_nat )
% 5.41/5.70 => ? [X6: nat] :
% 5.41/5.70 ( ( member_nat @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: nat] :
% 5.41/5.70 ( ( member_nat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_nat @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal
% 5.41/5.70 thf(fact_3815_finite__has__minimal,axiom,
% 5.41/5.70 ! [A2: set_int] :
% 5.41/5.70 ( ( finite_finite_int @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_int )
% 5.41/5.70 => ? [X6: int] :
% 5.41/5.70 ( ( member_int @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: int] :
% 5.41/5.70 ( ( member_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_int @ Xa @ X6 )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_minimal
% 5.41/5.70 thf(fact_3816_finite__has__maximal,axiom,
% 5.41/5.70 ! [A2: set_real] :
% 5.41/5.70 ( ( finite_finite_real @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_real )
% 5.41/5.70 => ? [X6: real] :
% 5.41/5.70 ( ( member_real @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: real] :
% 5.41/5.70 ( ( member_real @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_real @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal
% 5.41/5.70 thf(fact_3817_finite__has__maximal,axiom,
% 5.41/5.70 ! [A2: set_set_int] :
% 5.41/5.70 ( ( finite6197958912794628473et_int @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_set_int )
% 5.41/5.70 => ? [X6: set_int] :
% 5.41/5.70 ( ( member_set_int @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: set_int] :
% 5.41/5.70 ( ( member_set_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal
% 5.41/5.70 thf(fact_3818_finite__has__maximal,axiom,
% 5.41/5.70 ! [A2: set_rat] :
% 5.41/5.70 ( ( finite_finite_rat @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_rat )
% 5.41/5.70 => ? [X6: rat] :
% 5.41/5.70 ( ( member_rat @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: rat] :
% 5.41/5.70 ( ( member_rat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_rat @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal
% 5.41/5.70 thf(fact_3819_finite__has__maximal,axiom,
% 5.41/5.70 ! [A2: set_num] :
% 5.41/5.70 ( ( finite_finite_num @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_num )
% 5.41/5.70 => ? [X6: num] :
% 5.41/5.70 ( ( member_num @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: num] :
% 5.41/5.70 ( ( member_num @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_num @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal
% 5.41/5.70 thf(fact_3820_finite__has__maximal,axiom,
% 5.41/5.70 ! [A2: set_nat] :
% 5.41/5.70 ( ( finite_finite_nat @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_nat )
% 5.41/5.70 => ? [X6: nat] :
% 5.41/5.70 ( ( member_nat @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: nat] :
% 5.41/5.70 ( ( member_nat @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_nat @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal
% 5.41/5.70 thf(fact_3821_finite__has__maximal,axiom,
% 5.41/5.70 ! [A2: set_int] :
% 5.41/5.70 ( ( finite_finite_int @ A2 )
% 5.41/5.70 => ( ( A2 != bot_bot_set_int )
% 5.41/5.70 => ? [X6: int] :
% 5.41/5.70 ( ( member_int @ X6 @ A2 )
% 5.41/5.70 & ! [Xa: int] :
% 5.41/5.70 ( ( member_int @ Xa @ A2 )
% 5.41/5.70 => ( ( ord_less_eq_int @ X6 @ Xa )
% 5.41/5.70 => ( X6 = Xa ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_has_maximal
% 5.41/5.70 thf(fact_3822_arcosh__1,axiom,
% 5.41/5.70 ( ( arcosh_real @ one_one_real )
% 5.41/5.70 = zero_zero_real ) ).
% 5.41/5.70
% 5.41/5.70 % arcosh_1
% 5.41/5.70 thf(fact_3823_finite__nth__roots,axiom,
% 5.41/5.70 ! [N: nat,C: complex] :
% 5.41/5.70 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.70 => ( finite3207457112153483333omplex
% 5.41/5.70 @ ( collect_complex
% 5.41/5.70 @ ^ [Z3: complex] :
% 5.41/5.70 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.70 = C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % finite_nth_roots
% 5.41/5.70 thf(fact_3824_artanh__0,axiom,
% 5.41/5.70 ( ( artanh_real @ zero_zero_real )
% 5.41/5.70 = zero_zero_real ) ).
% 5.41/5.70
% 5.41/5.70 % artanh_0
% 5.41/5.70 thf(fact_3825_arsinh__0,axiom,
% 5.41/5.70 ( ( arsinh_real @ zero_zero_real )
% 5.41/5.70 = zero_zero_real ) ).
% 5.41/5.70
% 5.41/5.70 % arsinh_0
% 5.41/5.70 thf(fact_3826_prod_Oinject,axiom,
% 5.41/5.70 ! [X1: int,X22: int,Y1: int,Y22: int] :
% 5.41/5.70 ( ( ( product_Pair_int_int @ X1 @ X22 )
% 5.41/5.70 = ( product_Pair_int_int @ Y1 @ Y22 ) )
% 5.41/5.70 = ( ( X1 = Y1 )
% 5.41/5.70 & ( X22 = Y22 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod.inject
% 5.41/5.70 thf(fact_3827_prod_Oinject,axiom,
% 5.41/5.70 ! [X1: code_integer > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: code_integer > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 5.41/5.70 ( ( ( produc6137756002093451184nteger @ X1 @ X22 )
% 5.41/5.70 = ( produc6137756002093451184nteger @ Y1 @ Y22 ) )
% 5.41/5.70 = ( ( X1 = Y1 )
% 5.41/5.70 & ( X22 = Y22 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod.inject
% 5.41/5.70 thf(fact_3828_prod_Oinject,axiom,
% 5.41/5.70 ! [X1: produc6241069584506657477e_term > option6357759511663192854e_term,X22: produc8923325533196201883nteger,Y1: produc6241069584506657477e_term > option6357759511663192854e_term,Y22: produc8923325533196201883nteger] :
% 5.41/5.70 ( ( ( produc8603105652947943368nteger @ X1 @ X22 )
% 5.41/5.70 = ( produc8603105652947943368nteger @ Y1 @ Y22 ) )
% 5.41/5.70 = ( ( X1 = Y1 )
% 5.41/5.70 & ( X22 = Y22 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod.inject
% 5.41/5.70 thf(fact_3829_prod_Oinject,axiom,
% 5.41/5.70 ! [X1: produc8551481072490612790e_term > option6357759511663192854e_term,X22: product_prod_int_int,Y1: produc8551481072490612790e_term > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 5.41/5.70 ( ( ( produc5700946648718959541nt_int @ X1 @ X22 )
% 5.41/5.70 = ( produc5700946648718959541nt_int @ Y1 @ Y22 ) )
% 5.41/5.70 = ( ( X1 = Y1 )
% 5.41/5.70 & ( X22 = Y22 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod.inject
% 5.41/5.70 thf(fact_3830_prod_Oinject,axiom,
% 5.41/5.70 ! [X1: int > option6357759511663192854e_term,X22: product_prod_int_int,Y1: int > option6357759511663192854e_term,Y22: product_prod_int_int] :
% 5.41/5.70 ( ( ( produc4305682042979456191nt_int @ X1 @ X22 )
% 5.41/5.70 = ( produc4305682042979456191nt_int @ Y1 @ Y22 ) )
% 5.41/5.70 = ( ( X1 = Y1 )
% 5.41/5.70 & ( X22 = Y22 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod.inject
% 5.41/5.70 thf(fact_3831_old_Oprod_Oinject,axiom,
% 5.41/5.70 ! [A: int,B: int,A4: int,B4: int] :
% 5.41/5.70 ( ( ( product_Pair_int_int @ A @ B )
% 5.41/5.70 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.41/5.70 = ( ( A = A4 )
% 5.41/5.70 & ( B = B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.inject
% 5.41/5.70 thf(fact_3832_old_Oprod_Oinject,axiom,
% 5.41/5.70 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.41/5.70 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.41/5.70 = ( produc6137756002093451184nteger @ A4 @ B4 ) )
% 5.41/5.70 = ( ( A = A4 )
% 5.41/5.70 & ( B = B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.inject
% 5.41/5.70 thf(fact_3833_old_Oprod_Oinject,axiom,
% 5.41/5.70 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.41/5.70 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.41/5.70 = ( produc8603105652947943368nteger @ A4 @ B4 ) )
% 5.41/5.70 = ( ( A = A4 )
% 5.41/5.70 & ( B = B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.inject
% 5.41/5.70 thf(fact_3834_old_Oprod_Oinject,axiom,
% 5.41/5.70 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.41/5.70 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.41/5.70 = ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 5.41/5.70 = ( ( A = A4 )
% 5.41/5.70 & ( B = B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.inject
% 5.41/5.70 thf(fact_3835_old_Oprod_Oinject,axiom,
% 5.41/5.70 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.41/5.70 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.41/5.70 = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.41/5.70 = ( ( A = A4 )
% 5.41/5.70 & ( B = B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.inject
% 5.41/5.70 thf(fact_3836_old_Oprod_Oexhaust,axiom,
% 5.41/5.70 ! [Y: product_prod_int_int] :
% 5.41/5.70 ~ ! [A5: int,B5: int] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( product_Pair_int_int @ A5 @ B5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.exhaust
% 5.41/5.70 thf(fact_3837_old_Oprod_Oexhaust,axiom,
% 5.41/5.70 ! [Y: produc8763457246119570046nteger] :
% 5.41/5.70 ~ ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc6137756002093451184nteger @ A5 @ B5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.exhaust
% 5.41/5.70 thf(fact_3838_old_Oprod_Oexhaust,axiom,
% 5.41/5.70 ! [Y: produc1908205239877642774nteger] :
% 5.41/5.70 ~ ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc8603105652947943368nteger @ A5 @ B5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.exhaust
% 5.41/5.70 thf(fact_3839_old_Oprod_Oexhaust,axiom,
% 5.41/5.70 ! [Y: produc2285326912895808259nt_int] :
% 5.41/5.70 ~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc5700946648718959541nt_int @ A5 @ B5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.exhaust
% 5.41/5.70 thf(fact_3840_old_Oprod_Oexhaust,axiom,
% 5.41/5.70 ! [Y: produc7773217078559923341nt_int] :
% 5.41/5.70 ~ ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc4305682042979456191nt_int @ A5 @ B5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % old.prod.exhaust
% 5.41/5.70 thf(fact_3841_surj__pair,axiom,
% 5.41/5.70 ! [P5: product_prod_int_int] :
% 5.41/5.70 ? [X6: int,Y5: int] :
% 5.41/5.70 ( P5
% 5.41/5.70 = ( product_Pair_int_int @ X6 @ Y5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % surj_pair
% 5.41/5.70 thf(fact_3842_surj__pair,axiom,
% 5.41/5.70 ! [P5: produc8763457246119570046nteger] :
% 5.41/5.70 ? [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.70 ( P5
% 5.41/5.70 = ( produc6137756002093451184nteger @ X6 @ Y5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % surj_pair
% 5.41/5.70 thf(fact_3843_surj__pair,axiom,
% 5.41/5.70 ! [P5: produc1908205239877642774nteger] :
% 5.41/5.70 ? [X6: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.70 ( P5
% 5.41/5.70 = ( produc8603105652947943368nteger @ X6 @ Y5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % surj_pair
% 5.41/5.70 thf(fact_3844_surj__pair,axiom,
% 5.41/5.70 ! [P5: produc2285326912895808259nt_int] :
% 5.41/5.70 ? [X6: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 5.41/5.70 ( P5
% 5.41/5.70 = ( produc5700946648718959541nt_int @ X6 @ Y5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % surj_pair
% 5.41/5.70 thf(fact_3845_surj__pair,axiom,
% 5.41/5.70 ! [P5: produc7773217078559923341nt_int] :
% 5.41/5.70 ? [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 5.41/5.70 ( P5
% 5.41/5.70 = ( produc4305682042979456191nt_int @ X6 @ Y5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % surj_pair
% 5.41/5.70 thf(fact_3846_prod__cases,axiom,
% 5.41/5.70 ! [P: product_prod_int_int > $o,P5: product_prod_int_int] :
% 5.41/5.70 ( ! [A5: int,B5: int] : ( P @ ( product_Pair_int_int @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ P5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases
% 5.41/5.70 thf(fact_3847_prod__cases,axiom,
% 5.41/5.70 ! [P: produc8763457246119570046nteger > $o,P5: produc8763457246119570046nteger] :
% 5.41/5.70 ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] : ( P @ ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ P5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases
% 5.41/5.70 thf(fact_3848_prod__cases,axiom,
% 5.41/5.70 ! [P: produc1908205239877642774nteger > $o,P5: produc1908205239877642774nteger] :
% 5.41/5.70 ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] : ( P @ ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ P5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases
% 5.41/5.70 thf(fact_3849_prod__cases,axiom,
% 5.41/5.70 ! [P: produc2285326912895808259nt_int > $o,P5: produc2285326912895808259nt_int] :
% 5.41/5.70 ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ P5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases
% 5.41/5.70 thf(fact_3850_prod__cases,axiom,
% 5.41/5.70 ! [P: produc7773217078559923341nt_int > $o,P5: produc7773217078559923341nt_int] :
% 5.41/5.70 ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ P5 ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases
% 5.41/5.70 thf(fact_3851_Pair__inject,axiom,
% 5.41/5.70 ! [A: int,B: int,A4: int,B4: int] :
% 5.41/5.70 ( ( ( product_Pair_int_int @ A @ B )
% 5.41/5.70 = ( product_Pair_int_int @ A4 @ B4 ) )
% 5.41/5.70 => ~ ( ( A = A4 )
% 5.41/5.70 => ( B != B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Pair_inject
% 5.41/5.70 thf(fact_3852_Pair__inject,axiom,
% 5.41/5.70 ! [A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: code_integer > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.41/5.70 ( ( ( produc6137756002093451184nteger @ A @ B )
% 5.41/5.70 = ( produc6137756002093451184nteger @ A4 @ B4 ) )
% 5.41/5.70 => ~ ( ( A = A4 )
% 5.41/5.70 => ( B != B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Pair_inject
% 5.41/5.70 thf(fact_3853_Pair__inject,axiom,
% 5.41/5.70 ! [A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger,A4: produc6241069584506657477e_term > option6357759511663192854e_term,B4: produc8923325533196201883nteger] :
% 5.41/5.70 ( ( ( produc8603105652947943368nteger @ A @ B )
% 5.41/5.70 = ( produc8603105652947943368nteger @ A4 @ B4 ) )
% 5.41/5.70 => ~ ( ( A = A4 )
% 5.41/5.70 => ( B != B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Pair_inject
% 5.41/5.70 thf(fact_3854_Pair__inject,axiom,
% 5.41/5.70 ! [A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int,A4: produc8551481072490612790e_term > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.41/5.70 ( ( ( produc5700946648718959541nt_int @ A @ B )
% 5.41/5.70 = ( produc5700946648718959541nt_int @ A4 @ B4 ) )
% 5.41/5.70 => ~ ( ( A = A4 )
% 5.41/5.70 => ( B != B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Pair_inject
% 5.41/5.70 thf(fact_3855_Pair__inject,axiom,
% 5.41/5.70 ! [A: int > option6357759511663192854e_term,B: product_prod_int_int,A4: int > option6357759511663192854e_term,B4: product_prod_int_int] :
% 5.41/5.70 ( ( ( produc4305682042979456191nt_int @ A @ B )
% 5.41/5.70 = ( produc4305682042979456191nt_int @ A4 @ B4 ) )
% 5.41/5.70 => ~ ( ( A = A4 )
% 5.41/5.70 => ( B != B4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Pair_inject
% 5.41/5.70 thf(fact_3856_prod__cases3,axiom,
% 5.41/5.70 ! [Y: produc8763457246119570046nteger] :
% 5.41/5.70 ~ ! [A5: code_integer > option6357759511663192854e_term,B5: code_integer,C2: code_integer] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc6137756002093451184nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases3
% 5.41/5.70 thf(fact_3857_prod__cases3,axiom,
% 5.41/5.70 ! [Y: produc1908205239877642774nteger] :
% 5.41/5.70 ~ ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: code_integer,C2: code_integer] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc8603105652947943368nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases3
% 5.41/5.70 thf(fact_3858_prod__cases3,axiom,
% 5.41/5.70 ! [Y: produc2285326912895808259nt_int] :
% 5.41/5.70 ~ ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases3
% 5.41/5.70 thf(fact_3859_prod__cases3,axiom,
% 5.41/5.70 ! [Y: produc7773217078559923341nt_int] :
% 5.41/5.70 ~ ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] :
% 5.41/5.70 ( Y
% 5.41/5.70 != ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_cases3
% 5.41/5.70 thf(fact_3860_prod__induct3,axiom,
% 5.41/5.70 ! [P: produc8763457246119570046nteger > $o,X: produc8763457246119570046nteger] :
% 5.41/5.70 ( ! [A5: code_integer > option6357759511663192854e_term,B5: code_integer,C2: code_integer] : ( P @ ( produc6137756002093451184nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) )
% 5.41/5.70 => ( P @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_induct3
% 5.41/5.70 thf(fact_3861_prod__induct3,axiom,
% 5.41/5.70 ! [P: produc1908205239877642774nteger > $o,X: produc1908205239877642774nteger] :
% 5.41/5.70 ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: code_integer,C2: code_integer] : ( P @ ( produc8603105652947943368nteger @ A5 @ ( produc1086072967326762835nteger @ B5 @ C2 ) ) )
% 5.41/5.70 => ( P @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_induct3
% 5.41/5.70 thf(fact_3862_prod__induct3,axiom,
% 5.41/5.70 ! [P: produc2285326912895808259nt_int > $o,X: produc2285326912895808259nt_int] :
% 5.41/5.70 ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc5700946648718959541nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
% 5.41/5.70 => ( P @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_induct3
% 5.41/5.70 thf(fact_3863_prod__induct3,axiom,
% 5.41/5.70 ! [P: produc7773217078559923341nt_int > $o,X: produc7773217078559923341nt_int] :
% 5.41/5.70 ( ! [A5: int > option6357759511663192854e_term,B5: int,C2: int] : ( P @ ( produc4305682042979456191nt_int @ A5 @ ( product_Pair_int_int @ B5 @ C2 ) ) )
% 5.41/5.70 => ( P @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % prod_induct3
% 5.41/5.70 thf(fact_3864_artanh__def,axiom,
% 5.41/5.70 ( artanh_real
% 5.41/5.70 = ( ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ ( divide_divide_real @ ( plus_plus_real @ one_one_real @ X3 ) @ ( minus_minus_real @ one_one_real @ X3 ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % artanh_def
% 5.41/5.70 thf(fact_3865_gcd__nat__induct,axiom,
% 5.41/5.70 ! [P: nat > nat > $o,M: nat,N: nat] :
% 5.41/5.70 ( ! [M4: nat] : ( P @ M4 @ zero_zero_nat )
% 5.41/5.70 => ( ! [M4: nat,N3: nat] :
% 5.41/5.70 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.41/5.70 => ( ( P @ N3 @ ( modulo_modulo_nat @ M4 @ N3 ) )
% 5.41/5.70 => ( P @ M4 @ N3 ) ) )
% 5.41/5.70 => ( P @ M @ N ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % gcd_nat_induct
% 5.41/5.70 thf(fact_3866_concat__bit__Suc,axiom,
% 5.41/5.70 ! [N: nat,K: int,L2: int] :
% 5.41/5.70 ( ( bit_concat_bit @ ( suc @ N ) @ K @ L2 )
% 5.41/5.70 = ( plus_plus_int @ ( modulo_modulo_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_concat_bit @ N @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ L2 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % concat_bit_Suc
% 5.41/5.70 thf(fact_3867_dual__order_Orefl,axiom,
% 5.41/5.70 ! [A: set_int] : ( ord_less_eq_set_int @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.refl
% 5.41/5.70 thf(fact_3868_dual__order_Orefl,axiom,
% 5.41/5.70 ! [A: rat] : ( ord_less_eq_rat @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.refl
% 5.41/5.70 thf(fact_3869_dual__order_Orefl,axiom,
% 5.41/5.70 ! [A: num] : ( ord_less_eq_num @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.refl
% 5.41/5.70 thf(fact_3870_dual__order_Orefl,axiom,
% 5.41/5.70 ! [A: nat] : ( ord_less_eq_nat @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.refl
% 5.41/5.70 thf(fact_3871_dual__order_Orefl,axiom,
% 5.41/5.70 ! [A: int] : ( ord_less_eq_int @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.refl
% 5.41/5.70 thf(fact_3872_order__refl,axiom,
% 5.41/5.70 ! [X: set_int] : ( ord_less_eq_set_int @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_refl
% 5.41/5.70 thf(fact_3873_order__refl,axiom,
% 5.41/5.70 ! [X: rat] : ( ord_less_eq_rat @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_refl
% 5.41/5.70 thf(fact_3874_order__refl,axiom,
% 5.41/5.70 ! [X: num] : ( ord_less_eq_num @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_refl
% 5.41/5.70 thf(fact_3875_order__refl,axiom,
% 5.41/5.70 ! [X: nat] : ( ord_less_eq_nat @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_refl
% 5.41/5.70 thf(fact_3876_order__refl,axiom,
% 5.41/5.70 ! [X: int] : ( ord_less_eq_int @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_refl
% 5.41/5.70 thf(fact_3877_ln__less__cancel__iff,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.70 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.41/5.70 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_less_cancel_iff
% 5.41/5.70 thf(fact_3878_ln__inj__iff,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.70 => ( ( ( ln_ln_real @ X )
% 5.41/5.70 = ( ln_ln_real @ Y ) )
% 5.41/5.70 = ( X = Y ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_inj_iff
% 5.41/5.70 thf(fact_3879_concat__bit__0,axiom,
% 5.41/5.70 ! [K: int,L2: int] :
% 5.41/5.70 ( ( bit_concat_bit @ zero_zero_nat @ K @ L2 )
% 5.41/5.70 = L2 ) ).
% 5.41/5.70
% 5.41/5.70 % concat_bit_0
% 5.41/5.70 thf(fact_3880_ln__le__cancel__iff,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.70 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) )
% 5.41/5.70 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_le_cancel_iff
% 5.41/5.70 thf(fact_3881_ln__less__zero__iff,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.41/5.70 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_less_zero_iff
% 5.41/5.70 thf(fact_3882_ln__gt__zero__iff,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.41/5.70 = ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_gt_zero_iff
% 5.41/5.70 thf(fact_3883_ln__eq__zero__iff,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ( ln_ln_real @ X )
% 5.41/5.70 = zero_zero_real )
% 5.41/5.70 = ( X = one_one_real ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_eq_zero_iff
% 5.41/5.70 thf(fact_3884_ln__one,axiom,
% 5.41/5.70 ( ( ln_ln_real @ one_one_real )
% 5.41/5.70 = zero_zero_real ) ).
% 5.41/5.70
% 5.41/5.70 % ln_one
% 5.41/5.70 thf(fact_3885_concat__bit__nonnegative__iff,axiom,
% 5.41/5.70 ! [N: nat,K: int,L2: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_concat_bit @ N @ K @ L2 ) )
% 5.41/5.70 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ).
% 5.41/5.70
% 5.41/5.70 % concat_bit_nonnegative_iff
% 5.41/5.70 thf(fact_3886_concat__bit__negative__iff,axiom,
% 5.41/5.70 ! [N: nat,K: int,L2: int] :
% 5.41/5.70 ( ( ord_less_int @ ( bit_concat_bit @ N @ K @ L2 ) @ zero_zero_int )
% 5.41/5.70 = ( ord_less_int @ L2 @ zero_zero_int ) ) ).
% 5.41/5.70
% 5.41/5.70 % concat_bit_negative_iff
% 5.41/5.70 thf(fact_3887_ln__le__zero__iff,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_eq_real @ ( ln_ln_real @ X ) @ zero_zero_real )
% 5.41/5.70 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_le_zero_iff
% 5.41/5.70 thf(fact_3888_ln__ge__zero__iff,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.41/5.70 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_ge_zero_iff
% 5.41/5.70 thf(fact_3889_concat__bit__assoc,axiom,
% 5.41/5.70 ! [N: nat,K: int,M: nat,L2: int,R: int] :
% 5.41/5.70 ( ( bit_concat_bit @ N @ K @ ( bit_concat_bit @ M @ L2 @ R ) )
% 5.41/5.70 = ( bit_concat_bit @ ( plus_plus_nat @ M @ N ) @ ( bit_concat_bit @ N @ K @ L2 ) @ R ) ) ).
% 5.41/5.70
% 5.41/5.70 % concat_bit_assoc
% 5.41/5.70 thf(fact_3890_ln__less__self,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ord_less_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_less_self
% 5.41/5.70 thf(fact_3891_ln__bound,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_bound
% 5.41/5.70 thf(fact_3892_ln__gt__zero__imp__gt__one,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_gt_zero_imp_gt_one
% 5.41/5.70 thf(fact_3893_ln__less__zero,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.70 => ( ord_less_real @ ( ln_ln_real @ X ) @ zero_zero_real ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_less_zero
% 5.41/5.70 thf(fact_3894_ln__gt__zero,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.70 => ( ord_less_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_gt_zero
% 5.41/5.70 thf(fact_3895_ln__ge__zero,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.70 => ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_ge_zero
% 5.41/5.70 thf(fact_3896_order__antisym__conv,axiom,
% 5.41/5.70 ! [Y: set_int,X: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ Y @ X )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym_conv
% 5.41/5.70 thf(fact_3897_order__antisym__conv,axiom,
% 5.41/5.70 ! [Y: rat,X: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ Y @ X )
% 5.41/5.70 => ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym_conv
% 5.41/5.70 thf(fact_3898_order__antisym__conv,axiom,
% 5.41/5.70 ! [Y: num,X: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ Y @ X )
% 5.41/5.70 => ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym_conv
% 5.41/5.70 thf(fact_3899_order__antisym__conv,axiom,
% 5.41/5.70 ! [Y: nat,X: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ Y @ X )
% 5.41/5.70 => ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym_conv
% 5.41/5.70 thf(fact_3900_order__antisym__conv,axiom,
% 5.41/5.70 ! [Y: int,X: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ Y @ X )
% 5.41/5.70 => ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym_conv
% 5.41/5.70 thf(fact_3901_linorder__le__cases,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ~ ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_cases
% 5.41/5.70 thf(fact_3902_linorder__le__cases,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ~ ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_cases
% 5.41/5.70 thf(fact_3903_linorder__le__cases,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ~ ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_cases
% 5.41/5.70 thf(fact_3904_linorder__le__cases,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ~ ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_cases
% 5.41/5.70 thf(fact_3905_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3906_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3907_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3908_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3909_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3910_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3911_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3912_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3913_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3914_ord__le__eq__subst,axiom,
% 5.41/5.70 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_subst
% 5.41/5.70 thf(fact_3915_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3916_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3917_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3918_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3919_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3920_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: num,F: num > num,B: num,C: num] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3921_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3922_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: int,F: num > int,B: num,C: num] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3923_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3924_ord__eq__le__subst,axiom,
% 5.41/5.70 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_subst
% 5.41/5.70 thf(fact_3925_linorder__linear,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 | ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_linear
% 5.41/5.70 thf(fact_3926_linorder__linear,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 | ( ord_less_eq_num @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_linear
% 5.41/5.70 thf(fact_3927_linorder__linear,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 | ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_linear
% 5.41/5.70 thf(fact_3928_linorder__linear,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 | ( ord_less_eq_int @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_linear
% 5.41/5.70 thf(fact_3929_order__eq__refl,axiom,
% 5.41/5.70 ! [X: set_int,Y: set_int] :
% 5.41/5.70 ( ( X = Y )
% 5.41/5.70 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_eq_refl
% 5.41/5.70 thf(fact_3930_order__eq__refl,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( X = Y )
% 5.41/5.70 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_eq_refl
% 5.41/5.70 thf(fact_3931_order__eq__refl,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( X = Y )
% 5.41/5.70 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_eq_refl
% 5.41/5.70 thf(fact_3932_order__eq__refl,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( X = Y )
% 5.41/5.70 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_eq_refl
% 5.41/5.70 thf(fact_3933_order__eq__refl,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( X = Y )
% 5.41/5.70 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_eq_refl
% 5.41/5.70 thf(fact_3934_order__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3935_order__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3936_order__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3937_order__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3938_order__subst2,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3939_order__subst2,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3940_order__subst2,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_nat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3941_order__subst2,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_int @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3942_order__subst2,axiom,
% 5.41/5.70 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3943_order__subst2,axiom,
% 5.41/5.70 ! [A: nat,B: nat,F: nat > num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_num @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst2
% 5.41/5.70 thf(fact_3944_order__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3945_order__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3946_order__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3947_order__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_int @ B @ C )
% 5.41/5.70 => ( ! [X6: int,Y5: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3948_order__subst1,axiom,
% 5.41/5.70 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3949_order__subst1,axiom,
% 5.41/5.70 ! [A: num,F: num > num,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3950_order__subst1,axiom,
% 5.41/5.70 ! [A: num,F: nat > num,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3951_order__subst1,axiom,
% 5.41/5.70 ! [A: num,F: int > num,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_int @ B @ C )
% 5.41/5.70 => ( ! [X6: int,Y5: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3952_order__subst1,axiom,
% 5.41/5.70 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3953_order__subst1,axiom,
% 5.41/5.70 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_eq_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_subst1
% 5.41/5.70 thf(fact_3954_Orderings_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: set_int,B2: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.41/5.70 & ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Orderings.order_eq_iff
% 5.41/5.70 thf(fact_3955_Orderings_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.41/5.70 & ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Orderings.order_eq_iff
% 5.41/5.70 thf(fact_3956_Orderings_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: num,B2: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.41/5.70 & ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Orderings.order_eq_iff
% 5.41/5.70 thf(fact_3957_Orderings_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.41/5.70 & ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Orderings.order_eq_iff
% 5.41/5.70 thf(fact_3958_Orderings_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: int,B2: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.41/5.70 & ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % Orderings.order_eq_iff
% 5.41/5.70 thf(fact_3959_antisym,axiom,
% 5.41/5.70 ! [A: set_int,B: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ B @ A )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym
% 5.41/5.70 thf(fact_3960_antisym,axiom,
% 5.41/5.70 ! [A: rat,B: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym
% 5.41/5.70 thf(fact_3961_antisym,axiom,
% 5.41/5.70 ! [A: num,B: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ A )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym
% 5.41/5.70 thf(fact_3962_antisym,axiom,
% 5.41/5.70 ! [A: nat,B: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym
% 5.41/5.70 thf(fact_3963_antisym,axiom,
% 5.41/5.70 ! [A: int,B: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_int @ B @ A )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym
% 5.41/5.70 thf(fact_3964_dual__order_Otrans,axiom,
% 5.41/5.70 ! [B: set_int,A: set_int,C: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ C @ B )
% 5.41/5.70 => ( ord_less_eq_set_int @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.trans
% 5.41/5.70 thf(fact_3965_dual__order_Otrans,axiom,
% 5.41/5.70 ! [B: rat,A: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_rat @ C @ B )
% 5.41/5.70 => ( ord_less_eq_rat @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.trans
% 5.41/5.70 thf(fact_3966_dual__order_Otrans,axiom,
% 5.41/5.70 ! [B: num,A: num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_num @ C @ B )
% 5.41/5.70 => ( ord_less_eq_num @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.trans
% 5.41/5.70 thf(fact_3967_dual__order_Otrans,axiom,
% 5.41/5.70 ! [B: nat,A: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_nat @ C @ B )
% 5.41/5.70 => ( ord_less_eq_nat @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.trans
% 5.41/5.70 thf(fact_3968_dual__order_Otrans,axiom,
% 5.41/5.70 ! [B: int,A: int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_int @ C @ B )
% 5.41/5.70 => ( ord_less_eq_int @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.trans
% 5.41/5.70 thf(fact_3969_dual__order_Oantisym,axiom,
% 5.41/5.70 ! [B: set_int,A: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ A @ B )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.antisym
% 5.41/5.70 thf(fact_3970_dual__order_Oantisym,axiom,
% 5.41/5.70 ! [B: rat,A: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.antisym
% 5.41/5.70 thf(fact_3971_dual__order_Oantisym,axiom,
% 5.41/5.70 ! [B: num,A: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.antisym
% 5.41/5.70 thf(fact_3972_dual__order_Oantisym,axiom,
% 5.41/5.70 ! [B: nat,A: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.antisym
% 5.41/5.70 thf(fact_3973_dual__order_Oantisym,axiom,
% 5.41/5.70 ! [B: int,A: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.70 => ( ( ord_less_eq_int @ A @ B )
% 5.41/5.70 => ( A = B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.antisym
% 5.41/5.70 thf(fact_3974_dual__order_Oeq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: set_int,B2: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.41/5.70 & ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.eq_iff
% 5.41/5.70 thf(fact_3975_dual__order_Oeq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.41/5.70 & ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.eq_iff
% 5.41/5.70 thf(fact_3976_dual__order_Oeq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: num,B2: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.41/5.70 & ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.eq_iff
% 5.41/5.70 thf(fact_3977_dual__order_Oeq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.41/5.70 & ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.eq_iff
% 5.41/5.70 thf(fact_3978_dual__order_Oeq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [A3: int,B2: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.41/5.70 & ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.eq_iff
% 5.41/5.70 thf(fact_3979_linorder__wlog,axiom,
% 5.41/5.70 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.41/5.70 ( ! [A5: rat,B5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: rat,B5: rat] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_wlog
% 5.41/5.70 thf(fact_3980_linorder__wlog,axiom,
% 5.41/5.70 ! [P: num > num > $o,A: num,B: num] :
% 5.41/5.70 ( ! [A5: num,B5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: num,B5: num] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_wlog
% 5.41/5.70 thf(fact_3981_linorder__wlog,axiom,
% 5.41/5.70 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.41/5.70 ( ! [A5: nat,B5: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: nat,B5: nat] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_wlog
% 5.41/5.70 thf(fact_3982_linorder__wlog,axiom,
% 5.41/5.70 ! [P: int > int > $o,A: int,B: int] :
% 5.41/5.70 ( ! [A5: int,B5: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: int,B5: int] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_wlog
% 5.41/5.70 thf(fact_3983_order__trans,axiom,
% 5.41/5.70 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.41/5.70 => ( ord_less_eq_set_int @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_trans
% 5.41/5.70 thf(fact_3984_order__trans,axiom,
% 5.41/5.70 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.41/5.70 => ( ord_less_eq_rat @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_trans
% 5.41/5.70 thf(fact_3985_order__trans,axiom,
% 5.41/5.70 ! [X: num,Y: num,Z: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_num @ Y @ Z )
% 5.41/5.70 => ( ord_less_eq_num @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_trans
% 5.41/5.70 thf(fact_3986_order__trans,axiom,
% 5.41/5.70 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.41/5.70 => ( ord_less_eq_nat @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_trans
% 5.41/5.70 thf(fact_3987_order__trans,axiom,
% 5.41/5.70 ! [X: int,Y: int,Z: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_int @ Y @ Z )
% 5.41/5.70 => ( ord_less_eq_int @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_trans
% 5.41/5.70 thf(fact_3988_order_Otrans,axiom,
% 5.41/5.70 ! [A: set_int,B: set_int,C: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ B @ C )
% 5.41/5.70 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.trans
% 5.41/5.70 thf(fact_3989_order_Otrans,axiom,
% 5.41/5.70 ! [A: rat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.trans
% 5.41/5.70 thf(fact_3990_order_Otrans,axiom,
% 5.41/5.70 ! [A: num,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.trans
% 5.41/5.70 thf(fact_3991_order_Otrans,axiom,
% 5.41/5.70 ! [A: nat,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.70 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.trans
% 5.41/5.70 thf(fact_3992_order_Otrans,axiom,
% 5.41/5.70 ! [A: int,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_int @ B @ C )
% 5.41/5.70 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.trans
% 5.41/5.70 thf(fact_3993_order__antisym,axiom,
% 5.41/5.70 ! [X: set_int,Y: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ Y @ X )
% 5.41/5.70 => ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym
% 5.41/5.70 thf(fact_3994_order__antisym,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_rat @ Y @ X )
% 5.41/5.70 => ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym
% 5.41/5.70 thf(fact_3995_order__antisym,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_num @ Y @ X )
% 5.41/5.70 => ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym
% 5.41/5.70 thf(fact_3996_order__antisym,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_nat @ Y @ X )
% 5.41/5.70 => ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym
% 5.41/5.70 thf(fact_3997_order__antisym,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_eq_int @ Y @ X )
% 5.41/5.70 => ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_antisym
% 5.41/5.70 thf(fact_3998_ord__le__eq__trans,axiom,
% 5.41/5.70 ! [A: set_int,B: set_int,C: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_trans
% 5.41/5.70 thf(fact_3999_ord__le__eq__trans,axiom,
% 5.41/5.70 ! [A: rat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_trans
% 5.41/5.70 thf(fact_4000_ord__le__eq__trans,axiom,
% 5.41/5.70 ! [A: num,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_trans
% 5.41/5.70 thf(fact_4001_ord__le__eq__trans,axiom,
% 5.41/5.70 ! [A: nat,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_trans
% 5.41/5.70 thf(fact_4002_ord__le__eq__trans,axiom,
% 5.41/5.70 ! [A: int,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_le_eq_trans
% 5.41/5.70 thf(fact_4003_ord__eq__le__trans,axiom,
% 5.41/5.70 ! [A: set_int,B: set_int,C: set_int] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_eq_set_int @ B @ C )
% 5.41/5.70 => ( ord_less_eq_set_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_trans
% 5.41/5.70 thf(fact_4004_ord__eq__le__trans,axiom,
% 5.41/5.70 ! [A: rat,B: rat,C: rat] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ord_less_eq_rat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_trans
% 5.41/5.70 thf(fact_4005_ord__eq__le__trans,axiom,
% 5.41/5.70 ! [A: num,B: num,C: num] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ord_less_eq_num @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_trans
% 5.41/5.70 thf(fact_4006_ord__eq__le__trans,axiom,
% 5.41/5.70 ! [A: nat,B: nat,C: nat] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.70 => ( ord_less_eq_nat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_trans
% 5.41/5.70 thf(fact_4007_ord__eq__le__trans,axiom,
% 5.41/5.70 ! [A: int,B: int,C: int] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_eq_int @ B @ C )
% 5.41/5.70 => ( ord_less_eq_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_le_trans
% 5.41/5.70 thf(fact_4008_order__class_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: set_int,Z2: set_int] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [X3: set_int,Y3: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 5.41/5.70 & ( ord_less_eq_set_int @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_class.order_eq_iff
% 5.41/5.70 thf(fact_4009_order__class_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: rat,Z2: rat] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [X3: rat,Y3: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.41/5.70 & ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_class.order_eq_iff
% 5.41/5.70 thf(fact_4010_order__class_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: num,Z2: num] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [X3: num,Y3: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.41/5.70 & ( ord_less_eq_num @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_class.order_eq_iff
% 5.41/5.70 thf(fact_4011_order__class_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [X3: nat,Y3: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.41/5.70 & ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_class.order_eq_iff
% 5.41/5.70 thf(fact_4012_order__class_Oorder__eq__iff,axiom,
% 5.41/5.70 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.41/5.70 = ( ^ [X3: int,Y3: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.41/5.70 & ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_class.order_eq_iff
% 5.41/5.70 thf(fact_4013_le__cases3,axiom,
% 5.41/5.70 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.70 ( ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_rat @ Y @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_rat @ Y @ X )
% 5.41/5.70 => ~ ( ord_less_eq_rat @ X @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_rat @ X @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_rat @ Z @ Y ) )
% 5.41/5.70 => ( ( ( ord_less_eq_rat @ Z @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_rat @ Y @ X ) )
% 5.41/5.70 => ( ( ( ord_less_eq_rat @ Y @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_rat @ Z @ X ) )
% 5.41/5.70 => ~ ( ( ord_less_eq_rat @ Z @ X )
% 5.41/5.70 => ~ ( ord_less_eq_rat @ X @ Y ) ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % le_cases3
% 5.41/5.70 thf(fact_4014_le__cases3,axiom,
% 5.41/5.70 ! [X: num,Y: num,Z: num] :
% 5.41/5.70 ( ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_num @ Y @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_num @ Y @ X )
% 5.41/5.70 => ~ ( ord_less_eq_num @ X @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_num @ X @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_num @ Z @ Y ) )
% 5.41/5.70 => ( ( ( ord_less_eq_num @ Z @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_num @ Y @ X ) )
% 5.41/5.70 => ( ( ( ord_less_eq_num @ Y @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_num @ Z @ X ) )
% 5.41/5.70 => ~ ( ( ord_less_eq_num @ Z @ X )
% 5.41/5.70 => ~ ( ord_less_eq_num @ X @ Y ) ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % le_cases3
% 5.41/5.70 thf(fact_4015_le__cases3,axiom,
% 5.41/5.70 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.70 ( ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_nat @ Y @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_nat @ Y @ X )
% 5.41/5.70 => ~ ( ord_less_eq_nat @ X @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_nat @ X @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_nat @ Z @ Y ) )
% 5.41/5.70 => ( ( ( ord_less_eq_nat @ Z @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_nat @ Y @ X ) )
% 5.41/5.70 => ( ( ( ord_less_eq_nat @ Y @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_nat @ Z @ X ) )
% 5.41/5.70 => ~ ( ( ord_less_eq_nat @ Z @ X )
% 5.41/5.70 => ~ ( ord_less_eq_nat @ X @ Y ) ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % le_cases3
% 5.41/5.70 thf(fact_4016_le__cases3,axiom,
% 5.41/5.70 ! [X: int,Y: int,Z: int] :
% 5.41/5.70 ( ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_int @ Y @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_int @ Y @ X )
% 5.41/5.70 => ~ ( ord_less_eq_int @ X @ Z ) )
% 5.41/5.70 => ( ( ( ord_less_eq_int @ X @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_int @ Z @ Y ) )
% 5.41/5.70 => ( ( ( ord_less_eq_int @ Z @ Y )
% 5.41/5.70 => ~ ( ord_less_eq_int @ Y @ X ) )
% 5.41/5.70 => ( ( ( ord_less_eq_int @ Y @ Z )
% 5.41/5.70 => ~ ( ord_less_eq_int @ Z @ X ) )
% 5.41/5.70 => ~ ( ( ord_less_eq_int @ Z @ X )
% 5.41/5.70 => ~ ( ord_less_eq_int @ X @ Y ) ) ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % le_cases3
% 5.41/5.70 thf(fact_4017_nle__le,axiom,
% 5.41/5.70 ! [A: rat,B: rat] :
% 5.41/5.70 ( ( ~ ( ord_less_eq_rat @ A @ B ) )
% 5.41/5.70 = ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.70 & ( B != A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % nle_le
% 5.41/5.70 thf(fact_4018_nle__le,axiom,
% 5.41/5.70 ! [A: num,B: num] :
% 5.41/5.70 ( ( ~ ( ord_less_eq_num @ A @ B ) )
% 5.41/5.70 = ( ( ord_less_eq_num @ B @ A )
% 5.41/5.70 & ( B != A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % nle_le
% 5.41/5.70 thf(fact_4019_nle__le,axiom,
% 5.41/5.70 ! [A: nat,B: nat] :
% 5.41/5.70 ( ( ~ ( ord_less_eq_nat @ A @ B ) )
% 5.41/5.70 = ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.70 & ( B != A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % nle_le
% 5.41/5.70 thf(fact_4020_nle__le,axiom,
% 5.41/5.70 ! [A: int,B: int] :
% 5.41/5.70 ( ( ~ ( ord_less_eq_int @ A @ B ) )
% 5.41/5.70 = ( ( ord_less_eq_int @ B @ A )
% 5.41/5.70 & ( B != A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % nle_le
% 5.41/5.70 thf(fact_4021_order__less__imp__not__less,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_less
% 5.41/5.70 thf(fact_4022_order__less__imp__not__less,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_less
% 5.41/5.70 thf(fact_4023_order__less__imp__not__less,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_less
% 5.41/5.70 thf(fact_4024_order__less__imp__not__less,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_less
% 5.41/5.70 thf(fact_4025_order__less__imp__not__less,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_less
% 5.41/5.70 thf(fact_4026_order__less__imp__not__eq2,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ( Y != X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq2
% 5.41/5.70 thf(fact_4027_order__less__imp__not__eq2,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ( Y != X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq2
% 5.41/5.70 thf(fact_4028_order__less__imp__not__eq2,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ( Y != X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq2
% 5.41/5.70 thf(fact_4029_order__less__imp__not__eq2,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ( Y != X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq2
% 5.41/5.70 thf(fact_4030_order__less__imp__not__eq2,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ( Y != X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq2
% 5.41/5.70 thf(fact_4031_order__less__imp__not__eq,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq
% 5.41/5.70 thf(fact_4032_order__less__imp__not__eq,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq
% 5.41/5.70 thf(fact_4033_order__less__imp__not__eq,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq
% 5.41/5.70 thf(fact_4034_order__less__imp__not__eq,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq
% 5.41/5.70 thf(fact_4035_order__less__imp__not__eq,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_not_eq
% 5.41/5.70 thf(fact_4036_linorder__less__linear,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 | ( X = Y )
% 5.41/5.70 | ( ord_less_real @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_linear
% 5.41/5.70 thf(fact_4037_linorder__less__linear,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 | ( X = Y )
% 5.41/5.70 | ( ord_less_rat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_linear
% 5.41/5.70 thf(fact_4038_linorder__less__linear,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 | ( X = Y )
% 5.41/5.70 | ( ord_less_num @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_linear
% 5.41/5.70 thf(fact_4039_linorder__less__linear,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 | ( X = Y )
% 5.41/5.70 | ( ord_less_nat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_linear
% 5.41/5.70 thf(fact_4040_linorder__less__linear,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 | ( X = Y )
% 5.41/5.70 | ( ord_less_int @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_linear
% 5.41/5.70 thf(fact_4041_order__less__imp__triv,axiom,
% 5.41/5.70 ! [X: real,Y: real,P: $o] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ( ( ord_less_real @ Y @ X )
% 5.41/5.70 => P ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_triv
% 5.41/5.70 thf(fact_4042_order__less__imp__triv,axiom,
% 5.41/5.70 ! [X: rat,Y: rat,P: $o] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_rat @ Y @ X )
% 5.41/5.70 => P ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_triv
% 5.41/5.70 thf(fact_4043_order__less__imp__triv,axiom,
% 5.41/5.70 ! [X: num,Y: num,P: $o] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ( ( ord_less_num @ Y @ X )
% 5.41/5.70 => P ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_triv
% 5.41/5.70 thf(fact_4044_order__less__imp__triv,axiom,
% 5.41/5.70 ! [X: nat,Y: nat,P: $o] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_nat @ Y @ X )
% 5.41/5.70 => P ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_triv
% 5.41/5.70 thf(fact_4045_order__less__imp__triv,axiom,
% 5.41/5.70 ! [X: int,Y: int,P: $o] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_int @ Y @ X )
% 5.41/5.70 => P ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_imp_triv
% 5.41/5.70 thf(fact_4046_order__less__not__sym,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_not_sym
% 5.41/5.70 thf(fact_4047_order__less__not__sym,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_not_sym
% 5.41/5.70 thf(fact_4048_order__less__not__sym,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_not_sym
% 5.41/5.70 thf(fact_4049_order__less__not__sym,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_not_sym
% 5.41/5.70 thf(fact_4050_order__less__not__sym,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_not_sym
% 5.41/5.70 thf(fact_4051_order__less__subst2,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > real,C: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4052_order__less__subst2,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4053_order__less__subst2,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > num,C: num] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4054_order__less__subst2,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4055_order__less__subst2,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > int,C: int] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4056_order__less__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4057_order__less__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4058_order__less__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4059_order__less__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4060_order__less__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst2
% 5.41/5.70 thf(fact_4061_order__less__subst1,axiom,
% 5.41/5.70 ! [A: real,F: real > real,B: real,C: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4062_order__less__subst1,axiom,
% 5.41/5.70 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4063_order__less__subst1,axiom,
% 5.41/5.70 ! [A: real,F: num > real,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4064_order__less__subst1,axiom,
% 5.41/5.70 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_nat @ B @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4065_order__less__subst1,axiom,
% 5.41/5.70 ! [A: real,F: int > real,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_int @ B @ C )
% 5.41/5.70 => ( ! [X6: int,Y5: int] :
% 5.41/5.70 ( ( ord_less_int @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4066_order__less__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.41/5.70 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4067_order__less__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4068_order__less__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4069_order__less__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_nat @ B @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4070_order__less__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_int @ B @ C )
% 5.41/5.70 => ( ! [X6: int,Y5: int] :
% 5.41/5.70 ( ( ord_less_int @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_subst1
% 5.41/5.70 thf(fact_4071_order__less__irrefl,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ~ ( ord_less_real @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_irrefl
% 5.41/5.70 thf(fact_4072_order__less__irrefl,axiom,
% 5.41/5.70 ! [X: rat] :
% 5.41/5.70 ~ ( ord_less_rat @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_irrefl
% 5.41/5.70 thf(fact_4073_order__less__irrefl,axiom,
% 5.41/5.70 ! [X: num] :
% 5.41/5.70 ~ ( ord_less_num @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_irrefl
% 5.41/5.70 thf(fact_4074_order__less__irrefl,axiom,
% 5.41/5.70 ! [X: nat] :
% 5.41/5.70 ~ ( ord_less_nat @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_irrefl
% 5.41/5.70 thf(fact_4075_order__less__irrefl,axiom,
% 5.41/5.70 ! [X: int] :
% 5.41/5.70 ~ ( ord_less_int @ X @ X ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_irrefl
% 5.41/5.70 thf(fact_4076_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > real,C: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4077_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4078_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > num,C: num] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4079_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4080_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > int,C: int] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4081_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4082_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4083_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4084_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4085_ord__less__eq__subst,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ( F @ B )
% 5.41/5.70 = C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_subst
% 5.41/5.70 thf(fact_4086_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: real,F: real > real,B: real,C: real] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4087_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4088_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: num,F: real > num,B: real,C: real] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4089_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: nat,F: real > nat,B: real,C: real] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4090_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: int,F: real > int,B: real,C: real] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4091_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4092_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4093_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4094_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4095_ord__eq__less__subst,axiom,
% 5.41/5.70 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.41/5.70 ( ( A
% 5.41/5.70 = ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_subst
% 5.41/5.70 thf(fact_4096_order__less__trans,axiom,
% 5.41/5.70 ! [X: real,Y: real,Z: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ( ( ord_less_real @ Y @ Z )
% 5.41/5.70 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_trans
% 5.41/5.70 thf(fact_4097_order__less__trans,axiom,
% 5.41/5.70 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_rat @ Y @ Z )
% 5.41/5.70 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_trans
% 5.41/5.70 thf(fact_4098_order__less__trans,axiom,
% 5.41/5.70 ! [X: num,Y: num,Z: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ( ( ord_less_num @ Y @ Z )
% 5.41/5.70 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_trans
% 5.41/5.70 thf(fact_4099_order__less__trans,axiom,
% 5.41/5.70 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_nat @ Y @ Z )
% 5.41/5.70 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_trans
% 5.41/5.70 thf(fact_4100_order__less__trans,axiom,
% 5.41/5.70 ! [X: int,Y: int,Z: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_int @ Y @ Z )
% 5.41/5.70 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_trans
% 5.41/5.70 thf(fact_4101_order__less__asym_H,axiom,
% 5.41/5.70 ! [A: real,B: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym'
% 5.41/5.70 thf(fact_4102_order__less__asym_H,axiom,
% 5.41/5.70 ! [A: rat,B: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym'
% 5.41/5.70 thf(fact_4103_order__less__asym_H,axiom,
% 5.41/5.70 ! [A: num,B: num] :
% 5.41/5.70 ( ( ord_less_num @ A @ B )
% 5.41/5.70 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym'
% 5.41/5.70 thf(fact_4104_order__less__asym_H,axiom,
% 5.41/5.70 ! [A: nat,B: nat] :
% 5.41/5.70 ( ( ord_less_nat @ A @ B )
% 5.41/5.70 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym'
% 5.41/5.70 thf(fact_4105_order__less__asym_H,axiom,
% 5.41/5.70 ! [A: int,B: int] :
% 5.41/5.70 ( ( ord_less_int @ A @ B )
% 5.41/5.70 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym'
% 5.41/5.70 thf(fact_4106_linorder__neq__iff,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 = ( ( ord_less_real @ X @ Y )
% 5.41/5.70 | ( ord_less_real @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neq_iff
% 5.41/5.70 thf(fact_4107_linorder__neq__iff,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 = ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 | ( ord_less_rat @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neq_iff
% 5.41/5.70 thf(fact_4108_linorder__neq__iff,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 = ( ( ord_less_num @ X @ Y )
% 5.41/5.70 | ( ord_less_num @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neq_iff
% 5.41/5.70 thf(fact_4109_linorder__neq__iff,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 = ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 | ( ord_less_nat @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neq_iff
% 5.41/5.70 thf(fact_4110_linorder__neq__iff,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 = ( ( ord_less_int @ X @ Y )
% 5.41/5.70 | ( ord_less_int @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neq_iff
% 5.41/5.70 thf(fact_4111_order__less__asym,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_real @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym
% 5.41/5.70 thf(fact_4112_order__less__asym,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_rat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym
% 5.41/5.70 thf(fact_4113_order__less__asym,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_num @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym
% 5.41/5.70 thf(fact_4114_order__less__asym,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_nat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym
% 5.41/5.70 thf(fact_4115_order__less__asym,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ~ ( ord_less_int @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_asym
% 5.41/5.70 thf(fact_4116_linorder__neqE,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 => ( ~ ( ord_less_real @ X @ Y )
% 5.41/5.70 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neqE
% 5.41/5.70 thf(fact_4117_linorder__neqE,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 => ( ~ ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neqE
% 5.41/5.70 thf(fact_4118_linorder__neqE,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 => ( ~ ( ord_less_num @ X @ Y )
% 5.41/5.70 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neqE
% 5.41/5.70 thf(fact_4119_linorder__neqE,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 => ( ~ ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neqE
% 5.41/5.70 thf(fact_4120_linorder__neqE,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( X != Y )
% 5.41/5.70 => ( ~ ( ord_less_int @ X @ Y )
% 5.41/5.70 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_neqE
% 5.41/5.70 thf(fact_4121_dual__order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [B: real,A: real] :
% 5.41/5.70 ( ( ord_less_real @ B @ A )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4122_dual__order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [B: rat,A: rat] :
% 5.41/5.70 ( ( ord_less_rat @ B @ A )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4123_dual__order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [B: num,A: num] :
% 5.41/5.70 ( ( ord_less_num @ B @ A )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4124_dual__order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [B: nat,A: nat] :
% 5.41/5.70 ( ( ord_less_nat @ B @ A )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4125_dual__order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [B: int,A: int] :
% 5.41/5.70 ( ( ord_less_int @ B @ A )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4126_order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [A: real,B: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4127_order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [A: rat,B: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4128_order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [A: num,B: num] :
% 5.41/5.70 ( ( ord_less_num @ A @ B )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4129_order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [A: nat,B: nat] :
% 5.41/5.70 ( ( ord_less_nat @ A @ B )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4130_order_Ostrict__implies__not__eq,axiom,
% 5.41/5.70 ! [A: int,B: int] :
% 5.41/5.70 ( ( ord_less_int @ A @ B )
% 5.41/5.70 => ( A != B ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_implies_not_eq
% 5.41/5.70 thf(fact_4131_dual__order_Ostrict__trans,axiom,
% 5.41/5.70 ! [B: real,A: real,C: real] :
% 5.41/5.70 ( ( ord_less_real @ B @ A )
% 5.41/5.70 => ( ( ord_less_real @ C @ B )
% 5.41/5.70 => ( ord_less_real @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_trans
% 5.41/5.70 thf(fact_4132_dual__order_Ostrict__trans,axiom,
% 5.41/5.70 ! [B: rat,A: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ B @ A )
% 5.41/5.70 => ( ( ord_less_rat @ C @ B )
% 5.41/5.70 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_trans
% 5.41/5.70 thf(fact_4133_dual__order_Ostrict__trans,axiom,
% 5.41/5.70 ! [B: num,A: num,C: num] :
% 5.41/5.70 ( ( ord_less_num @ B @ A )
% 5.41/5.70 => ( ( ord_less_num @ C @ B )
% 5.41/5.70 => ( ord_less_num @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_trans
% 5.41/5.70 thf(fact_4134_dual__order_Ostrict__trans,axiom,
% 5.41/5.70 ! [B: nat,A: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_nat @ B @ A )
% 5.41/5.70 => ( ( ord_less_nat @ C @ B )
% 5.41/5.70 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_trans
% 5.41/5.70 thf(fact_4135_dual__order_Ostrict__trans,axiom,
% 5.41/5.70 ! [B: int,A: int,C: int] :
% 5.41/5.70 ( ( ord_less_int @ B @ A )
% 5.41/5.70 => ( ( ord_less_int @ C @ B )
% 5.41/5.70 => ( ord_less_int @ C @ A ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.strict_trans
% 5.41/5.70 thf(fact_4136_not__less__iff__gr__or__eq,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.41/5.70 = ( ( ord_less_real @ Y @ X )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % not_less_iff_gr_or_eq
% 5.41/5.70 thf(fact_4137_not__less__iff__gr__or__eq,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.41/5.70 = ( ( ord_less_rat @ Y @ X )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % not_less_iff_gr_or_eq
% 5.41/5.70 thf(fact_4138_not__less__iff__gr__or__eq,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.41/5.70 = ( ( ord_less_num @ Y @ X )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % not_less_iff_gr_or_eq
% 5.41/5.70 thf(fact_4139_not__less__iff__gr__or__eq,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.41/5.70 = ( ( ord_less_nat @ Y @ X )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % not_less_iff_gr_or_eq
% 5.41/5.70 thf(fact_4140_not__less__iff__gr__or__eq,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.41/5.70 = ( ( ord_less_int @ Y @ X )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % not_less_iff_gr_or_eq
% 5.41/5.70 thf(fact_4141_order_Ostrict__trans,axiom,
% 5.41/5.70 ! [A: real,B: real,C: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ord_less_real @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_trans
% 5.41/5.70 thf(fact_4142_order_Ostrict__trans,axiom,
% 5.41/5.70 ! [A: rat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_trans
% 5.41/5.70 thf(fact_4143_order_Ostrict__trans,axiom,
% 5.41/5.70 ! [A: num,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_num @ B @ C )
% 5.41/5.70 => ( ord_less_num @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_trans
% 5.41/5.70 thf(fact_4144_order_Ostrict__trans,axiom,
% 5.41/5.70 ! [A: nat,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_nat @ A @ B )
% 5.41/5.70 => ( ( ord_less_nat @ B @ C )
% 5.41/5.70 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_trans
% 5.41/5.70 thf(fact_4145_order_Ostrict__trans,axiom,
% 5.41/5.70 ! [A: int,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_int @ A @ B )
% 5.41/5.70 => ( ( ord_less_int @ B @ C )
% 5.41/5.70 => ( ord_less_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.strict_trans
% 5.41/5.70 thf(fact_4146_linorder__less__wlog,axiom,
% 5.41/5.70 ! [P: real > real > $o,A: real,B: real] :
% 5.41/5.70 ( ! [A5: real,B5: real] :
% 5.41/5.70 ( ( ord_less_real @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: real] : ( P @ A5 @ A5 )
% 5.41/5.70 => ( ! [A5: real,B5: real] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_wlog
% 5.41/5.70 thf(fact_4147_linorder__less__wlog,axiom,
% 5.41/5.70 ! [P: rat > rat > $o,A: rat,B: rat] :
% 5.41/5.70 ( ! [A5: rat,B5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: rat] : ( P @ A5 @ A5 )
% 5.41/5.70 => ( ! [A5: rat,B5: rat] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_wlog
% 5.41/5.70 thf(fact_4148_linorder__less__wlog,axiom,
% 5.41/5.70 ! [P: num > num > $o,A: num,B: num] :
% 5.41/5.70 ( ! [A5: num,B5: num] :
% 5.41/5.70 ( ( ord_less_num @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: num] : ( P @ A5 @ A5 )
% 5.41/5.70 => ( ! [A5: num,B5: num] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_wlog
% 5.41/5.70 thf(fact_4149_linorder__less__wlog,axiom,
% 5.41/5.70 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.41/5.70 ( ! [A5: nat,B5: nat] :
% 5.41/5.70 ( ( ord_less_nat @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: nat] : ( P @ A5 @ A5 )
% 5.41/5.70 => ( ! [A5: nat,B5: nat] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_wlog
% 5.41/5.70 thf(fact_4150_linorder__less__wlog,axiom,
% 5.41/5.70 ! [P: int > int > $o,A: int,B: int] :
% 5.41/5.70 ( ! [A5: int,B5: int] :
% 5.41/5.70 ( ( ord_less_int @ A5 @ B5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( ! [A5: int] : ( P @ A5 @ A5 )
% 5.41/5.70 => ( ! [A5: int,B5: int] :
% 5.41/5.70 ( ( P @ B5 @ A5 )
% 5.41/5.70 => ( P @ A5 @ B5 ) )
% 5.41/5.70 => ( P @ A @ B ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_less_wlog
% 5.41/5.70 thf(fact_4151_exists__least__iff,axiom,
% 5.41/5.70 ( ( ^ [P3: nat > $o] :
% 5.41/5.70 ? [X7: nat] : ( P3 @ X7 ) )
% 5.41/5.70 = ( ^ [P4: nat > $o] :
% 5.41/5.70 ? [N2: nat] :
% 5.41/5.70 ( ( P4 @ N2 )
% 5.41/5.70 & ! [M3: nat] :
% 5.41/5.70 ( ( ord_less_nat @ M3 @ N2 )
% 5.41/5.70 => ~ ( P4 @ M3 ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % exists_least_iff
% 5.41/5.70 thf(fact_4152_dual__order_Oirrefl,axiom,
% 5.41/5.70 ! [A: real] :
% 5.41/5.70 ~ ( ord_less_real @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.irrefl
% 5.41/5.70 thf(fact_4153_dual__order_Oirrefl,axiom,
% 5.41/5.70 ! [A: rat] :
% 5.41/5.70 ~ ( ord_less_rat @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.irrefl
% 5.41/5.70 thf(fact_4154_dual__order_Oirrefl,axiom,
% 5.41/5.70 ! [A: num] :
% 5.41/5.70 ~ ( ord_less_num @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.irrefl
% 5.41/5.70 thf(fact_4155_dual__order_Oirrefl,axiom,
% 5.41/5.70 ! [A: nat] :
% 5.41/5.70 ~ ( ord_less_nat @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.irrefl
% 5.41/5.70 thf(fact_4156_dual__order_Oirrefl,axiom,
% 5.41/5.70 ! [A: int] :
% 5.41/5.70 ~ ( ord_less_int @ A @ A ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.irrefl
% 5.41/5.70 thf(fact_4157_dual__order_Oasym,axiom,
% 5.41/5.70 ! [B: real,A: real] :
% 5.41/5.70 ( ( ord_less_real @ B @ A )
% 5.41/5.70 => ~ ( ord_less_real @ A @ B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.asym
% 5.41/5.70 thf(fact_4158_dual__order_Oasym,axiom,
% 5.41/5.70 ! [B: rat,A: rat] :
% 5.41/5.70 ( ( ord_less_rat @ B @ A )
% 5.41/5.70 => ~ ( ord_less_rat @ A @ B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.asym
% 5.41/5.70 thf(fact_4159_dual__order_Oasym,axiom,
% 5.41/5.70 ! [B: num,A: num] :
% 5.41/5.70 ( ( ord_less_num @ B @ A )
% 5.41/5.70 => ~ ( ord_less_num @ A @ B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.asym
% 5.41/5.70 thf(fact_4160_dual__order_Oasym,axiom,
% 5.41/5.70 ! [B: nat,A: nat] :
% 5.41/5.70 ( ( ord_less_nat @ B @ A )
% 5.41/5.70 => ~ ( ord_less_nat @ A @ B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.asym
% 5.41/5.70 thf(fact_4161_dual__order_Oasym,axiom,
% 5.41/5.70 ! [B: int,A: int] :
% 5.41/5.70 ( ( ord_less_int @ B @ A )
% 5.41/5.70 => ~ ( ord_less_int @ A @ B ) ) ).
% 5.41/5.70
% 5.41/5.70 % dual_order.asym
% 5.41/5.70 thf(fact_4162_linorder__cases,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ~ ( ord_less_real @ X @ Y )
% 5.41/5.70 => ( ( X != Y )
% 5.41/5.70 => ( ord_less_real @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_cases
% 5.41/5.70 thf(fact_4163_linorder__cases,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ~ ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ( ( X != Y )
% 5.41/5.70 => ( ord_less_rat @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_cases
% 5.41/5.70 thf(fact_4164_linorder__cases,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ~ ( ord_less_num @ X @ Y )
% 5.41/5.70 => ( ( X != Y )
% 5.41/5.70 => ( ord_less_num @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_cases
% 5.41/5.70 thf(fact_4165_linorder__cases,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ~ ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ( ( X != Y )
% 5.41/5.70 => ( ord_less_nat @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_cases
% 5.41/5.70 thf(fact_4166_linorder__cases,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ~ ( ord_less_int @ X @ Y )
% 5.41/5.70 => ( ( X != Y )
% 5.41/5.70 => ( ord_less_int @ Y @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_cases
% 5.41/5.70 thf(fact_4167_antisym__conv3,axiom,
% 5.41/5.70 ! [Y: real,X: real] :
% 5.41/5.70 ( ~ ( ord_less_real @ Y @ X )
% 5.41/5.70 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym_conv3
% 5.41/5.70 thf(fact_4168_antisym__conv3,axiom,
% 5.41/5.70 ! [Y: rat,X: rat] :
% 5.41/5.70 ( ~ ( ord_less_rat @ Y @ X )
% 5.41/5.70 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym_conv3
% 5.41/5.70 thf(fact_4169_antisym__conv3,axiom,
% 5.41/5.70 ! [Y: num,X: num] :
% 5.41/5.70 ( ~ ( ord_less_num @ Y @ X )
% 5.41/5.70 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym_conv3
% 5.41/5.70 thf(fact_4170_antisym__conv3,axiom,
% 5.41/5.70 ! [Y: nat,X: nat] :
% 5.41/5.70 ( ~ ( ord_less_nat @ Y @ X )
% 5.41/5.70 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym_conv3
% 5.41/5.70 thf(fact_4171_antisym__conv3,axiom,
% 5.41/5.70 ! [Y: int,X: int] :
% 5.41/5.70 ( ~ ( ord_less_int @ Y @ X )
% 5.41/5.70 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.41/5.70 = ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % antisym_conv3
% 5.41/5.70 thf(fact_4172_less__induct,axiom,
% 5.41/5.70 ! [P: nat > $o,A: nat] :
% 5.41/5.70 ( ! [X6: nat] :
% 5.41/5.70 ( ! [Y2: nat] :
% 5.41/5.70 ( ( ord_less_nat @ Y2 @ X6 )
% 5.41/5.70 => ( P @ Y2 ) )
% 5.41/5.70 => ( P @ X6 ) )
% 5.41/5.70 => ( P @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % less_induct
% 5.41/5.70 thf(fact_4173_ord__less__eq__trans,axiom,
% 5.41/5.70 ! [A: real,B: real,C: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_real @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_trans
% 5.41/5.70 thf(fact_4174_ord__less__eq__trans,axiom,
% 5.41/5.70 ! [A: rat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_trans
% 5.41/5.70 thf(fact_4175_ord__less__eq__trans,axiom,
% 5.41/5.70 ! [A: num,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_num @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_num @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_trans
% 5.41/5.70 thf(fact_4176_ord__less__eq__trans,axiom,
% 5.41/5.70 ! [A: nat,B: nat,C: nat] :
% 5.41/5.70 ( ( ord_less_nat @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_trans
% 5.41/5.70 thf(fact_4177_ord__less__eq__trans,axiom,
% 5.41/5.70 ! [A: int,B: int,C: int] :
% 5.41/5.70 ( ( ord_less_int @ A @ B )
% 5.41/5.70 => ( ( B = C )
% 5.41/5.70 => ( ord_less_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_less_eq_trans
% 5.41/5.70 thf(fact_4178_ord__eq__less__trans,axiom,
% 5.41/5.70 ! [A: real,B: real,C: real] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_real @ B @ C )
% 5.41/5.70 => ( ord_less_real @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_trans
% 5.41/5.70 thf(fact_4179_ord__eq__less__trans,axiom,
% 5.41/5.70 ! [A: rat,B: rat,C: rat] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_rat @ B @ C )
% 5.41/5.70 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_trans
% 5.41/5.70 thf(fact_4180_ord__eq__less__trans,axiom,
% 5.41/5.70 ! [A: num,B: num,C: num] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_num @ B @ C )
% 5.41/5.70 => ( ord_less_num @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_trans
% 5.41/5.70 thf(fact_4181_ord__eq__less__trans,axiom,
% 5.41/5.70 ! [A: nat,B: nat,C: nat] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_nat @ B @ C )
% 5.41/5.70 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_trans
% 5.41/5.70 thf(fact_4182_ord__eq__less__trans,axiom,
% 5.41/5.70 ! [A: int,B: int,C: int] :
% 5.41/5.70 ( ( A = B )
% 5.41/5.70 => ( ( ord_less_int @ B @ C )
% 5.41/5.70 => ( ord_less_int @ A @ C ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ord_eq_less_trans
% 5.41/5.70 thf(fact_4183_order_Oasym,axiom,
% 5.41/5.70 ! [A: real,B: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ~ ( ord_less_real @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.asym
% 5.41/5.70 thf(fact_4184_order_Oasym,axiom,
% 5.41/5.70 ! [A: rat,B: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ~ ( ord_less_rat @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.asym
% 5.41/5.70 thf(fact_4185_order_Oasym,axiom,
% 5.41/5.70 ! [A: num,B: num] :
% 5.41/5.70 ( ( ord_less_num @ A @ B )
% 5.41/5.70 => ~ ( ord_less_num @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.asym
% 5.41/5.70 thf(fact_4186_order_Oasym,axiom,
% 5.41/5.70 ! [A: nat,B: nat] :
% 5.41/5.70 ( ( ord_less_nat @ A @ B )
% 5.41/5.70 => ~ ( ord_less_nat @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.asym
% 5.41/5.70 thf(fact_4187_order_Oasym,axiom,
% 5.41/5.70 ! [A: int,B: int] :
% 5.41/5.70 ( ( ord_less_int @ A @ B )
% 5.41/5.70 => ~ ( ord_less_int @ B @ A ) ) ).
% 5.41/5.70
% 5.41/5.70 % order.asym
% 5.41/5.70 thf(fact_4188_less__imp__neq,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % less_imp_neq
% 5.41/5.70 thf(fact_4189_less__imp__neq,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % less_imp_neq
% 5.41/5.70 thf(fact_4190_less__imp__neq,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_num @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % less_imp_neq
% 5.41/5.70 thf(fact_4191_less__imp__neq,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % less_imp_neq
% 5.41/5.70 thf(fact_4192_less__imp__neq,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_int @ X @ Y )
% 5.41/5.70 => ( X != Y ) ) ).
% 5.41/5.70
% 5.41/5.70 % less_imp_neq
% 5.41/5.70 thf(fact_4193_dense,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Y )
% 5.41/5.70 => ? [Z5: real] :
% 5.41/5.70 ( ( ord_less_real @ X @ Z5 )
% 5.41/5.70 & ( ord_less_real @ Z5 @ Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dense
% 5.41/5.70 thf(fact_4194_dense,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 => ? [Z5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X @ Z5 )
% 5.41/5.70 & ( ord_less_rat @ Z5 @ Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % dense
% 5.41/5.70 thf(fact_4195_gt__ex,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ? [X_1: real] : ( ord_less_real @ X @ X_1 ) ).
% 5.41/5.70
% 5.41/5.70 % gt_ex
% 5.41/5.70 thf(fact_4196_gt__ex,axiom,
% 5.41/5.70 ! [X: rat] :
% 5.41/5.70 ? [X_1: rat] : ( ord_less_rat @ X @ X_1 ) ).
% 5.41/5.70
% 5.41/5.70 % gt_ex
% 5.41/5.70 thf(fact_4197_gt__ex,axiom,
% 5.41/5.70 ! [X: nat] :
% 5.41/5.70 ? [X_1: nat] : ( ord_less_nat @ X @ X_1 ) ).
% 5.41/5.70
% 5.41/5.70 % gt_ex
% 5.41/5.70 thf(fact_4198_gt__ex,axiom,
% 5.41/5.70 ! [X: int] :
% 5.41/5.70 ? [X_1: int] : ( ord_less_int @ X @ X_1 ) ).
% 5.41/5.70
% 5.41/5.70 % gt_ex
% 5.41/5.70 thf(fact_4199_lt__ex,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ? [Y5: real] : ( ord_less_real @ Y5 @ X ) ).
% 5.41/5.70
% 5.41/5.70 % lt_ex
% 5.41/5.70 thf(fact_4200_lt__ex,axiom,
% 5.41/5.70 ! [X: rat] :
% 5.41/5.70 ? [Y5: rat] : ( ord_less_rat @ Y5 @ X ) ).
% 5.41/5.70
% 5.41/5.70 % lt_ex
% 5.41/5.70 thf(fact_4201_lt__ex,axiom,
% 5.41/5.70 ! [X: int] :
% 5.41/5.70 ? [Y5: int] : ( ord_less_int @ Y5 @ X ) ).
% 5.41/5.70
% 5.41/5.70 % lt_ex
% 5.41/5.70 thf(fact_4202_small__lazy_H_Ocases,axiom,
% 5.41/5.70 ! [X: product_prod_int_int] :
% 5.41/5.70 ~ ! [D3: int,I4: int] :
% 5.41/5.70 ( X
% 5.41/5.70 != ( product_Pair_int_int @ D3 @ I4 ) ) ).
% 5.41/5.70
% 5.41/5.70 % small_lazy'.cases
% 5.41/5.70 thf(fact_4203_exhaustive__int_H_Ocases,axiom,
% 5.41/5.70 ! [X: produc7773217078559923341nt_int] :
% 5.41/5.70 ~ ! [F2: int > option6357759511663192854e_term,D3: int,I4: int] :
% 5.41/5.70 ( X
% 5.41/5.70 != ( produc4305682042979456191nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % exhaustive_int'.cases
% 5.41/5.70 thf(fact_4204_full__exhaustive__int_H_Ocases,axiom,
% 5.41/5.70 ! [X: produc2285326912895808259nt_int] :
% 5.41/5.70 ~ ! [F2: produc8551481072490612790e_term > option6357759511663192854e_term,D3: int,I4: int] :
% 5.41/5.70 ( X
% 5.41/5.70 != ( produc5700946648718959541nt_int @ F2 @ ( product_Pair_int_int @ D3 @ I4 ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % full_exhaustive_int'.cases
% 5.41/5.70 thf(fact_4205_ln__ge__zero__imp__ge__one,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_eq_real @ zero_zero_real @ ( ln_ln_real @ X ) )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_ge_zero_imp_ge_one
% 5.41/5.70 thf(fact_4206_ln__add__one__self__le__self,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_add_one_self_le_self
% 5.41/5.70 thf(fact_4207_ln__mult,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.70 => ( ( ln_ln_real @ ( times_times_real @ X @ Y ) )
% 5.41/5.70 = ( plus_plus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_mult
% 5.41/5.70 thf(fact_4208_ln__eq__minus__one,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ( ln_ln_real @ X )
% 5.41/5.70 = ( minus_minus_real @ X @ one_one_real ) )
% 5.41/5.70 => ( X = one_one_real ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_eq_minus_one
% 5.41/5.70 thf(fact_4209_ln__div,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.70 => ( ( ln_ln_real @ ( divide_divide_real @ X @ Y ) )
% 5.41/5.70 = ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_div
% 5.41/5.70 thf(fact_4210_ln__le__minus__one,axiom,
% 5.41/5.70 ! [X: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_le_minus_one
% 5.41/5.70 thf(fact_4211_ln__diff__le,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.70 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.70 => ( ord_less_eq_real @ ( minus_minus_real @ ( ln_ln_real @ X ) @ ( ln_ln_real @ Y ) ) @ ( divide_divide_real @ ( minus_minus_real @ X @ Y ) @ Y ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % ln_diff_le
% 5.41/5.70 thf(fact_4212_order__le__imp__less__or__eq,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.70 => ( ( ord_less_real @ X @ Y )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_le_imp_less_or_eq
% 5.41/5.70 thf(fact_4213_order__le__imp__less__or__eq,axiom,
% 5.41/5.70 ! [X: set_int,Y: set_int] :
% 5.41/5.70 ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_set_int @ X @ Y )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_le_imp_less_or_eq
% 5.41/5.70 thf(fact_4214_order__le__imp__less__or__eq,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_rat @ X @ Y )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_le_imp_less_or_eq
% 5.41/5.70 thf(fact_4215_order__le__imp__less__or__eq,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 => ( ( ord_less_num @ X @ Y )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_le_imp_less_or_eq
% 5.41/5.70 thf(fact_4216_order__le__imp__less__or__eq,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 => ( ( ord_less_nat @ X @ Y )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_le_imp_less_or_eq
% 5.41/5.70 thf(fact_4217_order__le__imp__less__or__eq,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 => ( ( ord_less_int @ X @ Y )
% 5.41/5.70 | ( X = Y ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_le_imp_less_or_eq
% 5.41/5.70 thf(fact_4218_linorder__le__less__linear,axiom,
% 5.41/5.70 ! [X: real,Y: real] :
% 5.41/5.70 ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.70 | ( ord_less_real @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_less_linear
% 5.41/5.70 thf(fact_4219_linorder__le__less__linear,axiom,
% 5.41/5.70 ! [X: rat,Y: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.70 | ( ord_less_rat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_less_linear
% 5.41/5.70 thf(fact_4220_linorder__le__less__linear,axiom,
% 5.41/5.70 ! [X: num,Y: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.70 | ( ord_less_num @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_less_linear
% 5.41/5.70 thf(fact_4221_linorder__le__less__linear,axiom,
% 5.41/5.70 ! [X: nat,Y: nat] :
% 5.41/5.70 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.70 | ( ord_less_nat @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_less_linear
% 5.41/5.70 thf(fact_4222_linorder__le__less__linear,axiom,
% 5.41/5.70 ! [X: int,Y: int] :
% 5.41/5.70 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.70 | ( ord_less_int @ Y @ X ) ) ).
% 5.41/5.70
% 5.41/5.70 % linorder_le_less_linear
% 5.41/5.70 thf(fact_4223_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > real,C: real] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4224_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4225_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > real,C: real] :
% 5.41/5.70 ( ( ord_less_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4226_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: nat,B: nat,F: nat > real,C: real] :
% 5.41/5.70 ( ( ord_less_nat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4227_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: int,B: int,F: int > real,C: real] :
% 5.41/5.70 ( ( ord_less_int @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_real @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: int,Y5: int] :
% 5.41/5.70 ( ( ord_less_int @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4228_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: real,B: real,F: real > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_real @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: real,Y5: real] :
% 5.41/5.70 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4229_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4230_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_num @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4231_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: nat,B: nat,F: nat > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_nat @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.70 ( ( ord_less_nat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4232_order__less__le__subst2,axiom,
% 5.41/5.70 ! [A: int,B: int,F: int > rat,C: rat] :
% 5.41/5.70 ( ( ord_less_int @ A @ B )
% 5.41/5.70 => ( ( ord_less_eq_rat @ ( F @ B ) @ C )
% 5.41/5.70 => ( ! [X6: int,Y5: int] :
% 5.41/5.70 ( ( ord_less_int @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst2
% 5.41/5.70 thf(fact_4233_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4234_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4235_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: num,F: rat > num,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4236_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: nat,F: rat > nat,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4237_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: int,F: rat > int,B: rat,C: rat] :
% 5.41/5.70 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.70 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.70 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4238_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: real,F: num > real,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_real @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4239_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_rat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4240_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: num,F: num > num,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_num @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_num @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4241_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: nat,F: num > nat,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_nat @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.70 => ( ! [X6: num,Y5: num] :
% 5.41/5.70 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.70 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.70 => ( ord_less_nat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.70
% 5.41/5.70 % order_less_le_subst1
% 5.41/5.70 thf(fact_4242_order__less__le__subst1,axiom,
% 5.41/5.70 ! [A: int,F: num > int,B: num,C: num] :
% 5.41/5.70 ( ( ord_less_int @ A @ ( F @ B ) )
% 5.41/5.70 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_int @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le_subst1
% 5.41/5.71 thf(fact_4243_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: rat,B: rat,F: rat > real,C: real] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4244_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: rat,B: rat,F: rat > rat,C: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4245_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: rat,B: rat,F: rat > num,C: num] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4246_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: rat,B: rat,F: rat > nat,C: nat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4247_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: rat,B: rat,F: rat > int,C: int] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4248_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: num,B: num,F: num > real,C: real] :
% 5.41/5.71 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ( ord_less_real @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_real @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4249_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: num,B: num,F: num > rat,C: rat] :
% 5.41/5.71 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ( ord_less_rat @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_rat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4250_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: num,B: num,F: num > num,C: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ( ord_less_num @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_num @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_num @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4251_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: num,B: num,F: num > nat,C: nat] :
% 5.41/5.71 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ( ord_less_nat @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_nat @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4252_order__le__less__subst2,axiom,
% 5.41/5.71 ! [A: num,B: num,F: num > int,C: int] :
% 5.41/5.71 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ( ord_less_int @ ( F @ B ) @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_eq_int @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_int @ ( F @ A ) @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst2
% 5.41/5.71 thf(fact_4253_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: real,F: real > real,B: real,C: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_real @ B @ C )
% 5.41/5.71 => ( ! [X6: real,Y5: real] :
% 5.41/5.71 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4254_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: real,F: rat > real,B: rat,C: rat] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_rat @ B @ C )
% 5.41/5.71 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4255_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: real,F: num > real,B: num,C: num] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_num @ B @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4256_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: real,F: nat > real,B: nat,C: nat] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_nat @ B @ C )
% 5.41/5.71 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.71 ( ( ord_less_nat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4257_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: real,F: int > real,B: int,C: int] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_int @ B @ C )
% 5.41/5.71 => ( ! [X6: int,Y5: int] :
% 5.41/5.71 ( ( ord_less_int @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_real @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_real @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4258_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: rat,F: real > rat,B: real,C: real] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_real @ B @ C )
% 5.41/5.71 => ( ! [X6: real,Y5: real] :
% 5.41/5.71 ( ( ord_less_real @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4259_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: rat,F: rat > rat,B: rat,C: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_rat @ B @ C )
% 5.41/5.71 => ( ! [X6: rat,Y5: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4260_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: rat,F: num > rat,B: num,C: num] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_num @ B @ C )
% 5.41/5.71 => ( ! [X6: num,Y5: num] :
% 5.41/5.71 ( ( ord_less_num @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4261_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: rat,F: nat > rat,B: nat,C: nat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_nat @ B @ C )
% 5.41/5.71 => ( ! [X6: nat,Y5: nat] :
% 5.41/5.71 ( ( ord_less_nat @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4262_order__le__less__subst1,axiom,
% 5.41/5.71 ! [A: rat,F: int > rat,B: int,C: int] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ ( F @ B ) )
% 5.41/5.71 => ( ( ord_less_int @ B @ C )
% 5.41/5.71 => ( ! [X6: int,Y5: int] :
% 5.41/5.71 ( ( ord_less_int @ X6 @ Y5 )
% 5.41/5.71 => ( ord_less_rat @ ( F @ X6 ) @ ( F @ Y5 ) ) )
% 5.41/5.71 => ( ord_less_rat @ A @ ( F @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_subst1
% 5.41/5.71 thf(fact_4263_order__less__le__trans,axiom,
% 5.41/5.71 ! [X: real,Y: real,Z: real] :
% 5.41/5.71 ( ( ord_less_real @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_real @ Y @ Z )
% 5.41/5.71 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le_trans
% 5.41/5.71 thf(fact_4264_order__less__le__trans,axiom,
% 5.41/5.71 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_set_int @ Y @ Z )
% 5.41/5.71 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le_trans
% 5.41/5.71 thf(fact_4265_order__less__le__trans,axiom,
% 5.41/5.71 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_rat @ Y @ Z )
% 5.41/5.71 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le_trans
% 5.41/5.71 thf(fact_4266_order__less__le__trans,axiom,
% 5.41/5.71 ! [X: num,Y: num,Z: num] :
% 5.41/5.71 ( ( ord_less_num @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_num @ Y @ Z )
% 5.41/5.71 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le_trans
% 5.41/5.71 thf(fact_4267_order__less__le__trans,axiom,
% 5.41/5.71 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.71 ( ( ord_less_nat @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_nat @ Y @ Z )
% 5.41/5.71 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le_trans
% 5.41/5.71 thf(fact_4268_order__less__le__trans,axiom,
% 5.41/5.71 ! [X: int,Y: int,Z: int] :
% 5.41/5.71 ( ( ord_less_int @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_int @ Y @ Z )
% 5.41/5.71 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le_trans
% 5.41/5.71 thf(fact_4269_order__le__less__trans,axiom,
% 5.41/5.71 ! [X: real,Y: real,Z: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.71 => ( ( ord_less_real @ Y @ Z )
% 5.41/5.71 => ( ord_less_real @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_trans
% 5.41/5.71 thf(fact_4270_order__le__less__trans,axiom,
% 5.41/5.71 ! [X: set_int,Y: set_int,Z: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.71 => ( ( ord_less_set_int @ Y @ Z )
% 5.41/5.71 => ( ord_less_set_int @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_trans
% 5.41/5.71 thf(fact_4271_order__le__less__trans,axiom,
% 5.41/5.71 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.71 => ( ( ord_less_rat @ Y @ Z )
% 5.41/5.71 => ( ord_less_rat @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_trans
% 5.41/5.71 thf(fact_4272_order__le__less__trans,axiom,
% 5.41/5.71 ! [X: num,Y: num,Z: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.71 => ( ( ord_less_num @ Y @ Z )
% 5.41/5.71 => ( ord_less_num @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_trans
% 5.41/5.71 thf(fact_4273_order__le__less__trans,axiom,
% 5.41/5.71 ! [X: nat,Y: nat,Z: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.71 => ( ( ord_less_nat @ Y @ Z )
% 5.41/5.71 => ( ord_less_nat @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_trans
% 5.41/5.71 thf(fact_4274_order__le__less__trans,axiom,
% 5.41/5.71 ! [X: int,Y: int,Z: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.71 => ( ( ord_less_int @ Y @ Z )
% 5.41/5.71 => ( ord_less_int @ X @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less_trans
% 5.41/5.71 thf(fact_4275_order__neq__le__trans,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( A != B )
% 5.41/5.71 => ( ( ord_less_eq_real @ A @ B )
% 5.41/5.71 => ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_neq_le_trans
% 5.41/5.71 thf(fact_4276_order__neq__le__trans,axiom,
% 5.41/5.71 ! [A: set_int,B: set_int] :
% 5.41/5.71 ( ( A != B )
% 5.41/5.71 => ( ( ord_less_eq_set_int @ A @ B )
% 5.41/5.71 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_neq_le_trans
% 5.41/5.71 thf(fact_4277_order__neq__le__trans,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( A != B )
% 5.41/5.71 => ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_neq_le_trans
% 5.41/5.71 thf(fact_4278_order__neq__le__trans,axiom,
% 5.41/5.71 ! [A: num,B: num] :
% 5.41/5.71 ( ( A != B )
% 5.41/5.71 => ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ord_less_num @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_neq_le_trans
% 5.41/5.71 thf(fact_4279_order__neq__le__trans,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( A != B )
% 5.41/5.71 => ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.71 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_neq_le_trans
% 5.41/5.71 thf(fact_4280_order__neq__le__trans,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( A != B )
% 5.41/5.71 => ( ( ord_less_eq_int @ A @ B )
% 5.41/5.71 => ( ord_less_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_neq_le_trans
% 5.41/5.71 thf(fact_4281_order__le__neq__trans,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.71 => ( ( A != B )
% 5.41/5.71 => ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_neq_trans
% 5.41/5.71 thf(fact_4282_order__le__neq__trans,axiom,
% 5.41/5.71 ! [A: set_int,B: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ A @ B )
% 5.41/5.71 => ( ( A != B )
% 5.41/5.71 => ( ord_less_set_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_neq_trans
% 5.41/5.71 thf(fact_4283_order__le__neq__trans,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ( A != B )
% 5.41/5.71 => ( ord_less_rat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_neq_trans
% 5.41/5.71 thf(fact_4284_order__le__neq__trans,axiom,
% 5.41/5.71 ! [A: num,B: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ( A != B )
% 5.41/5.71 => ( ord_less_num @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_neq_trans
% 5.41/5.71 thf(fact_4285_order__le__neq__trans,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.71 => ( ( A != B )
% 5.41/5.71 => ( ord_less_nat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_neq_trans
% 5.41/5.71 thf(fact_4286_order__le__neq__trans,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.71 => ( ( A != B )
% 5.41/5.71 => ( ord_less_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_neq_trans
% 5.41/5.71 thf(fact_4287_order__less__imp__le,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ( ord_less_real @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_imp_le
% 5.41/5.71 thf(fact_4288_order__less__imp__le,axiom,
% 5.41/5.71 ! [X: set_int,Y: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_imp_le
% 5.41/5.71 thf(fact_4289_order__less__imp__le,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_imp_le
% 5.41/5.71 thf(fact_4290_order__less__imp__le,axiom,
% 5.41/5.71 ! [X: num,Y: num] :
% 5.41/5.71 ( ( ord_less_num @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_num @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_imp_le
% 5.41/5.71 thf(fact_4291_order__less__imp__le,axiom,
% 5.41/5.71 ! [X: nat,Y: nat] :
% 5.41/5.71 ( ( ord_less_nat @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_imp_le
% 5.41/5.71 thf(fact_4292_order__less__imp__le,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ( ord_less_int @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_int @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_imp_le
% 5.41/5.71 thf(fact_4293_linorder__not__less,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.41/5.71 = ( ord_less_eq_real @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_less
% 5.41/5.71 thf(fact_4294_linorder__not__less,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.41/5.71 = ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_less
% 5.41/5.71 thf(fact_4295_linorder__not__less,axiom,
% 5.41/5.71 ! [X: num,Y: num] :
% 5.41/5.71 ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.41/5.71 = ( ord_less_eq_num @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_less
% 5.41/5.71 thf(fact_4296_linorder__not__less,axiom,
% 5.41/5.71 ! [X: nat,Y: nat] :
% 5.41/5.71 ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.41/5.71 = ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_less
% 5.41/5.71 thf(fact_4297_linorder__not__less,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.41/5.71 = ( ord_less_eq_int @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_less
% 5.41/5.71 thf(fact_4298_linorder__not__le,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ( ~ ( ord_less_eq_real @ X @ Y ) )
% 5.41/5.71 = ( ord_less_real @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_le
% 5.41/5.71 thf(fact_4299_linorder__not__le,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ( ~ ( ord_less_eq_rat @ X @ Y ) )
% 5.41/5.71 = ( ord_less_rat @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_le
% 5.41/5.71 thf(fact_4300_linorder__not__le,axiom,
% 5.41/5.71 ! [X: num,Y: num] :
% 5.41/5.71 ( ( ~ ( ord_less_eq_num @ X @ Y ) )
% 5.41/5.71 = ( ord_less_num @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_le
% 5.41/5.71 thf(fact_4301_linorder__not__le,axiom,
% 5.41/5.71 ! [X: nat,Y: nat] :
% 5.41/5.71 ( ( ~ ( ord_less_eq_nat @ X @ Y ) )
% 5.41/5.71 = ( ord_less_nat @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_le
% 5.41/5.71 thf(fact_4302_linorder__not__le,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ( ~ ( ord_less_eq_int @ X @ Y ) )
% 5.41/5.71 = ( ord_less_int @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % linorder_not_le
% 5.41/5.71 thf(fact_4303_order__less__le,axiom,
% 5.41/5.71 ( ord_less_real
% 5.41/5.71 = ( ^ [X3: real,Y3: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ X3 @ Y3 )
% 5.41/5.71 & ( X3 != Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le
% 5.41/5.71 thf(fact_4304_order__less__le,axiom,
% 5.41/5.71 ( ord_less_set_int
% 5.41/5.71 = ( ^ [X3: set_int,Y3: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 5.41/5.71 & ( X3 != Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le
% 5.41/5.71 thf(fact_4305_order__less__le,axiom,
% 5.41/5.71 ( ord_less_rat
% 5.41/5.71 = ( ^ [X3: rat,Y3: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.41/5.71 & ( X3 != Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le
% 5.41/5.71 thf(fact_4306_order__less__le,axiom,
% 5.41/5.71 ( ord_less_num
% 5.41/5.71 = ( ^ [X3: num,Y3: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.41/5.71 & ( X3 != Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le
% 5.41/5.71 thf(fact_4307_order__less__le,axiom,
% 5.41/5.71 ( ord_less_nat
% 5.41/5.71 = ( ^ [X3: nat,Y3: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.41/5.71 & ( X3 != Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le
% 5.41/5.71 thf(fact_4308_order__less__le,axiom,
% 5.41/5.71 ( ord_less_int
% 5.41/5.71 = ( ^ [X3: int,Y3: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.41/5.71 & ( X3 != Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_less_le
% 5.41/5.71 thf(fact_4309_order__le__less,axiom,
% 5.41/5.71 ( ord_less_eq_real
% 5.41/5.71 = ( ^ [X3: real,Y3: real] :
% 5.41/5.71 ( ( ord_less_real @ X3 @ Y3 )
% 5.41/5.71 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less
% 5.41/5.71 thf(fact_4310_order__le__less,axiom,
% 5.41/5.71 ( ord_less_eq_set_int
% 5.41/5.71 = ( ^ [X3: set_int,Y3: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ X3 @ Y3 )
% 5.41/5.71 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less
% 5.41/5.71 thf(fact_4311_order__le__less,axiom,
% 5.41/5.71 ( ord_less_eq_rat
% 5.41/5.71 = ( ^ [X3: rat,Y3: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X3 @ Y3 )
% 5.41/5.71 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less
% 5.41/5.71 thf(fact_4312_order__le__less,axiom,
% 5.41/5.71 ( ord_less_eq_num
% 5.41/5.71 = ( ^ [X3: num,Y3: num] :
% 5.41/5.71 ( ( ord_less_num @ X3 @ Y3 )
% 5.41/5.71 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less
% 5.41/5.71 thf(fact_4313_order__le__less,axiom,
% 5.41/5.71 ( ord_less_eq_nat
% 5.41/5.71 = ( ^ [X3: nat,Y3: nat] :
% 5.41/5.71 ( ( ord_less_nat @ X3 @ Y3 )
% 5.41/5.71 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less
% 5.41/5.71 thf(fact_4314_order__le__less,axiom,
% 5.41/5.71 ( ord_less_eq_int
% 5.41/5.71 = ( ^ [X3: int,Y3: int] :
% 5.41/5.71 ( ( ord_less_int @ X3 @ Y3 )
% 5.41/5.71 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order_le_less
% 5.41/5.71 thf(fact_4315_dual__order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [B: real,A: real] :
% 5.41/5.71 ( ( ord_less_real @ B @ A )
% 5.41/5.71 => ( ord_less_eq_real @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_implies_order
% 5.41/5.71 thf(fact_4316_dual__order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [B: set_int,A: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ B @ A )
% 5.41/5.71 => ( ord_less_eq_set_int @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_implies_order
% 5.41/5.71 thf(fact_4317_dual__order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [B: rat,A: rat] :
% 5.41/5.71 ( ( ord_less_rat @ B @ A )
% 5.41/5.71 => ( ord_less_eq_rat @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_implies_order
% 5.41/5.71 thf(fact_4318_dual__order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [B: num,A: num] :
% 5.41/5.71 ( ( ord_less_num @ B @ A )
% 5.41/5.71 => ( ord_less_eq_num @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_implies_order
% 5.41/5.71 thf(fact_4319_dual__order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [B: nat,A: nat] :
% 5.41/5.71 ( ( ord_less_nat @ B @ A )
% 5.41/5.71 => ( ord_less_eq_nat @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_implies_order
% 5.41/5.71 thf(fact_4320_dual__order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [B: int,A: int] :
% 5.41/5.71 ( ( ord_less_int @ B @ A )
% 5.41/5.71 => ( ord_less_eq_int @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_implies_order
% 5.41/5.71 thf(fact_4321_order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( ord_less_real @ A @ B )
% 5.41/5.71 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_implies_order
% 5.41/5.71 thf(fact_4322_order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [A: set_int,B: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ A @ B )
% 5.41/5.71 => ( ord_less_eq_set_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_implies_order
% 5.41/5.71 thf(fact_4323_order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( ord_less_rat @ A @ B )
% 5.41/5.71 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_implies_order
% 5.41/5.71 thf(fact_4324_order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [A: num,B: num] :
% 5.41/5.71 ( ( ord_less_num @ A @ B )
% 5.41/5.71 => ( ord_less_eq_num @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_implies_order
% 5.41/5.71 thf(fact_4325_order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( ord_less_nat @ A @ B )
% 5.41/5.71 => ( ord_less_eq_nat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_implies_order
% 5.41/5.71 thf(fact_4326_order_Ostrict__implies__order,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( ord_less_int @ A @ B )
% 5.41/5.71 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_implies_order
% 5.41/5.71 thf(fact_4327_dual__order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_real
% 5.41/5.71 = ( ^ [B2: real,A3: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.41/5.71 & ~ ( ord_less_eq_real @ A3 @ B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_not
% 5.41/5.71 thf(fact_4328_dual__order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_set_int
% 5.41/5.71 = ( ^ [B2: set_int,A3: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.41/5.71 & ~ ( ord_less_eq_set_int @ A3 @ B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_not
% 5.41/5.71 thf(fact_4329_dual__order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_rat
% 5.41/5.71 = ( ^ [B2: rat,A3: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.41/5.71 & ~ ( ord_less_eq_rat @ A3 @ B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_not
% 5.41/5.71 thf(fact_4330_dual__order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_num
% 5.41/5.71 = ( ^ [B2: num,A3: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.41/5.71 & ~ ( ord_less_eq_num @ A3 @ B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_not
% 5.41/5.71 thf(fact_4331_dual__order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_nat
% 5.41/5.71 = ( ^ [B2: nat,A3: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.41/5.71 & ~ ( ord_less_eq_nat @ A3 @ B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_not
% 5.41/5.71 thf(fact_4332_dual__order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_int
% 5.41/5.71 = ( ^ [B2: int,A3: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.41/5.71 & ~ ( ord_less_eq_int @ A3 @ B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_not
% 5.41/5.71 thf(fact_4333_dual__order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [B: real,A: real,C: real] :
% 5.41/5.71 ( ( ord_less_real @ B @ A )
% 5.41/5.71 => ( ( ord_less_eq_real @ C @ B )
% 5.41/5.71 => ( ord_less_real @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans2
% 5.41/5.71 thf(fact_4334_dual__order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [B: set_int,A: set_int,C: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ B @ A )
% 5.41/5.71 => ( ( ord_less_eq_set_int @ C @ B )
% 5.41/5.71 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans2
% 5.41/5.71 thf(fact_4335_dual__order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [B: rat,A: rat,C: rat] :
% 5.41/5.71 ( ( ord_less_rat @ B @ A )
% 5.41/5.71 => ( ( ord_less_eq_rat @ C @ B )
% 5.41/5.71 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans2
% 5.41/5.71 thf(fact_4336_dual__order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [B: num,A: num,C: num] :
% 5.41/5.71 ( ( ord_less_num @ B @ A )
% 5.41/5.71 => ( ( ord_less_eq_num @ C @ B )
% 5.41/5.71 => ( ord_less_num @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans2
% 5.41/5.71 thf(fact_4337_dual__order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [B: nat,A: nat,C: nat] :
% 5.41/5.71 ( ( ord_less_nat @ B @ A )
% 5.41/5.71 => ( ( ord_less_eq_nat @ C @ B )
% 5.41/5.71 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans2
% 5.41/5.71 thf(fact_4338_dual__order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [B: int,A: int,C: int] :
% 5.41/5.71 ( ( ord_less_int @ B @ A )
% 5.41/5.71 => ( ( ord_less_eq_int @ C @ B )
% 5.41/5.71 => ( ord_less_int @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans2
% 5.41/5.71 thf(fact_4339_dual__order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [B: real,A: real,C: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ B @ A )
% 5.41/5.71 => ( ( ord_less_real @ C @ B )
% 5.41/5.71 => ( ord_less_real @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans1
% 5.41/5.71 thf(fact_4340_dual__order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [B: set_int,A: set_int,C: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ B @ A )
% 5.41/5.71 => ( ( ord_less_set_int @ C @ B )
% 5.41/5.71 => ( ord_less_set_int @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans1
% 5.41/5.71 thf(fact_4341_dual__order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [B: rat,A: rat,C: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ B @ A )
% 5.41/5.71 => ( ( ord_less_rat @ C @ B )
% 5.41/5.71 => ( ord_less_rat @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans1
% 5.41/5.71 thf(fact_4342_dual__order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [B: num,A: num,C: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ B @ A )
% 5.41/5.71 => ( ( ord_less_num @ C @ B )
% 5.41/5.71 => ( ord_less_num @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans1
% 5.41/5.71 thf(fact_4343_dual__order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [B: nat,A: nat,C: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ B @ A )
% 5.41/5.71 => ( ( ord_less_nat @ C @ B )
% 5.41/5.71 => ( ord_less_nat @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans1
% 5.41/5.71 thf(fact_4344_dual__order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [B: int,A: int,C: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ B @ A )
% 5.41/5.71 => ( ( ord_less_int @ C @ B )
% 5.41/5.71 => ( ord_less_int @ C @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_trans1
% 5.41/5.71 thf(fact_4345_dual__order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_real
% 5.41/5.71 = ( ^ [B2: real,A3: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ B2 @ A3 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_order
% 5.41/5.71 thf(fact_4346_dual__order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_set_int
% 5.41/5.71 = ( ^ [B2: set_int,A3: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ B2 @ A3 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_order
% 5.41/5.71 thf(fact_4347_dual__order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_rat
% 5.41/5.71 = ( ^ [B2: rat,A3: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ B2 @ A3 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_order
% 5.41/5.71 thf(fact_4348_dual__order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_num
% 5.41/5.71 = ( ^ [B2: num,A3: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ B2 @ A3 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_order
% 5.41/5.71 thf(fact_4349_dual__order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_nat
% 5.41/5.71 = ( ^ [B2: nat,A3: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ B2 @ A3 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_order
% 5.41/5.71 thf(fact_4350_dual__order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_int
% 5.41/5.71 = ( ^ [B2: int,A3: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ B2 @ A3 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.strict_iff_order
% 5.41/5.71 thf(fact_4351_dual__order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_real
% 5.41/5.71 = ( ^ [B2: real,A3: real] :
% 5.41/5.71 ( ( ord_less_real @ B2 @ A3 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.order_iff_strict
% 5.41/5.71 thf(fact_4352_dual__order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_set_int
% 5.41/5.71 = ( ^ [B2: set_int,A3: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ B2 @ A3 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.order_iff_strict
% 5.41/5.71 thf(fact_4353_dual__order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_rat
% 5.41/5.71 = ( ^ [B2: rat,A3: rat] :
% 5.41/5.71 ( ( ord_less_rat @ B2 @ A3 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.order_iff_strict
% 5.41/5.71 thf(fact_4354_dual__order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_num
% 5.41/5.71 = ( ^ [B2: num,A3: num] :
% 5.41/5.71 ( ( ord_less_num @ B2 @ A3 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.order_iff_strict
% 5.41/5.71 thf(fact_4355_dual__order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_nat
% 5.41/5.71 = ( ^ [B2: nat,A3: nat] :
% 5.41/5.71 ( ( ord_less_nat @ B2 @ A3 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.order_iff_strict
% 5.41/5.71 thf(fact_4356_dual__order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_int
% 5.41/5.71 = ( ^ [B2: int,A3: int] :
% 5.41/5.71 ( ( ord_less_int @ B2 @ A3 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dual_order.order_iff_strict
% 5.41/5.71 thf(fact_4357_dense__le__bounded,axiom,
% 5.41/5.71 ! [X: real,Y: real,Z: real] :
% 5.41/5.71 ( ( ord_less_real @ X @ Y )
% 5.41/5.71 => ( ! [W2: real] :
% 5.41/5.71 ( ( ord_less_real @ X @ W2 )
% 5.41/5.71 => ( ( ord_less_real @ W2 @ Y )
% 5.41/5.71 => ( ord_less_eq_real @ W2 @ Z ) ) )
% 5.41/5.71 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_le_bounded
% 5.41/5.71 thf(fact_4358_dense__le__bounded,axiom,
% 5.41/5.71 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X @ Y )
% 5.41/5.71 => ( ! [W2: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X @ W2 )
% 5.41/5.71 => ( ( ord_less_rat @ W2 @ Y )
% 5.41/5.71 => ( ord_less_eq_rat @ W2 @ Z ) ) )
% 5.41/5.71 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_le_bounded
% 5.41/5.71 thf(fact_4359_dense__ge__bounded,axiom,
% 5.41/5.71 ! [Z: real,X: real,Y: real] :
% 5.41/5.71 ( ( ord_less_real @ Z @ X )
% 5.41/5.71 => ( ! [W2: real] :
% 5.41/5.71 ( ( ord_less_real @ Z @ W2 )
% 5.41/5.71 => ( ( ord_less_real @ W2 @ X )
% 5.41/5.71 => ( ord_less_eq_real @ Y @ W2 ) ) )
% 5.41/5.71 => ( ord_less_eq_real @ Y @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_ge_bounded
% 5.41/5.71 thf(fact_4360_dense__ge__bounded,axiom,
% 5.41/5.71 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.71 ( ( ord_less_rat @ Z @ X )
% 5.41/5.71 => ( ! [W2: rat] :
% 5.41/5.71 ( ( ord_less_rat @ Z @ W2 )
% 5.41/5.71 => ( ( ord_less_rat @ W2 @ X )
% 5.41/5.71 => ( ord_less_eq_rat @ Y @ W2 ) ) )
% 5.41/5.71 => ( ord_less_eq_rat @ Y @ Z ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_ge_bounded
% 5.41/5.71 thf(fact_4361_order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_real
% 5.41/5.71 = ( ^ [A3: real,B2: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.41/5.71 & ~ ( ord_less_eq_real @ B2 @ A3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_not
% 5.41/5.71 thf(fact_4362_order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_set_int
% 5.41/5.71 = ( ^ [A3: set_int,B2: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.41/5.71 & ~ ( ord_less_eq_set_int @ B2 @ A3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_not
% 5.41/5.71 thf(fact_4363_order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_rat
% 5.41/5.71 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.41/5.71 & ~ ( ord_less_eq_rat @ B2 @ A3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_not
% 5.41/5.71 thf(fact_4364_order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_num
% 5.41/5.71 = ( ^ [A3: num,B2: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.41/5.71 & ~ ( ord_less_eq_num @ B2 @ A3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_not
% 5.41/5.71 thf(fact_4365_order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_nat
% 5.41/5.71 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.41/5.71 & ~ ( ord_less_eq_nat @ B2 @ A3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_not
% 5.41/5.71 thf(fact_4366_order_Ostrict__iff__not,axiom,
% 5.41/5.71 ( ord_less_int
% 5.41/5.71 = ( ^ [A3: int,B2: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.41/5.71 & ~ ( ord_less_eq_int @ B2 @ A3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_not
% 5.41/5.71 thf(fact_4367_order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [A: real,B: real,C: real] :
% 5.41/5.71 ( ( ord_less_real @ A @ B )
% 5.41/5.71 => ( ( ord_less_eq_real @ B @ C )
% 5.41/5.71 => ( ord_less_real @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans2
% 5.41/5.71 thf(fact_4368_order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [A: set_int,B: set_int,C: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ A @ B )
% 5.41/5.71 => ( ( ord_less_eq_set_int @ B @ C )
% 5.41/5.71 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans2
% 5.41/5.71 thf(fact_4369_order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [A: rat,B: rat,C: rat] :
% 5.41/5.71 ( ( ord_less_rat @ A @ B )
% 5.41/5.71 => ( ( ord_less_eq_rat @ B @ C )
% 5.41/5.71 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans2
% 5.41/5.71 thf(fact_4370_order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [A: num,B: num,C: num] :
% 5.41/5.71 ( ( ord_less_num @ A @ B )
% 5.41/5.71 => ( ( ord_less_eq_num @ B @ C )
% 5.41/5.71 => ( ord_less_num @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans2
% 5.41/5.71 thf(fact_4371_order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [A: nat,B: nat,C: nat] :
% 5.41/5.71 ( ( ord_less_nat @ A @ B )
% 5.41/5.71 => ( ( ord_less_eq_nat @ B @ C )
% 5.41/5.71 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans2
% 5.41/5.71 thf(fact_4372_order_Ostrict__trans2,axiom,
% 5.41/5.71 ! [A: int,B: int,C: int] :
% 5.41/5.71 ( ( ord_less_int @ A @ B )
% 5.41/5.71 => ( ( ord_less_eq_int @ B @ C )
% 5.41/5.71 => ( ord_less_int @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans2
% 5.41/5.71 thf(fact_4373_order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [A: real,B: real,C: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.71 => ( ( ord_less_real @ B @ C )
% 5.41/5.71 => ( ord_less_real @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans1
% 5.41/5.71 thf(fact_4374_order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [A: set_int,B: set_int,C: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ A @ B )
% 5.41/5.71 => ( ( ord_less_set_int @ B @ C )
% 5.41/5.71 => ( ord_less_set_int @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans1
% 5.41/5.71 thf(fact_4375_order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [A: rat,B: rat,C: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 => ( ( ord_less_rat @ B @ C )
% 5.41/5.71 => ( ord_less_rat @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans1
% 5.41/5.71 thf(fact_4376_order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [A: num,B: num,C: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ A @ B )
% 5.41/5.71 => ( ( ord_less_num @ B @ C )
% 5.41/5.71 => ( ord_less_num @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans1
% 5.41/5.71 thf(fact_4377_order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [A: nat,B: nat,C: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.71 => ( ( ord_less_nat @ B @ C )
% 5.41/5.71 => ( ord_less_nat @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans1
% 5.41/5.71 thf(fact_4378_order_Ostrict__trans1,axiom,
% 5.41/5.71 ! [A: int,B: int,C: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.71 => ( ( ord_less_int @ B @ C )
% 5.41/5.71 => ( ord_less_int @ A @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_trans1
% 5.41/5.71 thf(fact_4379_order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_real
% 5.41/5.71 = ( ^ [A3: real,B2: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ A3 @ B2 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_order
% 5.41/5.71 thf(fact_4380_order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_set_int
% 5.41/5.71 = ( ^ [A3: set_int,B2: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ A3 @ B2 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_order
% 5.41/5.71 thf(fact_4381_order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_rat
% 5.41/5.71 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A3 @ B2 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_order
% 5.41/5.71 thf(fact_4382_order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_num
% 5.41/5.71 = ( ^ [A3: num,B2: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ A3 @ B2 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_order
% 5.41/5.71 thf(fact_4383_order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_nat
% 5.41/5.71 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ A3 @ B2 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_order
% 5.41/5.71 thf(fact_4384_order_Ostrict__iff__order,axiom,
% 5.41/5.71 ( ord_less_int
% 5.41/5.71 = ( ^ [A3: int,B2: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ A3 @ B2 )
% 5.41/5.71 & ( A3 != B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.strict_iff_order
% 5.41/5.71 thf(fact_4385_order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_real
% 5.41/5.71 = ( ^ [A3: real,B2: real] :
% 5.41/5.71 ( ( ord_less_real @ A3 @ B2 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.order_iff_strict
% 5.41/5.71 thf(fact_4386_order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_set_int
% 5.41/5.71 = ( ^ [A3: set_int,B2: set_int] :
% 5.41/5.71 ( ( ord_less_set_int @ A3 @ B2 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.order_iff_strict
% 5.41/5.71 thf(fact_4387_order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_rat
% 5.41/5.71 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.71 ( ( ord_less_rat @ A3 @ B2 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.order_iff_strict
% 5.41/5.71 thf(fact_4388_order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_num
% 5.41/5.71 = ( ^ [A3: num,B2: num] :
% 5.41/5.71 ( ( ord_less_num @ A3 @ B2 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.order_iff_strict
% 5.41/5.71 thf(fact_4389_order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_nat
% 5.41/5.71 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.71 ( ( ord_less_nat @ A3 @ B2 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.order_iff_strict
% 5.41/5.71 thf(fact_4390_order_Oorder__iff__strict,axiom,
% 5.41/5.71 ( ord_less_eq_int
% 5.41/5.71 = ( ^ [A3: int,B2: int] :
% 5.41/5.71 ( ( ord_less_int @ A3 @ B2 )
% 5.41/5.71 | ( A3 = B2 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % order.order_iff_strict
% 5.41/5.71 thf(fact_4391_not__le__imp__less,axiom,
% 5.41/5.71 ! [Y: real,X: real] :
% 5.41/5.71 ( ~ ( ord_less_eq_real @ Y @ X )
% 5.41/5.71 => ( ord_less_real @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % not_le_imp_less
% 5.41/5.71 thf(fact_4392_not__le__imp__less,axiom,
% 5.41/5.71 ! [Y: rat,X: rat] :
% 5.41/5.71 ( ~ ( ord_less_eq_rat @ Y @ X )
% 5.41/5.71 => ( ord_less_rat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % not_le_imp_less
% 5.41/5.71 thf(fact_4393_not__le__imp__less,axiom,
% 5.41/5.71 ! [Y: num,X: num] :
% 5.41/5.71 ( ~ ( ord_less_eq_num @ Y @ X )
% 5.41/5.71 => ( ord_less_num @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % not_le_imp_less
% 5.41/5.71 thf(fact_4394_not__le__imp__less,axiom,
% 5.41/5.71 ! [Y: nat,X: nat] :
% 5.41/5.71 ( ~ ( ord_less_eq_nat @ Y @ X )
% 5.41/5.71 => ( ord_less_nat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % not_le_imp_less
% 5.41/5.71 thf(fact_4395_not__le__imp__less,axiom,
% 5.41/5.71 ! [Y: int,X: int] :
% 5.41/5.71 ( ~ ( ord_less_eq_int @ Y @ X )
% 5.41/5.71 => ( ord_less_int @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % not_le_imp_less
% 5.41/5.71 thf(fact_4396_less__le__not__le,axiom,
% 5.41/5.71 ( ord_less_real
% 5.41/5.71 = ( ^ [X3: real,Y3: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ X3 @ Y3 )
% 5.41/5.71 & ~ ( ord_less_eq_real @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_le_not_le
% 5.41/5.71 thf(fact_4397_less__le__not__le,axiom,
% 5.41/5.71 ( ord_less_set_int
% 5.41/5.71 = ( ^ [X3: set_int,Y3: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ X3 @ Y3 )
% 5.41/5.71 & ~ ( ord_less_eq_set_int @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_le_not_le
% 5.41/5.71 thf(fact_4398_less__le__not__le,axiom,
% 5.41/5.71 ( ord_less_rat
% 5.41/5.71 = ( ^ [X3: rat,Y3: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X3 @ Y3 )
% 5.41/5.71 & ~ ( ord_less_eq_rat @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_le_not_le
% 5.41/5.71 thf(fact_4399_less__le__not__le,axiom,
% 5.41/5.71 ( ord_less_num
% 5.41/5.71 = ( ^ [X3: num,Y3: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X3 @ Y3 )
% 5.41/5.71 & ~ ( ord_less_eq_num @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_le_not_le
% 5.41/5.71 thf(fact_4400_less__le__not__le,axiom,
% 5.41/5.71 ( ord_less_nat
% 5.41/5.71 = ( ^ [X3: nat,Y3: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ X3 @ Y3 )
% 5.41/5.71 & ~ ( ord_less_eq_nat @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_le_not_le
% 5.41/5.71 thf(fact_4401_less__le__not__le,axiom,
% 5.41/5.71 ( ord_less_int
% 5.41/5.71 = ( ^ [X3: int,Y3: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ X3 @ Y3 )
% 5.41/5.71 & ~ ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_le_not_le
% 5.41/5.71 thf(fact_4402_dense__le,axiom,
% 5.41/5.71 ! [Y: real,Z: real] :
% 5.41/5.71 ( ! [X6: real] :
% 5.41/5.71 ( ( ord_less_real @ X6 @ Y )
% 5.41/5.71 => ( ord_less_eq_real @ X6 @ Z ) )
% 5.41/5.71 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_le
% 5.41/5.71 thf(fact_4403_dense__le,axiom,
% 5.41/5.71 ! [Y: rat,Z: rat] :
% 5.41/5.71 ( ! [X6: rat] :
% 5.41/5.71 ( ( ord_less_rat @ X6 @ Y )
% 5.41/5.71 => ( ord_less_eq_rat @ X6 @ Z ) )
% 5.41/5.71 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_le
% 5.41/5.71 thf(fact_4404_dense__ge,axiom,
% 5.41/5.71 ! [Z: real,Y: real] :
% 5.41/5.71 ( ! [X6: real] :
% 5.41/5.71 ( ( ord_less_real @ Z @ X6 )
% 5.41/5.71 => ( ord_less_eq_real @ Y @ X6 ) )
% 5.41/5.71 => ( ord_less_eq_real @ Y @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_ge
% 5.41/5.71 thf(fact_4405_dense__ge,axiom,
% 5.41/5.71 ! [Z: rat,Y: rat] :
% 5.41/5.71 ( ! [X6: rat] :
% 5.41/5.71 ( ( ord_less_rat @ Z @ X6 )
% 5.41/5.71 => ( ord_less_eq_rat @ Y @ X6 ) )
% 5.41/5.71 => ( ord_less_eq_rat @ Y @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % dense_ge
% 5.41/5.71 thf(fact_4406_antisym__conv2,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.71 => ( ( ~ ( ord_less_real @ X @ Y ) )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv2
% 5.41/5.71 thf(fact_4407_antisym__conv2,axiom,
% 5.41/5.71 ! [X: set_int,Y: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.71 => ( ( ~ ( ord_less_set_int @ X @ Y ) )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv2
% 5.41/5.71 thf(fact_4408_antisym__conv2,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.71 => ( ( ~ ( ord_less_rat @ X @ Y ) )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv2
% 5.41/5.71 thf(fact_4409_antisym__conv2,axiom,
% 5.41/5.71 ! [X: num,Y: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.71 => ( ( ~ ( ord_less_num @ X @ Y ) )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv2
% 5.41/5.71 thf(fact_4410_antisym__conv2,axiom,
% 5.41/5.71 ! [X: nat,Y: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.71 => ( ( ~ ( ord_less_nat @ X @ Y ) )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv2
% 5.41/5.71 thf(fact_4411_antisym__conv2,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.71 => ( ( ~ ( ord_less_int @ X @ Y ) )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv2
% 5.41/5.71 thf(fact_4412_antisym__conv1,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ~ ( ord_less_real @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv1
% 5.41/5.71 thf(fact_4413_antisym__conv1,axiom,
% 5.41/5.71 ! [X: set_int,Y: set_int] :
% 5.41/5.71 ( ~ ( ord_less_set_int @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv1
% 5.41/5.71 thf(fact_4414_antisym__conv1,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ~ ( ord_less_rat @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv1
% 5.41/5.71 thf(fact_4415_antisym__conv1,axiom,
% 5.41/5.71 ! [X: num,Y: num] :
% 5.41/5.71 ( ~ ( ord_less_num @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv1
% 5.41/5.71 thf(fact_4416_antisym__conv1,axiom,
% 5.41/5.71 ! [X: nat,Y: nat] :
% 5.41/5.71 ( ~ ( ord_less_nat @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv1
% 5.41/5.71 thf(fact_4417_antisym__conv1,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ~ ( ord_less_int @ X @ Y )
% 5.41/5.71 => ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.71 = ( X = Y ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % antisym_conv1
% 5.41/5.71 thf(fact_4418_nless__le,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( ~ ( ord_less_real @ A @ B ) )
% 5.41/5.71 = ( ~ ( ord_less_eq_real @ A @ B )
% 5.41/5.71 | ( A = B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % nless_le
% 5.41/5.71 thf(fact_4419_nless__le,axiom,
% 5.41/5.71 ! [A: set_int,B: set_int] :
% 5.41/5.71 ( ( ~ ( ord_less_set_int @ A @ B ) )
% 5.41/5.71 = ( ~ ( ord_less_eq_set_int @ A @ B )
% 5.41/5.71 | ( A = B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % nless_le
% 5.41/5.71 thf(fact_4420_nless__le,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( ~ ( ord_less_rat @ A @ B ) )
% 5.41/5.71 = ( ~ ( ord_less_eq_rat @ A @ B )
% 5.41/5.71 | ( A = B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % nless_le
% 5.41/5.71 thf(fact_4421_nless__le,axiom,
% 5.41/5.71 ! [A: num,B: num] :
% 5.41/5.71 ( ( ~ ( ord_less_num @ A @ B ) )
% 5.41/5.71 = ( ~ ( ord_less_eq_num @ A @ B )
% 5.41/5.71 | ( A = B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % nless_le
% 5.41/5.71 thf(fact_4422_nless__le,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( ~ ( ord_less_nat @ A @ B ) )
% 5.41/5.71 = ( ~ ( ord_less_eq_nat @ A @ B )
% 5.41/5.71 | ( A = B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % nless_le
% 5.41/5.71 thf(fact_4423_nless__le,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( ~ ( ord_less_int @ A @ B ) )
% 5.41/5.71 = ( ~ ( ord_less_eq_int @ A @ B )
% 5.41/5.71 | ( A = B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % nless_le
% 5.41/5.71 thf(fact_4424_leI,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ~ ( ord_less_real @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_real @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % leI
% 5.41/5.71 thf(fact_4425_leI,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ~ ( ord_less_rat @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_rat @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % leI
% 5.41/5.71 thf(fact_4426_leI,axiom,
% 5.41/5.71 ! [X: num,Y: num] :
% 5.41/5.71 ( ~ ( ord_less_num @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_num @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % leI
% 5.41/5.71 thf(fact_4427_leI,axiom,
% 5.41/5.71 ! [X: nat,Y: nat] :
% 5.41/5.71 ( ~ ( ord_less_nat @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_nat @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % leI
% 5.41/5.71 thf(fact_4428_leI,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ~ ( ord_less_int @ X @ Y )
% 5.41/5.71 => ( ord_less_eq_int @ Y @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % leI
% 5.41/5.71 thf(fact_4429_leD,axiom,
% 5.41/5.71 ! [Y: real,X: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ Y @ X )
% 5.41/5.71 => ~ ( ord_less_real @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % leD
% 5.41/5.71 thf(fact_4430_leD,axiom,
% 5.41/5.71 ! [Y: set_int,X: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ Y @ X )
% 5.41/5.71 => ~ ( ord_less_set_int @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % leD
% 5.41/5.71 thf(fact_4431_leD,axiom,
% 5.41/5.71 ! [Y: rat,X: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ Y @ X )
% 5.41/5.71 => ~ ( ord_less_rat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % leD
% 5.41/5.71 thf(fact_4432_leD,axiom,
% 5.41/5.71 ! [Y: num,X: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ Y @ X )
% 5.41/5.71 => ~ ( ord_less_num @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % leD
% 5.41/5.71 thf(fact_4433_leD,axiom,
% 5.41/5.71 ! [Y: nat,X: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ Y @ X )
% 5.41/5.71 => ~ ( ord_less_nat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % leD
% 5.41/5.71 thf(fact_4434_leD,axiom,
% 5.41/5.71 ! [Y: int,X: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ Y @ X )
% 5.41/5.71 => ~ ( ord_less_int @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % leD
% 5.41/5.71 thf(fact_4435_bot_Oextremum__uniqueI,axiom,
% 5.41/5.71 ! [A: set_nat] :
% 5.41/5.71 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.41/5.71 => ( A = bot_bot_set_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_uniqueI
% 5.41/5.71 thf(fact_4436_bot_Oextremum__uniqueI,axiom,
% 5.41/5.71 ! [A: extended_enat] :
% 5.41/5.71 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.41/5.71 => ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_uniqueI
% 5.41/5.71 thf(fact_4437_bot_Oextremum__uniqueI,axiom,
% 5.41/5.71 ! [A: set_real] :
% 5.41/5.71 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.41/5.71 => ( A = bot_bot_set_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_uniqueI
% 5.41/5.71 thf(fact_4438_bot_Oextremum__uniqueI,axiom,
% 5.41/5.71 ! [A: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.41/5.71 => ( A = bot_bot_set_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_uniqueI
% 5.41/5.71 thf(fact_4439_bot_Oextremum__uniqueI,axiom,
% 5.41/5.71 ! [A: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.41/5.71 => ( A = bot_bot_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_uniqueI
% 5.41/5.71 thf(fact_4440_bot_Oextremum__unique,axiom,
% 5.41/5.71 ! [A: set_nat] :
% 5.41/5.71 ( ( ord_less_eq_set_nat @ A @ bot_bot_set_nat )
% 5.41/5.71 = ( A = bot_bot_set_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_unique
% 5.41/5.71 thf(fact_4441_bot_Oextremum__unique,axiom,
% 5.41/5.71 ! [A: extended_enat] :
% 5.41/5.71 ( ( ord_le2932123472753598470d_enat @ A @ bot_bo4199563552545308370d_enat )
% 5.41/5.71 = ( A = bot_bo4199563552545308370d_enat ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_unique
% 5.41/5.71 thf(fact_4442_bot_Oextremum__unique,axiom,
% 5.41/5.71 ! [A: set_real] :
% 5.41/5.71 ( ( ord_less_eq_set_real @ A @ bot_bot_set_real )
% 5.41/5.71 = ( A = bot_bot_set_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_unique
% 5.41/5.71 thf(fact_4443_bot_Oextremum__unique,axiom,
% 5.41/5.71 ! [A: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ A @ bot_bot_set_int )
% 5.41/5.71 = ( A = bot_bot_set_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_unique
% 5.41/5.71 thf(fact_4444_bot_Oextremum__unique,axiom,
% 5.41/5.71 ! [A: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ A @ bot_bot_nat )
% 5.41/5.71 = ( A = bot_bot_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_unique
% 5.41/5.71 thf(fact_4445_bot_Oextremum,axiom,
% 5.41/5.71 ! [A: set_nat] : ( ord_less_eq_set_nat @ bot_bot_set_nat @ A ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum
% 5.41/5.71 thf(fact_4446_bot_Oextremum,axiom,
% 5.41/5.71 ! [A: extended_enat] : ( ord_le2932123472753598470d_enat @ bot_bo4199563552545308370d_enat @ A ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum
% 5.41/5.71 thf(fact_4447_bot_Oextremum,axiom,
% 5.41/5.71 ! [A: set_real] : ( ord_less_eq_set_real @ bot_bot_set_real @ A ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum
% 5.41/5.71 thf(fact_4448_bot_Oextremum,axiom,
% 5.41/5.71 ! [A: set_int] : ( ord_less_eq_set_int @ bot_bot_set_int @ A ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum
% 5.41/5.71 thf(fact_4449_bot_Oextremum,axiom,
% 5.41/5.71 ! [A: nat] : ( ord_less_eq_nat @ bot_bot_nat @ A ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum
% 5.41/5.71 thf(fact_4450_bot_Onot__eq__extremum,axiom,
% 5.41/5.71 ! [A: set_nat] :
% 5.41/5.71 ( ( A != bot_bot_set_nat )
% 5.41/5.71 = ( ord_less_set_nat @ bot_bot_set_nat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.not_eq_extremum
% 5.41/5.71 thf(fact_4451_bot_Onot__eq__extremum,axiom,
% 5.41/5.71 ! [A: extended_enat] :
% 5.41/5.71 ( ( A != bot_bo4199563552545308370d_enat )
% 5.41/5.71 = ( ord_le72135733267957522d_enat @ bot_bo4199563552545308370d_enat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.not_eq_extremum
% 5.41/5.71 thf(fact_4452_bot_Onot__eq__extremum,axiom,
% 5.41/5.71 ! [A: set_int] :
% 5.41/5.71 ( ( A != bot_bot_set_int )
% 5.41/5.71 = ( ord_less_set_int @ bot_bot_set_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.not_eq_extremum
% 5.41/5.71 thf(fact_4453_bot_Onot__eq__extremum,axiom,
% 5.41/5.71 ! [A: set_real] :
% 5.41/5.71 ( ( A != bot_bot_set_real )
% 5.41/5.71 = ( ord_less_set_real @ bot_bot_set_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.not_eq_extremum
% 5.41/5.71 thf(fact_4454_bot_Onot__eq__extremum,axiom,
% 5.41/5.71 ! [A: nat] :
% 5.41/5.71 ( ( A != bot_bot_nat )
% 5.41/5.71 = ( ord_less_nat @ bot_bot_nat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % bot.not_eq_extremum
% 5.41/5.71 thf(fact_4455_bot_Oextremum__strict,axiom,
% 5.41/5.71 ! [A: set_nat] :
% 5.41/5.71 ~ ( ord_less_set_nat @ A @ bot_bot_set_nat ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_strict
% 5.41/5.71 thf(fact_4456_bot_Oextremum__strict,axiom,
% 5.41/5.71 ! [A: extended_enat] :
% 5.41/5.71 ~ ( ord_le72135733267957522d_enat @ A @ bot_bo4199563552545308370d_enat ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_strict
% 5.41/5.71 thf(fact_4457_bot_Oextremum__strict,axiom,
% 5.41/5.71 ! [A: set_int] :
% 5.41/5.71 ~ ( ord_less_set_int @ A @ bot_bot_set_int ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_strict
% 5.41/5.71 thf(fact_4458_bot_Oextremum__strict,axiom,
% 5.41/5.71 ! [A: set_real] :
% 5.41/5.71 ~ ( ord_less_set_real @ A @ bot_bot_set_real ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_strict
% 5.41/5.71 thf(fact_4459_bot_Oextremum__strict,axiom,
% 5.41/5.71 ! [A: nat] :
% 5.41/5.71 ~ ( ord_less_nat @ A @ bot_bot_nat ) ).
% 5.41/5.71
% 5.41/5.71 % bot.extremum_strict
% 5.41/5.71 thf(fact_4460_Euclid__induct,axiom,
% 5.41/5.71 ! [P: nat > nat > $o,A: nat,B: nat] :
% 5.41/5.71 ( ! [A5: nat,B5: nat] :
% 5.41/5.71 ( ( P @ A5 @ B5 )
% 5.41/5.71 = ( P @ B5 @ A5 ) )
% 5.41/5.71 => ( ! [A5: nat] : ( P @ A5 @ zero_zero_nat )
% 5.41/5.71 => ( ! [A5: nat,B5: nat] :
% 5.41/5.71 ( ( P @ A5 @ B5 )
% 5.41/5.71 => ( P @ A5 @ ( plus_plus_nat @ A5 @ B5 ) ) )
% 5.41/5.71 => ( P @ A @ B ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % Euclid_induct
% 5.41/5.71 thf(fact_4461_max__def,axiom,
% 5.41/5.71 ( ord_ma741700101516333627d_enat
% 5.41/5.71 = ( ^ [A3: extended_enat,B2: extended_enat] : ( if_Extended_enat @ ( ord_le2932123472753598470d_enat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_def
% 5.41/5.71 thf(fact_4462_max__def,axiom,
% 5.41/5.71 ( ord_max_Code_integer
% 5.41/5.71 = ( ^ [A3: code_integer,B2: code_integer] : ( if_Code_integer @ ( ord_le3102999989581377725nteger @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_def
% 5.41/5.71 thf(fact_4463_max__def,axiom,
% 5.41/5.71 ( ord_max_set_int
% 5.41/5.71 = ( ^ [A3: set_int,B2: set_int] : ( if_set_int @ ( ord_less_eq_set_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_def
% 5.41/5.71 thf(fact_4464_max__def,axiom,
% 5.41/5.71 ( ord_max_rat
% 5.41/5.71 = ( ^ [A3: rat,B2: rat] : ( if_rat @ ( ord_less_eq_rat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_def
% 5.41/5.71 thf(fact_4465_max__def,axiom,
% 5.41/5.71 ( ord_max_num
% 5.41/5.71 = ( ^ [A3: num,B2: num] : ( if_num @ ( ord_less_eq_num @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_def
% 5.41/5.71 thf(fact_4466_max__def,axiom,
% 5.41/5.71 ( ord_max_nat
% 5.41/5.71 = ( ^ [A3: nat,B2: nat] : ( if_nat @ ( ord_less_eq_nat @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_def
% 5.41/5.71 thf(fact_4467_max__def,axiom,
% 5.41/5.71 ( ord_max_int
% 5.41/5.71 = ( ^ [A3: int,B2: int] : ( if_int @ ( ord_less_eq_int @ A3 @ B2 ) @ B2 @ A3 ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_def
% 5.41/5.71 thf(fact_4468_max__absorb1,axiom,
% 5.41/5.71 ! [Y: extended_enat,X: extended_enat] :
% 5.41/5.71 ( ( ord_le2932123472753598470d_enat @ Y @ X )
% 5.41/5.71 => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 5.41/5.71 = X ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb1
% 5.41/5.71 thf(fact_4469_max__absorb1,axiom,
% 5.41/5.71 ! [Y: code_integer,X: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ Y @ X )
% 5.41/5.71 => ( ( ord_max_Code_integer @ X @ Y )
% 5.41/5.71 = X ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb1
% 5.41/5.71 thf(fact_4470_max__absorb1,axiom,
% 5.41/5.71 ! [Y: set_int,X: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ Y @ X )
% 5.41/5.71 => ( ( ord_max_set_int @ X @ Y )
% 5.41/5.71 = X ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb1
% 5.41/5.71 thf(fact_4471_max__absorb1,axiom,
% 5.41/5.71 ! [Y: rat,X: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ Y @ X )
% 5.41/5.71 => ( ( ord_max_rat @ X @ Y )
% 5.41/5.71 = X ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb1
% 5.41/5.71 thf(fact_4472_max__absorb1,axiom,
% 5.41/5.71 ! [Y: num,X: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ Y @ X )
% 5.41/5.71 => ( ( ord_max_num @ X @ Y )
% 5.41/5.71 = X ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb1
% 5.41/5.71 thf(fact_4473_max__absorb1,axiom,
% 5.41/5.71 ! [Y: nat,X: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ Y @ X )
% 5.41/5.71 => ( ( ord_max_nat @ X @ Y )
% 5.41/5.71 = X ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb1
% 5.41/5.71 thf(fact_4474_max__absorb1,axiom,
% 5.41/5.71 ! [Y: int,X: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ Y @ X )
% 5.41/5.71 => ( ( ord_max_int @ X @ Y )
% 5.41/5.71 = X ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb1
% 5.41/5.71 thf(fact_4475_max__absorb2,axiom,
% 5.41/5.71 ! [X: extended_enat,Y: extended_enat] :
% 5.41/5.71 ( ( ord_le2932123472753598470d_enat @ X @ Y )
% 5.41/5.71 => ( ( ord_ma741700101516333627d_enat @ X @ Y )
% 5.41/5.71 = Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb2
% 5.41/5.71 thf(fact_4476_max__absorb2,axiom,
% 5.41/5.71 ! [X: code_integer,Y: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ X @ Y )
% 5.41/5.71 => ( ( ord_max_Code_integer @ X @ Y )
% 5.41/5.71 = Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb2
% 5.41/5.71 thf(fact_4477_max__absorb2,axiom,
% 5.41/5.71 ! [X: set_int,Y: set_int] :
% 5.41/5.71 ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.71 => ( ( ord_max_set_int @ X @ Y )
% 5.41/5.71 = Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb2
% 5.41/5.71 thf(fact_4478_max__absorb2,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.71 => ( ( ord_max_rat @ X @ Y )
% 5.41/5.71 = Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb2
% 5.41/5.71 thf(fact_4479_max__absorb2,axiom,
% 5.41/5.71 ! [X: num,Y: num] :
% 5.41/5.71 ( ( ord_less_eq_num @ X @ Y )
% 5.41/5.71 => ( ( ord_max_num @ X @ Y )
% 5.41/5.71 = Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb2
% 5.41/5.71 thf(fact_4480_max__absorb2,axiom,
% 5.41/5.71 ! [X: nat,Y: nat] :
% 5.41/5.71 ( ( ord_less_eq_nat @ X @ Y )
% 5.41/5.71 => ( ( ord_max_nat @ X @ Y )
% 5.41/5.71 = Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb2
% 5.41/5.71 thf(fact_4481_max__absorb2,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.71 => ( ( ord_max_int @ X @ Y )
% 5.41/5.71 = Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % max_absorb2
% 5.41/5.71 thf(fact_4482_ln__one__plus__pos__lower__bound,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.71 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.71 => ( ord_less_eq_real @ ( minus_minus_real @ X @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % ln_one_plus_pos_lower_bound
% 5.41/5.71 thf(fact_4483_ln__2__less__1,axiom,
% 5.41/5.71 ord_less_real @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ one_one_real ).
% 5.41/5.71
% 5.41/5.71 % ln_2_less_1
% 5.41/5.71 thf(fact_4484_tanh__ln__real,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.71 => ( ( tanh_real @ ( ln_ln_real @ X ) )
% 5.41/5.71 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_ln_real
% 5.41/5.71 thf(fact_4485_ln__one__minus__pos__lower__bound,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.71 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.71 => ( ord_less_eq_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % ln_one_minus_pos_lower_bound
% 5.41/5.71 thf(fact_4486_abs__ln__one__plus__x__minus__x__bound,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.71 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_ln_one_plus_x_minus_x_bound
% 5.41/5.71 thf(fact_4487_even__succ__mod__exp,axiom,
% 5.41/5.71 ! [A: nat,N: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.71 => ( ( modulo_modulo_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.71 = ( plus_plus_nat @ one_one_nat @ ( modulo_modulo_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_succ_mod_exp
% 5.41/5.71 thf(fact_4488_even__succ__mod__exp,axiom,
% 5.41/5.71 ! [A: int,N: nat] :
% 5.41/5.71 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.71 => ( ( modulo_modulo_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.71 = ( plus_plus_int @ one_one_int @ ( modulo_modulo_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_succ_mod_exp
% 5.41/5.71 thf(fact_4489_even__succ__mod__exp,axiom,
% 5.41/5.71 ! [A: code_integer,N: nat] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.71 => ( ( modulo364778990260209775nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.71 = ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( modulo364778990260209775nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_succ_mod_exp
% 5.41/5.71 thf(fact_4490_even__succ__div__exp,axiom,
% 5.41/5.71 ! [A: code_integer,N: nat] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.71 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.71 = ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_succ_div_exp
% 5.41/5.71 thf(fact_4491_even__succ__div__exp,axiom,
% 5.41/5.71 ! [A: nat,N: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.71 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.71 = ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_succ_div_exp
% 5.41/5.71 thf(fact_4492_even__succ__div__exp,axiom,
% 5.41/5.71 ! [A: int,N: nat] :
% 5.41/5.71 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.71 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.71 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.71 = ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_succ_div_exp
% 5.41/5.71 thf(fact_4493_neg__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( ( uminus_uminus_real @ A )
% 5.41/5.71 = ( uminus_uminus_real @ B ) )
% 5.41/5.71 = ( A = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_iff_equal
% 5.41/5.71 thf(fact_4494_neg__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( ( uminus_uminus_int @ A )
% 5.41/5.71 = ( uminus_uminus_int @ B ) )
% 5.41/5.71 = ( A = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_iff_equal
% 5.41/5.71 thf(fact_4495_neg__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( ( uminus1482373934393186551omplex @ A )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.71 = ( A = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_iff_equal
% 5.41/5.71 thf(fact_4496_neg__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( ( uminus1351360451143612070nteger @ A )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.71 = ( A = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_iff_equal
% 5.41/5.71 thf(fact_4497_neg__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( ( uminus_uminus_rat @ A )
% 5.41/5.71 = ( uminus_uminus_rat @ B ) )
% 5.41/5.71 = ( A = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_iff_equal
% 5.41/5.71 thf(fact_4498_add_Oinverse__inverse,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( uminus_uminus_real @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_inverse
% 5.41/5.71 thf(fact_4499_add_Oinverse__inverse,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( uminus_uminus_int @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_inverse
% 5.41/5.71 thf(fact_4500_add_Oinverse__inverse,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( uminus1482373934393186551omplex @ ( uminus1482373934393186551omplex @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_inverse
% 5.41/5.71 thf(fact_4501_add_Oinverse__inverse,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( uminus1351360451143612070nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_inverse
% 5.41/5.71 thf(fact_4502_add_Oinverse__inverse,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( uminus_uminus_rat @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_inverse
% 5.41/5.71 thf(fact_4503_abs__abs,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.41/5.71 = ( abs_abs_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_abs
% 5.41/5.71 thf(fact_4504_abs__abs,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.41/5.71 = ( abs_abs_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_abs
% 5.41/5.71 thf(fact_4505_abs__abs,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.41/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_abs
% 5.41/5.71 thf(fact_4506_abs__abs,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.41/5.71 = ( abs_abs_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_abs
% 5.41/5.71 thf(fact_4507_abs__idempotent,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( abs_abs_real @ ( abs_abs_real @ A ) )
% 5.41/5.71 = ( abs_abs_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_idempotent
% 5.41/5.71 thf(fact_4508_abs__idempotent,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( abs_abs_int @ ( abs_abs_int @ A ) )
% 5.41/5.71 = ( abs_abs_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_idempotent
% 5.41/5.71 thf(fact_4509_abs__idempotent,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( abs_abs_Code_integer @ A ) )
% 5.41/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_idempotent
% 5.41/5.71 thf(fact_4510_abs__idempotent,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( abs_abs_rat @ ( abs_abs_rat @ A ) )
% 5.41/5.71 = ( abs_abs_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_idempotent
% 5.41/5.71 thf(fact_4511_nat__dvd__1__iff__1,axiom,
% 5.41/5.71 ! [M: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ M @ one_one_nat )
% 5.41/5.71 = ( M = one_one_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % nat_dvd_1_iff_1
% 5.41/5.71 thf(fact_4512_neg__le__iff__le,axiom,
% 5.41/5.71 ! [B: real,A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( ord_less_eq_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_iff_le
% 5.41/5.71 thf(fact_4513_neg__le__iff__le,axiom,
% 5.41/5.71 ! [B: code_integer,A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_iff_le
% 5.41/5.71 thf(fact_4514_neg__le__iff__le,axiom,
% 5.41/5.71 ! [B: rat,A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( ord_less_eq_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_iff_le
% 5.41/5.71 thf(fact_4515_neg__le__iff__le,axiom,
% 5.41/5.71 ! [B: int,A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( ord_less_eq_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_iff_le
% 5.41/5.71 thf(fact_4516_neg__equal__zero,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ( uminus_uminus_real @ A )
% 5.41/5.71 = A )
% 5.41/5.71 = ( A = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_zero
% 5.41/5.71 thf(fact_4517_neg__equal__zero,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ( uminus_uminus_int @ A )
% 5.41/5.71 = A )
% 5.41/5.71 = ( A = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_zero
% 5.41/5.71 thf(fact_4518_neg__equal__zero,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ( uminus1351360451143612070nteger @ A )
% 5.41/5.71 = A )
% 5.41/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_zero
% 5.41/5.71 thf(fact_4519_neg__equal__zero,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ( uminus_uminus_rat @ A )
% 5.41/5.71 = A )
% 5.41/5.71 = ( A = zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_zero
% 5.41/5.71 thf(fact_4520_equal__neg__zero,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( A
% 5.41/5.71 = ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( A = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % equal_neg_zero
% 5.41/5.71 thf(fact_4521_equal__neg__zero,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( A
% 5.41/5.71 = ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( A = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % equal_neg_zero
% 5.41/5.71 thf(fact_4522_equal__neg__zero,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( A
% 5.41/5.71 = ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % equal_neg_zero
% 5.41/5.71 thf(fact_4523_equal__neg__zero,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( A
% 5.41/5.71 = ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( A = zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % equal_neg_zero
% 5.41/5.71 thf(fact_4524_neg__equal__0__iff__equal,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ( uminus_uminus_real @ A )
% 5.41/5.71 = zero_zero_real )
% 5.41/5.71 = ( A = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_0_iff_equal
% 5.41/5.71 thf(fact_4525_neg__equal__0__iff__equal,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ( uminus_uminus_int @ A )
% 5.41/5.71 = zero_zero_int )
% 5.41/5.71 = ( A = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_0_iff_equal
% 5.41/5.71 thf(fact_4526_neg__equal__0__iff__equal,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( ( uminus1482373934393186551omplex @ A )
% 5.41/5.71 = zero_zero_complex )
% 5.41/5.71 = ( A = zero_zero_complex ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_0_iff_equal
% 5.41/5.71 thf(fact_4527_neg__equal__0__iff__equal,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ( uminus1351360451143612070nteger @ A )
% 5.41/5.71 = zero_z3403309356797280102nteger )
% 5.41/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_0_iff_equal
% 5.41/5.71 thf(fact_4528_neg__equal__0__iff__equal,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ( uminus_uminus_rat @ A )
% 5.41/5.71 = zero_zero_rat )
% 5.41/5.71 = ( A = zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_equal_0_iff_equal
% 5.41/5.71 thf(fact_4529_neg__0__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( zero_zero_real
% 5.41/5.71 = ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( zero_zero_real = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_equal_iff_equal
% 5.41/5.71 thf(fact_4530_neg__0__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( zero_zero_int
% 5.41/5.71 = ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( zero_zero_int = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_equal_iff_equal
% 5.41/5.71 thf(fact_4531_neg__0__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( zero_zero_complex
% 5.41/5.71 = ( uminus1482373934393186551omplex @ A ) )
% 5.41/5.71 = ( zero_zero_complex = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_equal_iff_equal
% 5.41/5.71 thf(fact_4532_neg__0__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( zero_z3403309356797280102nteger
% 5.41/5.71 = ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( zero_z3403309356797280102nteger = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_equal_iff_equal
% 5.41/5.71 thf(fact_4533_neg__0__equal__iff__equal,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( zero_zero_rat
% 5.41/5.71 = ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( zero_zero_rat = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_equal_iff_equal
% 5.41/5.71 thf(fact_4534_add_Oinverse__neutral,axiom,
% 5.41/5.71 ( ( uminus_uminus_real @ zero_zero_real )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_neutral
% 5.41/5.71 thf(fact_4535_add_Oinverse__neutral,axiom,
% 5.41/5.71 ( ( uminus_uminus_int @ zero_zero_int )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_neutral
% 5.41/5.71 thf(fact_4536_add_Oinverse__neutral,axiom,
% 5.41/5.71 ( ( uminus1482373934393186551omplex @ zero_zero_complex )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_neutral
% 5.41/5.71 thf(fact_4537_add_Oinverse__neutral,axiom,
% 5.41/5.71 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_neutral
% 5.41/5.71 thf(fact_4538_add_Oinverse__neutral,axiom,
% 5.41/5.71 ( ( uminus_uminus_rat @ zero_zero_rat )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % add.inverse_neutral
% 5.41/5.71 thf(fact_4539_neg__less__iff__less,axiom,
% 5.41/5.71 ! [B: real,A: real] :
% 5.41/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( ord_less_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_iff_less
% 5.41/5.71 thf(fact_4540_neg__less__iff__less,axiom,
% 5.41/5.71 ! [B: int,A: int] :
% 5.41/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( ord_less_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_iff_less
% 5.41/5.71 thf(fact_4541_neg__less__iff__less,axiom,
% 5.41/5.71 ! [B: code_integer,A: code_integer] :
% 5.41/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( ord_le6747313008572928689nteger @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_iff_less
% 5.41/5.71 thf(fact_4542_neg__less__iff__less,axiom,
% 5.41/5.71 ! [B: rat,A: rat] :
% 5.41/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( ord_less_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_iff_less
% 5.41/5.71 thf(fact_4543_neg__numeral__eq__iff,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.41/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.71 = ( M = N ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_numeral_eq_iff
% 5.41/5.71 thf(fact_4544_neg__numeral__eq__iff,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.41/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.71 = ( M = N ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_numeral_eq_iff
% 5.41/5.71 thf(fact_4545_neg__numeral__eq__iff,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.71 = ( M = N ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_numeral_eq_iff
% 5.41/5.71 thf(fact_4546_neg__numeral__eq__iff,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.71 = ( M = N ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_numeral_eq_iff
% 5.41/5.71 thf(fact_4547_neg__numeral__eq__iff,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.41/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.71 = ( M = N ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_numeral_eq_iff
% 5.41/5.71 thf(fact_4548_mult__minus__left,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.41/5.71 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_left
% 5.41/5.71 thf(fact_4549_mult__minus__left,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.71 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_left
% 5.41/5.71 thf(fact_4550_mult__minus__left,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_left
% 5.41/5.71 thf(fact_4551_mult__minus__left,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_left
% 5.41/5.71 thf(fact_4552_mult__minus__left,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.41/5.71 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_left
% 5.41/5.71 thf(fact_4553_minus__mult__minus,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.41/5.71 = ( times_times_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_mult_minus
% 5.41/5.71 thf(fact_4554_minus__mult__minus,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.41/5.71 = ( times_times_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_mult_minus
% 5.41/5.71 thf(fact_4555_minus__mult__minus,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.71 = ( times_times_complex @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_mult_minus
% 5.41/5.71 thf(fact_4556_minus__mult__minus,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.71 = ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_mult_minus
% 5.41/5.71 thf(fact_4557_minus__mult__minus,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.41/5.71 = ( times_times_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_mult_minus
% 5.41/5.71 thf(fact_4558_mult__minus__right,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( times_times_real @ A @ ( uminus_uminus_real @ B ) )
% 5.41/5.71 = ( uminus_uminus_real @ ( times_times_real @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_right
% 5.41/5.71 thf(fact_4559_mult__minus__right,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( times_times_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.71 = ( uminus_uminus_int @ ( times_times_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_right
% 5.41/5.71 thf(fact_4560_mult__minus__right,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ ( times_times_complex @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_right
% 5.41/5.71 thf(fact_4561_mult__minus__right,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ ( times_3573771949741848930nteger @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_right
% 5.41/5.71 thf(fact_4562_mult__minus__right,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.41/5.71 = ( uminus_uminus_rat @ ( times_times_rat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus_right
% 5.41/5.71 thf(fact_4563_dvd__0__left__iff,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.41/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_left_iff
% 5.41/5.71 thf(fact_4564_dvd__0__left__iff,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.41/5.71 = ( A = zero_zero_complex ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_left_iff
% 5.41/5.71 thf(fact_4565_dvd__0__left__iff,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.41/5.71 = ( A = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_left_iff
% 5.41/5.71 thf(fact_4566_dvd__0__left__iff,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.41/5.71 = ( A = zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_left_iff
% 5.41/5.71 thf(fact_4567_dvd__0__left__iff,axiom,
% 5.41/5.71 ! [A: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.41/5.71 = ( A = zero_zero_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_left_iff
% 5.41/5.71 thf(fact_4568_dvd__0__left__iff,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.41/5.71 = ( A = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_left_iff
% 5.41/5.71 thf(fact_4569_dvd__0__right,axiom,
% 5.41/5.71 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_right
% 5.41/5.71 thf(fact_4570_dvd__0__right,axiom,
% 5.41/5.71 ! [A: complex] : ( dvd_dvd_complex @ A @ zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_right
% 5.41/5.71 thf(fact_4571_dvd__0__right,axiom,
% 5.41/5.71 ! [A: real] : ( dvd_dvd_real @ A @ zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_right
% 5.41/5.71 thf(fact_4572_dvd__0__right,axiom,
% 5.41/5.71 ! [A: rat] : ( dvd_dvd_rat @ A @ zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_right
% 5.41/5.71 thf(fact_4573_dvd__0__right,axiom,
% 5.41/5.71 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_right
% 5.41/5.71 thf(fact_4574_dvd__0__right,axiom,
% 5.41/5.71 ! [A: int] : ( dvd_dvd_int @ A @ zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_0_right
% 5.41/5.71 thf(fact_4575_add__minus__cancel,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( plus_plus_real @ A @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % add_minus_cancel
% 5.41/5.71 thf(fact_4576_add__minus__cancel,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( plus_plus_int @ A @ ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % add_minus_cancel
% 5.41/5.71 thf(fact_4577_add__minus__cancel,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( plus_plus_complex @ A @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % add_minus_cancel
% 5.41/5.71 thf(fact_4578_add__minus__cancel,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ A @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % add_minus_cancel
% 5.41/5.71 thf(fact_4579_add__minus__cancel,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( plus_plus_rat @ A @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % add_minus_cancel
% 5.41/5.71 thf(fact_4580_minus__add__cancel,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( plus_plus_real @ A @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_cancel
% 5.41/5.71 thf(fact_4581_minus__add__cancel,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( plus_plus_int @ A @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_cancel
% 5.41/5.71 thf(fact_4582_minus__add__cancel,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( plus_plus_complex @ A @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_cancel
% 5.41/5.71 thf(fact_4583_minus__add__cancel,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_cancel
% 5.41/5.71 thf(fact_4584_minus__add__cancel,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.71 = B ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_cancel
% 5.41/5.71 thf(fact_4585_minus__add__distrib,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.41/5.71 = ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_distrib
% 5.41/5.71 thf(fact_4586_minus__add__distrib,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.41/5.71 = ( plus_plus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_distrib
% 5.41/5.71 thf(fact_4587_minus__add__distrib,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.41/5.71 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_distrib
% 5.41/5.71 thf(fact_4588_minus__add__distrib,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.41/5.71 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_distrib
% 5.41/5.71 thf(fact_4589_minus__add__distrib,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.71 = ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_add_distrib
% 5.41/5.71 thf(fact_4590_minus__diff__eq,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) )
% 5.41/5.71 = ( minus_minus_real @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_diff_eq
% 5.41/5.71 thf(fact_4591_minus__diff__eq,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) )
% 5.41/5.71 = ( minus_minus_int @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_diff_eq
% 5.41/5.71 thf(fact_4592_minus__diff__eq,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) )
% 5.41/5.71 = ( minus_minus_complex @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_diff_eq
% 5.41/5.71 thf(fact_4593_minus__diff__eq,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.41/5.71 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_diff_eq
% 5.41/5.71 thf(fact_4594_minus__diff__eq,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) )
% 5.41/5.71 = ( minus_minus_rat @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_diff_eq
% 5.41/5.71 thf(fact_4595_div__minus__minus,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.41/5.71 = ( divide_divide_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_minus_minus
% 5.41/5.71 thf(fact_4596_div__minus__minus,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.71 = ( divide6298287555418463151nteger @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_minus_minus
% 5.41/5.71 thf(fact_4597_dvd__1__iff__1,axiom,
% 5.41/5.71 ! [M: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.41/5.71 = ( M
% 5.41/5.71 = ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_1_iff_1
% 5.41/5.71 thf(fact_4598_dvd__1__left,axiom,
% 5.41/5.71 ! [K: nat] : ( dvd_dvd_nat @ ( suc @ zero_zero_nat ) @ K ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_1_left
% 5.41/5.71 thf(fact_4599_dvd__add__triv__left__iff,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_left_iff
% 5.41/5.71 thf(fact_4600_dvd__add__triv__left__iff,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ A @ B ) )
% 5.41/5.71 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_left_iff
% 5.41/5.71 thf(fact_4601_dvd__add__triv__left__iff,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.71 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_left_iff
% 5.41/5.71 thf(fact_4602_dvd__add__triv__left__iff,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.71 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_left_iff
% 5.41/5.71 thf(fact_4603_dvd__add__triv__left__iff,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ A @ B ) )
% 5.41/5.71 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_left_iff
% 5.41/5.71 thf(fact_4604_dvd__add__triv__right__iff,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ A ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_right_iff
% 5.41/5.71 thf(fact_4605_dvd__add__triv__right__iff,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ A ) )
% 5.41/5.71 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_right_iff
% 5.41/5.71 thf(fact_4606_dvd__add__triv__right__iff,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ A ) )
% 5.41/5.71 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_right_iff
% 5.41/5.71 thf(fact_4607_dvd__add__triv__right__iff,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ A ) )
% 5.41/5.71 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_right_iff
% 5.41/5.71 thf(fact_4608_dvd__add__triv__right__iff,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ A ) )
% 5.41/5.71 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_triv_right_iff
% 5.41/5.71 thf(fact_4609_abs__0,axiom,
% 5.41/5.71 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0
% 5.41/5.71 thf(fact_4610_abs__0,axiom,
% 5.41/5.71 ( ( abs_abs_complex @ zero_zero_complex )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0
% 5.41/5.71 thf(fact_4611_abs__0,axiom,
% 5.41/5.71 ( ( abs_abs_real @ zero_zero_real )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0
% 5.41/5.71 thf(fact_4612_abs__0,axiom,
% 5.41/5.71 ( ( abs_abs_rat @ zero_zero_rat )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0
% 5.41/5.71 thf(fact_4613_abs__0,axiom,
% 5.41/5.71 ( ( abs_abs_int @ zero_zero_int )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0
% 5.41/5.71 thf(fact_4614_abs__zero,axiom,
% 5.41/5.71 ( ( abs_abs_Code_integer @ zero_z3403309356797280102nteger )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % abs_zero
% 5.41/5.71 thf(fact_4615_abs__zero,axiom,
% 5.41/5.71 ( ( abs_abs_real @ zero_zero_real )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % abs_zero
% 5.41/5.71 thf(fact_4616_abs__zero,axiom,
% 5.41/5.71 ( ( abs_abs_rat @ zero_zero_rat )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % abs_zero
% 5.41/5.71 thf(fact_4617_abs__zero,axiom,
% 5.41/5.71 ( ( abs_abs_int @ zero_zero_int )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % abs_zero
% 5.41/5.71 thf(fact_4618_abs__eq__0,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ( abs_abs_Code_integer @ A )
% 5.41/5.71 = zero_z3403309356797280102nteger )
% 5.41/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_eq_0
% 5.41/5.71 thf(fact_4619_abs__eq__0,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ( abs_abs_real @ A )
% 5.41/5.71 = zero_zero_real )
% 5.41/5.71 = ( A = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_eq_0
% 5.41/5.71 thf(fact_4620_abs__eq__0,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ( abs_abs_rat @ A )
% 5.41/5.71 = zero_zero_rat )
% 5.41/5.71 = ( A = zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_eq_0
% 5.41/5.71 thf(fact_4621_abs__eq__0,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ( abs_abs_int @ A )
% 5.41/5.71 = zero_zero_int )
% 5.41/5.71 = ( A = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_eq_0
% 5.41/5.71 thf(fact_4622_abs__0__eq,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( zero_z3403309356797280102nteger
% 5.41/5.71 = ( abs_abs_Code_integer @ A ) )
% 5.41/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0_eq
% 5.41/5.71 thf(fact_4623_abs__0__eq,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( zero_zero_real
% 5.41/5.71 = ( abs_abs_real @ A ) )
% 5.41/5.71 = ( A = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0_eq
% 5.41/5.71 thf(fact_4624_abs__0__eq,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( zero_zero_rat
% 5.41/5.71 = ( abs_abs_rat @ A ) )
% 5.41/5.71 = ( A = zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0_eq
% 5.41/5.71 thf(fact_4625_abs__0__eq,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( zero_zero_int
% 5.41/5.71 = ( abs_abs_int @ A ) )
% 5.41/5.71 = ( A = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_0_eq
% 5.41/5.71 thf(fact_4626_div__dvd__div,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ B @ A ) @ ( divide6298287555418463151nteger @ C @ A ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_dvd_div
% 5.41/5.71 thf(fact_4627_div__dvd__div,axiom,
% 5.41/5.71 ! [A: nat,B: nat,C: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.71 => ( ( dvd_dvd_nat @ A @ C )
% 5.41/5.71 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ B @ A ) @ ( divide_divide_nat @ C @ A ) )
% 5.41/5.71 = ( dvd_dvd_nat @ B @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_dvd_div
% 5.41/5.71 thf(fact_4628_div__dvd__div,axiom,
% 5.41/5.71 ! [A: int,B: int,C: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.71 => ( ( dvd_dvd_int @ A @ C )
% 5.41/5.71 => ( ( dvd_dvd_int @ ( divide_divide_int @ B @ A ) @ ( divide_divide_int @ C @ A ) )
% 5.41/5.71 = ( dvd_dvd_int @ B @ C ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_dvd_div
% 5.41/5.71 thf(fact_4629_minus__dvd__iff,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ ( uminus_uminus_real @ X ) @ Y )
% 5.41/5.71 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_dvd_iff
% 5.41/5.71 thf(fact_4630_minus__dvd__iff,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ ( uminus_uminus_int @ X ) @ Y )
% 5.41/5.71 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_dvd_iff
% 5.41/5.71 thf(fact_4631_minus__dvd__iff,axiom,
% 5.41/5.71 ! [X: complex,Y: complex] :
% 5.41/5.71 ( ( dvd_dvd_complex @ ( uminus1482373934393186551omplex @ X ) @ Y )
% 5.41/5.71 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_dvd_iff
% 5.41/5.71 thf(fact_4632_minus__dvd__iff,axiom,
% 5.41/5.71 ! [X: code_integer,Y: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ ( uminus1351360451143612070nteger @ X ) @ Y )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_dvd_iff
% 5.41/5.71 thf(fact_4633_minus__dvd__iff,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ ( uminus_uminus_rat @ X ) @ Y )
% 5.41/5.71 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_dvd_iff
% 5.41/5.71 thf(fact_4634_dvd__minus__iff,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ X @ ( uminus_uminus_real @ Y ) )
% 5.41/5.71 = ( dvd_dvd_real @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_minus_iff
% 5.41/5.71 thf(fact_4635_dvd__minus__iff,axiom,
% 5.41/5.71 ! [X: int,Y: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ X @ ( uminus_uminus_int @ Y ) )
% 5.41/5.71 = ( dvd_dvd_int @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_minus_iff
% 5.41/5.71 thf(fact_4636_dvd__minus__iff,axiom,
% 5.41/5.71 ! [X: complex,Y: complex] :
% 5.41/5.71 ( ( dvd_dvd_complex @ X @ ( uminus1482373934393186551omplex @ Y ) )
% 5.41/5.71 = ( dvd_dvd_complex @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_minus_iff
% 5.41/5.71 thf(fact_4637_dvd__minus__iff,axiom,
% 5.41/5.71 ! [X: code_integer,Y: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ X @ ( uminus1351360451143612070nteger @ Y ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_minus_iff
% 5.41/5.71 thf(fact_4638_dvd__minus__iff,axiom,
% 5.41/5.71 ! [X: rat,Y: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ X @ ( uminus_uminus_rat @ Y ) )
% 5.41/5.71 = ( dvd_dvd_rat @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_minus_iff
% 5.41/5.71 thf(fact_4639_abs__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( numera6620942414471956472nteger @ N ) )
% 5.41/5.71 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_numeral
% 5.41/5.71 thf(fact_4640_abs__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_real @ ( numeral_numeral_real @ N ) )
% 5.41/5.71 = ( numeral_numeral_real @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_numeral
% 5.41/5.71 thf(fact_4641_abs__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_rat @ ( numeral_numeral_rat @ N ) )
% 5.41/5.71 = ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_numeral
% 5.41/5.71 thf(fact_4642_abs__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_int @ ( numeral_numeral_int @ N ) )
% 5.41/5.71 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_numeral
% 5.41/5.71 thf(fact_4643_abs__mult__self__eq,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ A ) )
% 5.41/5.71 = ( times_3573771949741848930nteger @ A @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_mult_self_eq
% 5.41/5.71 thf(fact_4644_abs__mult__self__eq,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ A ) )
% 5.41/5.71 = ( times_times_real @ A @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_mult_self_eq
% 5.41/5.71 thf(fact_4645_abs__mult__self__eq,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ A ) )
% 5.41/5.71 = ( times_times_rat @ A @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_mult_self_eq
% 5.41/5.71 thf(fact_4646_abs__mult__self__eq,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ A ) )
% 5.41/5.71 = ( times_times_int @ A @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_mult_self_eq
% 5.41/5.71 thf(fact_4647_abs__add__abs,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) )
% 5.41/5.71 = ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_add_abs
% 5.41/5.71 thf(fact_4648_abs__add__abs,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( abs_abs_real @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) )
% 5.41/5.71 = ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_add_abs
% 5.41/5.71 thf(fact_4649_abs__add__abs,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( abs_abs_rat @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) )
% 5.41/5.71 = ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_add_abs
% 5.41/5.71 thf(fact_4650_abs__add__abs,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( abs_abs_int @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) )
% 5.41/5.71 = ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_add_abs
% 5.41/5.71 thf(fact_4651_abs__1,axiom,
% 5.41/5.71 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.41/5.71 = one_one_Code_integer ) ).
% 5.41/5.71
% 5.41/5.71 % abs_1
% 5.41/5.71 thf(fact_4652_abs__1,axiom,
% 5.41/5.71 ( ( abs_abs_complex @ one_one_complex )
% 5.41/5.71 = one_one_complex ) ).
% 5.41/5.71
% 5.41/5.71 % abs_1
% 5.41/5.71 thf(fact_4653_abs__1,axiom,
% 5.41/5.71 ( ( abs_abs_real @ one_one_real )
% 5.41/5.71 = one_one_real ) ).
% 5.41/5.71
% 5.41/5.71 % abs_1
% 5.41/5.71 thf(fact_4654_abs__1,axiom,
% 5.41/5.71 ( ( abs_abs_rat @ one_one_rat )
% 5.41/5.71 = one_one_rat ) ).
% 5.41/5.71
% 5.41/5.71 % abs_1
% 5.41/5.71 thf(fact_4655_abs__1,axiom,
% 5.41/5.71 ( ( abs_abs_int @ one_one_int )
% 5.41/5.71 = one_one_int ) ).
% 5.41/5.71
% 5.41/5.71 % abs_1
% 5.41/5.71 thf(fact_4656_abs__divide,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( abs_abs_complex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.71 = ( divide1717551699836669952omplex @ ( abs_abs_complex @ A ) @ ( abs_abs_complex @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_divide
% 5.41/5.71 thf(fact_4657_abs__divide,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.71 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_divide
% 5.41/5.71 thf(fact_4658_abs__divide,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.71 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_divide
% 5.41/5.71 thf(fact_4659_abs__minus,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( abs_abs_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus
% 5.41/5.71 thf(fact_4660_abs__minus,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( abs_abs_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus
% 5.41/5.71 thf(fact_4661_abs__minus,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( abs_abs_complex @ ( uminus1482373934393186551omplex @ A ) )
% 5.41/5.71 = ( abs_abs_complex @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus
% 5.41/5.71 thf(fact_4662_abs__minus,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus
% 5.41/5.71 thf(fact_4663_abs__minus,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( abs_abs_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus
% 5.41/5.71 thf(fact_4664_abs__minus__cancel,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( abs_abs_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus_cancel
% 5.41/5.71 thf(fact_4665_abs__minus__cancel,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( abs_abs_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus_cancel
% 5.41/5.71 thf(fact_4666_abs__minus__cancel,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( abs_abs_Code_integer @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus_cancel
% 5.41/5.71 thf(fact_4667_abs__minus__cancel,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( abs_abs_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_minus_cancel
% 5.41/5.71 thf(fact_4668_mod__minus__minus,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.41/5.71 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mod_minus_minus
% 5.41/5.71 thf(fact_4669_mod__minus__minus,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % mod_minus_minus
% 5.41/5.71 thf(fact_4670_nat__mult__dvd__cancel__disj,axiom,
% 5.41/5.71 ! [K: nat,M: nat,N: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.71 = ( ( K = zero_zero_nat )
% 5.41/5.71 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % nat_mult_dvd_cancel_disj
% 5.41/5.71 thf(fact_4671_dvd__abs__iff,axiom,
% 5.41/5.71 ! [M: real,K: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ M @ ( abs_abs_real @ K ) )
% 5.41/5.71 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_abs_iff
% 5.41/5.71 thf(fact_4672_dvd__abs__iff,axiom,
% 5.41/5.71 ! [M: int,K: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ M @ ( abs_abs_int @ K ) )
% 5.41/5.71 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_abs_iff
% 5.41/5.71 thf(fact_4673_dvd__abs__iff,axiom,
% 5.41/5.71 ! [M: code_integer,K: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ M @ ( abs_abs_Code_integer @ K ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_abs_iff
% 5.41/5.71 thf(fact_4674_dvd__abs__iff,axiom,
% 5.41/5.71 ! [M: rat,K: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ M @ ( abs_abs_rat @ K ) )
% 5.41/5.71 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_abs_iff
% 5.41/5.71 thf(fact_4675_abs__dvd__iff,axiom,
% 5.41/5.71 ! [M: real,K: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ ( abs_abs_real @ M ) @ K )
% 5.41/5.71 = ( dvd_dvd_real @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_dvd_iff
% 5.41/5.71 thf(fact_4676_abs__dvd__iff,axiom,
% 5.41/5.71 ! [M: int,K: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ ( abs_abs_int @ M ) @ K )
% 5.41/5.71 = ( dvd_dvd_int @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_dvd_iff
% 5.41/5.71 thf(fact_4677_abs__dvd__iff,axiom,
% 5.41/5.71 ! [M: code_integer,K: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ ( abs_abs_Code_integer @ M ) @ K )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_dvd_iff
% 5.41/5.71 thf(fact_4678_abs__dvd__iff,axiom,
% 5.41/5.71 ! [M: rat,K: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ ( abs_abs_rat @ M ) @ K )
% 5.41/5.71 = ( dvd_dvd_rat @ M @ K ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_dvd_iff
% 5.41/5.71 thf(fact_4679_tanh__0,axiom,
% 5.41/5.71 ( ( tanh_complex @ zero_zero_complex )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_0
% 5.41/5.71 thf(fact_4680_tanh__0,axiom,
% 5.41/5.71 ( ( tanh_real @ zero_zero_real )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_0
% 5.41/5.71 thf(fact_4681_tanh__real__zero__iff,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ( tanh_real @ X )
% 5.41/5.71 = zero_zero_real )
% 5.41/5.71 = ( X = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_real_zero_iff
% 5.41/5.71 thf(fact_4682_tanh__real__le__iff,axiom,
% 5.41/5.71 ! [X: real,Y: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ ( tanh_real @ Y ) )
% 5.41/5.71 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_real_le_iff
% 5.41/5.71 thf(fact_4683_neg__less__eq__nonneg,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ A )
% 5.41/5.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_eq_nonneg
% 5.41/5.71 thf(fact_4684_neg__less__eq__nonneg,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.41/5.71 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_eq_nonneg
% 5.41/5.71 thf(fact_4685_neg__less__eq__nonneg,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.41/5.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_eq_nonneg
% 5.41/5.71 thf(fact_4686_neg__less__eq__nonneg,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ A )
% 5.41/5.71 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_eq_nonneg
% 5.41/5.71 thf(fact_4687_less__eq__neg__nonpos,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_eq_neg_nonpos
% 5.41/5.71 thf(fact_4688_less__eq__neg__nonpos,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_eq_neg_nonpos
% 5.41/5.71 thf(fact_4689_less__eq__neg__nonpos,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_eq_neg_nonpos
% 5.41/5.71 thf(fact_4690_less__eq__neg__nonpos,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_eq_neg_nonpos
% 5.41/5.71 thf(fact_4691_neg__le__0__iff__le,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.41/5.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_0_iff_le
% 5.41/5.71 thf(fact_4692_neg__le__0__iff__le,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.41/5.71 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_0_iff_le
% 5.41/5.71 thf(fact_4693_neg__le__0__iff__le,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.41/5.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_0_iff_le
% 5.41/5.71 thf(fact_4694_neg__le__0__iff__le,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.41/5.71 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_le_0_iff_le
% 5.41/5.71 thf(fact_4695_neg__0__le__iff__le,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( ord_less_eq_real @ A @ zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_le_iff_le
% 5.41/5.71 thf(fact_4696_neg__0__le__iff__le,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_le_iff_le
% 5.41/5.71 thf(fact_4697_neg__0__le__iff__le,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_le_iff_le
% 5.41/5.71 thf(fact_4698_neg__0__le__iff__le,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_le_iff_le
% 5.41/5.71 thf(fact_4699_less__neg__neg,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_real @ A @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_neg_neg
% 5.41/5.71 thf(fact_4700_less__neg__neg,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_int @ A @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_neg_neg
% 5.41/5.71 thf(fact_4701_less__neg__neg,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_neg_neg
% 5.41/5.71 thf(fact_4702_less__neg__neg,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % less_neg_neg
% 5.41/5.71 thf(fact_4703_neg__less__pos,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ A )
% 5.41/5.71 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_pos
% 5.41/5.71 thf(fact_4704_neg__less__pos,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ A )
% 5.41/5.71 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_pos
% 5.41/5.71 thf(fact_4705_neg__less__pos,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.41/5.71 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_pos
% 5.41/5.71 thf(fact_4706_neg__less__pos,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.41/5.71 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_pos
% 5.41/5.71 thf(fact_4707_neg__0__less__iff__less,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = ( ord_less_real @ A @ zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_less_iff_less
% 5.41/5.71 thf(fact_4708_neg__0__less__iff__less,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = ( ord_less_int @ A @ zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_less_iff_less
% 5.41/5.71 thf(fact_4709_neg__0__less__iff__less,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_less_iff_less
% 5.41/5.71 thf(fact_4710_neg__0__less__iff__less,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = ( ord_less_rat @ A @ zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_0_less_iff_less
% 5.41/5.71 thf(fact_4711_neg__less__0__iff__less,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ zero_zero_real )
% 5.41/5.71 = ( ord_less_real @ zero_zero_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_0_iff_less
% 5.41/5.71 thf(fact_4712_neg__less__0__iff__less,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ zero_zero_int )
% 5.41/5.71 = ( ord_less_int @ zero_zero_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_0_iff_less
% 5.41/5.71 thf(fact_4713_neg__less__0__iff__less,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ zero_z3403309356797280102nteger )
% 5.41/5.71 = ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_0_iff_less
% 5.41/5.71 thf(fact_4714_neg__less__0__iff__less,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ zero_zero_rat )
% 5.41/5.71 = ( ord_less_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_less_0_iff_less
% 5.41/5.71 thf(fact_4715_ab__left__minus,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % ab_left_minus
% 5.41/5.71 thf(fact_4716_ab__left__minus,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % ab_left_minus
% 5.41/5.71 thf(fact_4717_ab__left__minus,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % ab_left_minus
% 5.41/5.71 thf(fact_4718_ab__left__minus,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % ab_left_minus
% 5.41/5.71 thf(fact_4719_ab__left__minus,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % ab_left_minus
% 5.41/5.71 thf(fact_4720_add_Oright__inverse,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( plus_plus_real @ A @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % add.right_inverse
% 5.41/5.71 thf(fact_4721_add_Oright__inverse,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( plus_plus_int @ A @ ( uminus_uminus_int @ A ) )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % add.right_inverse
% 5.41/5.71 thf(fact_4722_add_Oright__inverse,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( plus_plus_complex @ A @ ( uminus1482373934393186551omplex @ A ) )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % add.right_inverse
% 5.41/5.71 thf(fact_4723_add_Oright__inverse,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ A @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % add.right_inverse
% 5.41/5.71 thf(fact_4724_add_Oright__inverse,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( plus_plus_rat @ A @ ( uminus_uminus_rat @ A ) )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % add.right_inverse
% 5.41/5.71 thf(fact_4725_diff__0,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( minus_minus_real @ zero_zero_real @ A )
% 5.41/5.71 = ( uminus_uminus_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_0
% 5.41/5.71 thf(fact_4726_diff__0,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( minus_minus_int @ zero_zero_int @ A )
% 5.41/5.71 = ( uminus_uminus_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_0
% 5.41/5.71 thf(fact_4727_diff__0,axiom,
% 5.41/5.71 ! [A: complex] :
% 5.41/5.71 ( ( minus_minus_complex @ zero_zero_complex @ A )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_0
% 5.41/5.71 thf(fact_4728_diff__0,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_0
% 5.41/5.71 thf(fact_4729_diff__0,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( minus_minus_rat @ zero_zero_rat @ A )
% 5.41/5.71 = ( uminus_uminus_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_0
% 5.41/5.71 thf(fact_4730_verit__minus__simplify_I3_J,axiom,
% 5.41/5.71 ! [B: real] :
% 5.41/5.71 ( ( minus_minus_real @ zero_zero_real @ B )
% 5.41/5.71 = ( uminus_uminus_real @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % verit_minus_simplify(3)
% 5.41/5.71 thf(fact_4731_verit__minus__simplify_I3_J,axiom,
% 5.41/5.71 ! [B: int] :
% 5.41/5.71 ( ( minus_minus_int @ zero_zero_int @ B )
% 5.41/5.71 = ( uminus_uminus_int @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % verit_minus_simplify(3)
% 5.41/5.71 thf(fact_4732_verit__minus__simplify_I3_J,axiom,
% 5.41/5.71 ! [B: complex] :
% 5.41/5.71 ( ( minus_minus_complex @ zero_zero_complex @ B )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % verit_minus_simplify(3)
% 5.41/5.71 thf(fact_4733_verit__minus__simplify_I3_J,axiom,
% 5.41/5.71 ! [B: code_integer] :
% 5.41/5.71 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % verit_minus_simplify(3)
% 5.41/5.71 thf(fact_4734_verit__minus__simplify_I3_J,axiom,
% 5.41/5.71 ! [B: rat] :
% 5.41/5.71 ( ( minus_minus_rat @ zero_zero_rat @ B )
% 5.41/5.71 = ( uminus_uminus_rat @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % verit_minus_simplify(3)
% 5.41/5.71 thf(fact_4735_add__neg__numeral__simps_I3_J,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.71 = ( uminus_uminus_real @ ( plus_plus_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_simps(3)
% 5.41/5.71 thf(fact_4736_add__neg__numeral__simps_I3_J,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.71 = ( uminus_uminus_int @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_simps(3)
% 5.41/5.71 thf(fact_4737_add__neg__numeral__simps_I3_J,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ M ) @ ( numera6690914467698888265omplex @ N ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_simps(3)
% 5.41/5.71 thf(fact_4738_add__neg__numeral__simps_I3_J,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_simps(3)
% 5.41/5.71 thf(fact_4739_add__neg__numeral__simps_I3_J,axiom,
% 5.41/5.71 ! [M: num,N: num] :
% 5.41/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.71 = ( uminus_uminus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ M ) @ ( numeral_numeral_rat @ N ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_simps(3)
% 5.41/5.71 thf(fact_4740_dvd__times__right__cancel__iff,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.71 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ A ) @ ( times_3573771949741848930nteger @ C @ A ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_times_right_cancel_iff
% 5.41/5.71 thf(fact_4741_dvd__times__right__cancel__iff,axiom,
% 5.41/5.71 ! [A: nat,B: nat,C: nat] :
% 5.41/5.71 ( ( A != zero_zero_nat )
% 5.41/5.71 => ( ( dvd_dvd_nat @ ( times_times_nat @ B @ A ) @ ( times_times_nat @ C @ A ) )
% 5.41/5.71 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_times_right_cancel_iff
% 5.41/5.71 thf(fact_4742_dvd__times__right__cancel__iff,axiom,
% 5.41/5.71 ! [A: int,B: int,C: int] :
% 5.41/5.71 ( ( A != zero_zero_int )
% 5.41/5.71 => ( ( dvd_dvd_int @ ( times_times_int @ B @ A ) @ ( times_times_int @ C @ A ) )
% 5.41/5.71 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_times_right_cancel_iff
% 5.41/5.71 thf(fact_4743_dvd__times__left__cancel__iff,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.71 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ ( times_3573771949741848930nteger @ A @ C ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_times_left_cancel_iff
% 5.41/5.71 thf(fact_4744_dvd__times__left__cancel__iff,axiom,
% 5.41/5.71 ! [A: nat,B: nat,C: nat] :
% 5.41/5.71 ( ( A != zero_zero_nat )
% 5.41/5.71 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ ( times_times_nat @ A @ C ) )
% 5.41/5.71 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_times_left_cancel_iff
% 5.41/5.71 thf(fact_4745_dvd__times__left__cancel__iff,axiom,
% 5.41/5.71 ! [A: int,B: int,C: int] :
% 5.41/5.71 ( ( A != zero_zero_int )
% 5.41/5.71 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ ( times_times_int @ A @ C ) )
% 5.41/5.71 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_times_left_cancel_iff
% 5.41/5.71 thf(fact_4746_dvd__mult__cancel__right,axiom,
% 5.41/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.41/5.71 = ( ( C = zero_z3403309356797280102nteger )
% 5.41/5.71 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_right
% 5.41/5.71 thf(fact_4747_dvd__mult__cancel__right,axiom,
% 5.41/5.71 ! [A: complex,C: complex,B: complex] :
% 5.41/5.71 ( ( dvd_dvd_complex @ ( times_times_complex @ A @ C ) @ ( times_times_complex @ B @ C ) )
% 5.41/5.71 = ( ( C = zero_zero_complex )
% 5.41/5.71 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_right
% 5.41/5.71 thf(fact_4748_dvd__mult__cancel__right,axiom,
% 5.41/5.71 ! [A: real,C: real,B: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ C ) )
% 5.41/5.71 = ( ( C = zero_zero_real )
% 5.41/5.71 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_right
% 5.41/5.71 thf(fact_4749_dvd__mult__cancel__right,axiom,
% 5.41/5.71 ! [A: rat,C: rat,B: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ C ) )
% 5.41/5.71 = ( ( C = zero_zero_rat )
% 5.41/5.71 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_right
% 5.41/5.71 thf(fact_4750_dvd__mult__cancel__right,axiom,
% 5.41/5.71 ! [A: int,C: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ C ) )
% 5.41/5.71 = ( ( C = zero_zero_int )
% 5.41/5.71 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_right
% 5.41/5.71 thf(fact_4751_dvd__mult__cancel__left,axiom,
% 5.41/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ C @ A ) @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.41/5.71 = ( ( C = zero_z3403309356797280102nteger )
% 5.41/5.71 | ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_left
% 5.41/5.71 thf(fact_4752_dvd__mult__cancel__left,axiom,
% 5.41/5.71 ! [C: complex,A: complex,B: complex] :
% 5.41/5.71 ( ( dvd_dvd_complex @ ( times_times_complex @ C @ A ) @ ( times_times_complex @ C @ B ) )
% 5.41/5.71 = ( ( C = zero_zero_complex )
% 5.41/5.71 | ( dvd_dvd_complex @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_left
% 5.41/5.71 thf(fact_4753_dvd__mult__cancel__left,axiom,
% 5.41/5.71 ! [C: real,A: real,B: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ ( times_times_real @ C @ A ) @ ( times_times_real @ C @ B ) )
% 5.41/5.71 = ( ( C = zero_zero_real )
% 5.41/5.71 | ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_left
% 5.41/5.71 thf(fact_4754_dvd__mult__cancel__left,axiom,
% 5.41/5.71 ! [C: rat,A: rat,B: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ ( times_times_rat @ C @ A ) @ ( times_times_rat @ C @ B ) )
% 5.41/5.71 = ( ( C = zero_zero_rat )
% 5.41/5.71 | ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_left
% 5.41/5.71 thf(fact_4755_dvd__mult__cancel__left,axiom,
% 5.41/5.71 ! [C: int,A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.71 = ( ( C = zero_zero_int )
% 5.41/5.71 | ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_cancel_left
% 5.41/5.71 thf(fact_4756_mult__minus1__right,axiom,
% 5.41/5.71 ! [Z: real] :
% 5.41/5.71 ( ( times_times_real @ Z @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.71 = ( uminus_uminus_real @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1_right
% 5.41/5.71 thf(fact_4757_mult__minus1__right,axiom,
% 5.41/5.71 ! [Z: int] :
% 5.41/5.71 ( ( times_times_int @ Z @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.71 = ( uminus_uminus_int @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1_right
% 5.41/5.71 thf(fact_4758_mult__minus1__right,axiom,
% 5.41/5.71 ! [Z: complex] :
% 5.41/5.71 ( ( times_times_complex @ Z @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1_right
% 5.41/5.71 thf(fact_4759_mult__minus1__right,axiom,
% 5.41/5.71 ! [Z: code_integer] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ Z @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1_right
% 5.41/5.71 thf(fact_4760_mult__minus1__right,axiom,
% 5.41/5.71 ! [Z: rat] :
% 5.41/5.71 ( ( times_times_rat @ Z @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.71 = ( uminus_uminus_rat @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1_right
% 5.41/5.71 thf(fact_4761_mult__minus1,axiom,
% 5.41/5.71 ! [Z: real] :
% 5.41/5.71 ( ( times_times_real @ ( uminus_uminus_real @ one_one_real ) @ Z )
% 5.41/5.71 = ( uminus_uminus_real @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1
% 5.41/5.71 thf(fact_4762_mult__minus1,axiom,
% 5.41/5.71 ! [Z: int] :
% 5.41/5.71 ( ( times_times_int @ ( uminus_uminus_int @ one_one_int ) @ Z )
% 5.41/5.71 = ( uminus_uminus_int @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1
% 5.41/5.71 thf(fact_4763_mult__minus1,axiom,
% 5.41/5.71 ! [Z: complex] :
% 5.41/5.71 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ Z )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1
% 5.41/5.71 thf(fact_4764_mult__minus1,axiom,
% 5.41/5.71 ! [Z: code_integer] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ Z )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1
% 5.41/5.71 thf(fact_4765_mult__minus1,axiom,
% 5.41/5.71 ! [Z: rat] :
% 5.41/5.71 ( ( times_times_rat @ ( uminus_uminus_rat @ one_one_rat ) @ Z )
% 5.41/5.71 = ( uminus_uminus_rat @ Z ) ) ).
% 5.41/5.71
% 5.41/5.71 % mult_minus1
% 5.41/5.71 thf(fact_4766_abs__le__zero__iff,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger )
% 5.41/5.71 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_zero_iff
% 5.41/5.71 thf(fact_4767_abs__le__zero__iff,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ zero_zero_real )
% 5.41/5.71 = ( A = zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_zero_iff
% 5.41/5.71 thf(fact_4768_abs__le__zero__iff,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat )
% 5.41/5.71 = ( A = zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_zero_iff
% 5.41/5.71 thf(fact_4769_abs__le__zero__iff,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ zero_zero_int )
% 5.41/5.71 = ( A = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_zero_iff
% 5.41/5.71 thf(fact_4770_abs__le__self__iff,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ A )
% 5.41/5.71 = ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_self_iff
% 5.41/5.71 thf(fact_4771_abs__le__self__iff,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ A )
% 5.41/5.71 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_self_iff
% 5.41/5.71 thf(fact_4772_abs__le__self__iff,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ A )
% 5.41/5.71 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_self_iff
% 5.41/5.71 thf(fact_4773_abs__le__self__iff,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ A )
% 5.41/5.71 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_le_self_iff
% 5.41/5.71 thf(fact_4774_abs__of__nonneg,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.71 => ( ( abs_abs_Code_integer @ A )
% 5.41/5.71 = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonneg
% 5.41/5.71 thf(fact_4775_abs__of__nonneg,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.71 => ( ( abs_abs_real @ A )
% 5.41/5.71 = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonneg
% 5.41/5.71 thf(fact_4776_abs__of__nonneg,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.71 => ( ( abs_abs_rat @ A )
% 5.41/5.71 = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonneg
% 5.41/5.71 thf(fact_4777_abs__of__nonneg,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.71 => ( ( abs_abs_int @ A )
% 5.41/5.71 = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonneg
% 5.41/5.71 thf(fact_4778_zero__less__abs__iff,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) )
% 5.41/5.71 = ( A != zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % zero_less_abs_iff
% 5.41/5.71 thf(fact_4779_zero__less__abs__iff,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ A ) )
% 5.41/5.71 = ( A != zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % zero_less_abs_iff
% 5.41/5.71 thf(fact_4780_zero__less__abs__iff,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) )
% 5.41/5.71 = ( A != zero_zero_rat ) ) ).
% 5.41/5.71
% 5.41/5.71 % zero_less_abs_iff
% 5.41/5.71 thf(fact_4781_zero__less__abs__iff,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_int @ zero_zero_int @ ( abs_abs_int @ A ) )
% 5.41/5.71 = ( A != zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % zero_less_abs_iff
% 5.41/5.71 thf(fact_4782_uminus__add__conv__diff,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ B )
% 5.41/5.71 = ( minus_minus_real @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % uminus_add_conv_diff
% 5.41/5.71 thf(fact_4783_uminus__add__conv__diff,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.71 = ( minus_minus_int @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % uminus_add_conv_diff
% 5.41/5.71 thf(fact_4784_uminus__add__conv__diff,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.41/5.71 = ( minus_minus_complex @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % uminus_add_conv_diff
% 5.41/5.71 thf(fact_4785_uminus__add__conv__diff,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.71 = ( minus_8373710615458151222nteger @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % uminus_add_conv_diff
% 5.41/5.71 thf(fact_4786_uminus__add__conv__diff,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.41/5.71 = ( minus_minus_rat @ B @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % uminus_add_conv_diff
% 5.41/5.71 thf(fact_4787_diff__minus__eq__add,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( minus_minus_real @ A @ ( uminus_uminus_real @ B ) )
% 5.41/5.71 = ( plus_plus_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_minus_eq_add
% 5.41/5.71 thf(fact_4788_diff__minus__eq__add,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( minus_minus_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.71 = ( plus_plus_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_minus_eq_add
% 5.41/5.71 thf(fact_4789_diff__minus__eq__add,axiom,
% 5.41/5.71 ! [A: complex,B: complex] :
% 5.41/5.71 ( ( minus_minus_complex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.71 = ( plus_plus_complex @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_minus_eq_add
% 5.41/5.71 thf(fact_4790_diff__minus__eq__add,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( minus_8373710615458151222nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.71 = ( plus_p5714425477246183910nteger @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_minus_eq_add
% 5.41/5.71 thf(fact_4791_diff__minus__eq__add,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( minus_minus_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.41/5.71 = ( plus_plus_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % diff_minus_eq_add
% 5.41/5.71 thf(fact_4792_divide__minus1,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( divide_divide_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.71 = ( uminus_uminus_real @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % divide_minus1
% 5.41/5.71 thf(fact_4793_divide__minus1,axiom,
% 5.41/5.71 ! [X: complex] :
% 5.41/5.71 ( ( divide1717551699836669952omplex @ X @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % divide_minus1
% 5.41/5.71 thf(fact_4794_divide__minus1,axiom,
% 5.41/5.71 ! [X: rat] :
% 5.41/5.71 ( ( divide_divide_rat @ X @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.71 = ( uminus_uminus_rat @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % divide_minus1
% 5.41/5.71 thf(fact_4795_div__minus1__right,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.71 = ( uminus_uminus_int @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_minus1_right
% 5.41/5.71 thf(fact_4796_div__minus1__right,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ A ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_minus1_right
% 5.41/5.71 thf(fact_4797_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ ( times_3573771949741848930nteger @ C @ A ) ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_right_iff
% 5.41/5.71 thf(fact_4798_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.71 ! [A: real,B: real,C: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ ( times_times_real @ C @ A ) ) )
% 5.41/5.71 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_right_iff
% 5.41/5.71 thf(fact_4799_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.71 ! [A: rat,B: rat,C: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ ( times_times_rat @ C @ A ) ) )
% 5.41/5.71 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_right_iff
% 5.41/5.71 thf(fact_4800_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.71 ! [A: nat,B: nat,C: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ ( times_times_nat @ C @ A ) ) )
% 5.41/5.71 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_right_iff
% 5.41/5.71 thf(fact_4801_dvd__add__times__triv__right__iff,axiom,
% 5.41/5.71 ! [A: int,B: int,C: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ ( times_times_int @ C @ A ) ) )
% 5.41/5.71 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_right_iff
% 5.41/5.71 thf(fact_4802_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.71 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ C @ A ) @ B ) )
% 5.41/5.71 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_left_iff
% 5.41/5.71 thf(fact_4803_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.71 ! [A: real,C: real,B: real] :
% 5.41/5.71 ( ( dvd_dvd_real @ A @ ( plus_plus_real @ ( times_times_real @ C @ A ) @ B ) )
% 5.41/5.71 = ( dvd_dvd_real @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_left_iff
% 5.41/5.71 thf(fact_4804_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.71 ! [A: rat,C: rat,B: rat] :
% 5.41/5.71 ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ ( times_times_rat @ C @ A ) @ B ) )
% 5.41/5.71 = ( dvd_dvd_rat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_left_iff
% 5.41/5.71 thf(fact_4805_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.71 ! [A: nat,C: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ ( times_times_nat @ C @ A ) @ B ) )
% 5.41/5.71 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_left_iff
% 5.41/5.71 thf(fact_4806_dvd__add__times__triv__left__iff,axiom,
% 5.41/5.71 ! [A: int,C: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ ( plus_plus_int @ ( times_times_int @ C @ A ) @ B ) )
% 5.41/5.71 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_add_times_triv_left_iff
% 5.41/5.71 thf(fact_4807_unit__prod,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.71 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_prod
% 5.41/5.71 thf(fact_4808_unit__prod,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.71 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.71 => ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_prod
% 5.41/5.71 thf(fact_4809_unit__prod,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.71 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.71 => ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_prod
% 5.41/5.71 thf(fact_4810_dvd__div__mult__self,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.71 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.41/5.71 = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_div_mult_self
% 5.41/5.71 thf(fact_4811_dvd__div__mult__self,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.71 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.41/5.71 = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_div_mult_self
% 5.41/5.71 thf(fact_4812_dvd__div__mult__self,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.71 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.41/5.71 = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_div_mult_self
% 5.41/5.71 thf(fact_4813_dvd__mult__div__cancel,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.71 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ A ) )
% 5.41/5.71 = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_div_cancel
% 5.41/5.71 thf(fact_4814_dvd__mult__div__cancel,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.71 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ A ) )
% 5.41/5.71 = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_div_cancel
% 5.41/5.71 thf(fact_4815_dvd__mult__div__cancel,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.71 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ A ) )
% 5.41/5.71 = B ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_mult_div_cancel
% 5.41/5.71 thf(fact_4816_div__add,axiom,
% 5.41/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.71 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.41/5.71 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_add
% 5.41/5.71 thf(fact_4817_div__add,axiom,
% 5.41/5.71 ! [C: nat,A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ C @ A )
% 5.41/5.71 => ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.71 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.71 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_add
% 5.41/5.71 thf(fact_4818_div__add,axiom,
% 5.41/5.71 ! [C: int,A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ C @ A )
% 5.41/5.71 => ( ( dvd_dvd_int @ C @ B )
% 5.41/5.71 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.71 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_add
% 5.41/5.71 thf(fact_4819_unit__div,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.71 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div
% 5.41/5.71 thf(fact_4820_unit__div,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.71 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.71 => ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ one_one_nat ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div
% 5.41/5.71 thf(fact_4821_unit__div,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.71 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.71 => ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div
% 5.41/5.71 thf(fact_4822_unit__div__1__unit,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.71 => ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) @ one_one_Code_integer ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div_1_unit
% 5.41/5.71 thf(fact_4823_unit__div__1__unit,axiom,
% 5.41/5.71 ! [A: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.71 => ( dvd_dvd_nat @ ( divide_divide_nat @ one_one_nat @ A ) @ one_one_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div_1_unit
% 5.41/5.71 thf(fact_4824_unit__div__1__unit,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.71 => ( dvd_dvd_int @ ( divide_divide_int @ one_one_int @ A ) @ one_one_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div_1_unit
% 5.41/5.71 thf(fact_4825_unit__div__1__div__1,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.71 => ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.41/5.71 = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div_1_div_1
% 5.41/5.71 thf(fact_4826_unit__div__1__div__1,axiom,
% 5.41/5.71 ! [A: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.71 => ( ( divide_divide_nat @ one_one_nat @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.41/5.71 = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div_1_div_1
% 5.41/5.71 thf(fact_4827_unit__div__1__div__1,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.71 => ( ( divide_divide_int @ one_one_int @ ( divide_divide_int @ one_one_int @ A ) )
% 5.41/5.71 = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_div_1_div_1
% 5.41/5.71 thf(fact_4828_div__diff,axiom,
% 5.41/5.71 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.41/5.71 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.71 => ( ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ A @ B ) @ C )
% 5.41/5.71 = ( minus_8373710615458151222nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_diff
% 5.41/5.71 thf(fact_4829_div__diff,axiom,
% 5.41/5.71 ! [C: int,A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ C @ A )
% 5.41/5.71 => ( ( dvd_dvd_int @ C @ B )
% 5.41/5.71 => ( ( divide_divide_int @ ( minus_minus_int @ A @ B ) @ C )
% 5.41/5.71 = ( minus_minus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % div_diff
% 5.41/5.71 thf(fact_4830_abs__neg__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.71 = ( numeral_numeral_real @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_numeral
% 5.41/5.71 thf(fact_4831_abs__neg__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.71 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_numeral
% 5.41/5.71 thf(fact_4832_abs__neg__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.71 = ( numera6620942414471956472nteger @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_numeral
% 5.41/5.71 thf(fact_4833_abs__neg__numeral,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.71 = ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_numeral
% 5.41/5.71 thf(fact_4834_dvd__imp__mod__0,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.71 => ( ( modulo_modulo_nat @ B @ A )
% 5.41/5.71 = zero_zero_nat ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_imp_mod_0
% 5.41/5.71 thf(fact_4835_dvd__imp__mod__0,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.71 => ( ( modulo_modulo_int @ B @ A )
% 5.41/5.71 = zero_zero_int ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_imp_mod_0
% 5.41/5.71 thf(fact_4836_dvd__imp__mod__0,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.71 => ( ( modulo364778990260209775nteger @ B @ A )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.71
% 5.41/5.71 % dvd_imp_mod_0
% 5.41/5.71 thf(fact_4837_abs__neg__one,axiom,
% 5.41/5.71 ( ( abs_abs_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.71 = one_one_real ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_one
% 5.41/5.71 thf(fact_4838_abs__neg__one,axiom,
% 5.41/5.71 ( ( abs_abs_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.71 = one_one_int ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_one
% 5.41/5.71 thf(fact_4839_abs__neg__one,axiom,
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.71 = one_one_Code_integer ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_one
% 5.41/5.71 thf(fact_4840_abs__neg__one,axiom,
% 5.41/5.71 ( ( abs_abs_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.71 = one_one_rat ) ).
% 5.41/5.71
% 5.41/5.71 % abs_neg_one
% 5.41/5.71 thf(fact_4841_minus__mod__self1,axiom,
% 5.41/5.71 ! [B: int,A: int] :
% 5.41/5.71 ( ( modulo_modulo_int @ ( minus_minus_int @ B @ A ) @ B )
% 5.41/5.71 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_mod_self1
% 5.41/5.71 thf(fact_4842_minus__mod__self1,axiom,
% 5.41/5.71 ! [B: code_integer,A: code_integer] :
% 5.41/5.71 ( ( modulo364778990260209775nteger @ ( minus_8373710615458151222nteger @ B @ A ) @ B )
% 5.41/5.71 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.41/5.71
% 5.41/5.71 % minus_mod_self1
% 5.41/5.71 thf(fact_4843_abs__power__minus,axiom,
% 5.41/5.71 ! [A: real,N: nat] :
% 5.41/5.71 ( ( abs_abs_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.41/5.71 = ( abs_abs_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_power_minus
% 5.41/5.71 thf(fact_4844_abs__power__minus,axiom,
% 5.41/5.71 ! [A: int,N: nat] :
% 5.41/5.71 ( ( abs_abs_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.41/5.71 = ( abs_abs_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_power_minus
% 5.41/5.71 thf(fact_4845_abs__power__minus,axiom,
% 5.41/5.71 ! [A: code_integer,N: nat] :
% 5.41/5.71 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.41/5.71 = ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_power_minus
% 5.41/5.71 thf(fact_4846_abs__power__minus,axiom,
% 5.41/5.71 ! [A: rat,N: nat] :
% 5.41/5.71 ( ( abs_abs_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.41/5.71 = ( abs_abs_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_power_minus
% 5.41/5.71 thf(fact_4847_real__add__minus__iff,axiom,
% 5.41/5.71 ! [X: real,A: real] :
% 5.41/5.71 ( ( ( plus_plus_real @ X @ ( uminus_uminus_real @ A ) )
% 5.41/5.71 = zero_zero_real )
% 5.41/5.71 = ( X = A ) ) ).
% 5.41/5.71
% 5.41/5.71 % real_add_minus_iff
% 5.41/5.71 thf(fact_4848_tanh__real__neg__iff,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.41/5.71 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_real_neg_iff
% 5.41/5.71 thf(fact_4849_tanh__real__pos__iff,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.41/5.71 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_real_pos_iff
% 5.41/5.71 thf(fact_4850_tanh__real__nonpos__iff,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( tanh_real @ X ) @ zero_zero_real )
% 5.41/5.71 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_real_nonpos_iff
% 5.41/5.71 thf(fact_4851_tanh__real__nonneg__iff,axiom,
% 5.41/5.71 ! [X: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( tanh_real @ X ) )
% 5.41/5.71 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.41/5.71
% 5.41/5.71 % tanh_real_nonneg_iff
% 5.41/5.71 thf(fact_4852_dbl__simps_I1_J,axiom,
% 5.41/5.71 ! [K: num] :
% 5.41/5.71 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.41/5.71 = ( uminus_uminus_real @ ( neg_numeral_dbl_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dbl_simps(1)
% 5.41/5.71 thf(fact_4853_dbl__simps_I1_J,axiom,
% 5.41/5.71 ! [K: num] :
% 5.41/5.71 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.71 = ( uminus_uminus_int @ ( neg_numeral_dbl_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dbl_simps(1)
% 5.41/5.71 thf(fact_4854_dbl__simps_I1_J,axiom,
% 5.41/5.71 ! [K: num] :
% 5.41/5.71 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ ( neg_nu7009210354673126013omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dbl_simps(1)
% 5.41/5.71 thf(fact_4855_dbl__simps_I1_J,axiom,
% 5.41/5.71 ! [K: num] :
% 5.41/5.71 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ ( neg_nu8804712462038260780nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dbl_simps(1)
% 5.41/5.71 thf(fact_4856_dbl__simps_I1_J,axiom,
% 5.41/5.71 ! [K: num] :
% 5.41/5.71 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.41/5.71 = ( uminus_uminus_rat @ ( neg_numeral_dbl_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % dbl_simps(1)
% 5.41/5.71 thf(fact_4857_add__neg__numeral__special_I7_J,axiom,
% 5.41/5.71 ( ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(7)
% 5.41/5.71 thf(fact_4858_add__neg__numeral__special_I7_J,axiom,
% 5.41/5.71 ( ( plus_plus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(7)
% 5.41/5.71 thf(fact_4859_add__neg__numeral__special_I7_J,axiom,
% 5.41/5.71 ( ( plus_plus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(7)
% 5.41/5.71 thf(fact_4860_add__neg__numeral__special_I7_J,axiom,
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(7)
% 5.41/5.71 thf(fact_4861_add__neg__numeral__special_I7_J,axiom,
% 5.41/5.71 ( ( plus_plus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(7)
% 5.41/5.71 thf(fact_4862_add__neg__numeral__special_I8_J,axiom,
% 5.41/5.71 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(8)
% 5.41/5.71 thf(fact_4863_add__neg__numeral__special_I8_J,axiom,
% 5.41/5.71 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(8)
% 5.41/5.71 thf(fact_4864_add__neg__numeral__special_I8_J,axiom,
% 5.41/5.71 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(8)
% 5.41/5.71 thf(fact_4865_add__neg__numeral__special_I8_J,axiom,
% 5.41/5.71 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(8)
% 5.41/5.71 thf(fact_4866_add__neg__numeral__special_I8_J,axiom,
% 5.41/5.71 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % add_neg_numeral_special(8)
% 5.41/5.71 thf(fact_4867_diff__numeral__special_I12_J,axiom,
% 5.41/5.71 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.71 = zero_zero_real ) ).
% 5.41/5.71
% 5.41/5.71 % diff_numeral_special(12)
% 5.41/5.71 thf(fact_4868_diff__numeral__special_I12_J,axiom,
% 5.41/5.71 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.71 = zero_zero_int ) ).
% 5.41/5.71
% 5.41/5.71 % diff_numeral_special(12)
% 5.41/5.71 thf(fact_4869_diff__numeral__special_I12_J,axiom,
% 5.41/5.71 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.71 = zero_zero_complex ) ).
% 5.41/5.71
% 5.41/5.71 % diff_numeral_special(12)
% 5.41/5.71 thf(fact_4870_diff__numeral__special_I12_J,axiom,
% 5.41/5.71 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.71 = zero_z3403309356797280102nteger ) ).
% 5.41/5.71
% 5.41/5.71 % diff_numeral_special(12)
% 5.41/5.71 thf(fact_4871_diff__numeral__special_I12_J,axiom,
% 5.41/5.71 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.71 = zero_zero_rat ) ).
% 5.41/5.71
% 5.41/5.71 % diff_numeral_special(12)
% 5.41/5.71 thf(fact_4872_neg__one__eq__numeral__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_real @ one_one_real )
% 5.41/5.71 = ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_one_eq_numeral_iff
% 5.41/5.71 thf(fact_4873_neg__one__eq__numeral__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_int @ one_one_int )
% 5.41/5.71 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_one_eq_numeral_iff
% 5.41/5.71 thf(fact_4874_neg__one__eq__numeral__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus1482373934393186551omplex @ one_one_complex )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_one_eq_numeral_iff
% 5.41/5.71 thf(fact_4875_neg__one__eq__numeral__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus1351360451143612070nteger @ one_one_Code_integer )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_one_eq_numeral_iff
% 5.41/5.71 thf(fact_4876_neg__one__eq__numeral__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_rat @ one_one_rat )
% 5.41/5.71 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % neg_one_eq_numeral_iff
% 5.41/5.71 thf(fact_4877_numeral__eq__neg__one__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ N ) )
% 5.41/5.71 = ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % numeral_eq_neg_one_iff
% 5.41/5.71 thf(fact_4878_numeral__eq__neg__one__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_int @ ( numeral_numeral_int @ N ) )
% 5.41/5.71 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % numeral_eq_neg_one_iff
% 5.41/5.71 thf(fact_4879_numeral__eq__neg__one__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.71 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % numeral_eq_neg_one_iff
% 5.41/5.71 thf(fact_4880_numeral__eq__neg__one__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % numeral_eq_neg_one_iff
% 5.41/5.71 thf(fact_4881_numeral__eq__neg__one__iff,axiom,
% 5.41/5.71 ! [N: num] :
% 5.41/5.71 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) )
% 5.41/5.71 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.71 = ( N = one ) ) ).
% 5.41/5.71
% 5.41/5.71 % numeral_eq_neg_one_iff
% 5.41/5.71 thf(fact_4882_zero__le__divide__abs__iff,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) )
% 5.41/5.71 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.71 | ( B = zero_zero_real ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % zero_le_divide_abs_iff
% 5.41/5.71 thf(fact_4883_zero__le__divide__abs__iff,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ zero_zero_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) )
% 5.41/5.71 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.71 | ( B = zero_zero_rat ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % zero_le_divide_abs_iff
% 5.41/5.71 thf(fact_4884_divide__le__0__abs__iff,axiom,
% 5.41/5.71 ! [A: real,B: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ ( divide_divide_real @ A @ ( abs_abs_real @ B ) ) @ zero_zero_real )
% 5.41/5.71 = ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.71 | ( B = zero_zero_real ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % divide_le_0_abs_iff
% 5.41/5.71 thf(fact_4885_divide__le__0__abs__iff,axiom,
% 5.41/5.71 ! [A: rat,B: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ ( divide_divide_rat @ A @ ( abs_abs_rat @ B ) ) @ zero_zero_rat )
% 5.41/5.71 = ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.71 | ( B = zero_zero_rat ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % divide_le_0_abs_iff
% 5.41/5.71 thf(fact_4886_minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat] :
% 5.41/5.71 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) )
% 5.41/5.71 = one_one_real ) ).
% 5.41/5.71
% 5.41/5.71 % minus_one_mult_self
% 5.41/5.71 thf(fact_4887_minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat] :
% 5.41/5.71 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) )
% 5.41/5.71 = one_one_int ) ).
% 5.41/5.71
% 5.41/5.71 % minus_one_mult_self
% 5.41/5.71 thf(fact_4888_minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat] :
% 5.41/5.71 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) )
% 5.41/5.71 = one_one_complex ) ).
% 5.41/5.71
% 5.41/5.71 % minus_one_mult_self
% 5.41/5.71 thf(fact_4889_minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) )
% 5.41/5.71 = one_one_Code_integer ) ).
% 5.41/5.71
% 5.41/5.71 % minus_one_mult_self
% 5.41/5.71 thf(fact_4890_minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat] :
% 5.41/5.71 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) )
% 5.41/5.71 = one_one_rat ) ).
% 5.41/5.71
% 5.41/5.71 % minus_one_mult_self
% 5.41/5.71 thf(fact_4891_left__minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat,A: real] :
% 5.41/5.71 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % left_minus_one_mult_self
% 5.41/5.71 thf(fact_4892_left__minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat,A: int] :
% 5.41/5.71 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % left_minus_one_mult_self
% 5.41/5.71 thf(fact_4893_left__minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat,A: complex] :
% 5.41/5.71 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % left_minus_one_mult_self
% 5.41/5.71 thf(fact_4894_left__minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat,A: code_integer] :
% 5.41/5.71 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % left_minus_one_mult_self
% 5.41/5.71 thf(fact_4895_left__minus__one__mult__self,axiom,
% 5.41/5.71 ! [N: nat,A: rat] :
% 5.41/5.71 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ A ) )
% 5.41/5.71 = A ) ).
% 5.41/5.71
% 5.41/5.71 % left_minus_one_mult_self
% 5.41/5.71 thf(fact_4896_abs__of__nonpos,axiom,
% 5.41/5.71 ! [A: real] :
% 5.41/5.71 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.71 => ( ( abs_abs_real @ A )
% 5.41/5.71 = ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonpos
% 5.41/5.71 thf(fact_4897_abs__of__nonpos,axiom,
% 5.41/5.71 ! [A: code_integer] :
% 5.41/5.71 ( ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger )
% 5.41/5.71 => ( ( abs_abs_Code_integer @ A )
% 5.41/5.71 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonpos
% 5.41/5.71 thf(fact_4898_abs__of__nonpos,axiom,
% 5.41/5.71 ! [A: rat] :
% 5.41/5.71 ( ( ord_less_eq_rat @ A @ zero_zero_rat )
% 5.41/5.71 => ( ( abs_abs_rat @ A )
% 5.41/5.71 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonpos
% 5.41/5.71 thf(fact_4899_abs__of__nonpos,axiom,
% 5.41/5.71 ! [A: int] :
% 5.41/5.71 ( ( ord_less_eq_int @ A @ zero_zero_int )
% 5.41/5.71 => ( ( abs_abs_int @ A )
% 5.41/5.71 = ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % abs_of_nonpos
% 5.41/5.71 thf(fact_4900_even__Suc,axiom,
% 5.41/5.71 ! [N: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ N ) )
% 5.41/5.71 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_Suc
% 5.41/5.71 thf(fact_4901_even__Suc__Suc__iff,axiom,
% 5.41/5.71 ! [N: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ N ) ) )
% 5.41/5.71 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.71
% 5.41/5.71 % even_Suc_Suc_iff
% 5.41/5.71 thf(fact_4902_unit__mult__div__div,axiom,
% 5.41/5.71 ! [A: code_integer,B: code_integer] :
% 5.41/5.71 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.71 => ( ( times_3573771949741848930nteger @ B @ ( divide6298287555418463151nteger @ one_one_Code_integer @ A ) )
% 5.41/5.71 = ( divide6298287555418463151nteger @ B @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_mult_div_div
% 5.41/5.71 thf(fact_4903_unit__mult__div__div,axiom,
% 5.41/5.71 ! [A: nat,B: nat] :
% 5.41/5.71 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.71 => ( ( times_times_nat @ B @ ( divide_divide_nat @ one_one_nat @ A ) )
% 5.41/5.71 = ( divide_divide_nat @ B @ A ) ) ) ).
% 5.41/5.71
% 5.41/5.71 % unit_mult_div_div
% 5.41/5.71 thf(fact_4904_unit__mult__div__div,axiom,
% 5.41/5.71 ! [A: int,B: int] :
% 5.41/5.71 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.71 => ( ( times_times_int @ B @ ( divide_divide_int @ one_one_int @ A ) )
% 5.41/5.71 = ( divide_divide_int @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_mult_div_div
% 5.41/5.72 thf(fact_4905_unit__div__mult__self,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.72 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ A ) @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_div_mult_self
% 5.41/5.72 thf(fact_4906_unit__div__mult__self,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.72 => ( ( times_times_nat @ ( divide_divide_nat @ B @ A ) @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_div_mult_self
% 5.41/5.72 thf(fact_4907_unit__div__mult__self,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.72 => ( ( times_times_int @ ( divide_divide_int @ B @ A ) @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_div_mult_self
% 5.41/5.72 thf(fact_4908_mod__minus1__right,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.72 = zero_zero_int ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus1_right
% 5.41/5.72 thf(fact_4909_mod__minus1__right,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.72 = zero_z3403309356797280102nteger ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus1_right
% 5.41/5.72 thf(fact_4910_max__number__of_I2_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 => ( ( ord_max_real @ ( numeral_numeral_real @ U ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 = ( numeral_numeral_real @ U ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(2)
% 5.41/5.72 thf(fact_4911_max__number__of_I2_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 => ( ( ord_max_Code_integer @ ( numera6620942414471956472nteger @ U ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 = ( numera6620942414471956472nteger @ U ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(2)
% 5.41/5.72 thf(fact_4912_max__number__of_I2_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 => ( ( ord_max_rat @ ( numeral_numeral_rat @ U ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 = ( numeral_numeral_rat @ U ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(2)
% 5.41/5.72 thf(fact_4913_max__number__of_I2_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 => ( ( ord_max_int @ ( numeral_numeral_int @ U ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 = ( numeral_numeral_int @ U ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(2)
% 5.41/5.72 thf(fact_4914_max__number__of_I3_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.72 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.72 = ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.72 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( numeral_numeral_real @ V ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(3)
% 5.41/5.72 thf(fact_4915_max__number__of_I3_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.72 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.72 = ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.72 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( numera6620942414471956472nteger @ V ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(3)
% 5.41/5.72 thf(fact_4916_max__number__of_I3_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.72 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.72 = ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.72 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( numeral_numeral_rat @ V ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(3)
% 5.41/5.72 thf(fact_4917_max__number__of_I3_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.72 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.72 = ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.72 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( numeral_numeral_int @ V ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(3)
% 5.41/5.72 thf(fact_4918_max__number__of_I4_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 => ( ( ord_max_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(4)
% 5.41/5.72 thf(fact_4919_max__number__of_I4_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 => ( ( ord_max_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(4)
% 5.41/5.72 thf(fact_4920_max__number__of_I4_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 => ( ( ord_max_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(4)
% 5.41/5.72 thf(fact_4921_max__number__of_I4_J,axiom,
% 5.41/5.72 ! [U: num,V: num] :
% 5.41/5.72 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) ) )
% 5.41/5.72 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 => ( ( ord_max_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ U ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % max_number_of(4)
% 5.41/5.72 thf(fact_4922_pow__divides__pow__iff,axiom,
% 5.41/5.72 ! [N: nat,A: nat,B: nat] :
% 5.41/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.72 => ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pow_divides_pow_iff
% 5.41/5.72 thf(fact_4923_pow__divides__pow__iff,axiom,
% 5.41/5.72 ! [N: nat,A: int,B: int] :
% 5.41/5.72 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.72 => ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pow_divides_pow_iff
% 5.41/5.72 thf(fact_4924_semiring__norm_I168_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: real] :
% 5.41/5.72 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.41/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(168)
% 5.41/5.72 thf(fact_4925_semiring__norm_I168_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: int] :
% 5.41/5.72 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.41/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(168)
% 5.41/5.72 thf(fact_4926_semiring__norm_I168_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: complex] :
% 5.41/5.72 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.41/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(168)
% 5.41/5.72 thf(fact_4927_semiring__norm_I168_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: code_integer] :
% 5.41/5.72 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(168)
% 5.41/5.72 thf(fact_4928_semiring__norm_I168_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: rat] :
% 5.41/5.72 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.41/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(168)
% 5.41/5.72 thf(fact_4929_diff__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(3)
% 5.41/5.72 thf(fact_4930_diff__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(3)
% 5.41/5.72 thf(fact_4931_diff__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(3)
% 5.41/5.72 thf(fact_4932_diff__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(3)
% 5.41/5.72 thf(fact_4933_diff__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(3)
% 5.41/5.72 thf(fact_4934_diff__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_real @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(2)
% 5.41/5.72 thf(fact_4935_diff__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_int @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(2)
% 5.41/5.72 thf(fact_4936_diff__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.72 = ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(2)
% 5.41/5.72 thf(fact_4937_diff__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.72 = ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(2)
% 5.41/5.72 thf(fact_4938_diff__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_rat @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_simps(2)
% 5.41/5.72 thf(fact_4939_semiring__norm_I172_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: real] :
% 5.41/5.72 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(172)
% 5.41/5.72 thf(fact_4940_semiring__norm_I172_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: int] :
% 5.41/5.72 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(172)
% 5.41/5.72 thf(fact_4941_semiring__norm_I172_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: complex] :
% 5.41/5.72 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_complex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(172)
% 5.41/5.72 thf(fact_4942_semiring__norm_I172_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: code_integer] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(172)
% 5.41/5.72 thf(fact_4943_semiring__norm_I172_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: rat] :
% 5.41/5.72 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(172)
% 5.41/5.72 thf(fact_4944_semiring__norm_I171_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: real] :
% 5.41/5.72 ( ( times_times_real @ ( numeral_numeral_real @ V ) @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(171)
% 5.41/5.72 thf(fact_4945_semiring__norm_I171_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: int] :
% 5.41/5.72 ( ( times_times_int @ ( numeral_numeral_int @ V ) @ ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(171)
% 5.41/5.72 thf(fact_4946_semiring__norm_I171_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: complex] :
% 5.41/5.72 ( ( times_times_complex @ ( numera6690914467698888265omplex @ V ) @ ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(171)
% 5.41/5.72 thf(fact_4947_semiring__norm_I171_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: code_integer] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ V ) @ ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(171)
% 5.41/5.72 thf(fact_4948_semiring__norm_I171_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: rat] :
% 5.41/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ V ) @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ Y ) )
% 5.41/5.72 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(171)
% 5.41/5.72 thf(fact_4949_semiring__norm_I170_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: real] :
% 5.41/5.72 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ V ) ) @ ( times_times_real @ ( numeral_numeral_real @ W ) @ Y ) )
% 5.41/5.72 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(170)
% 5.41/5.72 thf(fact_4950_semiring__norm_I170_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: int] :
% 5.41/5.72 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ V ) ) @ ( times_times_int @ ( numeral_numeral_int @ W ) @ Y ) )
% 5.41/5.72 = ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(170)
% 5.41/5.72 thf(fact_4951_semiring__norm_I170_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: complex] :
% 5.41/5.72 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ V ) ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ Y ) )
% 5.41/5.72 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(170)
% 5.41/5.72 thf(fact_4952_semiring__norm_I170_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: code_integer] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ V ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ Y ) )
% 5.41/5.72 = ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(170)
% 5.41/5.72 thf(fact_4953_semiring__norm_I170_J,axiom,
% 5.41/5.72 ! [V: num,W: num,Y: rat] :
% 5.41/5.72 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ V ) ) @ ( times_times_rat @ ( numeral_numeral_rat @ W ) @ Y ) )
% 5.41/5.72 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ V @ W ) ) ) @ Y ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_norm(170)
% 5.41/5.72 thf(fact_4954_mult__neg__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(3)
% 5.41/5.72 thf(fact_4955_mult__neg__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(3)
% 5.41/5.72 thf(fact_4956_mult__neg__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(3)
% 5.41/5.72 thf(fact_4957_mult__neg__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(3)
% 5.41/5.72 thf(fact_4958_mult__neg__numeral__simps_I3_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(3)
% 5.41/5.72 thf(fact_4959_mult__neg__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(2)
% 5.41/5.72 thf(fact_4960_mult__neg__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(2)
% 5.41/5.72 thf(fact_4961_mult__neg__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(2)
% 5.41/5.72 thf(fact_4962_mult__neg__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(2)
% 5.41/5.72 thf(fact_4963_mult__neg__numeral__simps_I2_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(2)
% 5.41/5.72 thf(fact_4964_mult__neg__numeral__simps_I1_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_real @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(1)
% 5.41/5.72 thf(fact_4965_mult__neg__numeral__simps_I1_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_int @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(1)
% 5.41/5.72 thf(fact_4966_mult__neg__numeral__simps_I1_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.72 = ( numera6690914467698888265omplex @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(1)
% 5.41/5.72 thf(fact_4967_mult__neg__numeral__simps_I1_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.72 = ( numera6620942414471956472nteger @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(1)
% 5.41/5.72 thf(fact_4968_mult__neg__numeral__simps_I1_J,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_rat @ ( times_times_num @ M @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_neg_numeral_simps(1)
% 5.41/5.72 thf(fact_4969_artanh__minus__real,axiom,
% 5.41/5.72 ! [X: real] :
% 5.41/5.72 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.72 => ( ( artanh_real @ ( uminus_uminus_real @ X ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( artanh_real @ X ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % artanh_minus_real
% 5.41/5.72 thf(fact_4970_neg__numeral__le__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.72 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_iff
% 5.41/5.72 thf(fact_4971_neg__numeral__le__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.72 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_iff
% 5.41/5.72 thf(fact_4972_neg__numeral__le__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.72 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_iff
% 5.41/5.72 thf(fact_4973_neg__numeral__le__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.72 = ( ord_less_eq_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_iff
% 5.41/5.72 thf(fact_4974_neg__numeral__less__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.72 = ( ord_less_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_iff
% 5.41/5.72 thf(fact_4975_neg__numeral__less__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.72 = ( ord_less_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_iff
% 5.41/5.72 thf(fact_4976_neg__numeral__less__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.72 = ( ord_less_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_iff
% 5.41/5.72 thf(fact_4977_neg__numeral__less__iff,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.72 = ( ord_less_num @ N @ M ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_iff
% 5.41/5.72 thf(fact_4978_not__neg__one__le__neg__numeral__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ~ ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_neg_one_le_neg_numeral_iff
% 5.41/5.72 thf(fact_4979_not__neg__one__le__neg__numeral__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ~ ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_neg_one_le_neg_numeral_iff
% 5.41/5.72 thf(fact_4980_not__neg__one__le__neg__numeral__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ~ ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_neg_one_le_neg_numeral_iff
% 5.41/5.72 thf(fact_4981_not__neg__one__le__neg__numeral__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_neg_one_le_neg_numeral_iff
% 5.41/5.72 thf(fact_4982_le__divide__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [A: real,B: real,W: num] :
% 5.41/5.72 ( ( ord_less_eq_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.41/5.72 = ( ord_less_eq_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_divide_eq_numeral1(2)
% 5.41/5.72 thf(fact_4983_le__divide__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [A: rat,B: rat,W: num] :
% 5.41/5.72 ( ( ord_less_eq_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.41/5.72 = ( ord_less_eq_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_divide_eq_numeral1(2)
% 5.41/5.72 thf(fact_4984_divide__le__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [B: real,W: num,A: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.41/5.72 = ( ord_less_eq_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % divide_le_eq_numeral1(2)
% 5.41/5.72 thf(fact_4985_divide__le__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [B: rat,W: num,A: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.41/5.72 = ( ord_less_eq_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % divide_le_eq_numeral1(2)
% 5.41/5.72 thf(fact_4986_divide__eq__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [B: real,W: num,A: real] :
% 5.41/5.72 ( ( ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.72 = A )
% 5.41/5.72 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.72 != zero_zero_real )
% 5.41/5.72 => ( B
% 5.41/5.72 = ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) )
% 5.41/5.72 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.72 = zero_zero_real )
% 5.41/5.72 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % divide_eq_eq_numeral1(2)
% 5.41/5.72 thf(fact_4987_divide__eq__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [B: complex,W: num,A: complex] :
% 5.41/5.72 ( ( ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.72 = A )
% 5.41/5.72 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.72 != zero_zero_complex )
% 5.41/5.72 => ( B
% 5.41/5.72 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) )
% 5.41/5.72 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.72 = zero_zero_complex )
% 5.41/5.72 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % divide_eq_eq_numeral1(2)
% 5.41/5.72 thf(fact_4988_divide__eq__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [B: rat,W: num,A: rat] :
% 5.41/5.72 ( ( ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.72 = A )
% 5.41/5.72 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.41/5.72 != zero_zero_rat )
% 5.41/5.72 => ( B
% 5.41/5.72 = ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) )
% 5.41/5.72 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.41/5.72 = zero_zero_rat )
% 5.41/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % divide_eq_eq_numeral1(2)
% 5.41/5.72 thf(fact_4989_eq__divide__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [A: real,B: real,W: num] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.41/5.72 = ( ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.72 != zero_zero_real )
% 5.41/5.72 => ( ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.72 = B ) )
% 5.41/5.72 & ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.72 = zero_zero_real )
% 5.41/5.72 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_divide_eq_numeral1(2)
% 5.41/5.72 thf(fact_4990_eq__divide__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [A: complex,B: complex,W: num] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( divide1717551699836669952omplex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) )
% 5.41/5.72 = ( ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.72 != zero_zero_complex )
% 5.41/5.72 => ( ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.72 = B ) )
% 5.41/5.72 & ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.72 = zero_zero_complex )
% 5.41/5.72 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_divide_eq_numeral1(2)
% 5.41/5.72 thf(fact_4991_eq__divide__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [A: rat,B: rat,W: num] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.41/5.72 = ( ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.41/5.72 != zero_zero_rat )
% 5.41/5.72 => ( ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.72 = B ) )
% 5.41/5.72 & ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.41/5.72 = zero_zero_rat )
% 5.41/5.72 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_divide_eq_numeral1(2)
% 5.41/5.72 thf(fact_4992_neg__numeral__less__neg__one__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_neg_one_iff
% 5.41/5.72 thf(fact_4993_neg__numeral__less__neg__one__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_neg_one_iff
% 5.41/5.72 thf(fact_4994_neg__numeral__less__neg__one__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_neg_one_iff
% 5.41/5.72 thf(fact_4995_neg__numeral__less__neg__one__iff,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.72 = ( M != one ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_neg_one_iff
% 5.41/5.72 thf(fact_4996_divide__less__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [B: real,W: num,A: real] :
% 5.41/5.72 ( ( ord_less_real @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ A )
% 5.41/5.72 = ( ord_less_real @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % divide_less_eq_numeral1(2)
% 5.41/5.72 thf(fact_4997_divide__less__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [B: rat,W: num,A: rat] :
% 5.41/5.72 ( ( ord_less_rat @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ A )
% 5.41/5.72 = ( ord_less_rat @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % divide_less_eq_numeral1(2)
% 5.41/5.72 thf(fact_4998_less__divide__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [A: real,B: real,W: num] :
% 5.41/5.72 ( ( ord_less_real @ A @ ( divide_divide_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) )
% 5.41/5.72 = ( ord_less_real @ B @ ( times_times_real @ A @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_divide_eq_numeral1(2)
% 5.41/5.72 thf(fact_4999_less__divide__eq__numeral1_I2_J,axiom,
% 5.41/5.72 ! [A: rat,B: rat,W: num] :
% 5.41/5.72 ( ( ord_less_rat @ A @ ( divide_divide_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) )
% 5.41/5.72 = ( ord_less_rat @ B @ ( times_times_rat @ A @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_divide_eq_numeral1(2)
% 5.41/5.72 thf(fact_5000_even__mult__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.41/5.72 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_mult_iff
% 5.41/5.72 thf(fact_5001_even__mult__iff,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ A @ B ) )
% 5.41/5.72 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_mult_iff
% 5.41/5.72 thf(fact_5002_even__mult__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( times_times_int @ A @ B ) )
% 5.41/5.72 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_mult_iff
% 5.41/5.72 thf(fact_5003_odd__add,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) )
% 5.41/5.72 = ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.72 != ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_add
% 5.41/5.72 thf(fact_5004_odd__add,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) )
% 5.41/5.72 = ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.72 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_add
% 5.41/5.72 thf(fact_5005_odd__add,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) )
% 5.41/5.72 = ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.72 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_add
% 5.41/5.72 thf(fact_5006_even__add,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.41/5.72 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_add
% 5.41/5.72 thf(fact_5007_even__add,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.72 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_add
% 5.41/5.72 thf(fact_5008_even__add,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) )
% 5.41/5.72 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_add
% 5.41/5.72 thf(fact_5009_power__minus__odd,axiom,
% 5.41/5.72 ! [N: nat,A: real] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.41/5.72 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus_odd
% 5.41/5.72 thf(fact_5010_power__minus__odd,axiom,
% 5.41/5.72 ! [N: nat,A: int] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.41/5.72 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus_odd
% 5.41/5.72 thf(fact_5011_power__minus__odd,axiom,
% 5.41/5.72 ! [N: nat,A: complex] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus_odd
% 5.41/5.72 thf(fact_5012_power__minus__odd,axiom,
% 5.41/5.72 ! [N: nat,A: code_integer] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus_odd
% 5.41/5.72 thf(fact_5013_power__minus__odd,axiom,
% 5.41/5.72 ! [N: nat,A: rat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.41/5.72 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus_odd
% 5.41/5.72 thf(fact_5014_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [N: nat,A: real] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.41/5.72 = ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Parity.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5015_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [N: nat,A: int] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.41/5.72 = ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Parity.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5016_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [N: nat,A: complex] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.41/5.72 = ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Parity.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5017_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [N: nat,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Parity.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5018_Parity_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [N: nat,A: rat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.41/5.72 = ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Parity.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5019_power2__minus,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_minus
% 5.41/5.72 thf(fact_5020_power2__minus,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_minus
% 5.41/5.72 thf(fact_5021_power2__minus,axiom,
% 5.41/5.72 ! [A: complex] :
% 5.41/5.72 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_minus
% 5.41/5.72 thf(fact_5022_power2__minus,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_minus
% 5.41/5.72 thf(fact_5023_power2__minus,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_minus
% 5.41/5.72 thf(fact_5024_zero__less__power__abs__iff,axiom,
% 5.41/5.72 ! [A: code_integer,N: nat] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) )
% 5.41/5.72 = ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.72 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_less_power_abs_iff
% 5.41/5.72 thf(fact_5025_zero__less__power__abs__iff,axiom,
% 5.41/5.72 ! [A: real,N: nat] :
% 5.41/5.72 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.41/5.72 = ( ( A != zero_zero_real )
% 5.41/5.72 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_less_power_abs_iff
% 5.41/5.72 thf(fact_5026_zero__less__power__abs__iff,axiom,
% 5.41/5.72 ! [A: rat,N: nat] :
% 5.41/5.72 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) )
% 5.41/5.72 = ( ( A != zero_zero_rat )
% 5.41/5.72 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_less_power_abs_iff
% 5.41/5.72 thf(fact_5027_zero__less__power__abs__iff,axiom,
% 5.41/5.72 ! [A: int,N: nat] :
% 5.41/5.72 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) )
% 5.41/5.72 = ( ( A != zero_zero_int )
% 5.41/5.72 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_less_power_abs_iff
% 5.41/5.72 thf(fact_5028_even__mod__2__iff,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_mod_2_iff
% 5.41/5.72 thf(fact_5029_even__mod__2__iff,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_mod_2_iff
% 5.41/5.72 thf(fact_5030_even__mod__2__iff,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_mod_2_iff
% 5.41/5.72 thf(fact_5031_power__even__abs__numeral,axiom,
% 5.41/5.72 ! [W: num,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs_numeral
% 5.41/5.72 thf(fact_5032_power__even__abs__numeral,axiom,
% 5.41/5.72 ! [W: num,A: rat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 = ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs_numeral
% 5.41/5.72 thf(fact_5033_power__even__abs__numeral,axiom,
% 5.41/5.72 ! [W: num,A: real] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 => ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 = ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs_numeral
% 5.41/5.72 thf(fact_5034_power__even__abs__numeral,axiom,
% 5.41/5.72 ! [W: num,A: int] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 => ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 = ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs_numeral
% 5.41/5.72 thf(fact_5035_abs__power2,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_power2
% 5.41/5.72 thf(fact_5036_abs__power2,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( abs_abs_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_power2
% 5.41/5.72 thf(fact_5037_abs__power2,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( abs_abs_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_power2
% 5.41/5.72 thf(fact_5038_abs__power2,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( abs_abs_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_power2
% 5.41/5.72 thf(fact_5039_power2__abs,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_abs
% 5.41/5.72 thf(fact_5040_power2__abs,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( power_power_rat @ ( abs_abs_rat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_abs
% 5.41/5.72 thf(fact_5041_power2__abs,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( power_power_real @ ( abs_abs_real @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_abs
% 5.41/5.72 thf(fact_5042_power2__abs,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( power_power_int @ ( abs_abs_int @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power2_abs
% 5.41/5.72 thf(fact_5043_odd__Suc__div__two,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_Suc_div_two
% 5.41/5.72 thf(fact_5044_even__Suc__div__two,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( divide_divide_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_Suc_div_two
% 5.41/5.72 thf(fact_5045_zero__le__power__eq__numeral,axiom,
% 5.41/5.72 ! [A: real,W: num] :
% 5.41/5.72 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.72 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_le_power_eq_numeral
% 5.41/5.72 thf(fact_5046_zero__le__power__eq__numeral,axiom,
% 5.41/5.72 ! [A: rat,W: num] :
% 5.41/5.72 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.72 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_le_power_eq_numeral
% 5.41/5.72 thf(fact_5047_zero__le__power__eq__numeral,axiom,
% 5.41/5.72 ! [A: int,W: num] :
% 5.41/5.72 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.72 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_le_power_eq_numeral
% 5.41/5.72 thf(fact_5048_power__less__zero__eq,axiom,
% 5.41/5.72 ! [A: real,N: nat] :
% 5.41/5.72 ( ( ord_less_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_less_zero_eq
% 5.41/5.72 thf(fact_5049_power__less__zero__eq,axiom,
% 5.41/5.72 ! [A: rat,N: nat] :
% 5.41/5.72 ( ( ord_less_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_less_zero_eq
% 5.41/5.72 thf(fact_5050_power__less__zero__eq,axiom,
% 5.41/5.72 ! [A: int,N: nat] :
% 5.41/5.72 ( ( ord_less_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_less_zero_eq
% 5.41/5.72 thf(fact_5051_power__less__zero__eq__numeral,axiom,
% 5.41/5.72 ! [A: real,W: num] :
% 5.41/5.72 ( ( ord_less_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_real @ A @ zero_zero_real ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_less_zero_eq_numeral
% 5.41/5.72 thf(fact_5052_power__less__zero__eq__numeral,axiom,
% 5.41/5.72 ! [A: rat,W: num] :
% 5.41/5.72 ( ( ord_less_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_rat @ A @ zero_zero_rat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_less_zero_eq_numeral
% 5.41/5.72 thf(fact_5053_power__less__zero__eq__numeral,axiom,
% 5.41/5.72 ! [A: int,W: num] :
% 5.41/5.72 ( ( ord_less_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_less_zero_eq_numeral
% 5.41/5.72 thf(fact_5054_add__neg__numeral__special_I9_J,axiom,
% 5.41/5.72 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_neg_numeral_special(9)
% 5.41/5.72 thf(fact_5055_add__neg__numeral__special_I9_J,axiom,
% 5.41/5.72 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_neg_numeral_special(9)
% 5.41/5.72 thf(fact_5056_add__neg__numeral__special_I9_J,axiom,
% 5.41/5.72 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_neg_numeral_special(9)
% 5.41/5.72 thf(fact_5057_add__neg__numeral__special_I9_J,axiom,
% 5.41/5.72 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_neg_numeral_special(9)
% 5.41/5.72 thf(fact_5058_add__neg__numeral__special_I9_J,axiom,
% 5.41/5.72 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_neg_numeral_special(9)
% 5.41/5.72 thf(fact_5059_diff__numeral__special_I11_J,axiom,
% 5.41/5.72 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.72 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(11)
% 5.41/5.72 thf(fact_5060_diff__numeral__special_I11_J,axiom,
% 5.41/5.72 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.72 = ( numeral_numeral_int @ ( bit0 @ one ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(11)
% 5.41/5.72 thf(fact_5061_diff__numeral__special_I11_J,axiom,
% 5.41/5.72 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.72 = ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(11)
% 5.41/5.72 thf(fact_5062_diff__numeral__special_I11_J,axiom,
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.72 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(11)
% 5.41/5.72 thf(fact_5063_diff__numeral__special_I11_J,axiom,
% 5.41/5.72 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.72 = ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(11)
% 5.41/5.72 thf(fact_5064_diff__numeral__special_I10_J,axiom,
% 5.41/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(10)
% 5.41/5.72 thf(fact_5065_diff__numeral__special_I10_J,axiom,
% 5.41/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(10)
% 5.41/5.72 thf(fact_5066_diff__numeral__special_I10_J,axiom,
% 5.41/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ one_one_complex )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(10)
% 5.41/5.72 thf(fact_5067_diff__numeral__special_I10_J,axiom,
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(10)
% 5.41/5.72 thf(fact_5068_diff__numeral__special_I10_J,axiom,
% 5.41/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(10)
% 5.41/5.72 thf(fact_5069_minus__1__div__2__eq,axiom,
% 5.41/5.72 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_1_div_2_eq
% 5.41/5.72 thf(fact_5070_minus__1__div__2__eq,axiom,
% 5.41/5.72 ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_1_div_2_eq
% 5.41/5.72 thf(fact_5071_even__plus__one__iff,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_plus_one_iff
% 5.41/5.72 thf(fact_5072_even__plus__one__iff,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ one_one_nat ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_plus_one_iff
% 5.41/5.72 thf(fact_5073_even__plus__one__iff,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ one_one_int ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_plus_one_iff
% 5.41/5.72 thf(fact_5074_even__diff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_diff
% 5.41/5.72 thf(fact_5075_even__diff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ A @ B ) )
% 5.41/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_diff
% 5.41/5.72 thf(fact_5076_neg__one__odd__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.41/5.72 = ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_odd_power
% 5.41/5.72 thf(fact_5077_neg__one__odd__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.41/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_odd_power
% 5.41/5.72 thf(fact_5078_neg__one__odd__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_odd_power
% 5.41/5.72 thf(fact_5079_neg__one__odd__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_odd_power
% 5.41/5.72 thf(fact_5080_neg__one__odd__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.41/5.72 = ( uminus_uminus_rat @ one_one_rat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_odd_power
% 5.41/5.72 thf(fact_5081_neg__one__even__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.41/5.72 = one_one_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_even_power
% 5.41/5.72 thf(fact_5082_neg__one__even__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.41/5.72 = one_one_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_even_power
% 5.41/5.72 thf(fact_5083_neg__one__even__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.41/5.72 = one_one_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_even_power
% 5.41/5.72 thf(fact_5084_neg__one__even__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.41/5.72 = one_one_Code_integer ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_even_power
% 5.41/5.72 thf(fact_5085_neg__one__even__power,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.41/5.72 = one_one_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_one_even_power
% 5.41/5.72 thf(fact_5086_bits__minus__1__mod__2__eq,axiom,
% 5.41/5.72 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.72 = one_one_int ) ).
% 5.41/5.72
% 5.41/5.72 % bits_minus_1_mod_2_eq
% 5.41/5.72 thf(fact_5087_bits__minus__1__mod__2__eq,axiom,
% 5.41/5.72 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.72 = one_one_Code_integer ) ).
% 5.41/5.72
% 5.41/5.72 % bits_minus_1_mod_2_eq
% 5.41/5.72 thf(fact_5088_minus__1__mod__2__eq,axiom,
% 5.41/5.72 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.72 = one_one_int ) ).
% 5.41/5.72
% 5.41/5.72 % minus_1_mod_2_eq
% 5.41/5.72 thf(fact_5089_minus__1__mod__2__eq,axiom,
% 5.41/5.72 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.72 = one_one_Code_integer ) ).
% 5.41/5.72
% 5.41/5.72 % minus_1_mod_2_eq
% 5.41/5.72 thf(fact_5090_odd__Suc__minus__one,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( suc @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) )
% 5.41/5.72 = N ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_Suc_minus_one
% 5.41/5.72 thf(fact_5091_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [A: real,N: nat] :
% 5.41/5.72 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Power.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5092_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [A: int,N: nat] :
% 5.41/5.72 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Power.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5093_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [A: complex,N: nat] :
% 5.41/5.72 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Power.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5094_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [A: code_integer,N: nat] :
% 5.41/5.72 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Power.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5095_Power_Oring__1__class_Opower__minus__even,axiom,
% 5.41/5.72 ! [A: rat,N: nat] :
% 5.41/5.72 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % Power.ring_1_class.power_minus_even
% 5.41/5.72 thf(fact_5096_even__diff__nat,axiom,
% 5.41/5.72 ! [M: nat,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.72 = ( ( ord_less_nat @ M @ N )
% 5.41/5.72 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_diff_nat
% 5.41/5.72 thf(fact_5097_diff__numeral__special_I3_J,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( minus_minus_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_real @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(3)
% 5.41/5.72 thf(fact_5098_diff__numeral__special_I3_J,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( minus_minus_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_int @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(3)
% 5.41/5.72 thf(fact_5099_diff__numeral__special_I3_J,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( minus_minus_complex @ one_one_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.72 = ( numera6690914467698888265omplex @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(3)
% 5.41/5.72 thf(fact_5100_diff__numeral__special_I3_J,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.72 = ( numera6620942414471956472nteger @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(3)
% 5.41/5.72 thf(fact_5101_diff__numeral__special_I3_J,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( minus_minus_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.72 = ( numeral_numeral_rat @ ( plus_plus_num @ one @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(3)
% 5.41/5.72 thf(fact_5102_diff__numeral__special_I4_J,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(4)
% 5.41/5.72 thf(fact_5103_diff__numeral__special_I4_J,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(4)
% 5.41/5.72 thf(fact_5104_diff__numeral__special_I4_J,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ one_one_complex )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(4)
% 5.41/5.72 thf(fact_5105_diff__numeral__special_I4_J,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(4)
% 5.41/5.72 thf(fact_5106_diff__numeral__special_I4_J,axiom,
% 5.41/5.72 ! [M: num] :
% 5.41/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( plus_plus_num @ M @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % diff_numeral_special(4)
% 5.41/5.72 thf(fact_5107_dbl__simps_I4_J,axiom,
% 5.41/5.72 ( ( neg_numeral_dbl_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dbl_simps(4)
% 5.41/5.72 thf(fact_5108_dbl__simps_I4_J,axiom,
% 5.41/5.72 ( ( neg_numeral_dbl_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dbl_simps(4)
% 5.41/5.72 thf(fact_5109_dbl__simps_I4_J,axiom,
% 5.41/5.72 ( ( neg_nu7009210354673126013omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dbl_simps(4)
% 5.41/5.72 thf(fact_5110_dbl__simps_I4_J,axiom,
% 5.41/5.72 ( ( neg_nu8804712462038260780nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dbl_simps(4)
% 5.41/5.72 thf(fact_5111_dbl__simps_I4_J,axiom,
% 5.41/5.72 ( ( neg_numeral_dbl_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dbl_simps(4)
% 5.41/5.72 thf(fact_5112_zero__less__power__eq__numeral,axiom,
% 5.41/5.72 ! [A: real,W: num] :
% 5.41/5.72 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.72 = ( ( ( numeral_numeral_nat @ W )
% 5.41/5.72 = zero_zero_nat )
% 5.41/5.72 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( A != zero_zero_real ) )
% 5.41/5.72 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_less_power_eq_numeral
% 5.41/5.72 thf(fact_5113_zero__less__power__eq__numeral,axiom,
% 5.41/5.72 ! [A: rat,W: num] :
% 5.41/5.72 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.72 = ( ( ( numeral_numeral_nat @ W )
% 5.41/5.72 = zero_zero_nat )
% 5.41/5.72 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( A != zero_zero_rat ) )
% 5.41/5.72 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_less_power_eq_numeral
% 5.41/5.72 thf(fact_5114_zero__less__power__eq__numeral,axiom,
% 5.41/5.72 ! [A: int,W: num] :
% 5.41/5.72 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) )
% 5.41/5.72 = ( ( ( numeral_numeral_nat @ W )
% 5.41/5.72 = zero_zero_nat )
% 5.41/5.72 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( A != zero_zero_int ) )
% 5.41/5.72 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_less_power_eq_numeral
% 5.41/5.72 thf(fact_5115_even__succ__div__2,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ A ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_succ_div_2
% 5.41/5.72 thf(fact_5116_even__succ__div__2,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ one_one_nat @ A ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_succ_div_2
% 5.41/5.72 thf(fact_5117_even__succ__div__2,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ one_one_int @ A ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_succ_div_2
% 5.41/5.72 thf(fact_5118_odd__succ__div__two,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_succ_div_two
% 5.41/5.72 thf(fact_5119_odd__succ__div__two,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( plus_plus_nat @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_succ_div_two
% 5.41/5.72 thf(fact_5120_odd__succ__div__two,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( plus_plus_int @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_succ_div_two
% 5.41/5.72 thf(fact_5121_even__succ__div__two,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_succ_div_two
% 5.41/5.72 thf(fact_5122_even__succ__div__two,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_succ_div_two
% 5.41/5.72 thf(fact_5123_even__succ__div__two,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ A @ one_one_int ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.72 = ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_succ_div_two
% 5.41/5.72 thf(fact_5124_even__power,axiom,
% 5.41/5.72 ! [A: code_integer,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.41/5.72 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_power
% 5.41/5.72 thf(fact_5125_even__power,axiom,
% 5.41/5.72 ! [A: nat,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( power_power_nat @ A @ N ) )
% 5.41/5.72 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_power
% 5.41/5.72 thf(fact_5126_even__power,axiom,
% 5.41/5.72 ! [A: int,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( power_power_int @ A @ N ) )
% 5.41/5.72 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 & ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_power
% 5.41/5.72 thf(fact_5127_power__minus1__even,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = one_one_real ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus1_even
% 5.41/5.72 thf(fact_5128_power__minus1__even,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = one_one_int ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus1_even
% 5.41/5.72 thf(fact_5129_power__minus1__even,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = one_one_complex ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus1_even
% 5.41/5.72 thf(fact_5130_power__minus1__even,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = one_one_Code_integer ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus1_even
% 5.41/5.72 thf(fact_5131_power__minus1__even,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.72 = one_one_rat ) ).
% 5.41/5.72
% 5.41/5.72 % power_minus1_even
% 5.41/5.72 thf(fact_5132_odd__two__times__div__two__nat,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.72 = ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_two_times_div_two_nat
% 5.41/5.72 thf(fact_5133_odd__two__times__div__two__succ,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ one_one_Code_integer )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_two_times_div_two_succ
% 5.41/5.72 thf(fact_5134_odd__two__times__div__two__succ,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ one_one_nat )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_two_times_div_two_succ
% 5.41/5.72 thf(fact_5135_odd__two__times__div__two__succ,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.72 => ( ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ one_one_int )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % odd_two_times_div_two_succ
% 5.41/5.72 thf(fact_5136_power__le__zero__eq__numeral,axiom,
% 5.41/5.72 ! [A: real,W: num] :
% 5.41/5.72 ( ( ord_less_eq_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_real )
% 5.41/5.72 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.41/5.72 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_le_zero_eq_numeral
% 5.41/5.72 thf(fact_5137_power__le__zero__eq__numeral,axiom,
% 5.41/5.72 ! [A: rat,W: num] :
% 5.41/5.72 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_rat )
% 5.41/5.72 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.41/5.72 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_le_zero_eq_numeral
% 5.41/5.72 thf(fact_5138_power__le__zero__eq__numeral,axiom,
% 5.41/5.72 ! [A: int,W: num] :
% 5.41/5.72 ( ( ord_less_eq_int @ ( power_power_int @ A @ ( numeral_numeral_nat @ W ) ) @ zero_zero_int )
% 5.41/5.72 = ( ( ord_less_nat @ zero_zero_nat @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.41/5.72 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ W ) )
% 5.41/5.72 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_le_zero_eq_numeral
% 5.41/5.72 thf(fact_5139_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) )
% 5.41/5.72 = ( N = zero_zero_nat ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_parity_class.even_mask_iff
% 5.41/5.72 thf(fact_5140_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) )
% 5.41/5.72 = ( N = zero_zero_nat ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_parity_class.even_mask_iff
% 5.41/5.72 thf(fact_5141_semiring__parity__class_Oeven__mask__iff,axiom,
% 5.41/5.72 ! [N: nat] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.41/5.72 = ( N = zero_zero_nat ) ) ).
% 5.41/5.72
% 5.41/5.72 % semiring_parity_class.even_mask_iff
% 5.41/5.72 thf(fact_5142_dvd__div__neg,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ B @ A )
% 5.41/5.72 => ( ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_neg
% 5.41/5.72 thf(fact_5143_dvd__div__neg,axiom,
% 5.41/5.72 ! [B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_neg
% 5.41/5.72 thf(fact_5144_dvd__div__neg,axiom,
% 5.41/5.72 ! [B: complex,A: complex] :
% 5.41/5.72 ( ( dvd_dvd_complex @ B @ A )
% 5.41/5.72 => ( ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_neg
% 5.41/5.72 thf(fact_5145_dvd__div__neg,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_neg
% 5.41/5.72 thf(fact_5146_dvd__div__neg,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ B @ A )
% 5.41/5.72 => ( ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_neg
% 5.41/5.72 thf(fact_5147_dvd__neg__div,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ B @ A )
% 5.41/5.72 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B )
% 5.41/5.72 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_neg_div
% 5.41/5.72 thf(fact_5148_dvd__neg__div,axiom,
% 5.41/5.72 ! [B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.72 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_neg_div
% 5.41/5.72 thf(fact_5149_dvd__neg__div,axiom,
% 5.41/5.72 ! [B: complex,A: complex] :
% 5.41/5.72 ( ( dvd_dvd_complex @ B @ A )
% 5.41/5.72 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_neg_div
% 5.41/5.72 thf(fact_5150_dvd__neg__div,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_neg_div
% 5.41/5.72 thf(fact_5151_dvd__neg__div,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ B @ A )
% 5.41/5.72 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.41/5.72 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_neg_div
% 5.41/5.72 thf(fact_5152_dvd__if__abs__eq,axiom,
% 5.41/5.72 ! [L2: real,K: real] :
% 5.41/5.72 ( ( ( abs_abs_real @ L2 )
% 5.41/5.72 = ( abs_abs_real @ K ) )
% 5.41/5.72 => ( dvd_dvd_real @ L2 @ K ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_if_abs_eq
% 5.41/5.72 thf(fact_5153_dvd__if__abs__eq,axiom,
% 5.41/5.72 ! [L2: int,K: int] :
% 5.41/5.72 ( ( ( abs_abs_int @ L2 )
% 5.41/5.72 = ( abs_abs_int @ K ) )
% 5.41/5.72 => ( dvd_dvd_int @ L2 @ K ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_if_abs_eq
% 5.41/5.72 thf(fact_5154_dvd__if__abs__eq,axiom,
% 5.41/5.72 ! [L2: code_integer,K: code_integer] :
% 5.41/5.72 ( ( ( abs_abs_Code_integer @ L2 )
% 5.41/5.72 = ( abs_abs_Code_integer @ K ) )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ L2 @ K ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_if_abs_eq
% 5.41/5.72 thf(fact_5155_dvd__if__abs__eq,axiom,
% 5.41/5.72 ! [L2: rat,K: rat] :
% 5.41/5.72 ( ( ( abs_abs_rat @ L2 )
% 5.41/5.72 = ( abs_abs_rat @ K ) )
% 5.41/5.72 => ( dvd_dvd_rat @ L2 @ K ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_if_abs_eq
% 5.41/5.72 thf(fact_5156_abs__eq__iff,axiom,
% 5.41/5.72 ! [X: real,Y: real] :
% 5.41/5.72 ( ( ( abs_abs_real @ X )
% 5.41/5.72 = ( abs_abs_real @ Y ) )
% 5.41/5.72 = ( ( X = Y )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff
% 5.41/5.72 thf(fact_5157_abs__eq__iff,axiom,
% 5.41/5.72 ! [X: int,Y: int] :
% 5.41/5.72 ( ( ( abs_abs_int @ X )
% 5.41/5.72 = ( abs_abs_int @ Y ) )
% 5.41/5.72 = ( ( X = Y )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff
% 5.41/5.72 thf(fact_5158_abs__eq__iff,axiom,
% 5.41/5.72 ! [X: code_integer,Y: code_integer] :
% 5.41/5.72 ( ( ( abs_abs_Code_integer @ X )
% 5.41/5.72 = ( abs_abs_Code_integer @ Y ) )
% 5.41/5.72 = ( ( X = Y )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff
% 5.41/5.72 thf(fact_5159_abs__eq__iff,axiom,
% 5.41/5.72 ! [X: rat,Y: rat] :
% 5.41/5.72 ( ( ( abs_abs_rat @ X )
% 5.41/5.72 = ( abs_abs_rat @ Y ) )
% 5.41/5.72 = ( ( X = Y )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff
% 5.41/5.72 thf(fact_5160_dvd__trans,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ B @ C )
% 5.41/5.72 => ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_trans
% 5.41/5.72 thf(fact_5161_dvd__trans,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ B @ C )
% 5.41/5.72 => ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_trans
% 5.41/5.72 thf(fact_5162_dvd__trans,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ B @ C )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_trans
% 5.41/5.72 thf(fact_5163_dvd__refl,axiom,
% 5.41/5.72 ! [A: nat] : ( dvd_dvd_nat @ A @ A ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_refl
% 5.41/5.72 thf(fact_5164_dvd__refl,axiom,
% 5.41/5.72 ! [A: int] : ( dvd_dvd_int @ A @ A ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_refl
% 5.41/5.72 thf(fact_5165_dvd__refl,axiom,
% 5.41/5.72 ! [A: code_integer] : ( dvd_dvd_Code_integer @ A @ A ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_refl
% 5.41/5.72 thf(fact_5166_minus__equation__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ( uminus_uminus_real @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( uminus_uminus_real @ B )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_equation_iff
% 5.41/5.72 thf(fact_5167_minus__equation__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ( uminus_uminus_int @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( uminus_uminus_int @ B )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_equation_iff
% 5.41/5.72 thf(fact_5168_minus__equation__iff,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( ( uminus1482373934393186551omplex @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( uminus1482373934393186551omplex @ B )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_equation_iff
% 5.41/5.72 thf(fact_5169_minus__equation__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( uminus1351360451143612070nteger @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( uminus1351360451143612070nteger @ B )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_equation_iff
% 5.41/5.72 thf(fact_5170_minus__equation__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ( uminus_uminus_rat @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( uminus_uminus_rat @ B )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_equation_iff
% 5.41/5.72 thf(fact_5171_equation__minus__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % equation_minus_iff
% 5.41/5.72 thf(fact_5172_equation__minus__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % equation_minus_iff
% 5.41/5.72 thf(fact_5173_equation__minus__iff,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % equation_minus_iff
% 5.41/5.72 thf(fact_5174_equation__minus__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % equation_minus_iff
% 5.41/5.72 thf(fact_5175_equation__minus__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % equation_minus_iff
% 5.41/5.72 thf(fact_5176_abs__less__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_real @ ( abs_abs_real @ A ) @ B )
% 5.41/5.72 = ( ( ord_less_real @ A @ B )
% 5.41/5.72 & ( ord_less_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_less_iff
% 5.41/5.72 thf(fact_5177_abs__less__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_int @ ( abs_abs_int @ A ) @ B )
% 5.41/5.72 = ( ( ord_less_int @ A @ B )
% 5.41/5.72 & ( ord_less_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_less_iff
% 5.41/5.72 thf(fact_5178_abs__less__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.41/5.72 = ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.41/5.72 & ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_less_iff
% 5.41/5.72 thf(fact_5179_abs__less__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ B )
% 5.41/5.72 = ( ( ord_less_rat @ A @ B )
% 5.41/5.72 & ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_less_iff
% 5.41/5.72 thf(fact_5180_abs__leI,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.72 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_leI
% 5.41/5.72 thf(fact_5181_abs__leI,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.41/5.72 => ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.72 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_leI
% 5.41/5.72 thf(fact_5182_abs__leI,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.72 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_leI
% 5.41/5.72 thf(fact_5183_abs__leI,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.72 => ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_leI
% 5.41/5.72 thf(fact_5184_abs__le__D2,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D2
% 5.41/5.72 thf(fact_5185_abs__le__D2,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.41/5.72 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D2
% 5.41/5.72 thf(fact_5186_abs__le__D2,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D2
% 5.41/5.72 thf(fact_5187_abs__le__D2,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D2
% 5.41/5.72 thf(fact_5188_abs__le__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.41/5.72 = ( ( ord_less_eq_real @ A @ B )
% 5.41/5.72 & ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_iff
% 5.41/5.72 thf(fact_5189_abs__le__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.41/5.72 = ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.41/5.72 & ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_iff
% 5.41/5.72 thf(fact_5190_abs__le__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.41/5.72 = ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.72 & ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_iff
% 5.41/5.72 thf(fact_5191_abs__le__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.41/5.72 = ( ( ord_less_eq_int @ A @ B )
% 5.41/5.72 & ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_iff
% 5.41/5.72 thf(fact_5192_abs__ge__minus__self,axiom,
% 5.41/5.72 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ ( abs_abs_real @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_minus_self
% 5.41/5.72 thf(fact_5193_abs__ge__minus__self,axiom,
% 5.41/5.72 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ ( abs_abs_Code_integer @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_minus_self
% 5.41/5.72 thf(fact_5194_abs__ge__minus__self,axiom,
% 5.41/5.72 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ ( abs_abs_rat @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_minus_self
% 5.41/5.72 thf(fact_5195_abs__ge__minus__self,axiom,
% 5.41/5.72 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ ( abs_abs_int @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_minus_self
% 5.41/5.72 thf(fact_5196_abs__minus__le__zero,axiom,
% 5.41/5.72 ! [A: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( abs_abs_real @ A ) ) @ zero_zero_real ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_le_zero
% 5.41/5.72 thf(fact_5197_abs__minus__le__zero,axiom,
% 5.41/5.72 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( abs_abs_Code_integer @ A ) ) @ zero_z3403309356797280102nteger ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_le_zero
% 5.41/5.72 thf(fact_5198_abs__minus__le__zero,axiom,
% 5.41/5.72 ! [A: rat] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( abs_abs_rat @ A ) ) @ zero_zero_rat ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_le_zero
% 5.41/5.72 thf(fact_5199_abs__minus__le__zero,axiom,
% 5.41/5.72 ! [A: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( abs_abs_int @ A ) ) @ zero_zero_int ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_le_zero
% 5.41/5.72 thf(fact_5200_eq__abs__iff_H,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( abs_abs_real @ B ) )
% 5.41/5.72 = ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.72 & ( ( B = A )
% 5.41/5.72 | ( B
% 5.41/5.72 = ( uminus_uminus_real @ A ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_abs_iff'
% 5.41/5.72 thf(fact_5201_eq__abs__iff_H,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( abs_abs_Code_integer @ B ) )
% 5.41/5.72 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.72 & ( ( B = A )
% 5.41/5.72 | ( B
% 5.41/5.72 = ( uminus1351360451143612070nteger @ A ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_abs_iff'
% 5.41/5.72 thf(fact_5202_eq__abs__iff_H,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( abs_abs_rat @ B ) )
% 5.41/5.72 = ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.72 & ( ( B = A )
% 5.41/5.72 | ( B
% 5.41/5.72 = ( uminus_uminus_rat @ A ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_abs_iff'
% 5.41/5.72 thf(fact_5203_eq__abs__iff_H,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( abs_abs_int @ B ) )
% 5.41/5.72 = ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.72 & ( ( B = A )
% 5.41/5.72 | ( B
% 5.41/5.72 = ( uminus_uminus_int @ A ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_abs_iff'
% 5.41/5.72 thf(fact_5204_abs__eq__iff_H,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ( abs_abs_real @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.72 & ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus_uminus_real @ B ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff'
% 5.41/5.72 thf(fact_5205_abs__eq__iff_H,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( abs_abs_Code_integer @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.72 & ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus1351360451143612070nteger @ B ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff'
% 5.41/5.72 thf(fact_5206_abs__eq__iff_H,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ( abs_abs_rat @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.72 & ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus_uminus_rat @ B ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff'
% 5.41/5.72 thf(fact_5207_abs__eq__iff_H,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ( abs_abs_int @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.72 & ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus_uminus_int @ B ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_iff'
% 5.41/5.72 thf(fact_5208_abs__if,axiom,
% 5.41/5.72 ( abs_abs_real
% 5.41/5.72 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if
% 5.41/5.72 thf(fact_5209_abs__if,axiom,
% 5.41/5.72 ( abs_abs_int
% 5.41/5.72 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if
% 5.41/5.72 thf(fact_5210_abs__if,axiom,
% 5.41/5.72 ( abs_abs_Code_integer
% 5.41/5.72 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if
% 5.41/5.72 thf(fact_5211_abs__if,axiom,
% 5.41/5.72 ( abs_abs_rat
% 5.41/5.72 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if
% 5.41/5.72 thf(fact_5212_abs__of__neg,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.72 => ( ( abs_abs_real @ A )
% 5.41/5.72 = ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_neg
% 5.41/5.72 thf(fact_5213_abs__of__neg,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( ord_less_int @ A @ zero_zero_int )
% 5.41/5.72 => ( ( abs_abs_int @ A )
% 5.41/5.72 = ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_neg
% 5.41/5.72 thf(fact_5214_abs__of__neg,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ A @ zero_z3403309356797280102nteger )
% 5.41/5.72 => ( ( abs_abs_Code_integer @ A )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_neg
% 5.41/5.72 thf(fact_5215_abs__of__neg,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( ord_less_rat @ A @ zero_zero_rat )
% 5.41/5.72 => ( ( abs_abs_rat @ A )
% 5.41/5.72 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_neg
% 5.41/5.72 thf(fact_5216_abs__if__raw,axiom,
% 5.41/5.72 ( abs_abs_real
% 5.41/5.72 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if_raw
% 5.41/5.72 thf(fact_5217_abs__if__raw,axiom,
% 5.41/5.72 ( abs_abs_int
% 5.41/5.72 = ( ^ [A3: int] : ( if_int @ ( ord_less_int @ A3 @ zero_zero_int ) @ ( uminus_uminus_int @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if_raw
% 5.41/5.72 thf(fact_5218_abs__if__raw,axiom,
% 5.41/5.72 ( abs_abs_Code_integer
% 5.41/5.72 = ( ^ [A3: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ A3 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if_raw
% 5.41/5.72 thf(fact_5219_abs__if__raw,axiom,
% 5.41/5.72 ( abs_abs_rat
% 5.41/5.72 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_if_raw
% 5.41/5.72 thf(fact_5220_abs__real__def,axiom,
% 5.41/5.72 ( abs_abs_real
% 5.41/5.72 = ( ^ [A3: real] : ( if_real @ ( ord_less_real @ A3 @ zero_zero_real ) @ ( uminus_uminus_real @ A3 ) @ A3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_real_def
% 5.41/5.72 thf(fact_5221_abs__le__D1,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_real @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D1
% 5.41/5.72 thf(fact_5222_abs__le__D1,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ B )
% 5.41/5.72 => ( ord_le3102999989581377725nteger @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D1
% 5.41/5.72 thf(fact_5223_abs__le__D1,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_rat @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D1
% 5.41/5.72 thf(fact_5224_abs__le__D1,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ B )
% 5.41/5.72 => ( ord_less_eq_int @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_le_D1
% 5.41/5.72 thf(fact_5225_abs__ge__self,axiom,
% 5.41/5.72 ! [A: real] : ( ord_less_eq_real @ A @ ( abs_abs_real @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_self
% 5.41/5.72 thf(fact_5226_abs__ge__self,axiom,
% 5.41/5.72 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ A @ ( abs_abs_Code_integer @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_self
% 5.41/5.72 thf(fact_5227_abs__ge__self,axiom,
% 5.41/5.72 ! [A: rat] : ( ord_less_eq_rat @ A @ ( abs_abs_rat @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_self
% 5.41/5.72 thf(fact_5228_abs__ge__self,axiom,
% 5.41/5.72 ! [A: int] : ( ord_less_eq_int @ A @ ( abs_abs_int @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_self
% 5.41/5.72 thf(fact_5229_abs__eq__0__iff,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( ( abs_abs_Code_integer @ A )
% 5.41/5.72 = zero_z3403309356797280102nteger )
% 5.41/5.72 = ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_0_iff
% 5.41/5.72 thf(fact_5230_abs__eq__0__iff,axiom,
% 5.41/5.72 ! [A: complex] :
% 5.41/5.72 ( ( ( abs_abs_complex @ A )
% 5.41/5.72 = zero_zero_complex )
% 5.41/5.72 = ( A = zero_zero_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_0_iff
% 5.41/5.72 thf(fact_5231_abs__eq__0__iff,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( ( abs_abs_real @ A )
% 5.41/5.72 = zero_zero_real )
% 5.41/5.72 = ( A = zero_zero_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_0_iff
% 5.41/5.72 thf(fact_5232_abs__eq__0__iff,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( ( abs_abs_rat @ A )
% 5.41/5.72 = zero_zero_rat )
% 5.41/5.72 = ( A = zero_zero_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_0_iff
% 5.41/5.72 thf(fact_5233_abs__eq__0__iff,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( ( abs_abs_int @ A )
% 5.41/5.72 = zero_zero_int )
% 5.41/5.72 = ( A = zero_zero_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_eq_0_iff
% 5.41/5.72 thf(fact_5234_abs__mult,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.41/5.72 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult
% 5.41/5.72 thf(fact_5235_abs__mult,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.41/5.72 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult
% 5.41/5.72 thf(fact_5236_abs__mult,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.72 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult
% 5.41/5.72 thf(fact_5237_abs__mult,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.41/5.72 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult
% 5.41/5.72 thf(fact_5238_abs__one,axiom,
% 5.41/5.72 ( ( abs_abs_Code_integer @ one_one_Code_integer )
% 5.41/5.72 = one_one_Code_integer ) ).
% 5.41/5.72
% 5.41/5.72 % abs_one
% 5.41/5.72 thf(fact_5239_abs__one,axiom,
% 5.41/5.72 ( ( abs_abs_real @ one_one_real )
% 5.41/5.72 = one_one_real ) ).
% 5.41/5.72
% 5.41/5.72 % abs_one
% 5.41/5.72 thf(fact_5240_abs__one,axiom,
% 5.41/5.72 ( ( abs_abs_rat @ one_one_rat )
% 5.41/5.72 = one_one_rat ) ).
% 5.41/5.72
% 5.41/5.72 % abs_one
% 5.41/5.72 thf(fact_5241_abs__one,axiom,
% 5.41/5.72 ( ( abs_abs_int @ one_one_int )
% 5.41/5.72 = one_one_int ) ).
% 5.41/5.72
% 5.41/5.72 % abs_one
% 5.41/5.72 thf(fact_5242_abs__minus__commute,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) )
% 5.41/5.72 = ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_commute
% 5.41/5.72 thf(fact_5243_abs__minus__commute,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( abs_abs_real @ ( minus_minus_real @ A @ B ) )
% 5.41/5.72 = ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_commute
% 5.41/5.72 thf(fact_5244_abs__minus__commute,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) )
% 5.41/5.72 = ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_commute
% 5.41/5.72 thf(fact_5245_abs__minus__commute,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( abs_abs_int @ ( minus_minus_int @ A @ B ) )
% 5.41/5.72 = ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_minus_commute
% 5.41/5.72 thf(fact_5246_tanh__real__gt__neg1,axiom,
% 5.41/5.72 ! [X: real] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( tanh_real @ X ) ) ).
% 5.41/5.72
% 5.41/5.72 % tanh_real_gt_neg1
% 5.41/5.72 thf(fact_5247_power__abs,axiom,
% 5.41/5.72 ! [A: code_integer,N: nat] :
% 5.41/5.72 ( ( abs_abs_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) )
% 5.41/5.72 = ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_abs
% 5.41/5.72 thf(fact_5248_power__abs,axiom,
% 5.41/5.72 ! [A: rat,N: nat] :
% 5.41/5.72 ( ( abs_abs_rat @ ( power_power_rat @ A @ N ) )
% 5.41/5.72 = ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_abs
% 5.41/5.72 thf(fact_5249_power__abs,axiom,
% 5.41/5.72 ! [A: real,N: nat] :
% 5.41/5.72 ( ( abs_abs_real @ ( power_power_real @ A @ N ) )
% 5.41/5.72 = ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_abs
% 5.41/5.72 thf(fact_5250_power__abs,axiom,
% 5.41/5.72 ! [A: int,N: nat] :
% 5.41/5.72 ( ( abs_abs_int @ ( power_power_int @ A @ N ) )
% 5.41/5.72 = ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_abs
% 5.41/5.72 thf(fact_5251_bot__nat__def,axiom,
% 5.41/5.72 bot_bot_nat = zero_zero_nat ).
% 5.41/5.72
% 5.41/5.72 % bot_nat_def
% 5.41/5.72 thf(fact_5252_dvd__0__left,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ A )
% 5.41/5.72 => ( A = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_0_left
% 5.41/5.72 thf(fact_5253_dvd__0__left,axiom,
% 5.41/5.72 ! [A: complex] :
% 5.41/5.72 ( ( dvd_dvd_complex @ zero_zero_complex @ A )
% 5.41/5.72 => ( A = zero_zero_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_0_left
% 5.41/5.72 thf(fact_5254_dvd__0__left,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ zero_zero_real @ A )
% 5.41/5.72 => ( A = zero_zero_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_0_left
% 5.41/5.72 thf(fact_5255_dvd__0__left,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ zero_zero_rat @ A )
% 5.41/5.72 => ( A = zero_zero_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_0_left
% 5.41/5.72 thf(fact_5256_dvd__0__left,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.41/5.72 => ( A = zero_zero_nat ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_0_left
% 5.41/5.72 thf(fact_5257_dvd__0__left,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ zero_zero_int @ A )
% 5.41/5.72 => ( A = zero_zero_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_0_left
% 5.41/5.72 thf(fact_5258_dvd__field__iff,axiom,
% 5.41/5.72 ( dvd_dvd_complex
% 5.41/5.72 = ( ^ [A3: complex,B2: complex] :
% 5.41/5.72 ( ( A3 = zero_zero_complex )
% 5.41/5.72 => ( B2 = zero_zero_complex ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_field_iff
% 5.41/5.72 thf(fact_5259_dvd__field__iff,axiom,
% 5.41/5.72 ( dvd_dvd_real
% 5.41/5.72 = ( ^ [A3: real,B2: real] :
% 5.41/5.72 ( ( A3 = zero_zero_real )
% 5.41/5.72 => ( B2 = zero_zero_real ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_field_iff
% 5.41/5.72 thf(fact_5260_dvd__field__iff,axiom,
% 5.41/5.72 ( dvd_dvd_rat
% 5.41/5.72 = ( ^ [A3: rat,B2: rat] :
% 5.41/5.72 ( ( A3 = zero_zero_rat )
% 5.41/5.72 => ( B2 = zero_zero_rat ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_field_iff
% 5.41/5.72 thf(fact_5261_dvdE,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ~ ! [K3: code_integer] :
% 5.41/5.72 ( A
% 5.41/5.72 != ( times_3573771949741848930nteger @ B @ K3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdE
% 5.41/5.72 thf(fact_5262_dvdE,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ B @ A )
% 5.41/5.72 => ~ ! [K3: real] :
% 5.41/5.72 ( A
% 5.41/5.72 != ( times_times_real @ B @ K3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdE
% 5.41/5.72 thf(fact_5263_dvdE,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ B @ A )
% 5.41/5.72 => ~ ! [K3: rat] :
% 5.41/5.72 ( A
% 5.41/5.72 != ( times_times_rat @ B @ K3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdE
% 5.41/5.72 thf(fact_5264_dvdE,axiom,
% 5.41/5.72 ! [B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.72 => ~ ! [K3: nat] :
% 5.41/5.72 ( A
% 5.41/5.72 != ( times_times_nat @ B @ K3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdE
% 5.41/5.72 thf(fact_5265_dvdE,axiom,
% 5.41/5.72 ! [B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ~ ! [K3: int] :
% 5.41/5.72 ( A
% 5.41/5.72 != ( times_times_int @ B @ K3 ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdE
% 5.41/5.72 thf(fact_5266_dvdI,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,K: code_integer] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( times_3573771949741848930nteger @ B @ K ) )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdI
% 5.41/5.72 thf(fact_5267_dvdI,axiom,
% 5.41/5.72 ! [A: real,B: real,K: real] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( times_times_real @ B @ K ) )
% 5.41/5.72 => ( dvd_dvd_real @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdI
% 5.41/5.72 thf(fact_5268_dvdI,axiom,
% 5.41/5.72 ! [A: rat,B: rat,K: rat] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( times_times_rat @ B @ K ) )
% 5.41/5.72 => ( dvd_dvd_rat @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdI
% 5.41/5.72 thf(fact_5269_dvdI,axiom,
% 5.41/5.72 ! [A: nat,B: nat,K: nat] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( times_times_nat @ B @ K ) )
% 5.41/5.72 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdI
% 5.41/5.72 thf(fact_5270_dvdI,axiom,
% 5.41/5.72 ! [A: int,B: int,K: int] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( times_times_int @ B @ K ) )
% 5.41/5.72 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvdI
% 5.41/5.72 thf(fact_5271_dvd__def,axiom,
% 5.41/5.72 ( dvd_dvd_Code_integer
% 5.41/5.72 = ( ^ [B2: code_integer,A3: code_integer] :
% 5.41/5.72 ? [K2: code_integer] :
% 5.41/5.72 ( A3
% 5.41/5.72 = ( times_3573771949741848930nteger @ B2 @ K2 ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_def
% 5.41/5.72 thf(fact_5272_dvd__def,axiom,
% 5.41/5.72 ( dvd_dvd_real
% 5.41/5.72 = ( ^ [B2: real,A3: real] :
% 5.41/5.72 ? [K2: real] :
% 5.41/5.72 ( A3
% 5.41/5.72 = ( times_times_real @ B2 @ K2 ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_def
% 5.41/5.72 thf(fact_5273_dvd__def,axiom,
% 5.41/5.72 ( dvd_dvd_rat
% 5.41/5.72 = ( ^ [B2: rat,A3: rat] :
% 5.41/5.72 ? [K2: rat] :
% 5.41/5.72 ( A3
% 5.41/5.72 = ( times_times_rat @ B2 @ K2 ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_def
% 5.41/5.72 thf(fact_5274_dvd__def,axiom,
% 5.41/5.72 ( dvd_dvd_nat
% 5.41/5.72 = ( ^ [B2: nat,A3: nat] :
% 5.41/5.72 ? [K2: nat] :
% 5.41/5.72 ( A3
% 5.41/5.72 = ( times_times_nat @ B2 @ K2 ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_def
% 5.41/5.72 thf(fact_5275_dvd__def,axiom,
% 5.41/5.72 ( dvd_dvd_int
% 5.41/5.72 = ( ^ [B2: int,A3: int] :
% 5.41/5.72 ? [K2: int] :
% 5.41/5.72 ( A3
% 5.41/5.72 = ( times_times_int @ B2 @ K2 ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_def
% 5.41/5.72 thf(fact_5276_dvd__mult,axiom,
% 5.41/5.72 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult
% 5.41/5.72 thf(fact_5277_dvd__mult,axiom,
% 5.41/5.72 ! [A: real,C: real,B: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ A @ C )
% 5.41/5.72 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult
% 5.41/5.72 thf(fact_5278_dvd__mult,axiom,
% 5.41/5.72 ! [A: rat,C: rat,B: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ A @ C )
% 5.41/5.72 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult
% 5.41/5.72 thf(fact_5279_dvd__mult,axiom,
% 5.41/5.72 ! [A: nat,C: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ C )
% 5.41/5.72 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult
% 5.41/5.72 thf(fact_5280_dvd__mult,axiom,
% 5.41/5.72 ! [A: int,C: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ C )
% 5.41/5.72 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult
% 5.41/5.72 thf(fact_5281_dvd__mult2,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult2
% 5.41/5.72 thf(fact_5282_dvd__mult2,axiom,
% 5.41/5.72 ! [A: real,B: real,C: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ A @ B )
% 5.41/5.72 => ( dvd_dvd_real @ A @ ( times_times_real @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult2
% 5.41/5.72 thf(fact_5283_dvd__mult2,axiom,
% 5.41/5.72 ! [A: rat,B: rat,C: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ A @ B )
% 5.41/5.72 => ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult2
% 5.41/5.72 thf(fact_5284_dvd__mult2,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.72 => ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult2
% 5.41/5.72 thf(fact_5285_dvd__mult2,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.72 => ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult2
% 5.41/5.72 thf(fact_5286_dvd__mult__left,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ A @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_left
% 5.41/5.72 thf(fact_5287_dvd__mult__left,axiom,
% 5.41/5.72 ! [A: real,B: real,C: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_real @ A @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_left
% 5.41/5.72 thf(fact_5288_dvd__mult__left,axiom,
% 5.41/5.72 ! [A: rat,B: rat,C: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_rat @ A @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_left
% 5.41/5.72 thf(fact_5289_dvd__mult__left,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_nat @ A @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_left
% 5.41/5.72 thf(fact_5290_dvd__mult__left,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_int @ A @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_left
% 5.41/5.72 thf(fact_5291_dvd__triv__left,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_left
% 5.41/5.72 thf(fact_5292_dvd__triv__left,axiom,
% 5.41/5.72 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_left
% 5.41/5.72 thf(fact_5293_dvd__triv__left,axiom,
% 5.41/5.72 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_left
% 5.41/5.72 thf(fact_5294_dvd__triv__left,axiom,
% 5.41/5.72 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_left
% 5.41/5.72 thf(fact_5295_dvd__triv__left,axiom,
% 5.41/5.72 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_left
% 5.41/5.72 thf(fact_5296_mult__dvd__mono,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_dvd_mono
% 5.41/5.72 thf(fact_5297_mult__dvd__mono,axiom,
% 5.41/5.72 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_real @ C @ D )
% 5.41/5.72 => ( dvd_dvd_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_dvd_mono
% 5.41/5.72 thf(fact_5298_mult__dvd__mono,axiom,
% 5.41/5.72 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_rat @ C @ D )
% 5.41/5.72 => ( dvd_dvd_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_dvd_mono
% 5.41/5.72 thf(fact_5299_mult__dvd__mono,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ C @ D )
% 5.41/5.72 => ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_dvd_mono
% 5.41/5.72 thf(fact_5300_mult__dvd__mono,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ C @ D )
% 5.41/5.72 => ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_dvd_mono
% 5.41/5.72 thf(fact_5301_dvd__mult__right,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ B @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_right
% 5.41/5.72 thf(fact_5302_dvd__mult__right,axiom,
% 5.41/5.72 ! [A: real,B: real,C: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ ( times_times_real @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_real @ B @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_right
% 5.41/5.72 thf(fact_5303_dvd__mult__right,axiom,
% 5.41/5.72 ! [A: rat,B: rat,C: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ ( times_times_rat @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_rat @ B @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_right
% 5.41/5.72 thf(fact_5304_dvd__mult__right,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_nat @ B @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_right
% 5.41/5.72 thf(fact_5305_dvd__mult__right,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.72 => ( dvd_dvd_int @ B @ C ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_right
% 5.41/5.72 thf(fact_5306_dvd__triv__right,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] : ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_right
% 5.41/5.72 thf(fact_5307_dvd__triv__right,axiom,
% 5.41/5.72 ! [A: real,B: real] : ( dvd_dvd_real @ A @ ( times_times_real @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_right
% 5.41/5.72 thf(fact_5308_dvd__triv__right,axiom,
% 5.41/5.72 ! [A: rat,B: rat] : ( dvd_dvd_rat @ A @ ( times_times_rat @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_right
% 5.41/5.72 thf(fact_5309_dvd__triv__right,axiom,
% 5.41/5.72 ! [A: nat,B: nat] : ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_right
% 5.41/5.72 thf(fact_5310_dvd__triv__right,axiom,
% 5.41/5.72 ! [A: int,B: int] : ( dvd_dvd_int @ A @ ( times_times_int @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_triv_right
% 5.41/5.72 thf(fact_5311_division__decomp,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.41/5.72 => ? [B7: nat,C5: nat] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( times_times_nat @ B7 @ C5 ) )
% 5.41/5.72 & ( dvd_dvd_nat @ B7 @ B )
% 5.41/5.72 & ( dvd_dvd_nat @ C5 @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % division_decomp
% 5.41/5.72 thf(fact_5312_division__decomp,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.72 => ? [B7: int,C5: int] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( times_times_int @ B7 @ C5 ) )
% 5.41/5.72 & ( dvd_dvd_int @ B7 @ B )
% 5.41/5.72 & ( dvd_dvd_int @ C5 @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % division_decomp
% 5.41/5.72 thf(fact_5313_dvd__productE,axiom,
% 5.41/5.72 ! [P5: nat,A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ P5 @ ( times_times_nat @ A @ B ) )
% 5.41/5.72 => ~ ! [X6: nat,Y5: nat] :
% 5.41/5.72 ( ( P5
% 5.41/5.72 = ( times_times_nat @ X6 @ Y5 ) )
% 5.41/5.72 => ( ( dvd_dvd_nat @ X6 @ A )
% 5.41/5.72 => ~ ( dvd_dvd_nat @ Y5 @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_productE
% 5.41/5.72 thf(fact_5314_dvd__productE,axiom,
% 5.41/5.72 ! [P5: int,A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ P5 @ ( times_times_int @ A @ B ) )
% 5.41/5.72 => ~ ! [X6: int,Y5: int] :
% 5.41/5.72 ( ( P5
% 5.41/5.72 = ( times_times_int @ X6 @ Y5 ) )
% 5.41/5.72 => ( ( dvd_dvd_int @ X6 @ A )
% 5.41/5.72 => ~ ( dvd_dvd_int @ Y5 @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_productE
% 5.41/5.72 thf(fact_5315_dvd__add,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ A @ C )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add
% 5.41/5.72 thf(fact_5316_dvd__add,axiom,
% 5.41/5.72 ! [A: real,B: real,C: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_real @ A @ C )
% 5.41/5.72 => ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add
% 5.41/5.72 thf(fact_5317_dvd__add,axiom,
% 5.41/5.72 ! [A: rat,B: rat,C: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_rat @ A @ C )
% 5.41/5.72 => ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add
% 5.41/5.72 thf(fact_5318_dvd__add,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ A @ C )
% 5.41/5.72 => ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add
% 5.41/5.72 thf(fact_5319_dvd__add,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ A @ C )
% 5.41/5.72 => ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add
% 5.41/5.72 thf(fact_5320_dvd__add__left__iff,axiom,
% 5.41/5.72 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ C )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_left_iff
% 5.41/5.72 thf(fact_5321_dvd__add__left__iff,axiom,
% 5.41/5.72 ! [A: real,C: real,B: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ A @ C )
% 5.41/5.72 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_real @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_left_iff
% 5.41/5.72 thf(fact_5322_dvd__add__left__iff,axiom,
% 5.41/5.72 ! [A: rat,C: rat,B: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ A @ C )
% 5.41/5.72 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_rat @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_left_iff
% 5.41/5.72 thf(fact_5323_dvd__add__left__iff,axiom,
% 5.41/5.72 ! [A: nat,C: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ C )
% 5.41/5.72 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_left_iff
% 5.41/5.72 thf(fact_5324_dvd__add__left__iff,axiom,
% 5.41/5.72 ! [A: int,C: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ C )
% 5.41/5.72 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_left_iff
% 5.41/5.72 thf(fact_5325_dvd__add__right__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ A @ ( plus_p5714425477246183910nteger @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_right_iff
% 5.41/5.72 thf(fact_5326_dvd__add__right__iff,axiom,
% 5.41/5.72 ! [A: real,B: real,C: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_real @ A @ ( plus_plus_real @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_real @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_right_iff
% 5.41/5.72 thf(fact_5327_dvd__add__right__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat,C: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_rat @ A @ ( plus_plus_rat @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_rat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_right_iff
% 5.41/5.72 thf(fact_5328_dvd__add__right__iff,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ A @ ( plus_plus_nat @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_right_iff
% 5.41/5.72 thf(fact_5329_dvd__add__right__iff,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_add_right_iff
% 5.41/5.72 thf(fact_5330_one__dvd,axiom,
% 5.41/5.72 ! [A: code_integer] : ( dvd_dvd_Code_integer @ one_one_Code_integer @ A ) ).
% 5.41/5.72
% 5.41/5.72 % one_dvd
% 5.41/5.72 thf(fact_5331_one__dvd,axiom,
% 5.41/5.72 ! [A: complex] : ( dvd_dvd_complex @ one_one_complex @ A ) ).
% 5.41/5.72
% 5.41/5.72 % one_dvd
% 5.41/5.72 thf(fact_5332_one__dvd,axiom,
% 5.41/5.72 ! [A: real] : ( dvd_dvd_real @ one_one_real @ A ) ).
% 5.41/5.72
% 5.41/5.72 % one_dvd
% 5.41/5.72 thf(fact_5333_one__dvd,axiom,
% 5.41/5.72 ! [A: rat] : ( dvd_dvd_rat @ one_one_rat @ A ) ).
% 5.41/5.72
% 5.41/5.72 % one_dvd
% 5.41/5.72 thf(fact_5334_one__dvd,axiom,
% 5.41/5.72 ! [A: nat] : ( dvd_dvd_nat @ one_one_nat @ A ) ).
% 5.41/5.72
% 5.41/5.72 % one_dvd
% 5.41/5.72 thf(fact_5335_one__dvd,axiom,
% 5.41/5.72 ! [A: int] : ( dvd_dvd_int @ one_one_int @ A ) ).
% 5.41/5.72
% 5.41/5.72 % one_dvd
% 5.41/5.72 thf(fact_5336_unit__imp__dvd,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_imp_dvd
% 5.41/5.72 thf(fact_5337_unit__imp__dvd,axiom,
% 5.41/5.72 ! [B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.72 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_imp_dvd
% 5.41/5.72 thf(fact_5338_unit__imp__dvd,axiom,
% 5.41/5.72 ! [B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.72 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_imp_dvd
% 5.41/5.72 thf(fact_5339_dvd__unit__imp__unit,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ A @ one_one_Code_integer ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_unit_imp_unit
% 5.41/5.72 thf(fact_5340_dvd__unit__imp__unit,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.72 => ( dvd_dvd_nat @ A @ one_one_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_unit_imp_unit
% 5.41/5.72 thf(fact_5341_dvd__unit__imp__unit,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.72 => ( dvd_dvd_int @ A @ one_one_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_unit_imp_unit
% 5.41/5.72 thf(fact_5342_le__minus__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( ord_less_eq_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_iff
% 5.41/5.72 thf(fact_5343_le__minus__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( ord_le3102999989581377725nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_iff
% 5.41/5.72 thf(fact_5344_le__minus__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( ord_less_eq_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_iff
% 5.41/5.72 thf(fact_5345_le__minus__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( ord_less_eq_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_iff
% 5.41/5.72 thf(fact_5346_minus__le__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ ( uminus_uminus_real @ A ) @ B )
% 5.41/5.72 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_le_iff
% 5.41/5.72 thf(fact_5347_minus__le__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.72 = ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_le_iff
% 5.41/5.72 thf(fact_5348_minus__le__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.41/5.72 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_le_iff
% 5.41/5.72 thf(fact_5349_minus__le__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.72 = ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_le_iff
% 5.41/5.72 thf(fact_5350_le__imp__neg__le,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.72 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_imp_neg_le
% 5.41/5.72 thf(fact_5351_le__imp__neg__le,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le3102999989581377725nteger @ A @ B )
% 5.41/5.72 => ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_imp_neg_le
% 5.41/5.72 thf(fact_5352_le__imp__neg__le,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.72 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_imp_neg_le
% 5.41/5.72 thf(fact_5353_le__imp__neg__le,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_int @ A @ B )
% 5.41/5.72 => ( ord_less_eq_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_imp_neg_le
% 5.41/5.72 thf(fact_5354_dvd__diff__commute,axiom,
% 5.41/5.72 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ ( minus_8373710615458151222nteger @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_diff_commute
% 5.41/5.72 thf(fact_5355_dvd__diff__commute,axiom,
% 5.41/5.72 ! [A: int,C: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ ( minus_minus_int @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ ( minus_minus_int @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_diff_commute
% 5.41/5.72 thf(fact_5356_dvd__diff,axiom,
% 5.41/5.72 ! [X: code_integer,Y: code_integer,Z: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ X @ Z )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ X @ ( minus_8373710615458151222nteger @ Y @ Z ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_diff
% 5.41/5.72 thf(fact_5357_dvd__diff,axiom,
% 5.41/5.72 ! [X: real,Y: real,Z: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ X @ Y )
% 5.41/5.72 => ( ( dvd_dvd_real @ X @ Z )
% 5.41/5.72 => ( dvd_dvd_real @ X @ ( minus_minus_real @ Y @ Z ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_diff
% 5.41/5.72 thf(fact_5358_dvd__diff,axiom,
% 5.41/5.72 ! [X: rat,Y: rat,Z: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ X @ Y )
% 5.41/5.72 => ( ( dvd_dvd_rat @ X @ Z )
% 5.41/5.72 => ( dvd_dvd_rat @ X @ ( minus_minus_rat @ Y @ Z ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_diff
% 5.41/5.72 thf(fact_5359_dvd__diff,axiom,
% 5.41/5.72 ! [X: int,Y: int,Z: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ X @ Y )
% 5.41/5.72 => ( ( dvd_dvd_int @ X @ Z )
% 5.41/5.72 => ( dvd_dvd_int @ X @ ( minus_minus_int @ Y @ Z ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_diff
% 5.41/5.72 thf(fact_5360_less__minus__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_real @ A @ ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( ord_less_real @ B @ ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_iff
% 5.41/5.72 thf(fact_5361_less__minus__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( ord_less_int @ B @ ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_iff
% 5.41/5.72 thf(fact_5362_less__minus__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( ord_le6747313008572928689nteger @ B @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_iff
% 5.41/5.72 thf(fact_5363_less__minus__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( ord_less_rat @ B @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_iff
% 5.41/5.72 thf(fact_5364_minus__less__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_real @ ( uminus_uminus_real @ A ) @ B )
% 5.41/5.72 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_less_iff
% 5.41/5.72 thf(fact_5365_minus__less__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.72 = ( ord_less_int @ ( uminus_uminus_int @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_less_iff
% 5.41/5.72 thf(fact_5366_minus__less__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.72 = ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_less_iff
% 5.41/5.72 thf(fact_5367_minus__less__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.41/5.72 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_less_iff
% 5.41/5.72 thf(fact_5368_verit__negate__coefficient_I2_J,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ord_less_real @ A @ B )
% 5.41/5.72 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % verit_negate_coefficient(2)
% 5.41/5.72 thf(fact_5369_verit__negate__coefficient_I2_J,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_int @ A @ B )
% 5.41/5.72 => ( ord_less_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % verit_negate_coefficient(2)
% 5.41/5.72 thf(fact_5370_verit__negate__coefficient_I2_J,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ A @ B )
% 5.41/5.72 => ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % verit_negate_coefficient(2)
% 5.41/5.72 thf(fact_5371_verit__negate__coefficient_I2_J,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ord_less_rat @ A @ B )
% 5.41/5.72 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % verit_negate_coefficient(2)
% 5.41/5.72 thf(fact_5372_dvd__div__eq__iff,axiom,
% 5.41/5.72 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.41/5.72 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.41/5.72 = ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_iff
% 5.41/5.72 thf(fact_5373_dvd__div__eq__iff,axiom,
% 5.41/5.72 ! [C: complex,A: complex,B: complex] :
% 5.41/5.72 ( ( dvd_dvd_complex @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_complex @ C @ B )
% 5.41/5.72 => ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.41/5.72 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.72 = ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_iff
% 5.41/5.72 thf(fact_5374_dvd__div__eq__iff,axiom,
% 5.41/5.72 ! [C: real,A: real,B: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_real @ C @ B )
% 5.41/5.72 => ( ( ( divide_divide_real @ A @ C )
% 5.41/5.72 = ( divide_divide_real @ B @ C ) )
% 5.41/5.72 = ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_iff
% 5.41/5.72 thf(fact_5375_dvd__div__eq__iff,axiom,
% 5.41/5.72 ! [C: rat,A: rat,B: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_rat @ C @ B )
% 5.41/5.72 => ( ( ( divide_divide_rat @ A @ C )
% 5.41/5.72 = ( divide_divide_rat @ B @ C ) )
% 5.41/5.72 = ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_iff
% 5.41/5.72 thf(fact_5376_dvd__div__eq__iff,axiom,
% 5.41/5.72 ! [C: nat,A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( ( ( divide_divide_nat @ A @ C )
% 5.41/5.72 = ( divide_divide_nat @ B @ C ) )
% 5.41/5.72 = ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_iff
% 5.41/5.72 thf(fact_5377_dvd__div__eq__iff,axiom,
% 5.41/5.72 ! [C: int,A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( ( ( divide_divide_int @ A @ C )
% 5.41/5.72 = ( divide_divide_int @ B @ C ) )
% 5.41/5.72 = ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_iff
% 5.41/5.72 thf(fact_5378_dvd__div__eq__cancel,axiom,
% 5.41/5.72 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( divide6298287555418463151nteger @ A @ C )
% 5.41/5.72 = ( divide6298287555418463151nteger @ B @ C ) )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_cancel
% 5.41/5.72 thf(fact_5379_dvd__div__eq__cancel,axiom,
% 5.41/5.72 ! [A: complex,C: complex,B: complex] :
% 5.41/5.72 ( ( ( divide1717551699836669952omplex @ A @ C )
% 5.41/5.72 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.72 => ( ( dvd_dvd_complex @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_complex @ C @ B )
% 5.41/5.72 => ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_cancel
% 5.41/5.72 thf(fact_5380_dvd__div__eq__cancel,axiom,
% 5.41/5.72 ! [A: real,C: real,B: real] :
% 5.41/5.72 ( ( ( divide_divide_real @ A @ C )
% 5.41/5.72 = ( divide_divide_real @ B @ C ) )
% 5.41/5.72 => ( ( dvd_dvd_real @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_real @ C @ B )
% 5.41/5.72 => ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_cancel
% 5.41/5.72 thf(fact_5381_dvd__div__eq__cancel,axiom,
% 5.41/5.72 ! [A: rat,C: rat,B: rat] :
% 5.41/5.72 ( ( ( divide_divide_rat @ A @ C )
% 5.41/5.72 = ( divide_divide_rat @ B @ C ) )
% 5.41/5.72 => ( ( dvd_dvd_rat @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_rat @ C @ B )
% 5.41/5.72 => ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_cancel
% 5.41/5.72 thf(fact_5382_dvd__div__eq__cancel,axiom,
% 5.41/5.72 ! [A: nat,C: nat,B: nat] :
% 5.41/5.72 ( ( ( divide_divide_nat @ A @ C )
% 5.41/5.72 = ( divide_divide_nat @ B @ C ) )
% 5.41/5.72 => ( ( dvd_dvd_nat @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_cancel
% 5.41/5.72 thf(fact_5383_dvd__div__eq__cancel,axiom,
% 5.41/5.72 ! [A: int,C: int,B: int] :
% 5.41/5.72 ( ( ( divide_divide_int @ A @ C )
% 5.41/5.72 = ( divide_divide_int @ B @ C ) )
% 5.41/5.72 => ( ( dvd_dvd_int @ C @ A )
% 5.41/5.72 => ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( A = B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_cancel
% 5.41/5.72 thf(fact_5384_div__div__div__same,axiom,
% 5.41/5.72 ! [D: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ D @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ D ) @ ( divide6298287555418463151nteger @ B @ D ) )
% 5.41/5.72 = ( divide6298287555418463151nteger @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_div_div_same
% 5.41/5.72 thf(fact_5385_div__div__div__same,axiom,
% 5.41/5.72 ! [D: nat,B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ D @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.72 => ( ( divide_divide_nat @ ( divide_divide_nat @ A @ D ) @ ( divide_divide_nat @ B @ D ) )
% 5.41/5.72 = ( divide_divide_nat @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_div_div_same
% 5.41/5.72 thf(fact_5386_div__div__div__same,axiom,
% 5.41/5.72 ! [D: int,B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ D @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ( ( divide_divide_int @ ( divide_divide_int @ A @ D ) @ ( divide_divide_int @ B @ D ) )
% 5.41/5.72 = ( divide_divide_int @ A @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_div_div_same
% 5.41/5.72 thf(fact_5387_neg__numeral__neq__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( uminus_uminus_real @ ( numeral_numeral_real @ M ) )
% 5.41/5.72 != ( numeral_numeral_real @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_neq_numeral
% 5.41/5.72 thf(fact_5388_neg__numeral__neq__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( uminus_uminus_int @ ( numeral_numeral_int @ M ) )
% 5.41/5.72 != ( numeral_numeral_int @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_neq_numeral
% 5.41/5.72 thf(fact_5389_neg__numeral__neq__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) )
% 5.41/5.72 != ( numera6690914467698888265omplex @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_neq_numeral
% 5.41/5.72 thf(fact_5390_neg__numeral__neq__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) )
% 5.41/5.72 != ( numera6620942414471956472nteger @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_neq_numeral
% 5.41/5.72 thf(fact_5391_neg__numeral__neq__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) )
% 5.41/5.72 != ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_neq_numeral
% 5.41/5.72 thf(fact_5392_numeral__neq__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( numeral_numeral_real @ M )
% 5.41/5.72 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_numeral
% 5.41/5.72 thf(fact_5393_numeral__neq__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( numeral_numeral_int @ M )
% 5.41/5.72 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_numeral
% 5.41/5.72 thf(fact_5394_numeral__neq__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( numera6690914467698888265omplex @ M )
% 5.41/5.72 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_numeral
% 5.41/5.72 thf(fact_5395_numeral__neq__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( numera6620942414471956472nteger @ M )
% 5.41/5.72 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_numeral
% 5.41/5.72 thf(fact_5396_numeral__neq__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ( ( numeral_numeral_rat @ M )
% 5.41/5.72 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_numeral
% 5.41/5.72 thf(fact_5397_dvd__power__same,axiom,
% 5.41/5.72 ! [X: code_integer,Y: code_integer,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_power_same
% 5.41/5.72 thf(fact_5398_dvd__power__same,axiom,
% 5.41/5.72 ! [X: nat,Y: nat,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ X @ Y )
% 5.41/5.72 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_power_same
% 5.41/5.72 thf(fact_5399_dvd__power__same,axiom,
% 5.41/5.72 ! [X: real,Y: real,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_real @ X @ Y )
% 5.41/5.72 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_power_same
% 5.41/5.72 thf(fact_5400_dvd__power__same,axiom,
% 5.41/5.72 ! [X: int,Y: int,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_int @ X @ Y )
% 5.41/5.72 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_power_same
% 5.41/5.72 thf(fact_5401_dvd__power__same,axiom,
% 5.41/5.72 ! [X: complex,Y: complex,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_complex @ X @ Y )
% 5.41/5.72 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_power_same
% 5.41/5.72 thf(fact_5402_square__eq__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ( times_times_real @ A @ A )
% 5.41/5.72 = ( times_times_real @ B @ B ) )
% 5.41/5.72 = ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_iff
% 5.41/5.72 thf(fact_5403_square__eq__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ( times_times_int @ A @ A )
% 5.41/5.72 = ( times_times_int @ B @ B ) )
% 5.41/5.72 = ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus_uminus_int @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_iff
% 5.41/5.72 thf(fact_5404_square__eq__iff,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( ( times_times_complex @ A @ A )
% 5.41/5.72 = ( times_times_complex @ B @ B ) )
% 5.41/5.72 = ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_iff
% 5.41/5.72 thf(fact_5405_square__eq__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( times_3573771949741848930nteger @ A @ A )
% 5.41/5.72 = ( times_3573771949741848930nteger @ B @ B ) )
% 5.41/5.72 = ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus1351360451143612070nteger @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_iff
% 5.41/5.72 thf(fact_5406_square__eq__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ( times_times_rat @ A @ A )
% 5.41/5.72 = ( times_times_rat @ B @ B ) )
% 5.41/5.72 = ( ( A = B )
% 5.41/5.72 | ( A
% 5.41/5.72 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_iff
% 5.41/5.72 thf(fact_5407_minus__mult__commute,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( times_times_real @ ( uminus_uminus_real @ A ) @ B )
% 5.41/5.72 = ( times_times_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_mult_commute
% 5.41/5.72 thf(fact_5408_minus__mult__commute,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( times_times_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.72 = ( times_times_int @ A @ ( uminus_uminus_int @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_mult_commute
% 5.41/5.72 thf(fact_5409_minus__mult__commute,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ A ) @ B )
% 5.41/5.72 = ( times_times_complex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_mult_commute
% 5.41/5.72 thf(fact_5410_minus__mult__commute,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.72 = ( times_3573771949741848930nteger @ A @ ( uminus1351360451143612070nteger @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_mult_commute
% 5.41/5.72 thf(fact_5411_minus__mult__commute,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( times_times_rat @ ( uminus_uminus_rat @ A ) @ B )
% 5.41/5.72 = ( times_times_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_mult_commute
% 5.41/5.72 thf(fact_5412_group__cancel_Oneg1,axiom,
% 5.41/5.72 ! [A2: real,K: real,A: real] :
% 5.41/5.72 ( ( A2
% 5.41/5.72 = ( plus_plus_real @ K @ A ) )
% 5.41/5.72 => ( ( uminus_uminus_real @ A2 )
% 5.41/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( uminus_uminus_real @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % group_cancel.neg1
% 5.41/5.72 thf(fact_5413_group__cancel_Oneg1,axiom,
% 5.41/5.72 ! [A2: int,K: int,A: int] :
% 5.41/5.72 ( ( A2
% 5.41/5.72 = ( plus_plus_int @ K @ A ) )
% 5.41/5.72 => ( ( uminus_uminus_int @ A2 )
% 5.41/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( uminus_uminus_int @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % group_cancel.neg1
% 5.41/5.72 thf(fact_5414_group__cancel_Oneg1,axiom,
% 5.41/5.72 ! [A2: complex,K: complex,A: complex] :
% 5.41/5.72 ( ( A2
% 5.41/5.72 = ( plus_plus_complex @ K @ A ) )
% 5.41/5.72 => ( ( uminus1482373934393186551omplex @ A2 )
% 5.41/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % group_cancel.neg1
% 5.41/5.72 thf(fact_5415_group__cancel_Oneg1,axiom,
% 5.41/5.72 ! [A2: code_integer,K: code_integer,A: code_integer] :
% 5.41/5.72 ( ( A2
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ K @ A ) )
% 5.41/5.72 => ( ( uminus1351360451143612070nteger @ A2 )
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( uminus1351360451143612070nteger @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % group_cancel.neg1
% 5.41/5.72 thf(fact_5416_group__cancel_Oneg1,axiom,
% 5.41/5.72 ! [A2: rat,K: rat,A: rat] :
% 5.41/5.72 ( ( A2
% 5.41/5.72 = ( plus_plus_rat @ K @ A ) )
% 5.41/5.72 => ( ( uminus_uminus_rat @ A2 )
% 5.41/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % group_cancel.neg1
% 5.41/5.72 thf(fact_5417_add_Oinverse__distrib__swap,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.41/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_distrib_swap
% 5.41/5.72 thf(fact_5418_add_Oinverse__distrib__swap,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.41/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_distrib_swap
% 5.41/5.72 thf(fact_5419_add_Oinverse__distrib__swap,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.41/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_distrib_swap
% 5.41/5.72 thf(fact_5420_add_Oinverse__distrib__swap,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_distrib_swap
% 5.41/5.72 thf(fact_5421_add_Oinverse__distrib__swap,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_distrib_swap
% 5.41/5.72 thf(fact_5422_is__num__normalize_I8_J,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( uminus_uminus_real @ ( plus_plus_real @ A @ B ) )
% 5.41/5.72 = ( plus_plus_real @ ( uminus_uminus_real @ B ) @ ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_num_normalize(8)
% 5.41/5.72 thf(fact_5423_is__num__normalize_I8_J,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( uminus_uminus_int @ ( plus_plus_int @ A @ B ) )
% 5.41/5.72 = ( plus_plus_int @ ( uminus_uminus_int @ B ) @ ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_num_normalize(8)
% 5.41/5.72 thf(fact_5424_is__num__normalize_I8_J,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( uminus1482373934393186551omplex @ ( plus_plus_complex @ A @ B ) )
% 5.41/5.72 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ B ) @ ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_num_normalize(8)
% 5.41/5.72 thf(fact_5425_is__num__normalize_I8_J,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( uminus1351360451143612070nteger @ ( plus_p5714425477246183910nteger @ A @ B ) )
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ B ) @ ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_num_normalize(8)
% 5.41/5.72 thf(fact_5426_is__num__normalize_I8_J,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( uminus_uminus_rat @ ( plus_plus_rat @ A @ B ) )
% 5.41/5.72 = ( plus_plus_rat @ ( uminus_uminus_rat @ B ) @ ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_num_normalize(8)
% 5.41/5.72 thf(fact_5427_one__neq__neg__one,axiom,
% 5.41/5.72 ( one_one_real
% 5.41/5.72 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_one
% 5.41/5.72 thf(fact_5428_one__neq__neg__one,axiom,
% 5.41/5.72 ( one_one_int
% 5.41/5.72 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_one
% 5.41/5.72 thf(fact_5429_one__neq__neg__one,axiom,
% 5.41/5.72 ( one_one_complex
% 5.41/5.72 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_one
% 5.41/5.72 thf(fact_5430_one__neq__neg__one,axiom,
% 5.41/5.72 ( one_one_Code_integer
% 5.41/5.72 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_one
% 5.41/5.72 thf(fact_5431_one__neq__neg__one,axiom,
% 5.41/5.72 ( one_one_rat
% 5.41/5.72 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_one
% 5.41/5.72 thf(fact_5432_minus__diff__minus,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( uminus_uminus_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_minus
% 5.41/5.72 thf(fact_5433_minus__diff__minus,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ A ) @ ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_minus
% 5.41/5.72 thf(fact_5434_minus__diff__minus,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_minus
% 5.41/5.72 thf(fact_5435_minus__diff__minus,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_minus
% 5.41/5.72 thf(fact_5436_minus__diff__minus,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( uminus_uminus_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_minus
% 5.41/5.72 thf(fact_5437_minus__diff__commute,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( minus_minus_real @ ( uminus_uminus_real @ B ) @ A )
% 5.41/5.72 = ( minus_minus_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_commute
% 5.41/5.72 thf(fact_5438_minus__diff__commute,axiom,
% 5.41/5.72 ! [B: int,A: int] :
% 5.41/5.72 ( ( minus_minus_int @ ( uminus_uminus_int @ B ) @ A )
% 5.41/5.72 = ( minus_minus_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_commute
% 5.41/5.72 thf(fact_5439_minus__diff__commute,axiom,
% 5.41/5.72 ! [B: complex,A: complex] :
% 5.41/5.72 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ B ) @ A )
% 5.41/5.72 = ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_commute
% 5.41/5.72 thf(fact_5440_minus__diff__commute,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ B ) @ A )
% 5.41/5.72 = ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_commute
% 5.41/5.72 thf(fact_5441_minus__diff__commute,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( minus_minus_rat @ ( uminus_uminus_rat @ B ) @ A )
% 5.41/5.72 = ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_diff_commute
% 5.41/5.72 thf(fact_5442_minus__divide__right,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.72 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_right
% 5.41/5.72 thf(fact_5443_minus__divide__right,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.72 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_right
% 5.41/5.72 thf(fact_5444_minus__divide__right,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.72 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_right
% 5.41/5.72 thf(fact_5445_minus__divide__divide,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( divide_divide_real @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_divide
% 5.41/5.72 thf(fact_5446_minus__divide__divide,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.72 = ( divide1717551699836669952omplex @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_divide
% 5.41/5.72 thf(fact_5447_minus__divide__divide,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( divide_divide_rat @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_divide
% 5.41/5.72 thf(fact_5448_minus__divide__left,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.72 = ( divide_divide_real @ ( uminus_uminus_real @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_left
% 5.41/5.72 thf(fact_5449_minus__divide__left,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.72 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_left
% 5.41/5.72 thf(fact_5450_minus__divide__left,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.72 = ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % minus_divide_left
% 5.41/5.72 thf(fact_5451_div__minus__right,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_minus_right
% 5.41/5.72 thf(fact_5452_div__minus__right,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( divide6298287555418463151nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( divide6298287555418463151nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_minus_right
% 5.41/5.72 thf(fact_5453_gcd__nat_Oextremum,axiom,
% 5.41/5.72 ! [A: nat] : ( dvd_dvd_nat @ A @ zero_zero_nat ) ).
% 5.41/5.72
% 5.41/5.72 % gcd_nat.extremum
% 5.41/5.72 thf(fact_5454_gcd__nat_Oextremum__strict,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ~ ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.41/5.72 & ( zero_zero_nat != A ) ) ).
% 5.41/5.72
% 5.41/5.72 % gcd_nat.extremum_strict
% 5.41/5.72 thf(fact_5455_gcd__nat_Oextremum__unique,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.41/5.72 = ( A = zero_zero_nat ) ) ).
% 5.41/5.72
% 5.41/5.72 % gcd_nat.extremum_unique
% 5.41/5.72 thf(fact_5456_gcd__nat_Onot__eq__extremum,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( A != zero_zero_nat )
% 5.41/5.72 = ( ( dvd_dvd_nat @ A @ zero_zero_nat )
% 5.41/5.72 & ( A != zero_zero_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % gcd_nat.not_eq_extremum
% 5.41/5.72 thf(fact_5457_gcd__nat_Oextremum__uniqueI,axiom,
% 5.41/5.72 ! [A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ zero_zero_nat @ A )
% 5.41/5.72 => ( A = zero_zero_nat ) ) ).
% 5.41/5.72
% 5.41/5.72 % gcd_nat.extremum_uniqueI
% 5.41/5.72 thf(fact_5458_mod__mod__cancel,axiom,
% 5.41/5.72 ! [C: nat,B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( ( modulo_modulo_nat @ ( modulo_modulo_nat @ A @ B ) @ C )
% 5.41/5.72 = ( modulo_modulo_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_mod_cancel
% 5.41/5.72 thf(fact_5459_mod__mod__cancel,axiom,
% 5.41/5.72 ! [C: int,B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( ( modulo_modulo_int @ ( modulo_modulo_int @ A @ B ) @ C )
% 5.41/5.72 = ( modulo_modulo_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_mod_cancel
% 5.41/5.72 thf(fact_5460_mod__mod__cancel,axiom,
% 5.41/5.72 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( ( modulo364778990260209775nteger @ ( modulo364778990260209775nteger @ A @ B ) @ C )
% 5.41/5.72 = ( modulo364778990260209775nteger @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_mod_cancel
% 5.41/5.72 thf(fact_5461_dvd__mod,axiom,
% 5.41/5.72 ! [K: nat,M: nat,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ K @ M )
% 5.41/5.72 => ( ( dvd_dvd_nat @ K @ N )
% 5.41/5.72 => ( dvd_dvd_nat @ K @ ( modulo_modulo_nat @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod
% 5.41/5.72 thf(fact_5462_dvd__mod,axiom,
% 5.41/5.72 ! [K: int,M: int,N: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ K @ M )
% 5.41/5.72 => ( ( dvd_dvd_int @ K @ N )
% 5.41/5.72 => ( dvd_dvd_int @ K @ ( modulo_modulo_int @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod
% 5.41/5.72 thf(fact_5463_dvd__mod,axiom,
% 5.41/5.72 ! [K: code_integer,M: code_integer,N: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ K @ M )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ K @ N )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ K @ ( modulo364778990260209775nteger @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod
% 5.41/5.72 thf(fact_5464_dvd__mod__imp__dvd,axiom,
% 5.41/5.72 ! [C: nat,A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.72 => ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod_imp_dvd
% 5.41/5.72 thf(fact_5465_dvd__mod__imp__dvd,axiom,
% 5.41/5.72 ! [C: int,A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.72 => ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod_imp_dvd
% 5.41/5.72 thf(fact_5466_dvd__mod__imp__dvd,axiom,
% 5.41/5.72 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod_imp_dvd
% 5.41/5.72 thf(fact_5467_dvd__mod__iff,axiom,
% 5.41/5.72 ! [C: nat,B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ C @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.72 = ( dvd_dvd_nat @ C @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod_iff
% 5.41/5.72 thf(fact_5468_dvd__mod__iff,axiom,
% 5.41/5.72 ! [C: int,B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ C @ ( modulo_modulo_int @ A @ B ) )
% 5.41/5.72 = ( dvd_dvd_int @ C @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod_iff
% 5.41/5.72 thf(fact_5469_dvd__mod__iff,axiom,
% 5.41/5.72 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ C @ ( modulo364778990260209775nteger @ A @ B ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ C @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mod_iff
% 5.41/5.72 thf(fact_5470_mod__minus__right,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( uminus_uminus_int @ ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus_right
% 5.41/5.72 thf(fact_5471_mod__minus__right,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( modulo364778990260209775nteger @ A @ ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus_right
% 5.41/5.72 thf(fact_5472_mod__minus__cong,axiom,
% 5.41/5.72 ! [A: int,B: int,A4: int] :
% 5.41/5.72 ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.72 = ( modulo_modulo_int @ A4 @ B ) )
% 5.41/5.72 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.72 = ( modulo_modulo_int @ ( uminus_uminus_int @ A4 ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus_cong
% 5.41/5.72 thf(fact_5473_mod__minus__cong,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,A4: code_integer] :
% 5.41/5.72 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.41/5.72 = ( modulo364778990260209775nteger @ A4 @ B ) )
% 5.41/5.72 => ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B )
% 5.41/5.72 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A4 ) @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus_cong
% 5.41/5.72 thf(fact_5474_mod__minus__eq,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( modulo_modulo_int @ A @ B ) ) @ B )
% 5.41/5.72 = ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus_eq
% 5.41/5.72 thf(fact_5475_mod__minus__eq,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ B ) ) @ B )
% 5.41/5.72 = ( modulo364778990260209775nteger @ ( uminus1351360451143612070nteger @ A ) @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_minus_eq
% 5.41/5.72 thf(fact_5476_dvd__diff__nat,axiom,
% 5.41/5.72 ! [K: nat,M: nat,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ K @ M )
% 5.41/5.72 => ( ( dvd_dvd_nat @ K @ N )
% 5.41/5.72 => ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_diff_nat
% 5.41/5.72 thf(fact_5477_zdvd__zdiffD,axiom,
% 5.41/5.72 ! [K: int,M: int,N: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ K @ ( minus_minus_int @ M @ N ) )
% 5.41/5.72 => ( ( dvd_dvd_int @ K @ N )
% 5.41/5.72 => ( dvd_dvd_int @ K @ M ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zdvd_zdiffD
% 5.41/5.72 thf(fact_5478_bot__enat__def,axiom,
% 5.41/5.72 bot_bo4199563552545308370d_enat = zero_z5237406670263579293d_enat ).
% 5.41/5.72
% 5.41/5.72 % bot_enat_def
% 5.41/5.72 thf(fact_5479_even__minus,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( uminus_uminus_int @ A ) )
% 5.41/5.72 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_minus
% 5.41/5.72 thf(fact_5480_even__minus,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( uminus1351360451143612070nteger @ A ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % even_minus
% 5.41/5.72 thf(fact_5481_subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( ord_le211207098394363844omplex
% 5.41/5.72 @ ( collect_complex
% 5.41/5.72 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.41/5.72 @ ( collect_complex
% 5.41/5.72 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.41/5.72 = ( dvd_dvd_complex @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % subset_divisors_dvd
% 5.41/5.72 thf(fact_5482_subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( ord_less_eq_set_nat
% 5.41/5.72 @ ( collect_nat
% 5.41/5.72 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.41/5.72 @ ( collect_nat
% 5.41/5.72 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % subset_divisors_dvd
% 5.41/5.72 thf(fact_5483_subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le7084787975880047091nteger
% 5.41/5.72 @ ( collect_Code_integer
% 5.41/5.72 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.41/5.72 @ ( collect_Code_integer
% 5.41/5.72 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % subset_divisors_dvd
% 5.41/5.72 thf(fact_5484_subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_eq_set_int
% 5.41/5.72 @ ( collect_int
% 5.41/5.72 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.41/5.72 @ ( collect_int
% 5.41/5.72 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ B ) ) ).
% 5.41/5.72
% 5.41/5.72 % subset_divisors_dvd
% 5.41/5.72 thf(fact_5485_strict__subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( ord_less_set_complex
% 5.41/5.72 @ ( collect_complex
% 5.41/5.72 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ A ) )
% 5.41/5.72 @ ( collect_complex
% 5.41/5.72 @ ^ [C3: complex] : ( dvd_dvd_complex @ C3 @ B ) ) )
% 5.41/5.72 = ( ( dvd_dvd_complex @ A @ B )
% 5.41/5.72 & ~ ( dvd_dvd_complex @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % strict_subset_divisors_dvd
% 5.41/5.72 thf(fact_5486_strict__subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( ord_less_set_nat
% 5.41/5.72 @ ( collect_nat
% 5.41/5.72 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ A ) )
% 5.41/5.72 @ ( collect_nat
% 5.41/5.72 @ ^ [C3: nat] : ( dvd_dvd_nat @ C3 @ B ) ) )
% 5.41/5.72 = ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.72 & ~ ( dvd_dvd_nat @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % strict_subset_divisors_dvd
% 5.41/5.72 thf(fact_5487_strict__subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ord_less_set_int
% 5.41/5.72 @ ( collect_int
% 5.41/5.72 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ A ) )
% 5.41/5.72 @ ( collect_int
% 5.41/5.72 @ ^ [C3: int] : ( dvd_dvd_int @ C3 @ B ) ) )
% 5.41/5.72 = ( ( dvd_dvd_int @ A @ B )
% 5.41/5.72 & ~ ( dvd_dvd_int @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % strict_subset_divisors_dvd
% 5.41/5.72 thf(fact_5488_strict__subset__divisors__dvd,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ord_le1307284697595431911nteger
% 5.41/5.72 @ ( collect_Code_integer
% 5.41/5.72 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ A ) )
% 5.41/5.72 @ ( collect_Code_integer
% 5.41/5.72 @ ^ [C3: code_integer] : ( dvd_dvd_Code_integer @ C3 @ B ) ) )
% 5.41/5.72 = ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.72 & ~ ( dvd_dvd_Code_integer @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % strict_subset_divisors_dvd
% 5.41/5.72 thf(fact_5489_power__even__abs,axiom,
% 5.41/5.72 ! [N: nat,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs
% 5.41/5.72 thf(fact_5490_power__even__abs,axiom,
% 5.41/5.72 ! [N: nat,A: rat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_rat @ ( abs_abs_rat @ A ) @ N )
% 5.41/5.72 = ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs
% 5.41/5.72 thf(fact_5491_power__even__abs,axiom,
% 5.41/5.72 ! [N: nat,A: real] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_real @ ( abs_abs_real @ A ) @ N )
% 5.41/5.72 = ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs
% 5.41/5.72 thf(fact_5492_power__even__abs,axiom,
% 5.41/5.72 ! [N: nat,A: int] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_int @ ( abs_abs_int @ A ) @ N )
% 5.41/5.72 = ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % power_even_abs
% 5.41/5.72 thf(fact_5493_abs__ge__zero,axiom,
% 5.41/5.72 ! [A: code_integer] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_zero
% 5.41/5.72 thf(fact_5494_abs__ge__zero,axiom,
% 5.41/5.72 ! [A: real] : ( ord_less_eq_real @ zero_zero_real @ ( abs_abs_real @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_zero
% 5.41/5.72 thf(fact_5495_abs__ge__zero,axiom,
% 5.41/5.72 ! [A: rat] : ( ord_less_eq_rat @ zero_zero_rat @ ( abs_abs_rat @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_zero
% 5.41/5.72 thf(fact_5496_abs__ge__zero,axiom,
% 5.41/5.72 ! [A: int] : ( ord_less_eq_int @ zero_zero_int @ ( abs_abs_int @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_ge_zero
% 5.41/5.72 thf(fact_5497_abs__of__pos,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.72 => ( ( abs_abs_Code_integer @ A )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_pos
% 5.41/5.72 thf(fact_5498_abs__of__pos,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.72 => ( ( abs_abs_real @ A )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_pos
% 5.41/5.72 thf(fact_5499_abs__of__pos,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( ord_less_rat @ zero_zero_rat @ A )
% 5.41/5.72 => ( ( abs_abs_rat @ A )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_pos
% 5.41/5.72 thf(fact_5500_abs__of__pos,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.72 => ( ( abs_abs_int @ A )
% 5.41/5.72 = A ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_of_pos
% 5.41/5.72 thf(fact_5501_abs__not__less__zero,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ~ ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ zero_z3403309356797280102nteger ) ).
% 5.41/5.72
% 5.41/5.72 % abs_not_less_zero
% 5.41/5.72 thf(fact_5502_abs__not__less__zero,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ~ ( ord_less_real @ ( abs_abs_real @ A ) @ zero_zero_real ) ).
% 5.41/5.72
% 5.41/5.72 % abs_not_less_zero
% 5.41/5.72 thf(fact_5503_abs__not__less__zero,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ~ ( ord_less_rat @ ( abs_abs_rat @ A ) @ zero_zero_rat ) ).
% 5.41/5.72
% 5.41/5.72 % abs_not_less_zero
% 5.41/5.72 thf(fact_5504_abs__not__less__zero,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ~ ( ord_less_int @ ( abs_abs_int @ A ) @ zero_zero_int ) ).
% 5.41/5.72
% 5.41/5.72 % abs_not_less_zero
% 5.41/5.72 thf(fact_5505_uminus__power__if,axiom,
% 5.41/5.72 ! [N: nat,A: real] :
% 5.41/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.41/5.72 = ( power_power_real @ A @ N ) ) )
% 5.41/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.41/5.72 = ( uminus_uminus_real @ ( power_power_real @ A @ N ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % uminus_power_if
% 5.41/5.72 thf(fact_5506_uminus__power__if,axiom,
% 5.41/5.72 ! [N: nat,A: int] :
% 5.41/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.41/5.72 = ( power_power_int @ A @ N ) ) )
% 5.41/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.41/5.72 = ( uminus_uminus_int @ ( power_power_int @ A @ N ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % uminus_power_if
% 5.41/5.72 thf(fact_5507_uminus__power__if,axiom,
% 5.41/5.72 ! [N: nat,A: complex] :
% 5.41/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.41/5.72 = ( power_power_complex @ A @ N ) ) )
% 5.41/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.41/5.72 = ( uminus1482373934393186551omplex @ ( power_power_complex @ A @ N ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % uminus_power_if
% 5.41/5.72 thf(fact_5508_uminus__power__if,axiom,
% 5.41/5.72 ! [N: nat,A: code_integer] :
% 5.41/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.41/5.72 = ( power_8256067586552552935nteger @ A @ N ) ) )
% 5.41/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.41/5.72 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ A @ N ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % uminus_power_if
% 5.41/5.72 thf(fact_5509_uminus__power__if,axiom,
% 5.41/5.72 ! [N: nat,A: rat] :
% 5.41/5.72 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.41/5.72 = ( power_power_rat @ A @ N ) ) )
% 5.41/5.72 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.72 => ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.41/5.72 = ( uminus_uminus_rat @ ( power_power_rat @ A @ N ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % uminus_power_if
% 5.41/5.72 thf(fact_5510_abs__triangle__ineq,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( plus_p5714425477246183910nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq
% 5.41/5.72 thf(fact_5511_abs__triangle__ineq,axiom,
% 5.41/5.72 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq
% 5.41/5.72 thf(fact_5512_abs__triangle__ineq,axiom,
% 5.41/5.72 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( plus_plus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq
% 5.41/5.72 thf(fact_5513_abs__triangle__ineq,axiom,
% 5.41/5.72 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( plus_plus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq
% 5.41/5.72 thf(fact_5514_abs__mult__less,axiom,
% 5.41/5.72 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ A ) @ C )
% 5.41/5.72 => ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ B ) @ D )
% 5.41/5.72 => ( ord_le6747313008572928689nteger @ ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( times_3573771949741848930nteger @ C @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult_less
% 5.41/5.72 thf(fact_5515_abs__mult__less,axiom,
% 5.41/5.72 ! [A: real,C: real,B: real,D: real] :
% 5.41/5.72 ( ( ord_less_real @ ( abs_abs_real @ A ) @ C )
% 5.41/5.72 => ( ( ord_less_real @ ( abs_abs_real @ B ) @ D )
% 5.41/5.72 => ( ord_less_real @ ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( times_times_real @ C @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult_less
% 5.41/5.72 thf(fact_5516_abs__mult__less,axiom,
% 5.41/5.72 ! [A: rat,C: rat,B: rat,D: rat] :
% 5.41/5.72 ( ( ord_less_rat @ ( abs_abs_rat @ A ) @ C )
% 5.41/5.72 => ( ( ord_less_rat @ ( abs_abs_rat @ B ) @ D )
% 5.41/5.72 => ( ord_less_rat @ ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( times_times_rat @ C @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult_less
% 5.41/5.72 thf(fact_5517_abs__mult__less,axiom,
% 5.41/5.72 ! [A: int,C: int,B: int,D: int] :
% 5.41/5.72 ( ( ord_less_int @ ( abs_abs_int @ A ) @ C )
% 5.41/5.72 => ( ( ord_less_int @ ( abs_abs_int @ B ) @ D )
% 5.41/5.72 => ( ord_less_int @ ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( times_times_int @ C @ D ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_mult_less
% 5.41/5.72 thf(fact_5518_abs__triangle__ineq2__sym,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2_sym
% 5.41/5.72 thf(fact_5519_abs__triangle__ineq2__sym,axiom,
% 5.41/5.72 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2_sym
% 5.41/5.72 thf(fact_5520_abs__triangle__ineq2__sym,axiom,
% 5.41/5.72 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2_sym
% 5.41/5.72 thf(fact_5521_abs__triangle__ineq2__sym,axiom,
% 5.41/5.72 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2_sym
% 5.41/5.72 thf(fact_5522_abs__triangle__ineq3,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq3
% 5.41/5.72 thf(fact_5523_abs__triangle__ineq3,axiom,
% 5.41/5.72 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq3
% 5.41/5.72 thf(fact_5524_abs__triangle__ineq3,axiom,
% 5.41/5.72 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq3
% 5.41/5.72 thf(fact_5525_abs__triangle__ineq3,axiom,
% 5.41/5.72 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq3
% 5.41/5.72 thf(fact_5526_abs__triangle__ineq2,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2
% 5.41/5.72 thf(fact_5527_abs__triangle__ineq2,axiom,
% 5.41/5.72 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2
% 5.41/5.72 thf(fact_5528_abs__triangle__ineq2,axiom,
% 5.41/5.72 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2
% 5.41/5.72 thf(fact_5529_abs__triangle__ineq2,axiom,
% 5.41/5.72 ! [A: int,B: int] : ( ord_less_eq_int @ ( minus_minus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % abs_triangle_ineq2
% 5.41/5.72 thf(fact_5530_nonzero__abs__divide,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( B != zero_zero_real )
% 5.41/5.72 => ( ( abs_abs_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.72 = ( divide_divide_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_abs_divide
% 5.41/5.72 thf(fact_5531_nonzero__abs__divide,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( B != zero_zero_rat )
% 5.41/5.72 => ( ( abs_abs_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.72 = ( divide_divide_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_abs_divide
% 5.41/5.72 thf(fact_5532_not__is__unit__0,axiom,
% 5.41/5.72 ~ ( dvd_dvd_Code_integer @ zero_z3403309356797280102nteger @ one_one_Code_integer ) ).
% 5.41/5.72
% 5.41/5.72 % not_is_unit_0
% 5.41/5.72 thf(fact_5533_not__is__unit__0,axiom,
% 5.41/5.72 ~ ( dvd_dvd_nat @ zero_zero_nat @ one_one_nat ) ).
% 5.41/5.72
% 5.41/5.72 % not_is_unit_0
% 5.41/5.72 thf(fact_5534_not__is__unit__0,axiom,
% 5.41/5.72 ~ ( dvd_dvd_int @ zero_zero_int @ one_one_int ) ).
% 5.41/5.72
% 5.41/5.72 % not_is_unit_0
% 5.41/5.72 thf(fact_5535_pinf_I9_J,axiom,
% 5.41/5.72 ! [D: code_integer,S: code_integer] :
% 5.41/5.72 ? [Z5: code_integer] :
% 5.41/5.72 ! [X4: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ Z5 @ X4 )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(9)
% 5.41/5.72 thf(fact_5536_pinf_I9_J,axiom,
% 5.41/5.72 ! [D: real,S: real] :
% 5.41/5.72 ? [Z5: real] :
% 5.41/5.72 ! [X4: real] :
% 5.41/5.72 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.72 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(9)
% 5.41/5.72 thf(fact_5537_pinf_I9_J,axiom,
% 5.41/5.72 ! [D: rat,S: rat] :
% 5.41/5.72 ? [Z5: rat] :
% 5.41/5.72 ! [X4: rat] :
% 5.41/5.72 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.72 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(9)
% 5.41/5.72 thf(fact_5538_pinf_I9_J,axiom,
% 5.41/5.72 ! [D: nat,S: nat] :
% 5.41/5.72 ? [Z5: nat] :
% 5.41/5.72 ! [X4: nat] :
% 5.41/5.72 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.72 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(9)
% 5.41/5.72 thf(fact_5539_pinf_I9_J,axiom,
% 5.41/5.72 ! [D: int,S: int] :
% 5.41/5.72 ? [Z5: int] :
% 5.41/5.72 ! [X4: int] :
% 5.41/5.72 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.72 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(9)
% 5.41/5.72 thf(fact_5540_pinf_I10_J,axiom,
% 5.41/5.72 ! [D: code_integer,S: code_integer] :
% 5.41/5.72 ? [Z5: code_integer] :
% 5.41/5.72 ! [X4: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ Z5 @ X4 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(10)
% 5.41/5.72 thf(fact_5541_pinf_I10_J,axiom,
% 5.41/5.72 ! [D: real,S: real] :
% 5.41/5.72 ? [Z5: real] :
% 5.41/5.72 ! [X4: real] :
% 5.41/5.72 ( ( ord_less_real @ Z5 @ X4 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(10)
% 5.41/5.72 thf(fact_5542_pinf_I10_J,axiom,
% 5.41/5.72 ! [D: rat,S: rat] :
% 5.41/5.72 ? [Z5: rat] :
% 5.41/5.72 ! [X4: rat] :
% 5.41/5.72 ( ( ord_less_rat @ Z5 @ X4 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(10)
% 5.41/5.72 thf(fact_5543_pinf_I10_J,axiom,
% 5.41/5.72 ! [D: nat,S: nat] :
% 5.41/5.72 ? [Z5: nat] :
% 5.41/5.72 ! [X4: nat] :
% 5.41/5.72 ( ( ord_less_nat @ Z5 @ X4 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(10)
% 5.41/5.72 thf(fact_5544_pinf_I10_J,axiom,
% 5.41/5.72 ! [D: int,S: int] :
% 5.41/5.72 ? [Z5: int] :
% 5.41/5.72 ! [X4: int] :
% 5.41/5.72 ( ( ord_less_int @ Z5 @ X4 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % pinf(10)
% 5.41/5.72 thf(fact_5545_minf_I9_J,axiom,
% 5.41/5.72 ! [D: code_integer,S: code_integer] :
% 5.41/5.72 ? [Z5: code_integer] :
% 5.41/5.72 ! [X4: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ X4 @ Z5 )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(9)
% 5.41/5.72 thf(fact_5546_minf_I9_J,axiom,
% 5.41/5.72 ! [D: real,S: real] :
% 5.41/5.72 ? [Z5: real] :
% 5.41/5.72 ! [X4: real] :
% 5.41/5.72 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.72 => ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(9)
% 5.41/5.72 thf(fact_5547_minf_I9_J,axiom,
% 5.41/5.72 ! [D: rat,S: rat] :
% 5.41/5.72 ? [Z5: rat] :
% 5.41/5.72 ! [X4: rat] :
% 5.41/5.72 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.72 => ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(9)
% 5.41/5.72 thf(fact_5548_minf_I9_J,axiom,
% 5.41/5.72 ! [D: nat,S: nat] :
% 5.41/5.72 ? [Z5: nat] :
% 5.41/5.72 ! [X4: nat] :
% 5.41/5.72 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.72 => ( ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(9)
% 5.41/5.72 thf(fact_5549_minf_I9_J,axiom,
% 5.41/5.72 ! [D: int,S: int] :
% 5.41/5.72 ? [Z5: int] :
% 5.41/5.72 ! [X4: int] :
% 5.41/5.72 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.72 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) )
% 5.41/5.72 = ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(9)
% 5.41/5.72 thf(fact_5550_minf_I10_J,axiom,
% 5.41/5.72 ! [D: code_integer,S: code_integer] :
% 5.41/5.72 ? [Z5: code_integer] :
% 5.41/5.72 ! [X4: code_integer] :
% 5.41/5.72 ( ( ord_le6747313008572928689nteger @ X4 @ Z5 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(10)
% 5.41/5.72 thf(fact_5551_minf_I10_J,axiom,
% 5.41/5.72 ! [D: real,S: real] :
% 5.41/5.72 ? [Z5: real] :
% 5.41/5.72 ! [X4: real] :
% 5.41/5.72 ( ( ord_less_real @ X4 @ Z5 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(10)
% 5.41/5.72 thf(fact_5552_minf_I10_J,axiom,
% 5.41/5.72 ! [D: rat,S: rat] :
% 5.41/5.72 ? [Z5: rat] :
% 5.41/5.72 ! [X4: rat] :
% 5.41/5.72 ( ( ord_less_rat @ X4 @ Z5 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(10)
% 5.41/5.72 thf(fact_5553_minf_I10_J,axiom,
% 5.41/5.72 ! [D: nat,S: nat] :
% 5.41/5.72 ? [Z5: nat] :
% 5.41/5.72 ! [X4: nat] :
% 5.41/5.72 ( ( ord_less_nat @ X4 @ Z5 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_nat @ D @ ( plus_plus_nat @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(10)
% 5.41/5.72 thf(fact_5554_minf_I10_J,axiom,
% 5.41/5.72 ! [D: int,S: int] :
% 5.41/5.72 ? [Z5: int] :
% 5.41/5.72 ! [X4: int] :
% 5.41/5.72 ( ( ord_less_int @ X4 @ Z5 )
% 5.41/5.72 => ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) )
% 5.41/5.72 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ S ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % minf(10)
% 5.41/5.72 thf(fact_5555_dvd__div__eq__0__iff,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.41/5.72 = zero_z3403309356797280102nteger )
% 5.41/5.72 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_0_iff
% 5.41/5.72 thf(fact_5556_dvd__div__eq__0__iff,axiom,
% 5.41/5.72 ! [B: complex,A: complex] :
% 5.41/5.72 ( ( dvd_dvd_complex @ B @ A )
% 5.41/5.72 => ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.41/5.72 = zero_zero_complex )
% 5.41/5.72 = ( A = zero_zero_complex ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_0_iff
% 5.41/5.72 thf(fact_5557_dvd__div__eq__0__iff,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( dvd_dvd_real @ B @ A )
% 5.41/5.72 => ( ( ( divide_divide_real @ A @ B )
% 5.41/5.72 = zero_zero_real )
% 5.41/5.72 = ( A = zero_zero_real ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_0_iff
% 5.41/5.72 thf(fact_5558_dvd__div__eq__0__iff,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( dvd_dvd_rat @ B @ A )
% 5.41/5.72 => ( ( ( divide_divide_rat @ A @ B )
% 5.41/5.72 = zero_zero_rat )
% 5.41/5.72 = ( A = zero_zero_rat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_0_iff
% 5.41/5.72 thf(fact_5559_dvd__div__eq__0__iff,axiom,
% 5.41/5.72 ! [B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.72 => ( ( ( divide_divide_nat @ A @ B )
% 5.41/5.72 = zero_zero_nat )
% 5.41/5.72 = ( A = zero_zero_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_0_iff
% 5.41/5.72 thf(fact_5560_dvd__div__eq__0__iff,axiom,
% 5.41/5.72 ! [B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ( ( ( divide_divide_int @ A @ B )
% 5.41/5.72 = zero_zero_int )
% 5.41/5.72 = ( A = zero_zero_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_eq_0_iff
% 5.41/5.72 thf(fact_5561_is__unit__mult__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ one_one_Code_integer )
% 5.41/5.72 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.72 & ( dvd_dvd_Code_integer @ B @ one_one_Code_integer ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_unit_mult_iff
% 5.41/5.72 thf(fact_5562_is__unit__mult__iff,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ one_one_nat )
% 5.41/5.72 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.72 & ( dvd_dvd_nat @ B @ one_one_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_unit_mult_iff
% 5.41/5.72 thf(fact_5563_is__unit__mult__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ one_one_int )
% 5.41/5.72 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.72 & ( dvd_dvd_int @ B @ one_one_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % is_unit_mult_iff
% 5.41/5.72 thf(fact_5564_dvd__mult__unit__iff,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_unit_iff
% 5.41/5.72 thf(fact_5565_dvd__mult__unit__iff,axiom,
% 5.41/5.72 ! [B: nat,A: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.72 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_unit_iff
% 5.41/5.72 thf(fact_5566_dvd__mult__unit__iff,axiom,
% 5.41/5.72 ! [B: int,A: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.72 => ( ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_unit_iff
% 5.41/5.72 thf(fact_5567_mult__unit__dvd__iff,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_unit_dvd_iff
% 5.41/5.72 thf(fact_5568_mult__unit__dvd__iff,axiom,
% 5.41/5.72 ! [B: nat,A: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.72 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_unit_dvd_iff
% 5.41/5.72 thf(fact_5569_mult__unit__dvd__iff,axiom,
% 5.41/5.72 ! [B: int,A: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.72 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_unit_dvd_iff
% 5.41/5.72 thf(fact_5570_dvd__mult__unit__iff_H,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_unit_iff'
% 5.41/5.72 thf(fact_5571_dvd__mult__unit__iff_H,axiom,
% 5.41/5.72 ! [B: nat,A: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.72 => ( ( dvd_dvd_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_unit_iff'
% 5.41/5.72 thf(fact_5572_dvd__mult__unit__iff_H,axiom,
% 5.41/5.72 ! [B: int,A: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.72 => ( ( dvd_dvd_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_unit_iff'
% 5.41/5.72 thf(fact_5573_mult__unit__dvd__iff_H,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_unit_dvd_iff'
% 5.41/5.72 thf(fact_5574_mult__unit__dvd__iff_H,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.72 => ( ( dvd_dvd_nat @ ( times_times_nat @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_nat @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_unit_dvd_iff'
% 5.41/5.72 thf(fact_5575_mult__unit__dvd__iff_H,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.72 => ( ( dvd_dvd_int @ ( times_times_int @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_int @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % mult_unit_dvd_iff'
% 5.41/5.72 thf(fact_5576_unit__mult__left__cancel,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.72 => ( ( ( times_3573771949741848930nteger @ A @ B )
% 5.41/5.72 = ( times_3573771949741848930nteger @ A @ C ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_mult_left_cancel
% 5.41/5.72 thf(fact_5577_unit__mult__left__cancel,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.72 => ( ( ( times_times_nat @ A @ B )
% 5.41/5.72 = ( times_times_nat @ A @ C ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_mult_left_cancel
% 5.41/5.72 thf(fact_5578_unit__mult__left__cancel,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.72 => ( ( ( times_times_int @ A @ B )
% 5.41/5.72 = ( times_times_int @ A @ C ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_mult_left_cancel
% 5.41/5.72 thf(fact_5579_unit__mult__right__cancel,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.72 => ( ( ( times_3573771949741848930nteger @ B @ A )
% 5.41/5.72 = ( times_3573771949741848930nteger @ C @ A ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_mult_right_cancel
% 5.41/5.72 thf(fact_5580_unit__mult__right__cancel,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.72 => ( ( ( times_times_nat @ B @ A )
% 5.41/5.72 = ( times_times_nat @ C @ A ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_mult_right_cancel
% 5.41/5.72 thf(fact_5581_unit__mult__right__cancel,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.72 => ( ( ( times_times_int @ B @ A )
% 5.41/5.72 = ( times_times_int @ C @ A ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_mult_right_cancel
% 5.41/5.72 thf(fact_5582_dvd__div__mult,axiom,
% 5.41/5.72 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ B @ C ) @ A )
% 5.41/5.72 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ B @ A ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_mult
% 5.41/5.72 thf(fact_5583_dvd__div__mult,axiom,
% 5.41/5.72 ! [C: nat,B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( ( times_times_nat @ ( divide_divide_nat @ B @ C ) @ A )
% 5.41/5.72 = ( divide_divide_nat @ ( times_times_nat @ B @ A ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_mult
% 5.41/5.72 thf(fact_5584_dvd__div__mult,axiom,
% 5.41/5.72 ! [C: int,B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( ( times_times_int @ ( divide_divide_int @ B @ C ) @ A )
% 5.41/5.72 = ( divide_divide_int @ ( times_times_int @ B @ A ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_mult
% 5.41/5.72 thf(fact_5585_div__mult__swap,axiom,
% 5.41/5.72 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.41/5.72 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_mult_swap
% 5.41/5.72 thf(fact_5586_div__mult__swap,axiom,
% 5.41/5.72 ! [C: nat,B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.41/5.72 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_mult_swap
% 5.41/5.72 thf(fact_5587_div__mult__swap,axiom,
% 5.41/5.72 ! [C: int,B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.41/5.72 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_mult_swap
% 5.41/5.72 thf(fact_5588_div__div__eq__right,axiom,
% 5.41/5.72 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.41/5.72 = ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_div_eq_right
% 5.41/5.72 thf(fact_5589_div__div__eq__right,axiom,
% 5.41/5.72 ! [C: nat,B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.72 => ( ( divide_divide_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.41/5.72 = ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_div_eq_right
% 5.41/5.72 thf(fact_5590_div__div__eq__right,axiom,
% 5.41/5.72 ! [C: int,B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ( ( divide_divide_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.41/5.72 = ( times_times_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_div_eq_right
% 5.41/5.72 thf(fact_5591_dvd__div__mult2__eq,axiom,
% 5.41/5.72 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ B @ C ) @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.41/5.72 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_mult2_eq
% 5.41/5.72 thf(fact_5592_dvd__div__mult2__eq,axiom,
% 5.41/5.72 ! [B: nat,C: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( times_times_nat @ B @ C ) @ A )
% 5.41/5.72 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.41/5.72 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_mult2_eq
% 5.41/5.72 thf(fact_5593_dvd__div__mult2__eq,axiom,
% 5.41/5.72 ! [B: int,C: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( times_times_int @ B @ C ) @ A )
% 5.41/5.72 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.72 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_mult2_eq
% 5.41/5.72 thf(fact_5594_dvd__mult__imp__div,axiom,
% 5.41/5.72 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B )
% 5.41/5.72 => ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_imp_div
% 5.41/5.72 thf(fact_5595_dvd__mult__imp__div,axiom,
% 5.41/5.72 ! [A: nat,C: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B )
% 5.41/5.72 => ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_imp_div
% 5.41/5.72 thf(fact_5596_dvd__mult__imp__div,axiom,
% 5.41/5.72 ! [A: int,C: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B )
% 5.41/5.72 => ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_mult_imp_div
% 5.41/5.72 thf(fact_5597_div__mult__div__if__dvd,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer,D: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ D @ C )
% 5.41/5.72 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ ( divide6298287555418463151nteger @ C @ D ) )
% 5.41/5.72 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ ( times_3573771949741848930nteger @ B @ D ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_mult_div_if_dvd
% 5.41/5.72 thf(fact_5598_div__mult__div__if__dvd,axiom,
% 5.41/5.72 ! [B: nat,A: nat,D: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.72 => ( ( dvd_dvd_nat @ D @ C )
% 5.41/5.72 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ ( divide_divide_nat @ C @ D ) )
% 5.41/5.72 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_mult_div_if_dvd
% 5.41/5.72 thf(fact_5599_div__mult__div__if__dvd,axiom,
% 5.41/5.72 ! [B: int,A: int,D: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ( ( dvd_dvd_int @ D @ C )
% 5.41/5.72 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ ( divide_divide_int @ C @ D ) )
% 5.41/5.72 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_mult_div_if_dvd
% 5.41/5.72 thf(fact_5600_not__numeral__le__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_le_neg_numeral
% 5.41/5.72 thf(fact_5601_not__numeral__le__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_le_neg_numeral
% 5.41/5.72 thf(fact_5602_not__numeral__le__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_le_neg_numeral
% 5.41/5.72 thf(fact_5603_not__numeral__le__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_le_neg_numeral
% 5.41/5.72 thf(fact_5604_neg__numeral__le__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_numeral
% 5.41/5.72 thf(fact_5605_neg__numeral__le__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_numeral
% 5.41/5.72 thf(fact_5606_neg__numeral__le__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_numeral
% 5.41/5.72 thf(fact_5607_neg__numeral__le__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_le_numeral
% 5.41/5.72 thf(fact_5608_zero__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( zero_zero_real
% 5.41/5.72 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_numeral
% 5.41/5.72 thf(fact_5609_zero__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( zero_zero_int
% 5.41/5.72 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_numeral
% 5.41/5.72 thf(fact_5610_zero__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( zero_zero_complex
% 5.41/5.72 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_numeral
% 5.41/5.72 thf(fact_5611_zero__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( zero_z3403309356797280102nteger
% 5.41/5.72 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_numeral
% 5.41/5.72 thf(fact_5612_zero__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( zero_zero_rat
% 5.41/5.72 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_numeral
% 5.41/5.72 thf(fact_5613_div__plus__div__distrib__dvd__right,axiom,
% 5.41/5.72 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_plus_div_distrib_dvd_right
% 5.41/5.72 thf(fact_5614_div__plus__div__distrib__dvd__right,axiom,
% 5.41/5.72 ! [C: nat,B: nat,A: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.72 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_plus_div_distrib_dvd_right
% 5.41/5.72 thf(fact_5615_div__plus__div__distrib__dvd__right,axiom,
% 5.41/5.72 ! [C: int,B: int,A: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ B )
% 5.41/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.72 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_plus_div_distrib_dvd_right
% 5.41/5.72 thf(fact_5616_div__plus__div__distrib__dvd__left,axiom,
% 5.41/5.72 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ C @ A )
% 5.41/5.72 => ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ C )
% 5.41/5.72 = ( plus_p5714425477246183910nteger @ ( divide6298287555418463151nteger @ A @ C ) @ ( divide6298287555418463151nteger @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_plus_div_distrib_dvd_left
% 5.41/5.72 thf(fact_5617_div__plus__div__distrib__dvd__left,axiom,
% 5.41/5.72 ! [C: nat,A: nat,B: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ C @ A )
% 5.41/5.72 => ( ( divide_divide_nat @ ( plus_plus_nat @ A @ B ) @ C )
% 5.41/5.72 = ( plus_plus_nat @ ( divide_divide_nat @ A @ C ) @ ( divide_divide_nat @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_plus_div_distrib_dvd_left
% 5.41/5.72 thf(fact_5618_div__plus__div__distrib__dvd__left,axiom,
% 5.41/5.72 ! [C: int,A: int,B: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ C @ A )
% 5.41/5.72 => ( ( divide_divide_int @ ( plus_plus_int @ A @ B ) @ C )
% 5.41/5.72 = ( plus_plus_int @ ( divide_divide_int @ A @ C ) @ ( divide_divide_int @ B @ C ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_plus_div_distrib_dvd_left
% 5.41/5.72 thf(fact_5619_unit__div__cancel,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.72 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.41/5.72 = ( divide6298287555418463151nteger @ C @ A ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_div_cancel
% 5.41/5.72 thf(fact_5620_unit__div__cancel,axiom,
% 5.41/5.72 ! [A: nat,B: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.72 => ( ( ( divide_divide_nat @ B @ A )
% 5.41/5.72 = ( divide_divide_nat @ C @ A ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_div_cancel
% 5.41/5.72 thf(fact_5621_unit__div__cancel,axiom,
% 5.41/5.72 ! [A: int,B: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.72 => ( ( ( divide_divide_int @ B @ A )
% 5.41/5.72 = ( divide_divide_int @ C @ A ) )
% 5.41/5.72 = ( B = C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % unit_div_cancel
% 5.41/5.72 thf(fact_5622_div__unit__dvd__iff,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_unit_dvd_iff
% 5.41/5.72 thf(fact_5623_div__unit__dvd__iff,axiom,
% 5.41/5.72 ! [B: nat,A: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.72 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_unit_dvd_iff
% 5.41/5.72 thf(fact_5624_div__unit__dvd__iff,axiom,
% 5.41/5.72 ! [B: int,A: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.72 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.41/5.72 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_unit_dvd_iff
% 5.41/5.72 thf(fact_5625_dvd__div__unit__iff,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.72 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_unit_iff
% 5.41/5.72 thf(fact_5626_dvd__div__unit__iff,axiom,
% 5.41/5.72 ! [B: nat,A: nat,C: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.72 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_nat @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_unit_iff
% 5.41/5.72 thf(fact_5627_dvd__div__unit__iff,axiom,
% 5.41/5.72 ! [B: int,A: int,C: int] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.72 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ C @ B ) )
% 5.41/5.72 = ( dvd_dvd_int @ A @ C ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_div_unit_iff
% 5.41/5.72 thf(fact_5628_neg__numeral__less__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( numeral_numeral_real @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_numeral
% 5.41/5.72 thf(fact_5629_neg__numeral__less__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_numeral
% 5.41/5.72 thf(fact_5630_neg__numeral__less__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( numera6620942414471956472nteger @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_numeral
% 5.41/5.72 thf(fact_5631_neg__numeral__less__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_numeral_less_numeral
% 5.41/5.72 thf(fact_5632_not__numeral__less__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_less_neg_numeral
% 5.41/5.72 thf(fact_5633_not__numeral__less__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_less_neg_numeral
% 5.41/5.72 thf(fact_5634_not__numeral__less__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_less_neg_numeral
% 5.41/5.72 thf(fact_5635_not__numeral__less__neg__numeral,axiom,
% 5.41/5.72 ! [M: num,N: num] :
% 5.41/5.72 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % not_numeral_less_neg_numeral
% 5.41/5.72 thf(fact_5636_le__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(4)
% 5.41/5.72 thf(fact_5637_le__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(4)
% 5.41/5.72 thf(fact_5638_le__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(4)
% 5.41/5.72 thf(fact_5639_le__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(4)
% 5.41/5.72 thf(fact_5640_le__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(2)
% 5.41/5.72 thf(fact_5641_le__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(2)
% 5.41/5.72 thf(fact_5642_le__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(2)
% 5.41/5.72 thf(fact_5643_le__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.41/5.72
% 5.41/5.72 % le_minus_one_simps(2)
% 5.41/5.72 thf(fact_5644_neg__eq__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ( uminus_uminus_real @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( plus_plus_real @ A @ B )
% 5.41/5.72 = zero_zero_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_eq_iff_add_eq_0
% 5.41/5.72 thf(fact_5645_neg__eq__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ( uminus_uminus_int @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( plus_plus_int @ A @ B )
% 5.41/5.72 = zero_zero_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_eq_iff_add_eq_0
% 5.41/5.72 thf(fact_5646_neg__eq__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( ( uminus1482373934393186551omplex @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( plus_plus_complex @ A @ B )
% 5.41/5.72 = zero_zero_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_eq_iff_add_eq_0
% 5.41/5.72 thf(fact_5647_neg__eq__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( uminus1351360451143612070nteger @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.41/5.72 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_eq_iff_add_eq_0
% 5.41/5.72 thf(fact_5648_neg__eq__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ( uminus_uminus_rat @ A )
% 5.41/5.72 = B )
% 5.41/5.72 = ( ( plus_plus_rat @ A @ B )
% 5.41/5.72 = zero_zero_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % neg_eq_iff_add_eq_0
% 5.41/5.72 thf(fact_5649_eq__neg__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( ( plus_plus_real @ A @ B )
% 5.41/5.72 = zero_zero_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_neg_iff_add_eq_0
% 5.41/5.72 thf(fact_5650_eq__neg__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus_uminus_int @ B ) )
% 5.41/5.72 = ( ( plus_plus_int @ A @ B )
% 5.41/5.72 = zero_zero_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_neg_iff_add_eq_0
% 5.41/5.72 thf(fact_5651_eq__neg__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.72 = ( ( plus_plus_complex @ A @ B )
% 5.41/5.72 = zero_zero_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_neg_iff_add_eq_0
% 5.41/5.72 thf(fact_5652_eq__neg__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus1351360451143612070nteger @ B ) )
% 5.41/5.72 = ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.41/5.72 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_neg_iff_add_eq_0
% 5.41/5.72 thf(fact_5653_eq__neg__iff__add__eq__0,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( A
% 5.41/5.72 = ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( ( plus_plus_rat @ A @ B )
% 5.41/5.72 = zero_zero_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % eq_neg_iff_add_eq_0
% 5.41/5.72 thf(fact_5654_add_Oinverse__unique,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ( plus_plus_real @ A @ B )
% 5.41/5.72 = zero_zero_real )
% 5.41/5.72 => ( ( uminus_uminus_real @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_unique
% 5.41/5.72 thf(fact_5655_add_Oinverse__unique,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ( plus_plus_int @ A @ B )
% 5.41/5.72 = zero_zero_int )
% 5.41/5.72 => ( ( uminus_uminus_int @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_unique
% 5.41/5.72 thf(fact_5656_add_Oinverse__unique,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( ( plus_plus_complex @ A @ B )
% 5.41/5.72 = zero_zero_complex )
% 5.41/5.72 => ( ( uminus1482373934393186551omplex @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_unique
% 5.41/5.72 thf(fact_5657_add_Oinverse__unique,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.41/5.72 = zero_z3403309356797280102nteger )
% 5.41/5.72 => ( ( uminus1351360451143612070nteger @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_unique
% 5.41/5.72 thf(fact_5658_add_Oinverse__unique,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ( plus_plus_rat @ A @ B )
% 5.41/5.72 = zero_zero_rat )
% 5.41/5.72 => ( ( uminus_uminus_rat @ A )
% 5.41/5.72 = B ) ) ).
% 5.41/5.72
% 5.41/5.72 % add.inverse_unique
% 5.41/5.72 thf(fact_5659_ab__group__add__class_Oab__left__minus,axiom,
% 5.41/5.72 ! [A: real] :
% 5.41/5.72 ( ( plus_plus_real @ ( uminus_uminus_real @ A ) @ A )
% 5.41/5.72 = zero_zero_real ) ).
% 5.41/5.72
% 5.41/5.72 % ab_group_add_class.ab_left_minus
% 5.41/5.72 thf(fact_5660_ab__group__add__class_Oab__left__minus,axiom,
% 5.41/5.72 ! [A: int] :
% 5.41/5.72 ( ( plus_plus_int @ ( uminus_uminus_int @ A ) @ A )
% 5.41/5.72 = zero_zero_int ) ).
% 5.41/5.72
% 5.41/5.72 % ab_group_add_class.ab_left_minus
% 5.41/5.72 thf(fact_5661_ab__group__add__class_Oab__left__minus,axiom,
% 5.41/5.72 ! [A: complex] :
% 5.41/5.72 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ A )
% 5.41/5.72 = zero_zero_complex ) ).
% 5.41/5.72
% 5.41/5.72 % ab_group_add_class.ab_left_minus
% 5.41/5.72 thf(fact_5662_ab__group__add__class_Oab__left__minus,axiom,
% 5.41/5.72 ! [A: code_integer] :
% 5.41/5.72 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ A ) @ A )
% 5.41/5.72 = zero_z3403309356797280102nteger ) ).
% 5.41/5.72
% 5.41/5.72 % ab_group_add_class.ab_left_minus
% 5.41/5.72 thf(fact_5663_ab__group__add__class_Oab__left__minus,axiom,
% 5.41/5.72 ! [A: rat] :
% 5.41/5.72 ( ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ A )
% 5.41/5.72 = zero_zero_rat ) ).
% 5.41/5.72
% 5.41/5.72 % ab_group_add_class.ab_left_minus
% 5.41/5.72 thf(fact_5664_add__eq__0__iff,axiom,
% 5.41/5.72 ! [A: real,B: real] :
% 5.41/5.72 ( ( ( plus_plus_real @ A @ B )
% 5.41/5.72 = zero_zero_real )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus_uminus_real @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_eq_0_iff
% 5.41/5.72 thf(fact_5665_add__eq__0__iff,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ( plus_plus_int @ A @ B )
% 5.41/5.72 = zero_zero_int )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus_uminus_int @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_eq_0_iff
% 5.41/5.72 thf(fact_5666_add__eq__0__iff,axiom,
% 5.41/5.72 ! [A: complex,B: complex] :
% 5.41/5.72 ( ( ( plus_plus_complex @ A @ B )
% 5.41/5.72 = zero_zero_complex )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus1482373934393186551omplex @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_eq_0_iff
% 5.41/5.72 thf(fact_5667_add__eq__0__iff,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( plus_p5714425477246183910nteger @ A @ B )
% 5.41/5.72 = zero_z3403309356797280102nteger )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus1351360451143612070nteger @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_eq_0_iff
% 5.41/5.72 thf(fact_5668_add__eq__0__iff,axiom,
% 5.41/5.72 ! [A: rat,B: rat] :
% 5.41/5.72 ( ( ( plus_plus_rat @ A @ B )
% 5.41/5.72 = zero_zero_rat )
% 5.41/5.72 = ( B
% 5.41/5.72 = ( uminus_uminus_rat @ A ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % add_eq_0_iff
% 5.41/5.72 thf(fact_5669_zero__neq__neg__one,axiom,
% 5.41/5.72 ( zero_zero_real
% 5.41/5.72 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_one
% 5.41/5.72 thf(fact_5670_zero__neq__neg__one,axiom,
% 5.41/5.72 ( zero_zero_int
% 5.41/5.72 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_one
% 5.41/5.72 thf(fact_5671_zero__neq__neg__one,axiom,
% 5.41/5.72 ( zero_zero_complex
% 5.41/5.72 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_one
% 5.41/5.72 thf(fact_5672_zero__neq__neg__one,axiom,
% 5.41/5.72 ( zero_z3403309356797280102nteger
% 5.41/5.72 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_one
% 5.41/5.72 thf(fact_5673_zero__neq__neg__one,axiom,
% 5.41/5.72 ( zero_zero_rat
% 5.41/5.72 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % zero_neq_neg_one
% 5.41/5.72 thf(fact_5674_less__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(2)
% 5.41/5.72 thf(fact_5675_less__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(2)
% 5.41/5.72 thf(fact_5676_less__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(2)
% 5.41/5.72 thf(fact_5677_less__minus__one__simps_I2_J,axiom,
% 5.41/5.72 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ one_one_rat ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(2)
% 5.41/5.72 thf(fact_5678_less__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(4)
% 5.41/5.72 thf(fact_5679_less__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(4)
% 5.41/5.72 thf(fact_5680_less__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(4)
% 5.41/5.72 thf(fact_5681_less__minus__one__simps_I4_J,axiom,
% 5.41/5.72 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % less_minus_one_simps(4)
% 5.41/5.72 thf(fact_5682_numeral__times__minus__swap,axiom,
% 5.41/5.72 ! [W: num,X: real] :
% 5.41/5.72 ( ( times_times_real @ ( numeral_numeral_real @ W ) @ ( uminus_uminus_real @ X ) )
% 5.41/5.72 = ( times_times_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_times_minus_swap
% 5.41/5.72 thf(fact_5683_numeral__times__minus__swap,axiom,
% 5.41/5.72 ! [W: num,X: int] :
% 5.41/5.72 ( ( times_times_int @ ( numeral_numeral_int @ W ) @ ( uminus_uminus_int @ X ) )
% 5.41/5.72 = ( times_times_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_times_minus_swap
% 5.41/5.72 thf(fact_5684_numeral__times__minus__swap,axiom,
% 5.41/5.72 ! [W: num,X: complex] :
% 5.41/5.72 ( ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ ( uminus1482373934393186551omplex @ X ) )
% 5.41/5.72 = ( times_times_complex @ X @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_times_minus_swap
% 5.41/5.72 thf(fact_5685_numeral__times__minus__swap,axiom,
% 5.41/5.72 ! [W: num,X: code_integer] :
% 5.41/5.72 ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ W ) @ ( uminus1351360451143612070nteger @ X ) )
% 5.41/5.72 = ( times_3573771949741848930nteger @ X @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_times_minus_swap
% 5.41/5.72 thf(fact_5686_numeral__times__minus__swap,axiom,
% 5.41/5.72 ! [W: num,X: rat] :
% 5.41/5.72 ( ( times_times_rat @ ( numeral_numeral_rat @ W ) @ ( uminus_uminus_rat @ X ) )
% 5.41/5.72 = ( times_times_rat @ X @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_times_minus_swap
% 5.41/5.72 thf(fact_5687_div__power,axiom,
% 5.41/5.72 ! [B: code_integer,A: code_integer,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.72 => ( ( power_8256067586552552935nteger @ ( divide6298287555418463151nteger @ A @ B ) @ N )
% 5.41/5.72 = ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_power
% 5.41/5.72 thf(fact_5688_div__power,axiom,
% 5.41/5.72 ! [B: nat,A: nat,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.72 => ( ( power_power_nat @ ( divide_divide_nat @ A @ B ) @ N )
% 5.41/5.72 = ( divide_divide_nat @ ( power_power_nat @ A @ N ) @ ( power_power_nat @ B @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_power
% 5.41/5.72 thf(fact_5689_div__power,axiom,
% 5.41/5.72 ! [B: int,A: int,N: nat] :
% 5.41/5.72 ( ( dvd_dvd_int @ B @ A )
% 5.41/5.72 => ( ( power_power_int @ ( divide_divide_int @ A @ B ) @ N )
% 5.41/5.72 = ( divide_divide_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % div_power
% 5.41/5.72 thf(fact_5690_nonzero__minus__divide__divide,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( B != zero_zero_real )
% 5.41/5.72 => ( ( divide_divide_real @ ( uminus_uminus_real @ A ) @ ( uminus_uminus_real @ B ) )
% 5.41/5.72 = ( divide_divide_real @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_minus_divide_divide
% 5.41/5.72 thf(fact_5691_nonzero__minus__divide__divide,axiom,
% 5.41/5.72 ! [B: complex,A: complex] :
% 5.41/5.72 ( ( B != zero_zero_complex )
% 5.41/5.72 => ( ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ A ) @ ( uminus1482373934393186551omplex @ B ) )
% 5.41/5.72 = ( divide1717551699836669952omplex @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_minus_divide_divide
% 5.41/5.72 thf(fact_5692_nonzero__minus__divide__divide,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( B != zero_zero_rat )
% 5.41/5.72 => ( ( divide_divide_rat @ ( uminus_uminus_rat @ A ) @ ( uminus_uminus_rat @ B ) )
% 5.41/5.72 = ( divide_divide_rat @ A @ B ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_minus_divide_divide
% 5.41/5.72 thf(fact_5693_nonzero__minus__divide__right,axiom,
% 5.41/5.72 ! [B: real,A: real] :
% 5.41/5.72 ( ( B != zero_zero_real )
% 5.41/5.72 => ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.72 = ( divide_divide_real @ A @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_minus_divide_right
% 5.41/5.72 thf(fact_5694_nonzero__minus__divide__right,axiom,
% 5.41/5.72 ! [B: complex,A: complex] :
% 5.41/5.72 ( ( B != zero_zero_complex )
% 5.41/5.72 => ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.72 = ( divide1717551699836669952omplex @ A @ ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_minus_divide_right
% 5.41/5.72 thf(fact_5695_nonzero__minus__divide__right,axiom,
% 5.41/5.72 ! [B: rat,A: rat] :
% 5.41/5.72 ( ( B != zero_zero_rat )
% 5.41/5.72 => ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.72 = ( divide_divide_rat @ A @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % nonzero_minus_divide_right
% 5.41/5.72 thf(fact_5696_one__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( one_one_real
% 5.41/5.72 != ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_numeral
% 5.41/5.72 thf(fact_5697_one__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( one_one_int
% 5.41/5.72 != ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_numeral
% 5.41/5.72 thf(fact_5698_one__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( one_one_complex
% 5.41/5.72 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_numeral
% 5.41/5.72 thf(fact_5699_one__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( one_one_Code_integer
% 5.41/5.72 != ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_numeral
% 5.41/5.72 thf(fact_5700_one__neq__neg__numeral,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( one_one_rat
% 5.41/5.72 != ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % one_neq_neg_numeral
% 5.41/5.72 thf(fact_5701_numeral__neq__neg__one,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( numeral_numeral_real @ N )
% 5.41/5.72 != ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_one
% 5.41/5.72 thf(fact_5702_numeral__neq__neg__one,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( numeral_numeral_int @ N )
% 5.41/5.72 != ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_one
% 5.41/5.72 thf(fact_5703_numeral__neq__neg__one,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( numera6690914467698888265omplex @ N )
% 5.41/5.72 != ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_one
% 5.41/5.72 thf(fact_5704_numeral__neq__neg__one,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( numera6620942414471956472nteger @ N )
% 5.41/5.72 != ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_one
% 5.41/5.72 thf(fact_5705_numeral__neq__neg__one,axiom,
% 5.41/5.72 ! [N: num] :
% 5.41/5.72 ( ( numeral_numeral_rat @ N )
% 5.41/5.72 != ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.72
% 5.41/5.72 % numeral_neq_neg_one
% 5.41/5.72 thf(fact_5706_square__eq__1__iff,axiom,
% 5.41/5.72 ! [X: real] :
% 5.41/5.72 ( ( ( times_times_real @ X @ X )
% 5.41/5.72 = one_one_real )
% 5.41/5.72 = ( ( X = one_one_real )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_1_iff
% 5.41/5.72 thf(fact_5707_square__eq__1__iff,axiom,
% 5.41/5.72 ! [X: int] :
% 5.41/5.72 ( ( ( times_times_int @ X @ X )
% 5.41/5.72 = one_one_int )
% 5.41/5.72 = ( ( X = one_one_int )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_1_iff
% 5.41/5.72 thf(fact_5708_square__eq__1__iff,axiom,
% 5.41/5.72 ! [X: complex] :
% 5.41/5.72 ( ( ( times_times_complex @ X @ X )
% 5.41/5.72 = one_one_complex )
% 5.41/5.72 = ( ( X = one_one_complex )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_1_iff
% 5.41/5.72 thf(fact_5709_square__eq__1__iff,axiom,
% 5.41/5.72 ! [X: code_integer] :
% 5.41/5.72 ( ( ( times_3573771949741848930nteger @ X @ X )
% 5.41/5.72 = one_one_Code_integer )
% 5.41/5.72 = ( ( X = one_one_Code_integer )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_1_iff
% 5.41/5.72 thf(fact_5710_square__eq__1__iff,axiom,
% 5.41/5.72 ! [X: rat] :
% 5.41/5.72 ( ( ( times_times_rat @ X @ X )
% 5.41/5.72 = one_one_rat )
% 5.41/5.72 = ( ( X = one_one_rat )
% 5.41/5.72 | ( X
% 5.41/5.72 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % square_eq_1_iff
% 5.41/5.72 thf(fact_5711_mod__eq__0__iff__dvd,axiom,
% 5.41/5.72 ! [A: nat,B: nat] :
% 5.41/5.72 ( ( ( modulo_modulo_nat @ A @ B )
% 5.41/5.72 = zero_zero_nat )
% 5.41/5.72 = ( dvd_dvd_nat @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_eq_0_iff_dvd
% 5.41/5.72 thf(fact_5712_mod__eq__0__iff__dvd,axiom,
% 5.41/5.72 ! [A: int,B: int] :
% 5.41/5.72 ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.72 = zero_zero_int )
% 5.41/5.72 = ( dvd_dvd_int @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_eq_0_iff_dvd
% 5.41/5.72 thf(fact_5713_mod__eq__0__iff__dvd,axiom,
% 5.41/5.72 ! [A: code_integer,B: code_integer] :
% 5.41/5.72 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.41/5.72 = zero_z3403309356797280102nteger )
% 5.41/5.72 = ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.41/5.72
% 5.41/5.72 % mod_eq_0_iff_dvd
% 5.41/5.72 thf(fact_5714_dvd__eq__mod__eq__0,axiom,
% 5.41/5.72 ( dvd_dvd_nat
% 5.41/5.72 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.72 ( ( modulo_modulo_nat @ B2 @ A3 )
% 5.41/5.72 = zero_zero_nat ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_eq_mod_eq_0
% 5.41/5.72 thf(fact_5715_dvd__eq__mod__eq__0,axiom,
% 5.41/5.72 ( dvd_dvd_int
% 5.41/5.72 = ( ^ [A3: int,B2: int] :
% 5.41/5.72 ( ( modulo_modulo_int @ B2 @ A3 )
% 5.41/5.72 = zero_zero_int ) ) ) ).
% 5.41/5.72
% 5.41/5.72 % dvd_eq_mod_eq_0
% 5.41/5.72 thf(fact_5716_dvd__eq__mod__eq__0,axiom,
% 5.41/5.72 ( dvd_dvd_Code_integer
% 5.41/5.72 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.41/5.72 ( ( modulo364778990260209775nteger @ B2 @ A3 )
% 5.41/5.72 = zero_z3403309356797280102nteger ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_eq_mod_eq_0
% 5.41/5.73 thf(fact_5717_mod__0__imp__dvd,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ( ( ( modulo_modulo_nat @ A @ B )
% 5.41/5.73 = zero_zero_nat )
% 5.41/5.73 => ( dvd_dvd_nat @ B @ A ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_0_imp_dvd
% 5.41/5.73 thf(fact_5718_mod__0__imp__dvd,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 => ( dvd_dvd_int @ B @ A ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_0_imp_dvd
% 5.41/5.73 thf(fact_5719_mod__0__imp__dvd,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer] :
% 5.41/5.73 ( ( ( modulo364778990260209775nteger @ A @ B )
% 5.41/5.73 = zero_z3403309356797280102nteger )
% 5.41/5.73 => ( dvd_dvd_Code_integer @ B @ A ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_0_imp_dvd
% 5.41/5.73 thf(fact_5720_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_real
% 5.41/5.73 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.41/5.73 thf(fact_5721_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_int
% 5.41/5.73 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.41/5.73 thf(fact_5722_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_complex
% 5.41/5.73 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.41/5.73 thf(fact_5723_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_8373710615458151222nteger
% 5.41/5.73 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.41/5.73 thf(fact_5724_ab__group__add__class_Oab__diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_rat
% 5.41/5.73 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % ab_group_add_class.ab_diff_conv_add_uminus
% 5.41/5.73 thf(fact_5725_diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_real
% 5.41/5.73 = ( ^ [A3: real,B2: real] : ( plus_plus_real @ A3 @ ( uminus_uminus_real @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % diff_conv_add_uminus
% 5.41/5.73 thf(fact_5726_diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_int
% 5.41/5.73 = ( ^ [A3: int,B2: int] : ( plus_plus_int @ A3 @ ( uminus_uminus_int @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % diff_conv_add_uminus
% 5.41/5.73 thf(fact_5727_diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_complex
% 5.41/5.73 = ( ^ [A3: complex,B2: complex] : ( plus_plus_complex @ A3 @ ( uminus1482373934393186551omplex @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % diff_conv_add_uminus
% 5.41/5.73 thf(fact_5728_diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_8373710615458151222nteger
% 5.41/5.73 = ( ^ [A3: code_integer,B2: code_integer] : ( plus_p5714425477246183910nteger @ A3 @ ( uminus1351360451143612070nteger @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % diff_conv_add_uminus
% 5.41/5.73 thf(fact_5729_diff__conv__add__uminus,axiom,
% 5.41/5.73 ( minus_minus_rat
% 5.41/5.73 = ( ^ [A3: rat,B2: rat] : ( plus_plus_rat @ A3 @ ( uminus_uminus_rat @ B2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % diff_conv_add_uminus
% 5.41/5.73 thf(fact_5730_group__cancel_Osub2,axiom,
% 5.41/5.73 ! [B3: real,K: real,B: real,A: real] :
% 5.41/5.73 ( ( B3
% 5.41/5.73 = ( plus_plus_real @ K @ B ) )
% 5.41/5.73 => ( ( minus_minus_real @ A @ B3 )
% 5.41/5.73 = ( plus_plus_real @ ( uminus_uminus_real @ K ) @ ( minus_minus_real @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % group_cancel.sub2
% 5.41/5.73 thf(fact_5731_group__cancel_Osub2,axiom,
% 5.41/5.73 ! [B3: int,K: int,B: int,A: int] :
% 5.41/5.73 ( ( B3
% 5.41/5.73 = ( plus_plus_int @ K @ B ) )
% 5.41/5.73 => ( ( minus_minus_int @ A @ B3 )
% 5.41/5.73 = ( plus_plus_int @ ( uminus_uminus_int @ K ) @ ( minus_minus_int @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % group_cancel.sub2
% 5.41/5.73 thf(fact_5732_group__cancel_Osub2,axiom,
% 5.41/5.73 ! [B3: complex,K: complex,B: complex,A: complex] :
% 5.41/5.73 ( ( B3
% 5.41/5.73 = ( plus_plus_complex @ K @ B ) )
% 5.41/5.73 => ( ( minus_minus_complex @ A @ B3 )
% 5.41/5.73 = ( plus_plus_complex @ ( uminus1482373934393186551omplex @ K ) @ ( minus_minus_complex @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % group_cancel.sub2
% 5.41/5.73 thf(fact_5733_group__cancel_Osub2,axiom,
% 5.41/5.73 ! [B3: code_integer,K: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.73 ( ( B3
% 5.41/5.73 = ( plus_p5714425477246183910nteger @ K @ B ) )
% 5.41/5.73 => ( ( minus_8373710615458151222nteger @ A @ B3 )
% 5.41/5.73 = ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ K ) @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % group_cancel.sub2
% 5.41/5.73 thf(fact_5734_group__cancel_Osub2,axiom,
% 5.41/5.73 ! [B3: rat,K: rat,B: rat,A: rat] :
% 5.41/5.73 ( ( B3
% 5.41/5.73 = ( plus_plus_rat @ K @ B ) )
% 5.41/5.73 => ( ( minus_minus_rat @ A @ B3 )
% 5.41/5.73 = ( plus_plus_rat @ ( uminus_uminus_rat @ K ) @ ( minus_minus_rat @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % group_cancel.sub2
% 5.41/5.73 thf(fact_5735_le__imp__power__dvd,axiom,
% 5.41/5.73 ! [M: nat,N: nat,A: code_integer] :
% 5.41/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_imp_power_dvd
% 5.41/5.73 thf(fact_5736_le__imp__power__dvd,axiom,
% 5.41/5.73 ! [M: nat,N: nat,A: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ ( power_power_nat @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_imp_power_dvd
% 5.41/5.73 thf(fact_5737_le__imp__power__dvd,axiom,
% 5.41/5.73 ! [M: nat,N: nat,A: real] :
% 5.41/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_imp_power_dvd
% 5.41/5.73 thf(fact_5738_le__imp__power__dvd,axiom,
% 5.41/5.73 ! [M: nat,N: nat,A: int] :
% 5.41/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_imp_power_dvd
% 5.41/5.73 thf(fact_5739_le__imp__power__dvd,axiom,
% 5.41/5.73 ! [M: nat,N: nat,A: complex] :
% 5.41/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_imp_power_dvd
% 5.41/5.73 thf(fact_5740_power__le__dvd,axiom,
% 5.41/5.73 ! [A: code_integer,N: nat,B: code_integer,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ B )
% 5.41/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ M ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_dvd
% 5.41/5.73 thf(fact_5741_power__le__dvd,axiom,
% 5.41/5.73 ! [A: nat,N: nat,B: nat,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ B )
% 5.41/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_nat @ ( power_power_nat @ A @ M ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_dvd
% 5.41/5.73 thf(fact_5742_power__le__dvd,axiom,
% 5.41/5.73 ! [A: real,N: nat,B: real,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_real @ ( power_power_real @ A @ N ) @ B )
% 5.41/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_real @ ( power_power_real @ A @ M ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_dvd
% 5.41/5.73 thf(fact_5743_power__le__dvd,axiom,
% 5.41/5.73 ! [A: int,N: nat,B: int,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ B )
% 5.41/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_int @ ( power_power_int @ A @ M ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_dvd
% 5.41/5.73 thf(fact_5744_power__le__dvd,axiom,
% 5.41/5.73 ! [A: complex,N: nat,B: complex,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_complex @ ( power_power_complex @ A @ N ) @ B )
% 5.41/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( dvd_dvd_complex @ ( power_power_complex @ A @ M ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_dvd
% 5.41/5.73 thf(fact_5745_dvd__power__le,axiom,
% 5.41/5.73 ! [X: code_integer,Y: code_integer,N: nat,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ X @ Y )
% 5.41/5.73 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ N ) @ ( power_8256067586552552935nteger @ Y @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_le
% 5.41/5.73 thf(fact_5746_dvd__power__le,axiom,
% 5.41/5.73 ! [X: nat,Y: nat,N: nat,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ X @ Y )
% 5.41/5.73 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( dvd_dvd_nat @ ( power_power_nat @ X @ N ) @ ( power_power_nat @ Y @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_le
% 5.41/5.73 thf(fact_5747_dvd__power__le,axiom,
% 5.41/5.73 ! [X: real,Y: real,N: nat,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_real @ X @ Y )
% 5.41/5.73 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( dvd_dvd_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_le
% 5.41/5.73 thf(fact_5748_dvd__power__le,axiom,
% 5.41/5.73 ! [X: int,Y: int,N: nat,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_int @ X @ Y )
% 5.41/5.73 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( dvd_dvd_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_le
% 5.41/5.73 thf(fact_5749_dvd__power__le,axiom,
% 5.41/5.73 ! [X: complex,Y: complex,N: nat,M: nat] :
% 5.41/5.73 ( ( dvd_dvd_complex @ X @ Y )
% 5.41/5.73 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( dvd_dvd_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_le
% 5.41/5.73 thf(fact_5750_mod__eq__dvd__iff,axiom,
% 5.41/5.73 ! [A: int,C: int,B: int] :
% 5.41/5.73 ( ( ( modulo_modulo_int @ A @ C )
% 5.41/5.73 = ( modulo_modulo_int @ B @ C ) )
% 5.41/5.73 = ( dvd_dvd_int @ C @ ( minus_minus_int @ A @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_eq_dvd_iff
% 5.41/5.73 thf(fact_5751_mod__eq__dvd__iff,axiom,
% 5.41/5.73 ! [A: code_integer,C: code_integer,B: code_integer] :
% 5.41/5.73 ( ( ( modulo364778990260209775nteger @ A @ C )
% 5.41/5.73 = ( modulo364778990260209775nteger @ B @ C ) )
% 5.41/5.73 = ( dvd_dvd_Code_integer @ C @ ( minus_8373710615458151222nteger @ A @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_eq_dvd_iff
% 5.41/5.73 thf(fact_5752_dvd__minus__mod,axiom,
% 5.41/5.73 ! [B: nat,A: nat] : ( dvd_dvd_nat @ B @ ( minus_minus_nat @ A @ ( modulo_modulo_nat @ A @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_minus_mod
% 5.41/5.73 thf(fact_5753_dvd__minus__mod,axiom,
% 5.41/5.73 ! [B: int,A: int] : ( dvd_dvd_int @ B @ ( minus_minus_int @ A @ ( modulo_modulo_int @ A @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_minus_mod
% 5.41/5.73 thf(fact_5754_dvd__minus__mod,axiom,
% 5.41/5.73 ! [B: code_integer,A: code_integer] : ( dvd_dvd_Code_integer @ B @ ( minus_8373710615458151222nteger @ A @ ( modulo364778990260209775nteger @ A @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_minus_mod
% 5.41/5.73 thf(fact_5755_nat__dvd__not__less,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.73 => ( ( ord_less_nat @ M @ N )
% 5.41/5.73 => ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nat_dvd_not_less
% 5.41/5.73 thf(fact_5756_dvd__pos__nat,axiom,
% 5.41/5.73 ! [N: nat,M: nat] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 => ( ( dvd_dvd_nat @ M @ N )
% 5.41/5.73 => ( ord_less_nat @ zero_zero_nat @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_pos_nat
% 5.41/5.73 thf(fact_5757_sin__bound__lemma,axiom,
% 5.41/5.73 ! [X: real,Y: real,U: real,V: real] :
% 5.41/5.73 ( ( X = Y )
% 5.41/5.73 => ( ( ord_less_eq_real @ ( abs_abs_real @ U ) @ V )
% 5.41/5.73 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ X @ U ) @ Y ) ) @ V ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % sin_bound_lemma
% 5.41/5.73 thf(fact_5758_dvd__minus__self,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) )
% 5.41/5.73 = ( ( ord_less_nat @ N @ M )
% 5.41/5.73 | ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_minus_self
% 5.41/5.73 thf(fact_5759_zdvd__antisym__nonneg,axiom,
% 5.41/5.73 ! [M: int,N: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ zero_zero_int @ M )
% 5.41/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.41/5.73 => ( ( dvd_dvd_int @ M @ N )
% 5.41/5.73 => ( ( dvd_dvd_int @ N @ M )
% 5.41/5.73 => ( M = N ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_antisym_nonneg
% 5.41/5.73 thf(fact_5760_less__eq__dvd__minus,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( ( dvd_dvd_nat @ M @ N )
% 5.41/5.73 = ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_eq_dvd_minus
% 5.41/5.73 thf(fact_5761_dvd__diffD1,axiom,
% 5.41/5.73 ! [K: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.73 => ( ( dvd_dvd_nat @ K @ M )
% 5.41/5.73 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( dvd_dvd_nat @ K @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_diffD1
% 5.41/5.73 thf(fact_5762_dvd__diffD,axiom,
% 5.41/5.73 ! [K: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ K @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.73 => ( ( dvd_dvd_nat @ K @ N )
% 5.41/5.73 => ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( dvd_dvd_nat @ K @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_diffD
% 5.41/5.73 thf(fact_5763_zdvd__not__zless,axiom,
% 5.41/5.73 ! [M: int,N: int] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ M )
% 5.41/5.73 => ( ( ord_less_int @ M @ N )
% 5.41/5.73 => ~ ( dvd_dvd_int @ N @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_not_zless
% 5.41/5.73 thf(fact_5764_bezout__lemma__nat,axiom,
% 5.41/5.73 ! [D: nat,A: nat,B: nat,X: nat,Y: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ D @ A )
% 5.41/5.73 => ( ( dvd_dvd_nat @ D @ B )
% 5.41/5.73 => ( ( ( ( times_times_nat @ A @ X )
% 5.41/5.73 = ( plus_plus_nat @ ( times_times_nat @ B @ Y ) @ D ) )
% 5.41/5.73 | ( ( times_times_nat @ B @ X )
% 5.41/5.73 = ( plus_plus_nat @ ( times_times_nat @ A @ Y ) @ D ) ) )
% 5.41/5.73 => ? [X6: nat,Y5: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ D @ A )
% 5.41/5.73 & ( dvd_dvd_nat @ D @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.73 & ( ( ( times_times_nat @ A @ X6 )
% 5.41/5.73 = ( plus_plus_nat @ ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ Y5 ) @ D ) )
% 5.41/5.73 | ( ( times_times_nat @ ( plus_plus_nat @ A @ B ) @ X6 )
% 5.41/5.73 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bezout_lemma_nat
% 5.41/5.73 thf(fact_5765_bezout__add__nat,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ? [D3: nat,X6: nat,Y5: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ D3 @ A )
% 5.41/5.73 & ( dvd_dvd_nat @ D3 @ B )
% 5.41/5.73 & ( ( ( times_times_nat @ A @ X6 )
% 5.41/5.73 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) )
% 5.41/5.73 | ( ( times_times_nat @ B @ X6 )
% 5.41/5.73 = ( plus_plus_nat @ ( times_times_nat @ A @ Y5 ) @ D3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bezout_add_nat
% 5.41/5.73 thf(fact_5766_zdvd__mult__cancel,axiom,
% 5.41/5.73 ! [K: int,M: int,N: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) )
% 5.41/5.73 => ( ( K != zero_zero_int )
% 5.41/5.73 => ( dvd_dvd_int @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_mult_cancel
% 5.41/5.73 thf(fact_5767_zdvd__mono,axiom,
% 5.41/5.73 ! [K: int,M: int,T: int] :
% 5.41/5.73 ( ( K != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ M @ T )
% 5.41/5.73 = ( dvd_dvd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ T ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_mono
% 5.41/5.73 thf(fact_5768_bezout1__nat,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ? [D3: nat,X6: nat,Y5: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ D3 @ A )
% 5.41/5.73 & ( dvd_dvd_nat @ D3 @ B )
% 5.41/5.73 & ( ( ( minus_minus_nat @ ( times_times_nat @ A @ X6 ) @ ( times_times_nat @ B @ Y5 ) )
% 5.41/5.73 = D3 )
% 5.41/5.73 | ( ( minus_minus_nat @ ( times_times_nat @ B @ X6 ) @ ( times_times_nat @ A @ Y5 ) )
% 5.41/5.73 = D3 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bezout1_nat
% 5.41/5.73 thf(fact_5769_real__minus__mult__self__le,axiom,
% 5.41/5.73 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( times_times_real @ U @ U ) ) @ ( times_times_real @ X @ X ) ) ).
% 5.41/5.73
% 5.41/5.73 % real_minus_mult_self_le
% 5.41/5.73 thf(fact_5770_zdvd__period,axiom,
% 5.41/5.73 ! [A: int,D: int,X: int,T: int,C: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ A @ D )
% 5.41/5.73 => ( ( dvd_dvd_int @ A @ ( plus_plus_int @ X @ T ) )
% 5.41/5.73 = ( dvd_dvd_int @ A @ ( plus_plus_int @ ( plus_plus_int @ X @ ( times_times_int @ C @ D ) ) @ T ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_period
% 5.41/5.73 thf(fact_5771_zdvd__reduce,axiom,
% 5.41/5.73 ! [K: int,N: int,M: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ K @ ( plus_plus_int @ N @ ( times_times_int @ K @ M ) ) )
% 5.41/5.73 = ( dvd_dvd_int @ K @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_reduce
% 5.41/5.73 thf(fact_5772_power__mono__even,axiom,
% 5.41/5.73 ! [N: nat,A: code_integer,B: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) )
% 5.41/5.73 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ A @ N ) @ ( power_8256067586552552935nteger @ B @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_mono_even
% 5.41/5.73 thf(fact_5773_power__mono__even,axiom,
% 5.41/5.73 ! [N: nat,A: real,B: real] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) )
% 5.41/5.73 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_mono_even
% 5.41/5.73 thf(fact_5774_power__mono__even,axiom,
% 5.41/5.73 ! [N: nat,A: rat,B: rat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) )
% 5.41/5.73 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_mono_even
% 5.41/5.73 thf(fact_5775_power__mono__even,axiom,
% 5.41/5.73 ! [N: nat,A: int,B: int] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) )
% 5.41/5.73 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_mono_even
% 5.41/5.73 thf(fact_5776_minus__real__def,axiom,
% 5.41/5.73 ( minus_minus_real
% 5.41/5.73 = ( ^ [X3: real,Y3: real] : ( plus_plus_real @ X3 @ ( uminus_uminus_real @ Y3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_real_def
% 5.41/5.73 thf(fact_5777_minus__one__power__iff,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.41/5.73 = one_one_real ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N )
% 5.41/5.73 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_one_power_iff
% 5.41/5.73 thf(fact_5778_minus__one__power__iff,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.41/5.73 = one_one_int ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N )
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_one_power_iff
% 5.41/5.73 thf(fact_5779_minus__one__power__iff,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.41/5.73 = one_one_complex ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_one_power_iff
% 5.41/5.73 thf(fact_5780_minus__one__power__iff,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.41/5.73 = one_one_Code_integer ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N )
% 5.41/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_one_power_iff
% 5.41/5.73 thf(fact_5781_minus__one__power__iff,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.41/5.73 = one_one_rat ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N )
% 5.41/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_one_power_iff
% 5.41/5.73 thf(fact_5782_tanh__real__lt__1,axiom,
% 5.41/5.73 ! [X: real] : ( ord_less_real @ ( tanh_real @ X ) @ one_one_real ) ).
% 5.41/5.73
% 5.41/5.73 % tanh_real_lt_1
% 5.41/5.73 thf(fact_5783_dense__eq0__I,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ! [E2: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.41/5.73 => ( ord_less_eq_real @ ( abs_abs_real @ X ) @ E2 ) )
% 5.41/5.73 => ( X = zero_zero_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % dense_eq0_I
% 5.41/5.73 thf(fact_5784_dense__eq0__I,axiom,
% 5.41/5.73 ! [X: rat] :
% 5.41/5.73 ( ! [E2: rat] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ E2 )
% 5.41/5.73 => ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ E2 ) )
% 5.41/5.73 => ( X = zero_zero_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % dense_eq0_I
% 5.41/5.73 thf(fact_5785_abs__eq__mult,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer] :
% 5.41/5.73 ( ( ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ A )
% 5.41/5.73 | ( ord_le3102999989581377725nteger @ A @ zero_z3403309356797280102nteger ) )
% 5.41/5.73 & ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ B )
% 5.41/5.73 | ( ord_le3102999989581377725nteger @ B @ zero_z3403309356797280102nteger ) ) )
% 5.41/5.73 => ( ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.41/5.73 = ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_eq_mult
% 5.41/5.73 thf(fact_5786_abs__eq__mult,axiom,
% 5.41/5.73 ! [A: real,B: real] :
% 5.41/5.73 ( ( ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.73 | ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.41/5.73 & ( ( ord_less_eq_real @ zero_zero_real @ B )
% 5.41/5.73 | ( ord_less_eq_real @ B @ zero_zero_real ) ) )
% 5.41/5.73 => ( ( abs_abs_real @ ( times_times_real @ A @ B ) )
% 5.41/5.73 = ( times_times_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_eq_mult
% 5.41/5.73 thf(fact_5787_abs__eq__mult,axiom,
% 5.41/5.73 ! [A: rat,B: rat] :
% 5.41/5.73 ( ( ( ( ord_less_eq_rat @ zero_zero_rat @ A )
% 5.41/5.73 | ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.41/5.73 & ( ( ord_less_eq_rat @ zero_zero_rat @ B )
% 5.41/5.73 | ( ord_less_eq_rat @ B @ zero_zero_rat ) ) )
% 5.41/5.73 => ( ( abs_abs_rat @ ( times_times_rat @ A @ B ) )
% 5.41/5.73 = ( times_times_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_eq_mult
% 5.41/5.73 thf(fact_5788_abs__eq__mult,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ( ( ( ord_less_eq_int @ zero_zero_int @ A )
% 5.41/5.73 | ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.41/5.73 & ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.73 | ( ord_less_eq_int @ B @ zero_zero_int ) ) )
% 5.41/5.73 => ( ( abs_abs_int @ ( times_times_int @ A @ B ) )
% 5.41/5.73 = ( times_times_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_eq_mult
% 5.41/5.73 thf(fact_5789_abs__mult__pos,axiom,
% 5.41/5.73 ! [X: code_integer,Y: code_integer] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X )
% 5.41/5.73 => ( ( times_3573771949741848930nteger @ ( abs_abs_Code_integer @ Y ) @ X )
% 5.41/5.73 = ( abs_abs_Code_integer @ ( times_3573771949741848930nteger @ Y @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_mult_pos
% 5.41/5.73 thf(fact_5790_abs__mult__pos,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.73 => ( ( times_times_real @ ( abs_abs_real @ Y ) @ X )
% 5.41/5.73 = ( abs_abs_real @ ( times_times_real @ Y @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_mult_pos
% 5.41/5.73 thf(fact_5791_abs__mult__pos,axiom,
% 5.41/5.73 ! [X: rat,Y: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ zero_zero_rat @ X )
% 5.41/5.73 => ( ( times_times_rat @ ( abs_abs_rat @ Y ) @ X )
% 5.41/5.73 = ( abs_abs_rat @ ( times_times_rat @ Y @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_mult_pos
% 5.41/5.73 thf(fact_5792_abs__mult__pos,axiom,
% 5.41/5.73 ! [X: int,Y: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.73 => ( ( times_times_int @ ( abs_abs_int @ Y ) @ X )
% 5.41/5.73 = ( abs_abs_int @ ( times_times_int @ Y @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_mult_pos
% 5.41/5.73 thf(fact_5793_abs__div__pos,axiom,
% 5.41/5.73 ! [Y: real,X: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.73 => ( ( divide_divide_real @ ( abs_abs_real @ X ) @ Y )
% 5.41/5.73 = ( abs_abs_real @ ( divide_divide_real @ X @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_div_pos
% 5.41/5.73 thf(fact_5794_abs__div__pos,axiom,
% 5.41/5.73 ! [Y: rat,X: rat] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ Y )
% 5.41/5.73 => ( ( divide_divide_rat @ ( abs_abs_rat @ X ) @ Y )
% 5.41/5.73 = ( abs_abs_rat @ ( divide_divide_rat @ X @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_div_pos
% 5.41/5.73 thf(fact_5795_zero__le__power__abs,axiom,
% 5.41/5.73 ! [A: code_integer,N: nat] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( power_8256067586552552935nteger @ ( abs_abs_Code_integer @ A ) @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_power_abs
% 5.41/5.73 thf(fact_5796_zero__le__power__abs,axiom,
% 5.41/5.73 ! [A: real,N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_power_abs
% 5.41/5.73 thf(fact_5797_zero__le__power__abs,axiom,
% 5.41/5.73 ! [A: rat,N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ ( abs_abs_rat @ A ) @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_power_abs
% 5.41/5.73 thf(fact_5798_zero__le__power__abs,axiom,
% 5.41/5.73 ! [A: int,N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ ( abs_abs_int @ A ) @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_power_abs
% 5.41/5.73 thf(fact_5799_abs__triangle__ineq4,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ B ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ A ) @ ( abs_abs_Code_integer @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_triangle_ineq4
% 5.41/5.73 thf(fact_5800_abs__triangle__ineq4,axiom,
% 5.41/5.73 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( abs_abs_real @ A ) @ ( abs_abs_real @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_triangle_ineq4
% 5.41/5.73 thf(fact_5801_abs__triangle__ineq4,axiom,
% 5.41/5.73 ! [A: rat,B: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ B ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ A ) @ ( abs_abs_rat @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_triangle_ineq4
% 5.41/5.73 thf(fact_5802_abs__triangle__ineq4,axiom,
% 5.41/5.73 ! [A: int,B: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ A @ B ) ) @ ( plus_plus_int @ ( abs_abs_int @ A ) @ ( abs_abs_int @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_triangle_ineq4
% 5.41/5.73 thf(fact_5803_abs__diff__triangle__ineq,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer,C: code_integer,D: code_integer] : ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( plus_p5714425477246183910nteger @ A @ B ) @ ( plus_p5714425477246183910nteger @ C @ D ) ) ) @ ( plus_p5714425477246183910nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ A @ C ) ) @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ B @ D ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_triangle_ineq
% 5.41/5.73 thf(fact_5804_abs__diff__triangle__ineq,axiom,
% 5.41/5.73 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ ( minus_minus_real @ A @ C ) ) @ ( abs_abs_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_triangle_ineq
% 5.41/5.73 thf(fact_5805_abs__diff__triangle__ineq,axiom,
% 5.41/5.73 ! [A: rat,B: rat,C: rat,D: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( plus_plus_rat @ A @ B ) @ ( plus_plus_rat @ C @ D ) ) ) @ ( plus_plus_rat @ ( abs_abs_rat @ ( minus_minus_rat @ A @ C ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ B @ D ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_triangle_ineq
% 5.41/5.73 thf(fact_5806_abs__diff__triangle__ineq,axiom,
% 5.41/5.73 ! [A: int,B: int,C: int,D: int] : ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( plus_plus_int @ A @ B ) @ ( plus_plus_int @ C @ D ) ) ) @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ A @ C ) ) @ ( abs_abs_int @ ( minus_minus_int @ B @ D ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_triangle_ineq
% 5.41/5.73 thf(fact_5807_abs__diff__le__iff,axiom,
% 5.41/5.73 ! [X: code_integer,A: code_integer,R: code_integer] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_le3102999989581377725nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 5.41/5.73 & ( ord_le3102999989581377725nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_le_iff
% 5.41/5.73 thf(fact_5808_abs__diff__le__iff,axiom,
% 5.41/5.73 ! [X: real,A: real,R: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_less_eq_real @ ( minus_minus_real @ A @ R ) @ X )
% 5.41/5.73 & ( ord_less_eq_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_le_iff
% 5.41/5.73 thf(fact_5809_abs__diff__le__iff,axiom,
% 5.41/5.73 ! [X: rat,A: rat,R: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_less_eq_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 5.41/5.73 & ( ord_less_eq_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_le_iff
% 5.41/5.73 thf(fact_5810_abs__diff__le__iff,axiom,
% 5.41/5.73 ! [X: int,A: int,R: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_less_eq_int @ ( minus_minus_int @ A @ R ) @ X )
% 5.41/5.73 & ( ord_less_eq_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_le_iff
% 5.41/5.73 thf(fact_5811_abs__diff__less__iff,axiom,
% 5.41/5.73 ! [X: code_integer,A: code_integer,R: code_integer] :
% 5.41/5.73 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_le6747313008572928689nteger @ ( minus_8373710615458151222nteger @ A @ R ) @ X )
% 5.41/5.73 & ( ord_le6747313008572928689nteger @ X @ ( plus_p5714425477246183910nteger @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_less_iff
% 5.41/5.73 thf(fact_5812_abs__diff__less__iff,axiom,
% 5.41/5.73 ! [X: real,A: real,R: real] :
% 5.41/5.73 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_less_real @ ( minus_minus_real @ A @ R ) @ X )
% 5.41/5.73 & ( ord_less_real @ X @ ( plus_plus_real @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_less_iff
% 5.41/5.73 thf(fact_5813_abs__diff__less__iff,axiom,
% 5.41/5.73 ! [X: rat,A: rat,R: rat] :
% 5.41/5.73 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_less_rat @ ( minus_minus_rat @ A @ R ) @ X )
% 5.41/5.73 & ( ord_less_rat @ X @ ( plus_plus_rat @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_less_iff
% 5.41/5.73 thf(fact_5814_abs__diff__less__iff,axiom,
% 5.41/5.73 ! [X: int,A: int,R: int] :
% 5.41/5.73 ( ( ord_less_int @ ( abs_abs_int @ ( minus_minus_int @ X @ A ) ) @ R )
% 5.41/5.73 = ( ( ord_less_int @ ( minus_minus_int @ A @ R ) @ X )
% 5.41/5.73 & ( ord_less_int @ X @ ( plus_plus_int @ A @ R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_diff_less_iff
% 5.41/5.73 thf(fact_5815_finite__divisors__int,axiom,
% 5.41/5.73 ! [I: int] :
% 5.41/5.73 ( ( I != zero_zero_int )
% 5.41/5.73 => ( finite_finite_int
% 5.41/5.73 @ ( collect_int
% 5.41/5.73 @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ I ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % finite_divisors_int
% 5.41/5.73 thf(fact_5816_div2__even__ext__nat,axiom,
% 5.41/5.73 ! [X: nat,Y: nat] :
% 5.41/5.73 ( ( ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( divide_divide_nat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X )
% 5.41/5.73 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Y ) )
% 5.41/5.73 => ( X = Y ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div2_even_ext_nat
% 5.41/5.73 thf(fact_5817_unity__coeff__ex,axiom,
% 5.41/5.73 ! [P: code_integer > $o,L2: code_integer] :
% 5.41/5.73 ( ( ? [X3: code_integer] : ( P @ ( times_3573771949741848930nteger @ L2 @ X3 ) ) )
% 5.41/5.73 = ( ? [X3: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ L2 @ ( plus_p5714425477246183910nteger @ X3 @ zero_z3403309356797280102nteger ) )
% 5.41/5.73 & ( P @ X3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unity_coeff_ex
% 5.41/5.73 thf(fact_5818_unity__coeff__ex,axiom,
% 5.41/5.73 ! [P: complex > $o,L2: complex] :
% 5.41/5.73 ( ( ? [X3: complex] : ( P @ ( times_times_complex @ L2 @ X3 ) ) )
% 5.41/5.73 = ( ? [X3: complex] :
% 5.41/5.73 ( ( dvd_dvd_complex @ L2 @ ( plus_plus_complex @ X3 @ zero_zero_complex ) )
% 5.41/5.73 & ( P @ X3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unity_coeff_ex
% 5.41/5.73 thf(fact_5819_unity__coeff__ex,axiom,
% 5.41/5.73 ! [P: real > $o,L2: real] :
% 5.41/5.73 ( ( ? [X3: real] : ( P @ ( times_times_real @ L2 @ X3 ) ) )
% 5.41/5.73 = ( ? [X3: real] :
% 5.41/5.73 ( ( dvd_dvd_real @ L2 @ ( plus_plus_real @ X3 @ zero_zero_real ) )
% 5.41/5.73 & ( P @ X3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unity_coeff_ex
% 5.41/5.73 thf(fact_5820_unity__coeff__ex,axiom,
% 5.41/5.73 ! [P: rat > $o,L2: rat] :
% 5.41/5.73 ( ( ? [X3: rat] : ( P @ ( times_times_rat @ L2 @ X3 ) ) )
% 5.41/5.73 = ( ? [X3: rat] :
% 5.41/5.73 ( ( dvd_dvd_rat @ L2 @ ( plus_plus_rat @ X3 @ zero_zero_rat ) )
% 5.41/5.73 & ( P @ X3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unity_coeff_ex
% 5.41/5.73 thf(fact_5821_unity__coeff__ex,axiom,
% 5.41/5.73 ! [P: nat > $o,L2: nat] :
% 5.41/5.73 ( ( ? [X3: nat] : ( P @ ( times_times_nat @ L2 @ X3 ) ) )
% 5.41/5.73 = ( ? [X3: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ L2 @ ( plus_plus_nat @ X3 @ zero_zero_nat ) )
% 5.41/5.73 & ( P @ X3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unity_coeff_ex
% 5.41/5.73 thf(fact_5822_unity__coeff__ex,axiom,
% 5.41/5.73 ! [P: int > $o,L2: int] :
% 5.41/5.73 ( ( ? [X3: int] : ( P @ ( times_times_int @ L2 @ X3 ) ) )
% 5.41/5.73 = ( ? [X3: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ L2 @ ( plus_plus_int @ X3 @ zero_zero_int ) )
% 5.41/5.73 & ( P @ X3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unity_coeff_ex
% 5.41/5.73 thf(fact_5823_unit__dvdE,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.73 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.73 => ! [C2: code_integer] :
% 5.41/5.73 ( B
% 5.41/5.73 != ( times_3573771949741848930nteger @ A @ C2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_dvdE
% 5.41/5.73 thf(fact_5824_unit__dvdE,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.73 => ~ ( ( A != zero_zero_nat )
% 5.41/5.73 => ! [C2: nat] :
% 5.41/5.73 ( B
% 5.41/5.73 != ( times_times_nat @ A @ C2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_dvdE
% 5.41/5.73 thf(fact_5825_unit__dvdE,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.73 => ~ ( ( A != zero_zero_int )
% 5.41/5.73 => ! [C2: int] :
% 5.41/5.73 ( B
% 5.41/5.73 != ( times_times_int @ A @ C2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_dvdE
% 5.41/5.73 thf(fact_5826_dvd__div__eq__mult,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer,C: code_integer] :
% 5.41/5.73 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.73 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.41/5.73 = C )
% 5.41/5.73 = ( B
% 5.41/5.73 = ( times_3573771949741848930nteger @ C @ A ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_eq_mult
% 5.41/5.73 thf(fact_5827_dvd__div__eq__mult,axiom,
% 5.41/5.73 ! [A: nat,B: nat,C: nat] :
% 5.41/5.73 ( ( A != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.73 => ( ( ( divide_divide_nat @ B @ A )
% 5.41/5.73 = C )
% 5.41/5.73 = ( B
% 5.41/5.73 = ( times_times_nat @ C @ A ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_eq_mult
% 5.41/5.73 thf(fact_5828_dvd__div__eq__mult,axiom,
% 5.41/5.73 ! [A: int,B: int,C: int] :
% 5.41/5.73 ( ( A != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ A @ B )
% 5.41/5.73 => ( ( ( divide_divide_int @ B @ A )
% 5.41/5.73 = C )
% 5.41/5.73 = ( B
% 5.41/5.73 = ( times_times_int @ C @ A ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_eq_mult
% 5.41/5.73 thf(fact_5829_div__dvd__iff__mult,axiom,
% 5.41/5.73 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.73 ( ( B != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.41/5.73 = ( dvd_dvd_Code_integer @ A @ ( times_3573771949741848930nteger @ C @ B ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_dvd_iff_mult
% 5.41/5.73 thf(fact_5830_div__dvd__iff__mult,axiom,
% 5.41/5.73 ! [B: nat,A: nat,C: nat] :
% 5.41/5.73 ( ( B != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.73 => ( ( dvd_dvd_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.41/5.73 = ( dvd_dvd_nat @ A @ ( times_times_nat @ C @ B ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_dvd_iff_mult
% 5.41/5.73 thf(fact_5831_div__dvd__iff__mult,axiom,
% 5.41/5.73 ! [B: int,A: int,C: int] :
% 5.41/5.73 ( ( B != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ B @ A )
% 5.41/5.73 => ( ( dvd_dvd_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.41/5.73 = ( dvd_dvd_int @ A @ ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_dvd_iff_mult
% 5.41/5.73 thf(fact_5832_dvd__div__iff__mult,axiom,
% 5.41/5.73 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.73 ( ( C != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ C @ B )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.41/5.73 = ( dvd_dvd_Code_integer @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_iff_mult
% 5.41/5.73 thf(fact_5833_dvd__div__iff__mult,axiom,
% 5.41/5.73 ! [C: nat,B: nat,A: nat] :
% 5.41/5.73 ( ( C != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ C @ B )
% 5.41/5.73 => ( ( dvd_dvd_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.41/5.73 = ( dvd_dvd_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_iff_mult
% 5.41/5.73 thf(fact_5834_dvd__div__iff__mult,axiom,
% 5.41/5.73 ! [C: int,B: int,A: int] :
% 5.41/5.73 ( ( C != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ C @ B )
% 5.41/5.73 => ( ( dvd_dvd_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.41/5.73 = ( dvd_dvd_int @ ( times_times_int @ A @ C ) @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_iff_mult
% 5.41/5.73 thf(fact_5835_dvd__div__div__eq__mult,axiom,
% 5.41/5.73 ! [A: code_integer,C: code_integer,B: code_integer,D: code_integer] :
% 5.41/5.73 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( C != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ A @ B )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ C @ D )
% 5.41/5.73 => ( ( ( divide6298287555418463151nteger @ B @ A )
% 5.41/5.73 = ( divide6298287555418463151nteger @ D @ C ) )
% 5.41/5.73 = ( ( times_3573771949741848930nteger @ B @ C )
% 5.41/5.73 = ( times_3573771949741848930nteger @ A @ D ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_div_eq_mult
% 5.41/5.73 thf(fact_5836_dvd__div__div__eq__mult,axiom,
% 5.41/5.73 ! [A: nat,C: nat,B: nat,D: nat] :
% 5.41/5.73 ( ( A != zero_zero_nat )
% 5.41/5.73 => ( ( C != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ A @ B )
% 5.41/5.73 => ( ( dvd_dvd_nat @ C @ D )
% 5.41/5.73 => ( ( ( divide_divide_nat @ B @ A )
% 5.41/5.73 = ( divide_divide_nat @ D @ C ) )
% 5.41/5.73 = ( ( times_times_nat @ B @ C )
% 5.41/5.73 = ( times_times_nat @ A @ D ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_div_eq_mult
% 5.41/5.73 thf(fact_5837_dvd__div__div__eq__mult,axiom,
% 5.41/5.73 ! [A: int,C: int,B: int,D: int] :
% 5.41/5.73 ( ( A != zero_zero_int )
% 5.41/5.73 => ( ( C != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ A @ B )
% 5.41/5.73 => ( ( dvd_dvd_int @ C @ D )
% 5.41/5.73 => ( ( ( divide_divide_int @ B @ A )
% 5.41/5.73 = ( divide_divide_int @ D @ C ) )
% 5.41/5.73 = ( ( times_times_int @ B @ C )
% 5.41/5.73 = ( times_times_int @ A @ D ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_div_div_eq_mult
% 5.41/5.73 thf(fact_5838_unit__div__eq__0__iff,axiom,
% 5.41/5.73 ! [B: code_integer,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.41/5.73 = zero_z3403309356797280102nteger )
% 5.41/5.73 = ( A = zero_z3403309356797280102nteger ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_eq_0_iff
% 5.41/5.73 thf(fact_5839_unit__div__eq__0__iff,axiom,
% 5.41/5.73 ! [B: nat,A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( ( divide_divide_nat @ A @ B )
% 5.41/5.73 = zero_zero_nat )
% 5.41/5.73 = ( A = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_eq_0_iff
% 5.41/5.73 thf(fact_5840_unit__div__eq__0__iff,axiom,
% 5.41/5.73 ! [B: int,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( ( divide_divide_int @ A @ B )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 = ( A = zero_zero_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_eq_0_iff
% 5.41/5.73 thf(fact_5841_even__numeral,axiom,
% 5.41/5.73 ! [N: num] : ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_numeral
% 5.41/5.73 thf(fact_5842_even__numeral,axiom,
% 5.41/5.73 ! [N: num] : ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_numeral
% 5.41/5.73 thf(fact_5843_even__numeral,axiom,
% 5.41/5.73 ! [N: num] : ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_numeral
% 5.41/5.73 thf(fact_5844_inf__period_I3_J,axiom,
% 5.41/5.73 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.41/5.73 => ! [X4: code_integer,K4: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) )
% 5.41/5.73 = ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(3)
% 5.41/5.73 thf(fact_5845_inf__period_I3_J,axiom,
% 5.41/5.73 ! [D: real,D4: real,T: real] :
% 5.41/5.73 ( ( dvd_dvd_real @ D @ D4 )
% 5.41/5.73 => ! [X4: real,K4: real] :
% 5.41/5.73 ( ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) )
% 5.41/5.73 = ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(3)
% 5.41/5.73 thf(fact_5846_inf__period_I3_J,axiom,
% 5.41/5.73 ! [D: rat,D4: rat,T: rat] :
% 5.41/5.73 ( ( dvd_dvd_rat @ D @ D4 )
% 5.41/5.73 => ! [X4: rat,K4: rat] :
% 5.41/5.73 ( ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) )
% 5.41/5.73 = ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(3)
% 5.41/5.73 thf(fact_5847_inf__period_I3_J,axiom,
% 5.41/5.73 ! [D: int,D4: int,T: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ D @ D4 )
% 5.41/5.73 => ! [X4: int,K4: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.41/5.73 = ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(3)
% 5.41/5.73 thf(fact_5848_inf__period_I4_J,axiom,
% 5.41/5.73 ! [D: code_integer,D4: code_integer,T: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ D @ D4 )
% 5.41/5.73 => ! [X4: code_integer,K4: code_integer] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ X4 @ T ) ) )
% 5.41/5.73 = ( ~ ( dvd_dvd_Code_integer @ D @ ( plus_p5714425477246183910nteger @ ( minus_8373710615458151222nteger @ X4 @ ( times_3573771949741848930nteger @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(4)
% 5.41/5.73 thf(fact_5849_inf__period_I4_J,axiom,
% 5.41/5.73 ! [D: real,D4: real,T: real] :
% 5.41/5.73 ( ( dvd_dvd_real @ D @ D4 )
% 5.41/5.73 => ! [X4: real,K4: real] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ X4 @ T ) ) )
% 5.41/5.73 = ( ~ ( dvd_dvd_real @ D @ ( plus_plus_real @ ( minus_minus_real @ X4 @ ( times_times_real @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(4)
% 5.41/5.73 thf(fact_5850_inf__period_I4_J,axiom,
% 5.41/5.73 ! [D: rat,D4: rat,T: rat] :
% 5.41/5.73 ( ( dvd_dvd_rat @ D @ D4 )
% 5.41/5.73 => ! [X4: rat,K4: rat] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ X4 @ T ) ) )
% 5.41/5.73 = ( ~ ( dvd_dvd_rat @ D @ ( plus_plus_rat @ ( minus_minus_rat @ X4 @ ( times_times_rat @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(4)
% 5.41/5.73 thf(fact_5851_inf__period_I4_J,axiom,
% 5.41/5.73 ! [D: int,D4: int,T: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ D @ D4 )
% 5.41/5.73 => ! [X4: int,K4: int] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) ) )
% 5.41/5.73 = ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ ( times_times_int @ K4 @ D4 ) ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % inf_period(4)
% 5.41/5.73 thf(fact_5852_not__zero__le__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_le_neg_numeral
% 5.41/5.73 thf(fact_5853_not__zero__le__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_le_neg_numeral
% 5.41/5.73 thf(fact_5854_not__zero__le__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_le_neg_numeral
% 5.41/5.73 thf(fact_5855_not__zero__le__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_le_neg_numeral
% 5.41/5.73 thf(fact_5856_neg__numeral__le__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_zero
% 5.41/5.73 thf(fact_5857_neg__numeral__le__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_zero
% 5.41/5.73 thf(fact_5858_neg__numeral__le__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_zero
% 5.41/5.73 thf(fact_5859_neg__numeral__le__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_zero
% 5.41/5.73 thf(fact_5860_unit__eq__div1,axiom,
% 5.41/5.73 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( ( divide6298287555418463151nteger @ A @ B )
% 5.41/5.73 = C )
% 5.41/5.73 = ( A
% 5.41/5.73 = ( times_3573771949741848930nteger @ C @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_eq_div1
% 5.41/5.73 thf(fact_5861_unit__eq__div1,axiom,
% 5.41/5.73 ! [B: nat,A: nat,C: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( ( divide_divide_nat @ A @ B )
% 5.41/5.73 = C )
% 5.41/5.73 = ( A
% 5.41/5.73 = ( times_times_nat @ C @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_eq_div1
% 5.41/5.73 thf(fact_5862_unit__eq__div1,axiom,
% 5.41/5.73 ! [B: int,A: int,C: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( ( divide_divide_int @ A @ B )
% 5.41/5.73 = C )
% 5.41/5.73 = ( A
% 5.41/5.73 = ( times_times_int @ C @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_eq_div1
% 5.41/5.73 thf(fact_5863_unit__eq__div2,axiom,
% 5.41/5.73 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( A
% 5.41/5.73 = ( divide6298287555418463151nteger @ C @ B ) )
% 5.41/5.73 = ( ( times_3573771949741848930nteger @ A @ B )
% 5.41/5.73 = C ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_eq_div2
% 5.41/5.73 thf(fact_5864_unit__eq__div2,axiom,
% 5.41/5.73 ! [B: nat,A: nat,C: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( A
% 5.41/5.73 = ( divide_divide_nat @ C @ B ) )
% 5.41/5.73 = ( ( times_times_nat @ A @ B )
% 5.41/5.73 = C ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_eq_div2
% 5.41/5.73 thf(fact_5865_unit__eq__div2,axiom,
% 5.41/5.73 ! [B: int,A: int,C: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( A
% 5.41/5.73 = ( divide_divide_int @ C @ B ) )
% 5.41/5.73 = ( ( times_times_int @ A @ B )
% 5.41/5.73 = C ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_eq_div2
% 5.41/5.73 thf(fact_5866_div__mult__unit2,axiom,
% 5.41/5.73 ! [C: code_integer,B: code_integer,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ B @ A )
% 5.41/5.73 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.41/5.73 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_mult_unit2
% 5.41/5.73 thf(fact_5867_div__mult__unit2,axiom,
% 5.41/5.73 ! [C: nat,B: nat,A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ B @ A )
% 5.41/5.73 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.41/5.73 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_mult_unit2
% 5.41/5.73 thf(fact_5868_div__mult__unit2,axiom,
% 5.41/5.73 ! [C: int,B: int,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ B @ A )
% 5.41/5.73 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.73 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_mult_unit2
% 5.41/5.73 thf(fact_5869_unit__div__commute,axiom,
% 5.41/5.73 ! [B: code_integer,A: code_integer,C: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( times_3573771949741848930nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C )
% 5.41/5.73 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ C ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_commute
% 5.41/5.73 thf(fact_5870_unit__div__commute,axiom,
% 5.41/5.73 ! [B: nat,A: nat,C: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( times_times_nat @ ( divide_divide_nat @ A @ B ) @ C )
% 5.41/5.73 = ( divide_divide_nat @ ( times_times_nat @ A @ C ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_commute
% 5.41/5.73 thf(fact_5871_unit__div__commute,axiom,
% 5.41/5.73 ! [B: int,A: int,C: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( times_times_int @ ( divide_divide_int @ A @ B ) @ C )
% 5.41/5.73 = ( divide_divide_int @ ( times_times_int @ A @ C ) @ B ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_commute
% 5.41/5.73 thf(fact_5872_unit__div__mult__swap,axiom,
% 5.41/5.73 ! [C: code_integer,A: code_integer,B: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.41/5.73 => ( ( times_3573771949741848930nteger @ A @ ( divide6298287555418463151nteger @ B @ C ) )
% 5.41/5.73 = ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ B ) @ C ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_mult_swap
% 5.41/5.73 thf(fact_5873_unit__div__mult__swap,axiom,
% 5.41/5.73 ! [C: nat,A: nat,B: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.41/5.73 => ( ( times_times_nat @ A @ ( divide_divide_nat @ B @ C ) )
% 5.41/5.73 = ( divide_divide_nat @ ( times_times_nat @ A @ B ) @ C ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_mult_swap
% 5.41/5.73 thf(fact_5874_unit__div__mult__swap,axiom,
% 5.41/5.73 ! [C: int,A: int,B: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ C @ one_one_int )
% 5.41/5.73 => ( ( times_times_int @ A @ ( divide_divide_int @ B @ C ) )
% 5.41/5.73 = ( divide_divide_int @ ( times_times_int @ A @ B ) @ C ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_div_mult_swap
% 5.41/5.73 thf(fact_5875_is__unit__div__mult2__eq,axiom,
% 5.41/5.73 ! [B: code_integer,C: code_integer,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ C @ one_one_Code_integer )
% 5.41/5.73 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ C ) )
% 5.41/5.73 = ( divide6298287555418463151nteger @ ( divide6298287555418463151nteger @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult2_eq
% 5.41/5.73 thf(fact_5876_is__unit__div__mult2__eq,axiom,
% 5.41/5.73 ! [B: nat,C: nat,A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ C @ one_one_nat )
% 5.41/5.73 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ C ) )
% 5.41/5.73 = ( divide_divide_nat @ ( divide_divide_nat @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult2_eq
% 5.41/5.73 thf(fact_5877_is__unit__div__mult2__eq,axiom,
% 5.41/5.73 ! [B: int,C: int,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ C @ one_one_int )
% 5.41/5.73 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ C ) )
% 5.41/5.73 = ( divide_divide_int @ ( divide_divide_int @ A @ B ) @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult2_eq
% 5.41/5.73 thf(fact_5878_neg__numeral__less__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) @ zero_zero_real ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_zero
% 5.41/5.73 thf(fact_5879_neg__numeral__less__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ zero_zero_int ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_zero
% 5.41/5.73 thf(fact_5880_neg__numeral__less__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) @ zero_z3403309356797280102nteger ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_zero
% 5.41/5.73 thf(fact_5881_neg__numeral__less__zero,axiom,
% 5.41/5.73 ! [N: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) @ zero_zero_rat ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_zero
% 5.41/5.73 thf(fact_5882_not__zero__less__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_less_neg_numeral
% 5.41/5.73 thf(fact_5883_not__zero__less__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_less_neg_numeral
% 5.41/5.73 thf(fact_5884_not__zero__less__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_less_neg_numeral
% 5.41/5.73 thf(fact_5885_not__zero__less__neg__numeral,axiom,
% 5.41/5.73 ! [N: num] :
% 5.41/5.73 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_zero_less_neg_numeral
% 5.41/5.73 thf(fact_5886_le__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(1)
% 5.41/5.73 thf(fact_5887_le__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(1)
% 5.41/5.73 thf(fact_5888_le__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(1)
% 5.41/5.73 thf(fact_5889_le__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(1)
% 5.41/5.73 thf(fact_5890_le__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(3)
% 5.41/5.73 thf(fact_5891_le__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(3)
% 5.41/5.73 thf(fact_5892_le__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(3)
% 5.41/5.73 thf(fact_5893_le__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_minus_one_simps(3)
% 5.41/5.73 thf(fact_5894_less__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(3)
% 5.41/5.73 thf(fact_5895_less__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(3)
% 5.41/5.73 thf(fact_5896_less__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(3)
% 5.41/5.73 thf(fact_5897_less__minus__one__simps_I3_J,axiom,
% 5.41/5.73 ~ ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(3)
% 5.41/5.73 thf(fact_5898_less__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ zero_zero_real ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(1)
% 5.41/5.73 thf(fact_5899_less__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ zero_zero_int ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(1)
% 5.41/5.73 thf(fact_5900_less__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ zero_z3403309356797280102nteger ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(1)
% 5.41/5.73 thf(fact_5901_less__minus__one__simps_I1_J,axiom,
% 5.41/5.73 ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ zero_zero_rat ).
% 5.41/5.73
% 5.41/5.73 % less_minus_one_simps(1)
% 5.41/5.73 thf(fact_5902_not__one__le__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_eq_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_le_neg_numeral
% 5.41/5.73 thf(fact_5903_not__one__le__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_le3102999989581377725nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_le_neg_numeral
% 5.41/5.73 thf(fact_5904_not__one__le__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_eq_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_le_neg_numeral
% 5.41/5.73 thf(fact_5905_not__one__le__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_eq_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_le_neg_numeral
% 5.41/5.73 thf(fact_5906_not__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_eq_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_le_neg_one
% 5.41/5.73 thf(fact_5907_not__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_le_neg_one
% 5.41/5.73 thf(fact_5908_not__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_eq_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_le_neg_one
% 5.41/5.73 thf(fact_5909_not__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_le_neg_one
% 5.41/5.73 thf(fact_5910_neg__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_neg_one
% 5.41/5.73 thf(fact_5911_neg__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_neg_one
% 5.41/5.73 thf(fact_5912_neg__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_neg_one
% 5.41/5.73 thf(fact_5913_neg__numeral__le__neg__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_neg_one
% 5.41/5.73 thf(fact_5914_neg__one__le__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_le_numeral
% 5.41/5.73 thf(fact_5915_neg__one__le__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_le_numeral
% 5.41/5.73 thf(fact_5916_neg__one__le__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_le_numeral
% 5.41/5.73 thf(fact_5917_neg__one__le__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_le_numeral
% 5.41/5.73 thf(fact_5918_neg__numeral__le__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_one
% 5.41/5.73 thf(fact_5919_neg__numeral__le__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_one
% 5.41/5.73 thf(fact_5920_neg__numeral__le__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_one
% 5.41/5.73 thf(fact_5921_neg__numeral__le__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_le_one
% 5.41/5.73 thf(fact_5922_neg__numeral__less__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ one_one_real ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_one
% 5.41/5.73 thf(fact_5923_neg__numeral__less__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_one
% 5.41/5.73 thf(fact_5924_neg__numeral__less__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ one_one_Code_integer ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_one
% 5.41/5.73 thf(fact_5925_neg__numeral__less__one,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ one_one_rat ) ).
% 5.41/5.73
% 5.41/5.73 % neg_numeral_less_one
% 5.41/5.73 thf(fact_5926_neg__one__less__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_less_numeral
% 5.41/5.73 thf(fact_5927_neg__one__less__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_less_numeral
% 5.41/5.73 thf(fact_5928_neg__one__less__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_less_numeral
% 5.41/5.73 thf(fact_5929_neg__one__less__numeral,axiom,
% 5.41/5.73 ! [M: num] : ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ M ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_less_numeral
% 5.41/5.73 thf(fact_5930_not__numeral__less__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_less_neg_one
% 5.41/5.73 thf(fact_5931_not__numeral__less__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_less_neg_one
% 5.41/5.73 thf(fact_5932_not__numeral__less__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_le6747313008572928689nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_less_neg_one
% 5.41/5.73 thf(fact_5933_not__numeral__less__neg__one,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_numeral_less_neg_one
% 5.41/5.73 thf(fact_5934_not__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_real @ one_one_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_less_neg_numeral
% 5.41/5.73 thf(fact_5935_not__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_less_neg_numeral
% 5.41/5.73 thf(fact_5936_not__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_le6747313008572928689nteger @ one_one_Code_integer @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_less_neg_numeral
% 5.41/5.73 thf(fact_5937_not__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_rat @ one_one_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_one_less_neg_numeral
% 5.41/5.73 thf(fact_5938_not__neg__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_neg_one_less_neg_numeral
% 5.41/5.73 thf(fact_5939_not__neg__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_neg_one_less_neg_numeral
% 5.41/5.73 thf(fact_5940_not__neg__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_le6747313008572928689nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_neg_one_less_neg_numeral
% 5.41/5.73 thf(fact_5941_not__neg__one__less__neg__numeral,axiom,
% 5.41/5.73 ! [M: num] :
% 5.41/5.73 ~ ( ord_less_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % not_neg_one_less_neg_numeral
% 5.41/5.73 thf(fact_5942_is__unit__power__iff,axiom,
% 5.41/5.73 ! [A: code_integer,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ A @ N ) @ one_one_Code_integer )
% 5.41/5.73 = ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.73 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_power_iff
% 5.41/5.73 thf(fact_5943_is__unit__power__iff,axiom,
% 5.41/5.73 ! [A: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( power_power_nat @ A @ N ) @ one_one_nat )
% 5.41/5.73 = ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.73 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_power_iff
% 5.41/5.73 thf(fact_5944_is__unit__power__iff,axiom,
% 5.41/5.73 ! [A: int,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( power_power_int @ A @ N ) @ one_one_int )
% 5.41/5.73 = ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.73 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_power_iff
% 5.41/5.73 thf(fact_5945_unit__imp__mod__eq__0,axiom,
% 5.41/5.73 ! [B: nat,A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( modulo_modulo_nat @ A @ B )
% 5.41/5.73 = zero_zero_nat ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_imp_mod_eq_0
% 5.41/5.73 thf(fact_5946_unit__imp__mod__eq__0,axiom,
% 5.41/5.73 ! [B: int,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 = zero_zero_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_imp_mod_eq_0
% 5.41/5.73 thf(fact_5947_unit__imp__mod__eq__0,axiom,
% 5.41/5.73 ! [B: code_integer,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( modulo364778990260209775nteger @ A @ B )
% 5.41/5.73 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.73
% 5.41/5.73 % unit_imp_mod_eq_0
% 5.41/5.73 thf(fact_5948_eq__minus__divide__eq,axiom,
% 5.41/5.73 ! [A: real,B: real,C: real] :
% 5.41/5.73 ( ( A
% 5.41/5.73 = ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.41/5.73 = ( ( ( C != zero_zero_real )
% 5.41/5.73 => ( ( times_times_real @ A @ C )
% 5.41/5.73 = ( uminus_uminus_real @ B ) ) )
% 5.41/5.73 & ( ( C = zero_zero_real )
% 5.41/5.73 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % eq_minus_divide_eq
% 5.41/5.73 thf(fact_5949_eq__minus__divide__eq,axiom,
% 5.41/5.73 ! [A: complex,B: complex,C: complex] :
% 5.41/5.73 ( ( A
% 5.41/5.73 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) ) )
% 5.41/5.73 = ( ( ( C != zero_zero_complex )
% 5.41/5.73 => ( ( times_times_complex @ A @ C )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.41/5.73 & ( ( C = zero_zero_complex )
% 5.41/5.73 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % eq_minus_divide_eq
% 5.41/5.73 thf(fact_5950_eq__minus__divide__eq,axiom,
% 5.41/5.73 ! [A: rat,B: rat,C: rat] :
% 5.41/5.73 ( ( A
% 5.41/5.73 = ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.41/5.73 = ( ( ( C != zero_zero_rat )
% 5.41/5.73 => ( ( times_times_rat @ A @ C )
% 5.41/5.73 = ( uminus_uminus_rat @ B ) ) )
% 5.41/5.73 & ( ( C = zero_zero_rat )
% 5.41/5.73 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % eq_minus_divide_eq
% 5.41/5.73 thf(fact_5951_minus__divide__eq__eq,axiom,
% 5.41/5.73 ! [B: real,C: real,A: real] :
% 5.41/5.73 ( ( ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) )
% 5.41/5.73 = A )
% 5.41/5.73 = ( ( ( C != zero_zero_real )
% 5.41/5.73 => ( ( uminus_uminus_real @ B )
% 5.41/5.73 = ( times_times_real @ A @ C ) ) )
% 5.41/5.73 & ( ( C = zero_zero_real )
% 5.41/5.73 => ( A = zero_zero_real ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_eq_eq
% 5.41/5.73 thf(fact_5952_minus__divide__eq__eq,axiom,
% 5.41/5.73 ! [B: complex,C: complex,A: complex] :
% 5.41/5.73 ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.73 = A )
% 5.41/5.73 = ( ( ( C != zero_zero_complex )
% 5.41/5.73 => ( ( uminus1482373934393186551omplex @ B )
% 5.41/5.73 = ( times_times_complex @ A @ C ) ) )
% 5.41/5.73 & ( ( C = zero_zero_complex )
% 5.41/5.73 => ( A = zero_zero_complex ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_eq_eq
% 5.41/5.73 thf(fact_5953_minus__divide__eq__eq,axiom,
% 5.41/5.73 ! [B: rat,C: rat,A: rat] :
% 5.41/5.73 ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.73 = A )
% 5.41/5.73 = ( ( ( C != zero_zero_rat )
% 5.41/5.73 => ( ( uminus_uminus_rat @ B )
% 5.41/5.73 = ( times_times_rat @ A @ C ) ) )
% 5.41/5.73 & ( ( C = zero_zero_rat )
% 5.41/5.73 => ( A = zero_zero_rat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_eq_eq
% 5.41/5.73 thf(fact_5954_nonzero__neg__divide__eq__eq,axiom,
% 5.41/5.73 ! [B: real,A: real,C: real] :
% 5.41/5.73 ( ( B != zero_zero_real )
% 5.41/5.73 => ( ( ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.73 = C )
% 5.41/5.73 = ( ( uminus_uminus_real @ A )
% 5.41/5.73 = ( times_times_real @ C @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nonzero_neg_divide_eq_eq
% 5.41/5.73 thf(fact_5955_nonzero__neg__divide__eq__eq,axiom,
% 5.41/5.73 ! [B: complex,A: complex,C: complex] :
% 5.41/5.73 ( ( B != zero_zero_complex )
% 5.41/5.73 => ( ( ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.73 = C )
% 5.41/5.73 = ( ( uminus1482373934393186551omplex @ A )
% 5.41/5.73 = ( times_times_complex @ C @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nonzero_neg_divide_eq_eq
% 5.41/5.73 thf(fact_5956_nonzero__neg__divide__eq__eq,axiom,
% 5.41/5.73 ! [B: rat,A: rat,C: rat] :
% 5.41/5.73 ( ( B != zero_zero_rat )
% 5.41/5.73 => ( ( ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) )
% 5.41/5.73 = C )
% 5.41/5.73 = ( ( uminus_uminus_rat @ A )
% 5.41/5.73 = ( times_times_rat @ C @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nonzero_neg_divide_eq_eq
% 5.41/5.73 thf(fact_5957_nonzero__neg__divide__eq__eq2,axiom,
% 5.41/5.73 ! [B: real,C: real,A: real] :
% 5.41/5.73 ( ( B != zero_zero_real )
% 5.41/5.73 => ( ( C
% 5.41/5.73 = ( uminus_uminus_real @ ( divide_divide_real @ A @ B ) ) )
% 5.41/5.73 = ( ( times_times_real @ C @ B )
% 5.41/5.73 = ( uminus_uminus_real @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nonzero_neg_divide_eq_eq2
% 5.41/5.73 thf(fact_5958_nonzero__neg__divide__eq__eq2,axiom,
% 5.41/5.73 ! [B: complex,C: complex,A: complex] :
% 5.41/5.73 ( ( B != zero_zero_complex )
% 5.41/5.73 => ( ( C
% 5.41/5.73 = ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.41/5.73 = ( ( times_times_complex @ C @ B )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nonzero_neg_divide_eq_eq2
% 5.41/5.73 thf(fact_5959_nonzero__neg__divide__eq__eq2,axiom,
% 5.41/5.73 ! [B: rat,C: rat,A: rat] :
% 5.41/5.73 ( ( B != zero_zero_rat )
% 5.41/5.73 => ( ( C
% 5.41/5.73 = ( uminus_uminus_rat @ ( divide_divide_rat @ A @ B ) ) )
% 5.41/5.73 = ( ( times_times_rat @ C @ B )
% 5.41/5.73 = ( uminus_uminus_rat @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nonzero_neg_divide_eq_eq2
% 5.41/5.73 thf(fact_5960_mult__1s__ring__1_I2_J,axiom,
% 5.41/5.73 ! [B: real] :
% 5.41/5.73 ( ( times_times_real @ B @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) )
% 5.41/5.73 = ( uminus_uminus_real @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(2)
% 5.41/5.73 thf(fact_5961_mult__1s__ring__1_I2_J,axiom,
% 5.41/5.73 ! [B: int] :
% 5.41/5.73 ( ( times_times_int @ B @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) )
% 5.41/5.73 = ( uminus_uminus_int @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(2)
% 5.41/5.73 thf(fact_5962_mult__1s__ring__1_I2_J,axiom,
% 5.41/5.73 ! [B: complex] :
% 5.41/5.73 ( ( times_times_complex @ B @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(2)
% 5.41/5.73 thf(fact_5963_mult__1s__ring__1_I2_J,axiom,
% 5.41/5.73 ! [B: code_integer] :
% 5.41/5.73 ( ( times_3573771949741848930nteger @ B @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) )
% 5.41/5.73 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(2)
% 5.41/5.73 thf(fact_5964_mult__1s__ring__1_I2_J,axiom,
% 5.41/5.73 ! [B: rat] :
% 5.41/5.73 ( ( times_times_rat @ B @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) )
% 5.41/5.73 = ( uminus_uminus_rat @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(2)
% 5.41/5.73 thf(fact_5965_mult__1s__ring__1_I1_J,axiom,
% 5.41/5.73 ! [B: real] :
% 5.41/5.73 ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ one ) ) @ B )
% 5.41/5.73 = ( uminus_uminus_real @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(1)
% 5.41/5.73 thf(fact_5966_mult__1s__ring__1_I1_J,axiom,
% 5.41/5.73 ! [B: int] :
% 5.41/5.73 ( ( times_times_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ one ) ) @ B )
% 5.41/5.73 = ( uminus_uminus_int @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(1)
% 5.41/5.73 thf(fact_5967_mult__1s__ring__1_I1_J,axiom,
% 5.41/5.73 ! [B: complex] :
% 5.41/5.73 ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) ) @ B )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(1)
% 5.41/5.73 thf(fact_5968_mult__1s__ring__1_I1_J,axiom,
% 5.41/5.73 ! [B: code_integer] :
% 5.41/5.73 ( ( times_3573771949741848930nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) ) @ B )
% 5.41/5.73 = ( uminus1351360451143612070nteger @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(1)
% 5.41/5.73 thf(fact_5969_mult__1s__ring__1_I1_J,axiom,
% 5.41/5.73 ! [B: rat] :
% 5.41/5.73 ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) ) @ B )
% 5.41/5.73 = ( uminus_uminus_rat @ B ) ) ).
% 5.41/5.73
% 5.41/5.73 % mult_1s_ring_1(1)
% 5.41/5.73 thf(fact_5970_divide__eq__minus__1__iff,axiom,
% 5.41/5.73 ! [A: real,B: real] :
% 5.41/5.73 ( ( ( divide_divide_real @ A @ B )
% 5.41/5.73 = ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.73 = ( ( B != zero_zero_real )
% 5.41/5.73 & ( A
% 5.41/5.73 = ( uminus_uminus_real @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_eq_minus_1_iff
% 5.41/5.73 thf(fact_5971_divide__eq__minus__1__iff,axiom,
% 5.41/5.73 ! [A: complex,B: complex] :
% 5.41/5.73 ( ( ( divide1717551699836669952omplex @ A @ B )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.73 = ( ( B != zero_zero_complex )
% 5.41/5.73 & ( A
% 5.41/5.73 = ( uminus1482373934393186551omplex @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_eq_minus_1_iff
% 5.41/5.73 thf(fact_5972_divide__eq__minus__1__iff,axiom,
% 5.41/5.73 ! [A: rat,B: rat] :
% 5.41/5.73 ( ( ( divide_divide_rat @ A @ B )
% 5.41/5.73 = ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.73 = ( ( B != zero_zero_rat )
% 5.41/5.73 & ( A
% 5.41/5.73 = ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_eq_minus_1_iff
% 5.41/5.73 thf(fact_5973_uminus__numeral__One,axiom,
% 5.41/5.73 ( ( uminus_uminus_real @ ( numeral_numeral_real @ one ) )
% 5.41/5.73 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % uminus_numeral_One
% 5.41/5.73 thf(fact_5974_uminus__numeral__One,axiom,
% 5.41/5.73 ( ( uminus_uminus_int @ ( numeral_numeral_int @ one ) )
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % uminus_numeral_One
% 5.41/5.73 thf(fact_5975_uminus__numeral__One,axiom,
% 5.41/5.73 ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ one ) )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.73
% 5.41/5.73 % uminus_numeral_One
% 5.41/5.73 thf(fact_5976_uminus__numeral__One,axiom,
% 5.41/5.73 ( ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ one ) )
% 5.41/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % uminus_numeral_One
% 5.41/5.73 thf(fact_5977_uminus__numeral__One,axiom,
% 5.41/5.73 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ one ) )
% 5.41/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % uminus_numeral_One
% 5.41/5.73 thf(fact_5978_power__minus,axiom,
% 5.41/5.73 ! [A: real,N: nat] :
% 5.41/5.73 ( ( power_power_real @ ( uminus_uminus_real @ A ) @ N )
% 5.41/5.73 = ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus
% 5.41/5.73 thf(fact_5979_power__minus,axiom,
% 5.41/5.73 ! [A: int,N: nat] :
% 5.41/5.73 ( ( power_power_int @ ( uminus_uminus_int @ A ) @ N )
% 5.41/5.73 = ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ N ) @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus
% 5.41/5.73 thf(fact_5980_power__minus,axiom,
% 5.41/5.73 ! [A: complex,N: nat] :
% 5.41/5.73 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N )
% 5.41/5.73 = ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) @ ( power_power_complex @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus
% 5.41/5.73 thf(fact_5981_power__minus,axiom,
% 5.41/5.73 ! [A: code_integer,N: nat] :
% 5.41/5.73 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N )
% 5.41/5.73 = ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ N ) @ ( power_8256067586552552935nteger @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus
% 5.41/5.73 thf(fact_5982_power__minus,axiom,
% 5.41/5.73 ! [A: rat,N: nat] :
% 5.41/5.73 ( ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N )
% 5.41/5.73 = ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ N ) @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus
% 5.41/5.73 thf(fact_5983_power__minus__Bit0,axiom,
% 5.41/5.73 ! [X: real,K: num] :
% 5.41/5.73 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.41/5.73 = ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus_Bit0
% 5.41/5.73 thf(fact_5984_power__minus__Bit0,axiom,
% 5.41/5.73 ! [X: int,K: num] :
% 5.41/5.73 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.41/5.73 = ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus_Bit0
% 5.41/5.73 thf(fact_5985_power__minus__Bit0,axiom,
% 5.41/5.73 ! [X: complex,K: num] :
% 5.41/5.73 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.41/5.73 = ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus_Bit0
% 5.41/5.73 thf(fact_5986_power__minus__Bit0,axiom,
% 5.41/5.73 ! [X: code_integer,K: num] :
% 5.41/5.73 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.41/5.73 = ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus_Bit0
% 5.41/5.73 thf(fact_5987_power__minus__Bit0,axiom,
% 5.41/5.73 ! [X: rat,K: num] :
% 5.41/5.73 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.41/5.73 = ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus_Bit0
% 5.41/5.73 thf(fact_5988_lemma__interval__lt,axiom,
% 5.41/5.73 ! [A: real,X: real,B: real] :
% 5.41/5.73 ( ( ord_less_real @ A @ X )
% 5.41/5.73 => ( ( ord_less_real @ X @ B )
% 5.41/5.73 => ? [D3: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.73 & ! [Y2: real] :
% 5.41/5.73 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 5.41/5.73 => ( ( ord_less_real @ A @ Y2 )
% 5.41/5.73 & ( ord_less_real @ Y2 @ B ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % lemma_interval_lt
% 5.41/5.73 thf(fact_5989_dvd__imp__le,axiom,
% 5.41/5.73 ! [K: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ K @ N )
% 5.41/5.73 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 => ( ord_less_eq_nat @ K @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_imp_le
% 5.41/5.73 thf(fact_5990_dvd__mult__cancel,axiom,
% 5.41/5.73 ! [K: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.73 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.73 => ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_mult_cancel
% 5.41/5.73 thf(fact_5991_nat__mult__dvd__cancel1,axiom,
% 5.41/5.73 ! [K: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.73 => ( ( dvd_dvd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) )
% 5.41/5.73 = ( dvd_dvd_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nat_mult_dvd_cancel1
% 5.41/5.73 thf(fact_5992_bezout__add__strong__nat,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ( ( A != zero_zero_nat )
% 5.41/5.73 => ? [D3: nat,X6: nat,Y5: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ D3 @ A )
% 5.41/5.73 & ( dvd_dvd_nat @ D3 @ B )
% 5.41/5.73 & ( ( times_times_nat @ A @ X6 )
% 5.41/5.73 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ D3 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bezout_add_strong_nat
% 5.41/5.73 thf(fact_5993_zdvd__imp__le,axiom,
% 5.41/5.73 ! [Z: int,N: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ Z @ N )
% 5.41/5.73 => ( ( ord_less_int @ zero_zero_int @ N )
% 5.41/5.73 => ( ord_less_eq_int @ Z @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_imp_le
% 5.41/5.73 thf(fact_5994_mod__greater__zero__iff__not__dvd,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.41/5.73 = ( ~ ( dvd_dvd_nat @ N @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_greater_zero_iff_not_dvd
% 5.41/5.73 thf(fact_5995_real__0__less__add__iff,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.41/5.73 = ( ord_less_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.41/5.73
% 5.41/5.73 % real_0_less_add_iff
% 5.41/5.73 thf(fact_5996_real__add__less__0__iff,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.41/5.73 = ( ord_less_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % real_add_less_0_iff
% 5.41/5.73 thf(fact_5997_real__add__le__0__iff,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( plus_plus_real @ X @ Y ) @ zero_zero_real )
% 5.41/5.73 = ( ord_less_eq_real @ Y @ ( uminus_uminus_real @ X ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % real_add_le_0_iff
% 5.41/5.73 thf(fact_5998_real__0__le__add__iff,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( plus_plus_real @ X @ Y ) )
% 5.41/5.73 = ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ Y ) ) ).
% 5.41/5.73
% 5.41/5.73 % real_0_le_add_iff
% 5.41/5.73 thf(fact_5999_mod__eq__dvd__iff__nat,axiom,
% 5.41/5.73 ! [N: nat,M: nat,Q2: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.73 => ( ( ( modulo_modulo_nat @ M @ Q2 )
% 5.41/5.73 = ( modulo_modulo_nat @ N @ Q2 ) )
% 5.41/5.73 = ( dvd_dvd_nat @ Q2 @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_eq_dvd_iff_nat
% 5.41/5.73 thf(fact_6000_prod__decode__aux_Ocases,axiom,
% 5.41/5.73 ! [X: product_prod_nat_nat] :
% 5.41/5.73 ~ ! [K3: nat,M4: nat] :
% 5.41/5.73 ( X
% 5.41/5.73 != ( product_Pair_nat_nat @ K3 @ M4 ) ) ).
% 5.41/5.73
% 5.41/5.73 % prod_decode_aux.cases
% 5.41/5.73 thf(fact_6001_finite__divisors__nat,axiom,
% 5.41/5.73 ! [M: nat] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.73 => ( finite_finite_nat
% 5.41/5.73 @ ( collect_nat
% 5.41/5.73 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % finite_divisors_nat
% 5.41/5.73 thf(fact_6002_abs__add__one__gt__zero,axiom,
% 5.41/5.73 ! [X: code_integer] : ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ one_one_Code_integer @ ( abs_abs_Code_integer @ X ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_add_one_gt_zero
% 5.41/5.73 thf(fact_6003_abs__add__one__gt__zero,axiom,
% 5.41/5.73 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ one_one_real @ ( abs_abs_real @ X ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_add_one_gt_zero
% 5.41/5.73 thf(fact_6004_abs__add__one__gt__zero,axiom,
% 5.41/5.73 ! [X: rat] : ( ord_less_rat @ zero_zero_rat @ ( plus_plus_rat @ one_one_rat @ ( abs_abs_rat @ X ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_add_one_gt_zero
% 5.41/5.73 thf(fact_6005_abs__add__one__gt__zero,axiom,
% 5.41/5.73 ! [X: int] : ( ord_less_int @ zero_zero_int @ ( plus_plus_int @ one_one_int @ ( abs_abs_int @ X ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_add_one_gt_zero
% 5.41/5.73 thf(fact_6006_even__zero,axiom,
% 5.41/5.73 dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ zero_z3403309356797280102nteger ).
% 5.41/5.73
% 5.41/5.73 % even_zero
% 5.41/5.73 thf(fact_6007_even__zero,axiom,
% 5.41/5.73 dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ zero_zero_nat ).
% 5.41/5.73
% 5.41/5.73 % even_zero
% 5.41/5.73 thf(fact_6008_even__zero,axiom,
% 5.41/5.73 dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ zero_zero_int ).
% 5.41/5.73
% 5.41/5.73 % even_zero
% 5.41/5.73 thf(fact_6009_is__unitE,axiom,
% 5.41/5.73 ! [A: code_integer,C: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ A @ one_one_Code_integer )
% 5.41/5.73 => ~ ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.73 => ! [B5: code_integer] :
% 5.41/5.73 ( ( B5 != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ B5 @ one_one_Code_integer )
% 5.41/5.73 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ A )
% 5.41/5.73 = B5 )
% 5.41/5.73 => ( ( ( divide6298287555418463151nteger @ one_one_Code_integer @ B5 )
% 5.41/5.73 = A )
% 5.41/5.73 => ( ( ( times_3573771949741848930nteger @ A @ B5 )
% 5.41/5.73 = one_one_Code_integer )
% 5.41/5.73 => ( ( divide6298287555418463151nteger @ C @ A )
% 5.41/5.73 != ( times_3573771949741848930nteger @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unitE
% 5.41/5.73 thf(fact_6010_is__unitE,axiom,
% 5.41/5.73 ! [A: nat,C: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ A @ one_one_nat )
% 5.41/5.73 => ~ ( ( A != zero_zero_nat )
% 5.41/5.73 => ! [B5: nat] :
% 5.41/5.73 ( ( B5 != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ B5 @ one_one_nat )
% 5.41/5.73 => ( ( ( divide_divide_nat @ one_one_nat @ A )
% 5.41/5.73 = B5 )
% 5.41/5.73 => ( ( ( divide_divide_nat @ one_one_nat @ B5 )
% 5.41/5.73 = A )
% 5.41/5.73 => ( ( ( times_times_nat @ A @ B5 )
% 5.41/5.73 = one_one_nat )
% 5.41/5.73 => ( ( divide_divide_nat @ C @ A )
% 5.41/5.73 != ( times_times_nat @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unitE
% 5.41/5.73 thf(fact_6011_is__unitE,axiom,
% 5.41/5.73 ! [A: int,C: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ A @ one_one_int )
% 5.41/5.73 => ~ ( ( A != zero_zero_int )
% 5.41/5.73 => ! [B5: int] :
% 5.41/5.73 ( ( B5 != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ B5 @ one_one_int )
% 5.41/5.73 => ( ( ( divide_divide_int @ one_one_int @ A )
% 5.41/5.73 = B5 )
% 5.41/5.73 => ( ( ( divide_divide_int @ one_one_int @ B5 )
% 5.41/5.73 = A )
% 5.41/5.73 => ( ( ( times_times_int @ A @ B5 )
% 5.41/5.73 = one_one_int )
% 5.41/5.73 => ( ( divide_divide_int @ C @ A )
% 5.41/5.73 != ( times_times_int @ C @ B5 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unitE
% 5.41/5.73 thf(fact_6012_is__unit__div__mult__cancel__left,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer] :
% 5.41/5.73 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ A @ B ) )
% 5.41/5.73 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult_cancel_left
% 5.41/5.73 thf(fact_6013_is__unit__div__mult__cancel__left,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ( ( A != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( divide_divide_nat @ A @ ( times_times_nat @ A @ B ) )
% 5.41/5.73 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult_cancel_left
% 5.41/5.73 thf(fact_6014_is__unit__div__mult__cancel__left,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ( A != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( divide_divide_int @ A @ ( times_times_int @ A @ B ) )
% 5.41/5.73 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult_cancel_left
% 5.41/5.73 thf(fact_6015_is__unit__div__mult__cancel__right,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer] :
% 5.41/5.73 ( ( A != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ B @ one_one_Code_integer )
% 5.41/5.73 => ( ( divide6298287555418463151nteger @ A @ ( times_3573771949741848930nteger @ B @ A ) )
% 5.41/5.73 = ( divide6298287555418463151nteger @ one_one_Code_integer @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult_cancel_right
% 5.41/5.73 thf(fact_6016_is__unit__div__mult__cancel__right,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ( ( A != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ B @ one_one_nat )
% 5.41/5.73 => ( ( divide_divide_nat @ A @ ( times_times_nat @ B @ A ) )
% 5.41/5.73 = ( divide_divide_nat @ one_one_nat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult_cancel_right
% 5.41/5.73 thf(fact_6017_is__unit__div__mult__cancel__right,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ( A != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ B @ one_one_int )
% 5.41/5.73 => ( ( divide_divide_int @ A @ ( times_times_int @ B @ A ) )
% 5.41/5.73 = ( divide_divide_int @ one_one_int @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % is_unit_div_mult_cancel_right
% 5.41/5.73 thf(fact_6018_evenE,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ~ ! [B5: code_integer] :
% 5.41/5.73 ( A
% 5.41/5.73 != ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % evenE
% 5.41/5.73 thf(fact_6019_evenE,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ~ ! [B5: nat] :
% 5.41/5.73 ( A
% 5.41/5.73 != ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % evenE
% 5.41/5.73 thf(fact_6020_evenE,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ~ ! [B5: int] :
% 5.41/5.73 ( A
% 5.41/5.73 != ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % evenE
% 5.41/5.73 thf(fact_6021_odd__even__add,axiom,
% 5.41/5.73 ! [A: code_integer,B: code_integer] :
% 5.41/5.73 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B )
% 5.41/5.73 => ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( plus_p5714425477246183910nteger @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % odd_even_add
% 5.41/5.73 thf(fact_6022_odd__even__add,axiom,
% 5.41/5.73 ! [A: nat,B: nat] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.41/5.73 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( plus_plus_nat @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % odd_even_add
% 5.41/5.73 thf(fact_6023_odd__even__add,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B )
% 5.41/5.73 => ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ A @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % odd_even_add
% 5.41/5.73 thf(fact_6024_odd__one,axiom,
% 5.41/5.73 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ one_one_Code_integer ) ).
% 5.41/5.73
% 5.41/5.73 % odd_one
% 5.41/5.73 thf(fact_6025_odd__one,axiom,
% 5.41/5.73 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ one_one_nat ) ).
% 5.41/5.73
% 5.41/5.73 % odd_one
% 5.41/5.73 thf(fact_6026_odd__one,axiom,
% 5.41/5.73 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ one_one_int ) ).
% 5.41/5.73
% 5.41/5.73 % odd_one
% 5.41/5.73 thf(fact_6027_bit__eq__rec,axiom,
% 5.41/5.73 ( ( ^ [Y4: code_integer,Z2: code_integer] : ( Y4 = Z2 ) )
% 5.41/5.73 = ( ^ [A3: code_integer,B2: code_integer] :
% 5.41/5.73 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A3 )
% 5.41/5.73 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B2 ) )
% 5.41/5.73 & ( ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( divide6298287555418463151nteger @ B2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bit_eq_rec
% 5.41/5.73 thf(fact_6028_bit__eq__rec,axiom,
% 5.41/5.73 ( ( ^ [Y4: nat,Z2: nat] : ( Y4 = Z2 ) )
% 5.41/5.73 = ( ^ [A3: nat,B2: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A3 )
% 5.41/5.73 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B2 ) )
% 5.41/5.73 & ( ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( divide_divide_nat @ B2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bit_eq_rec
% 5.41/5.73 thf(fact_6029_bit__eq__rec,axiom,
% 5.41/5.73 ( ( ^ [Y4: int,Z2: int] : ( Y4 = Z2 ) )
% 5.41/5.73 = ( ^ [A3: int,B2: int] :
% 5.41/5.73 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A3 )
% 5.41/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B2 ) )
% 5.41/5.73 & ( ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( divide_divide_int @ B2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bit_eq_rec
% 5.41/5.73 thf(fact_6030_dvd__power__iff,axiom,
% 5.41/5.73 ! [X: code_integer,M: nat,N: nat] :
% 5.41/5.73 ( ( X != zero_z3403309356797280102nteger )
% 5.41/5.73 => ( ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ X @ M ) @ ( power_8256067586552552935nteger @ X @ N ) )
% 5.41/5.73 = ( ( dvd_dvd_Code_integer @ X @ one_one_Code_integer )
% 5.41/5.73 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_iff
% 5.41/5.73 thf(fact_6031_dvd__power__iff,axiom,
% 5.41/5.73 ! [X: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( X != zero_zero_nat )
% 5.41/5.73 => ( ( dvd_dvd_nat @ ( power_power_nat @ X @ M ) @ ( power_power_nat @ X @ N ) )
% 5.41/5.73 = ( ( dvd_dvd_nat @ X @ one_one_nat )
% 5.41/5.73 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_iff
% 5.41/5.73 thf(fact_6032_dvd__power__iff,axiom,
% 5.41/5.73 ! [X: int,M: nat,N: nat] :
% 5.41/5.73 ( ( X != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ N ) )
% 5.41/5.73 = ( ( dvd_dvd_int @ X @ one_one_int )
% 5.41/5.73 | ( ord_less_eq_nat @ M @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_iff
% 5.41/5.73 thf(fact_6033_less__minus__divide__eq,axiom,
% 5.41/5.73 ! [A: real,B: real,C: real] :
% 5.41/5.73 ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_minus_divide_eq
% 5.41/5.73 thf(fact_6034_less__minus__divide__eq,axiom,
% 5.41/5.73 ! [A: rat,B: rat,C: rat] :
% 5.41/5.73 ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_minus_divide_eq
% 5.41/5.73 thf(fact_6035_minus__divide__less__eq,axiom,
% 5.41/5.73 ! [B: real,C: real,A: real] :
% 5.41/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_less_eq
% 5.41/5.73 thf(fact_6036_minus__divide__less__eq,axiom,
% 5.41/5.73 ! [B: rat,C: rat,A: rat] :
% 5.41/5.73 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_less_eq
% 5.41/5.73 thf(fact_6037_neg__less__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: real,A: real,B: real] :
% 5.41/5.73 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_less_minus_divide_eq
% 5.41/5.73 thf(fact_6038_neg__less__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: rat,A: rat,B: rat] :
% 5.41/5.73 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_less_minus_divide_eq
% 5.41/5.73 thf(fact_6039_neg__minus__divide__less__eq,axiom,
% 5.41/5.73 ! [C: real,B: real,A: real] :
% 5.41/5.73 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_minus_divide_less_eq
% 5.41/5.73 thf(fact_6040_neg__minus__divide__less__eq,axiom,
% 5.41/5.73 ! [C: rat,B: rat,A: rat] :
% 5.41/5.73 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_minus_divide_less_eq
% 5.41/5.73 thf(fact_6041_pos__less__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: real,A: real,B: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ord_less_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_less_minus_divide_eq
% 5.41/5.73 thf(fact_6042_pos__less__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: rat,A: rat,B: rat] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ord_less_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_less_minus_divide_eq
% 5.41/5.73 thf(fact_6043_pos__minus__divide__less__eq,axiom,
% 5.41/5.73 ! [C: real,B: real,A: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_minus_divide_less_eq
% 5.41/5.73 thf(fact_6044_pos__minus__divide__less__eq,axiom,
% 5.41/5.73 ! [C: rat,B: rat,A: rat] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ord_less_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_minus_divide_less_eq
% 5.41/5.73 thf(fact_6045_divide__eq__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [B: real,C: real,W: num] :
% 5.41/5.73 ( ( ( divide_divide_real @ B @ C )
% 5.41/5.73 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.73 = ( ( ( C != zero_zero_real )
% 5.41/5.73 => ( B
% 5.41/5.73 = ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ( C = zero_zero_real )
% 5.41/5.73 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.73 = zero_zero_real ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_eq_eq_numeral(2)
% 5.41/5.73 thf(fact_6046_divide__eq__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [B: complex,C: complex,W: num] :
% 5.41/5.73 ( ( ( divide1717551699836669952omplex @ B @ C )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.73 = ( ( ( C != zero_zero_complex )
% 5.41/5.73 => ( B
% 5.41/5.73 = ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ( C = zero_zero_complex )
% 5.41/5.73 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.73 = zero_zero_complex ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_eq_eq_numeral(2)
% 5.41/5.73 thf(fact_6047_divide__eq__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [B: rat,C: rat,W: num] :
% 5.41/5.73 ( ( ( divide_divide_rat @ B @ C )
% 5.41/5.73 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.73 = ( ( ( C != zero_zero_rat )
% 5.41/5.73 => ( B
% 5.41/5.73 = ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ( C = zero_zero_rat )
% 5.41/5.73 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.41/5.73 = zero_zero_rat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_eq_eq_numeral(2)
% 5.41/5.73 thf(fact_6048_eq__divide__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [W: num,B: real,C: real] :
% 5.41/5.73 ( ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.73 = ( divide_divide_real @ B @ C ) )
% 5.41/5.73 = ( ( ( C != zero_zero_real )
% 5.41/5.73 => ( ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C )
% 5.41/5.73 = B ) )
% 5.41/5.73 & ( ( C = zero_zero_real )
% 5.41/5.73 => ( ( uminus_uminus_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.73 = zero_zero_real ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % eq_divide_eq_numeral(2)
% 5.41/5.73 thf(fact_6049_eq__divide__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [W: num,B: complex,C: complex] :
% 5.41/5.73 ( ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.73 = ( divide1717551699836669952omplex @ B @ C ) )
% 5.41/5.73 = ( ( ( C != zero_zero_complex )
% 5.41/5.73 => ( ( times_times_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) @ C )
% 5.41/5.73 = B ) )
% 5.41/5.73 & ( ( C = zero_zero_complex )
% 5.41/5.73 => ( ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.73 = zero_zero_complex ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % eq_divide_eq_numeral(2)
% 5.41/5.73 thf(fact_6050_eq__divide__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [W: num,B: rat,C: rat] :
% 5.41/5.73 ( ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.41/5.73 = ( divide_divide_rat @ B @ C ) )
% 5.41/5.73 = ( ( ( C != zero_zero_rat )
% 5.41/5.73 => ( ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C )
% 5.41/5.73 = B ) )
% 5.41/5.73 & ( ( C = zero_zero_rat )
% 5.41/5.73 => ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) )
% 5.41/5.73 = zero_zero_rat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % eq_divide_eq_numeral(2)
% 5.41/5.73 thf(fact_6051_minus__divide__add__eq__iff,axiom,
% 5.41/5.73 ! [Z: real,X: real,Y: real] :
% 5.41/5.73 ( ( Z != zero_zero_real )
% 5.41/5.73 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.41/5.73 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_add_eq_iff
% 5.41/5.73 thf(fact_6052_minus__divide__add__eq__iff,axiom,
% 5.41/5.73 ! [Z: complex,X: complex,Y: complex] :
% 5.41/5.73 ( ( Z != zero_zero_complex )
% 5.41/5.73 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.41/5.73 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_add_eq_iff
% 5.41/5.73 thf(fact_6053_minus__divide__add__eq__iff,axiom,
% 5.41/5.73 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.73 ( ( Z != zero_zero_rat )
% 5.41/5.73 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.41/5.73 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_add_eq_iff
% 5.41/5.73 thf(fact_6054_add__divide__eq__if__simps_I3_J,axiom,
% 5.41/5.73 ! [Z: real,A: real,B: real] :
% 5.41/5.73 ( ( ( Z = zero_zero_real )
% 5.41/5.73 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.41/5.73 = B ) )
% 5.41/5.73 & ( ( Z != zero_zero_real )
% 5.41/5.73 => ( ( plus_plus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.41/5.73 = ( divide_divide_real @ ( plus_plus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(3)
% 5.41/5.73 thf(fact_6055_add__divide__eq__if__simps_I3_J,axiom,
% 5.41/5.73 ! [Z: complex,A: complex,B: complex] :
% 5.41/5.73 ( ( ( Z = zero_zero_complex )
% 5.41/5.73 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.41/5.73 = B ) )
% 5.41/5.73 & ( ( Z != zero_zero_complex )
% 5.41/5.73 => ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.41/5.73 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(3)
% 5.41/5.73 thf(fact_6056_add__divide__eq__if__simps_I3_J,axiom,
% 5.41/5.73 ! [Z: rat,A: rat,B: rat] :
% 5.41/5.73 ( ( ( Z = zero_zero_rat )
% 5.41/5.73 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.41/5.73 = B ) )
% 5.41/5.73 & ( ( Z != zero_zero_rat )
% 5.41/5.73 => ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.41/5.73 = ( divide_divide_rat @ ( plus_plus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(3)
% 5.41/5.73 thf(fact_6057_dvd__power,axiom,
% 5.41/5.73 ! [N: nat,X: code_integer] :
% 5.41/5.73 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 | ( X = one_one_Code_integer ) )
% 5.41/5.73 => ( dvd_dvd_Code_integer @ X @ ( power_8256067586552552935nteger @ X @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power
% 5.41/5.73 thf(fact_6058_dvd__power,axiom,
% 5.41/5.73 ! [N: nat,X: rat] :
% 5.41/5.73 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 | ( X = one_one_rat ) )
% 5.41/5.73 => ( dvd_dvd_rat @ X @ ( power_power_rat @ X @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power
% 5.41/5.73 thf(fact_6059_dvd__power,axiom,
% 5.41/5.73 ! [N: nat,X: nat] :
% 5.41/5.73 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 | ( X = one_one_nat ) )
% 5.41/5.73 => ( dvd_dvd_nat @ X @ ( power_power_nat @ X @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power
% 5.41/5.73 thf(fact_6060_dvd__power,axiom,
% 5.41/5.73 ! [N: nat,X: real] :
% 5.41/5.73 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 | ( X = one_one_real ) )
% 5.41/5.73 => ( dvd_dvd_real @ X @ ( power_power_real @ X @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power
% 5.41/5.73 thf(fact_6061_dvd__power,axiom,
% 5.41/5.73 ! [N: nat,X: int] :
% 5.41/5.73 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 | ( X = one_one_int ) )
% 5.41/5.73 => ( dvd_dvd_int @ X @ ( power_power_int @ X @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power
% 5.41/5.73 thf(fact_6062_dvd__power,axiom,
% 5.41/5.73 ! [N: nat,X: complex] :
% 5.41/5.73 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 | ( X = one_one_complex ) )
% 5.41/5.73 => ( dvd_dvd_complex @ X @ ( power_power_complex @ X @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power
% 5.41/5.73 thf(fact_6063_add__divide__eq__if__simps_I6_J,axiom,
% 5.41/5.73 ! [Z: real,A: real,B: real] :
% 5.41/5.73 ( ( ( Z = zero_zero_real )
% 5.41/5.73 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.41/5.73 = ( uminus_uminus_real @ B ) ) )
% 5.41/5.73 & ( ( Z != zero_zero_real )
% 5.41/5.73 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ A @ Z ) ) @ B )
% 5.41/5.73 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ A ) @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(6)
% 5.41/5.73 thf(fact_6064_add__divide__eq__if__simps_I6_J,axiom,
% 5.41/5.73 ! [Z: complex,A: complex,B: complex] :
% 5.41/5.73 ( ( ( Z = zero_zero_complex )
% 5.41/5.73 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.41/5.73 & ( ( Z != zero_zero_complex )
% 5.41/5.73 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ A @ Z ) ) @ B )
% 5.41/5.73 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ A ) @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(6)
% 5.41/5.73 thf(fact_6065_add__divide__eq__if__simps_I6_J,axiom,
% 5.41/5.73 ! [Z: rat,A: rat,B: rat] :
% 5.41/5.73 ( ( ( Z = zero_zero_rat )
% 5.41/5.73 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.41/5.73 = ( uminus_uminus_rat @ B ) ) )
% 5.41/5.73 & ( ( Z != zero_zero_rat )
% 5.41/5.73 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ A @ Z ) ) @ B )
% 5.41/5.73 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ A ) @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(6)
% 5.41/5.73 thf(fact_6066_add__divide__eq__if__simps_I5_J,axiom,
% 5.41/5.73 ! [Z: real,A: real,B: real] :
% 5.41/5.73 ( ( ( Z = zero_zero_real )
% 5.41/5.73 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.41/5.73 = ( uminus_uminus_real @ B ) ) )
% 5.41/5.73 & ( ( Z != zero_zero_real )
% 5.41/5.73 => ( ( minus_minus_real @ ( divide_divide_real @ A @ Z ) @ B )
% 5.41/5.73 = ( divide_divide_real @ ( minus_minus_real @ A @ ( times_times_real @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(5)
% 5.41/5.73 thf(fact_6067_add__divide__eq__if__simps_I5_J,axiom,
% 5.41/5.73 ! [Z: complex,A: complex,B: complex] :
% 5.41/5.73 ( ( ( Z = zero_zero_complex )
% 5.41/5.73 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ B ) ) )
% 5.41/5.73 & ( ( Z != zero_zero_complex )
% 5.41/5.73 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ A @ Z ) @ B )
% 5.41/5.73 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ A @ ( times_times_complex @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(5)
% 5.41/5.73 thf(fact_6068_add__divide__eq__if__simps_I5_J,axiom,
% 5.41/5.73 ! [Z: rat,A: rat,B: rat] :
% 5.41/5.73 ( ( ( Z = zero_zero_rat )
% 5.41/5.73 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.41/5.73 = ( uminus_uminus_rat @ B ) ) )
% 5.41/5.73 & ( ( Z != zero_zero_rat )
% 5.41/5.73 => ( ( minus_minus_rat @ ( divide_divide_rat @ A @ Z ) @ B )
% 5.41/5.73 = ( divide_divide_rat @ ( minus_minus_rat @ A @ ( times_times_rat @ B @ Z ) ) @ Z ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % add_divide_eq_if_simps(5)
% 5.41/5.73 thf(fact_6069_minus__divide__diff__eq__iff,axiom,
% 5.41/5.73 ! [Z: real,X: real,Y: real] :
% 5.41/5.73 ( ( Z != zero_zero_real )
% 5.41/5.73 => ( ( minus_minus_real @ ( uminus_uminus_real @ ( divide_divide_real @ X @ Z ) ) @ Y )
% 5.41/5.73 = ( divide_divide_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ ( times_times_real @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_diff_eq_iff
% 5.41/5.73 thf(fact_6070_minus__divide__diff__eq__iff,axiom,
% 5.41/5.73 ! [Z: complex,X: complex,Y: complex] :
% 5.41/5.73 ( ( Z != zero_zero_complex )
% 5.41/5.73 => ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ ( divide1717551699836669952omplex @ X @ Z ) ) @ Y )
% 5.41/5.73 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ ( times_times_complex @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_diff_eq_iff
% 5.41/5.73 thf(fact_6071_minus__divide__diff__eq__iff,axiom,
% 5.41/5.73 ! [Z: rat,X: rat,Y: rat] :
% 5.41/5.73 ( ( Z != zero_zero_rat )
% 5.41/5.73 => ( ( minus_minus_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ X @ Z ) ) @ Y )
% 5.41/5.73 = ( divide_divide_rat @ ( minus_minus_rat @ ( uminus_uminus_rat @ X ) @ ( times_times_rat @ Y @ Z ) ) @ Z ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_diff_eq_iff
% 5.41/5.73 thf(fact_6072_power2__eq__iff,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 | ( X
% 5.41/5.73 = ( uminus_uminus_real @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_iff
% 5.41/5.73 thf(fact_6073_power2__eq__iff,axiom,
% 5.41/5.73 ! [X: int,Y: int] :
% 5.41/5.73 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 | ( X
% 5.41/5.73 = ( uminus_uminus_int @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_iff
% 5.41/5.73 thf(fact_6074_power2__eq__iff,axiom,
% 5.41/5.73 ! [X: complex,Y: complex] :
% 5.41/5.73 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( power_power_complex @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 | ( X
% 5.41/5.73 = ( uminus1482373934393186551omplex @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_iff
% 5.41/5.73 thf(fact_6075_power2__eq__iff,axiom,
% 5.41/5.73 ! [X: code_integer,Y: code_integer] :
% 5.41/5.73 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 | ( X
% 5.41/5.73 = ( uminus1351360451143612070nteger @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_iff
% 5.41/5.73 thf(fact_6076_power2__eq__iff,axiom,
% 5.41/5.73 ! [X: rat,Y: rat] :
% 5.41/5.73 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 | ( X
% 5.41/5.73 = ( uminus_uminus_rat @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_iff
% 5.41/5.73 thf(fact_6077_lemma__interval,axiom,
% 5.41/5.73 ! [A: real,X: real,B: real] :
% 5.41/5.73 ( ( ord_less_real @ A @ X )
% 5.41/5.73 => ( ( ord_less_real @ X @ B )
% 5.41/5.73 => ? [D3: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.73 & ! [Y2: real] :
% 5.41/5.73 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y2 ) ) @ D3 )
% 5.41/5.73 => ( ( ord_less_eq_real @ A @ Y2 )
% 5.41/5.73 & ( ord_less_eq_real @ Y2 @ B ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % lemma_interval
% 5.41/5.73 thf(fact_6078_even__even__mod__4__iff,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_even_mod_4_iff
% 5.41/5.73 thf(fact_6079_dvd__mult__cancel1,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.73 => ( ( dvd_dvd_nat @ ( times_times_nat @ M @ N ) @ M )
% 5.41/5.73 = ( N = one_one_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_mult_cancel1
% 5.41/5.73 thf(fact_6080_dvd__mult__cancel2,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.73 => ( ( dvd_dvd_nat @ ( times_times_nat @ N @ M ) @ M )
% 5.41/5.73 = ( N = one_one_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_mult_cancel2
% 5.41/5.73 thf(fact_6081_dvd__minus__add,axiom,
% 5.41/5.73 ! [Q2: nat,N: nat,R: nat,M: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ Q2 @ N )
% 5.41/5.73 => ( ( ord_less_eq_nat @ Q2 @ ( times_times_nat @ R @ M ) )
% 5.41/5.73 => ( ( dvd_dvd_nat @ M @ ( minus_minus_nat @ N @ Q2 ) )
% 5.41/5.73 = ( dvd_dvd_nat @ M @ ( plus_plus_nat @ N @ ( minus_minus_nat @ ( times_times_nat @ R @ M ) @ Q2 ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_minus_add
% 5.41/5.73 thf(fact_6082_power__dvd__imp__le,axiom,
% 5.41/5.73 ! [I: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( power_power_nat @ I @ M ) @ ( power_power_nat @ I @ N ) )
% 5.41/5.73 => ( ( ord_less_nat @ one_one_nat @ I )
% 5.41/5.73 => ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_dvd_imp_le
% 5.41/5.73 thf(fact_6083_mod__nat__eqI,axiom,
% 5.41/5.73 ! [R: nat,N: nat,M: nat] :
% 5.41/5.73 ( ( ord_less_nat @ R @ N )
% 5.41/5.73 => ( ( ord_less_eq_nat @ R @ M )
% 5.41/5.73 => ( ( dvd_dvd_nat @ N @ ( minus_minus_nat @ M @ R ) )
% 5.41/5.73 => ( ( modulo_modulo_nat @ M @ N )
% 5.41/5.73 = R ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_nat_eqI
% 5.41/5.73 thf(fact_6084_ln__add__one__self__le__self2,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.73 => ( ord_less_eq_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) ).
% 5.41/5.73
% 5.41/5.73 % ln_add_one_self_le_self2
% 5.41/5.73 thf(fact_6085_mod__int__pos__iff,axiom,
% 5.41/5.73 ! [K: int,L2: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.41/5.73 = ( ( dvd_dvd_int @ L2 @ K )
% 5.41/5.73 | ( ( L2 = zero_zero_int )
% 5.41/5.73 & ( ord_less_eq_int @ zero_zero_int @ K ) )
% 5.41/5.73 | ( ord_less_int @ zero_zero_int @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod_int_pos_iff
% 5.41/5.73 thf(fact_6086_aset_I10_J,axiom,
% 5.41/5.73 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ D @ D4 )
% 5.41/5.73 => ! [X4: int] :
% 5.41/5.73 ( ! [Xa3: int] :
% 5.41/5.73 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.73 => ! [Xb2: int] :
% 5.41/5.73 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.73 => ( X4
% 5.41/5.73 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.73 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.41/5.73 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % aset(10)
% 5.41/5.73 thf(fact_6087_aset_I9_J,axiom,
% 5.41/5.73 ! [D: int,D4: int,A2: set_int,T: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ D @ D4 )
% 5.41/5.73 => ! [X4: int] :
% 5.41/5.73 ( ! [Xa3: int] :
% 5.41/5.73 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.73 => ! [Xb2: int] :
% 5.41/5.73 ( ( member_int @ Xb2 @ A2 )
% 5.41/5.73 => ( X4
% 5.41/5.73 != ( minus_minus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.73 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.41/5.73 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( plus_plus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % aset(9)
% 5.41/5.73 thf(fact_6088_bset_I10_J,axiom,
% 5.41/5.73 ! [D: int,D4: int,B3: set_int,T: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ D @ D4 )
% 5.41/5.73 => ! [X4: int] :
% 5.41/5.73 ( ! [Xa3: int] :
% 5.41/5.73 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.73 => ! [Xb2: int] :
% 5.41/5.73 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.73 => ( X4
% 5.41/5.73 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.73 => ( ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.41/5.73 => ~ ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bset(10)
% 5.41/5.73 thf(fact_6089_bset_I9_J,axiom,
% 5.41/5.73 ! [D: int,D4: int,B3: set_int,T: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ D @ D4 )
% 5.41/5.73 => ! [X4: int] :
% 5.41/5.73 ( ! [Xa3: int] :
% 5.41/5.73 ( ( member_int @ Xa3 @ ( set_or1266510415728281911st_int @ one_one_int @ D4 ) )
% 5.41/5.73 => ! [Xb2: int] :
% 5.41/5.73 ( ( member_int @ Xb2 @ B3 )
% 5.41/5.73 => ( X4
% 5.41/5.73 != ( plus_plus_int @ Xb2 @ Xa3 ) ) ) )
% 5.41/5.73 => ( ( dvd_dvd_int @ D @ ( plus_plus_int @ X4 @ T ) )
% 5.41/5.73 => ( dvd_dvd_int @ D @ ( plus_plus_int @ ( minus_minus_int @ X4 @ D4 ) @ T ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bset(9)
% 5.41/5.73 thf(fact_6090_abs__le__square__iff,axiom,
% 5.41/5.73 ! [X: code_integer,Y: code_integer] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ ( abs_abs_Code_integer @ Y ) )
% 5.41/5.73 = ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_le_square_iff
% 5.41/5.73 thf(fact_6091_abs__le__square__iff,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) )
% 5.41/5.73 = ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_le_square_iff
% 5.41/5.73 thf(fact_6092_abs__le__square__iff,axiom,
% 5.41/5.73 ! [X: rat,Y: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ ( abs_abs_rat @ Y ) )
% 5.41/5.73 = ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_le_square_iff
% 5.41/5.73 thf(fact_6093_abs__le__square__iff,axiom,
% 5.41/5.73 ! [X: int,Y: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) )
% 5.41/5.73 = ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_le_square_iff
% 5.41/5.73 thf(fact_6094_abs__square__eq__1,axiom,
% 5.41/5.73 ! [X: code_integer] :
% 5.41/5.73 ( ( ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_Code_integer )
% 5.41/5.73 = ( ( abs_abs_Code_integer @ X )
% 5.41/5.73 = one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_eq_1
% 5.41/5.73 thf(fact_6095_abs__square__eq__1,axiom,
% 5.41/5.73 ! [X: rat] :
% 5.41/5.73 ( ( ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_rat )
% 5.41/5.73 = ( ( abs_abs_rat @ X )
% 5.41/5.73 = one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_eq_1
% 5.41/5.73 thf(fact_6096_abs__square__eq__1,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_real )
% 5.41/5.73 = ( ( abs_abs_real @ X )
% 5.41/5.73 = one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_eq_1
% 5.41/5.73 thf(fact_6097_abs__square__eq__1,axiom,
% 5.41/5.73 ! [X: int] :
% 5.41/5.73 ( ( ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_int )
% 5.41/5.73 = ( ( abs_abs_int @ X )
% 5.41/5.73 = one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_eq_1
% 5.41/5.73 thf(fact_6098_even__two__times__div__two,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = A ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_two_times_div_two
% 5.41/5.73 thf(fact_6099_even__two__times__div__two,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = A ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_two_times_div_two
% 5.41/5.73 thf(fact_6100_even__two__times__div__two,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = A ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_two_times_div_two
% 5.41/5.73 thf(fact_6101_even__iff__mod__2__eq__zero,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_zero_nat ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_iff_mod_2_eq_zero
% 5.41/5.73 thf(fact_6102_even__iff__mod__2__eq__zero,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_zero_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_iff_mod_2_eq_zero
% 5.41/5.73 thf(fact_6103_even__iff__mod__2__eq__zero,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_iff_mod_2_eq_zero
% 5.41/5.73 thf(fact_6104_le__minus__divide__eq,axiom,
% 5.41/5.73 ! [A: real,B: real,C: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ A @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_minus_divide_eq
% 5.41/5.73 thf(fact_6105_le__minus__divide__eq,axiom,
% 5.41/5.73 ! [A: rat,B: rat,C: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ A @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_minus_divide_eq
% 5.41/5.73 thf(fact_6106_minus__divide__le__eq,axiom,
% 5.41/5.73 ! [B: real,C: real,A: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_le_eq
% 5.41/5.73 thf(fact_6107_minus__divide__le__eq,axiom,
% 5.41/5.73 ! [B: rat,C: rat,A: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_divide_le_eq
% 5.41/5.73 thf(fact_6108_neg__le__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: real,A: real,B: real] :
% 5.41/5.73 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_le_minus_divide_eq
% 5.41/5.73 thf(fact_6109_neg__le__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: rat,A: rat,B: rat] :
% 5.41/5.73 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_le_minus_divide_eq
% 5.41/5.73 thf(fact_6110_neg__minus__divide__le__eq,axiom,
% 5.41/5.73 ! [C: real,B: real,A: real] :
% 5.41/5.73 ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_minus_divide_le_eq
% 5.41/5.73 thf(fact_6111_neg__minus__divide__le__eq,axiom,
% 5.41/5.73 ! [C: rat,B: rat,A: rat] :
% 5.41/5.73 ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_minus_divide_le_eq
% 5.41/5.73 thf(fact_6112_pos__le__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: real,A: real,B: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ord_less_eq_real @ A @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_eq_real @ ( times_times_real @ A @ C ) @ ( uminus_uminus_real @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_le_minus_divide_eq
% 5.41/5.73 thf(fact_6113_pos__le__minus__divide__eq,axiom,
% 5.41/5.73 ! [C: rat,A: rat,B: rat] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ord_less_eq_rat @ A @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) )
% 5.41/5.73 = ( ord_less_eq_rat @ ( times_times_rat @ A @ C ) @ ( uminus_uminus_rat @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_le_minus_divide_eq
% 5.41/5.73 thf(fact_6114_pos__minus__divide__le__eq,axiom,
% 5.41/5.73 ! [C: real,B: real,A: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_eq_real @ ( uminus_uminus_real @ B ) @ ( times_times_real @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_minus_divide_le_eq
% 5.41/5.73 thf(fact_6115_pos__minus__divide__le__eq,axiom,
% 5.41/5.73 ! [C: rat,B: rat,A: rat] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( divide_divide_rat @ B @ C ) ) @ A )
% 5.41/5.73 = ( ord_less_eq_rat @ ( uminus_uminus_rat @ B ) @ ( times_times_rat @ A @ C ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_minus_divide_le_eq
% 5.41/5.73 thf(fact_6116_odd__iff__mod__2__eq__one,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.73 = ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_nat ) ) ).
% 5.41/5.73
% 5.41/5.73 % odd_iff_mod_2_eq_one
% 5.41/5.73 thf(fact_6117_odd__iff__mod__2__eq__one,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.73 = ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % odd_iff_mod_2_eq_one
% 5.41/5.73 thf(fact_6118_odd__iff__mod__2__eq__one,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.73 = ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % odd_iff_mod_2_eq_one
% 5.41/5.73 thf(fact_6119_less__divide__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [W: num,B: real,C: real] :
% 5.41/5.73 ( ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_divide_eq_numeral(2)
% 5.41/5.73 thf(fact_6120_less__divide__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [W: num,B: rat,C: rat] :
% 5.41/5.73 ( ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % less_divide_eq_numeral(2)
% 5.41/5.73 thf(fact_6121_divide__less__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [B: real,C: real,W: num] :
% 5.41/5.73 ( ( ord_less_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_less_eq_numeral(2)
% 5.41/5.73 thf(fact_6122_divide__less__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [B: rat,C: rat,W: num] :
% 5.41/5.73 ( ( ord_less_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_less_eq_numeral(2)
% 5.41/5.73 thf(fact_6123_power__mono__odd,axiom,
% 5.41/5.73 ! [N: nat,A: real,B: real] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_real @ A @ B )
% 5.41/5.73 => ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ ( power_power_real @ B @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_mono_odd
% 5.41/5.73 thf(fact_6124_power__mono__odd,axiom,
% 5.41/5.73 ! [N: nat,A: rat,B: rat] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_rat @ A @ B )
% 5.41/5.73 => ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ ( power_power_rat @ B @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_mono_odd
% 5.41/5.73 thf(fact_6125_power__mono__odd,axiom,
% 5.41/5.73 ! [N: nat,A: int,B: int] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_int @ A @ B )
% 5.41/5.73 => ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ ( power_power_int @ B @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_mono_odd
% 5.41/5.73 thf(fact_6126_power2__eq__1__iff,axiom,
% 5.41/5.73 ! [A: real] :
% 5.41/5.73 ( ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_real )
% 5.41/5.73 = ( ( A = one_one_real )
% 5.41/5.73 | ( A
% 5.41/5.73 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_1_iff
% 5.41/5.73 thf(fact_6127_power2__eq__1__iff,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_int )
% 5.41/5.73 = ( ( A = one_one_int )
% 5.41/5.73 | ( A
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_1_iff
% 5.41/5.73 thf(fact_6128_power2__eq__1__iff,axiom,
% 5.41/5.73 ! [A: complex] :
% 5.41/5.73 ( ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_complex )
% 5.41/5.73 = ( ( A = one_one_complex )
% 5.41/5.73 | ( A
% 5.41/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_1_iff
% 5.41/5.73 thf(fact_6129_power2__eq__1__iff,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( ( power_8256067586552552935nteger @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_Code_integer )
% 5.41/5.73 = ( ( A = one_one_Code_integer )
% 5.41/5.73 | ( A
% 5.41/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_1_iff
% 5.41/5.73 thf(fact_6130_power2__eq__1__iff,axiom,
% 5.41/5.73 ! [A: rat] :
% 5.41/5.73 ( ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_rat )
% 5.41/5.73 = ( ( A = one_one_rat )
% 5.41/5.73 | ( A
% 5.41/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_eq_1_iff
% 5.41/5.73 thf(fact_6131_odd__pos,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % odd_pos
% 5.41/5.73 thf(fact_6132_dvd__power__iff__le,axiom,
% 5.41/5.73 ! [K: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.73 => ( ( dvd_dvd_nat @ ( power_power_nat @ K @ M ) @ ( power_power_nat @ K @ N ) )
% 5.41/5.73 = ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_power_iff_le
% 5.41/5.73 thf(fact_6133_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.41/5.73 ! [K: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.73 => ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( plus_plus_nat @ N @ K ) )
% 5.41/5.73 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_power_add_eq_neg_one_power_diff
% 5.41/5.73 thf(fact_6134_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.41/5.73 ! [K: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.73 => ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( plus_plus_nat @ N @ K ) )
% 5.41/5.73 = ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_power_add_eq_neg_one_power_diff
% 5.41/5.73 thf(fact_6135_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.41/5.73 ! [K: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.73 => ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( plus_plus_nat @ N @ K ) )
% 5.41/5.73 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_power_add_eq_neg_one_power_diff
% 5.41/5.73 thf(fact_6136_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.41/5.73 ! [K: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.73 => ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( plus_plus_nat @ N @ K ) )
% 5.41/5.73 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_power_add_eq_neg_one_power_diff
% 5.41/5.73 thf(fact_6137_neg__one__power__add__eq__neg__one__power__diff,axiom,
% 5.41/5.73 ! [K: nat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.73 => ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( plus_plus_nat @ N @ K ) )
% 5.41/5.73 = ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % neg_one_power_add_eq_neg_one_power_diff
% 5.41/5.73 thf(fact_6138_even__unset__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se8260200283734997820nteger @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 | ( M = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_unset_bit_iff
% 5.41/5.73 thf(fact_6139_even__unset__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 | ( M = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_unset_bit_iff
% 5.41/5.73 thf(fact_6140_even__unset__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 | ( M = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_unset_bit_iff
% 5.41/5.73 thf(fact_6141_even__set__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2793503036327961859nteger @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 & ( M != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_set_bit_iff
% 5.41/5.73 thf(fact_6142_even__set__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 & ( M != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_set_bit_iff
% 5.41/5.73 thf(fact_6143_even__set__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 & ( M != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_set_bit_iff
% 5.41/5.73 thf(fact_6144_realpow__square__minus__le,axiom,
% 5.41/5.73 ! [U: real,X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( power_power_real @ U @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % realpow_square_minus_le
% 5.41/5.73 thf(fact_6145_even__flip__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1345352211410354436nteger @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 != ( M = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_flip_bit_iff
% 5.41/5.73 thf(fact_6146_even__flip__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 != ( M = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_flip_bit_iff
% 5.41/5.73 thf(fact_6147_even__flip__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.41/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 != ( M = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_flip_bit_iff
% 5.41/5.73 thf(fact_6148_even__diff__iff,axiom,
% 5.41/5.73 ! [K: int,L2: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_int @ K @ L2 ) )
% 5.41/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_diff_iff
% 5.41/5.73 thf(fact_6149_ln__one__minus__pos__upper__bound,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.73 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( ln_ln_real @ ( minus_minus_real @ one_one_real @ X ) ) @ ( uminus_uminus_real @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % ln_one_minus_pos_upper_bound
% 5.41/5.73 thf(fact_6150_abs__sqrt__wlog,axiom,
% 5.41/5.73 ! [P: code_integer > code_integer > $o,X: code_integer] :
% 5.41/5.73 ( ! [X6: code_integer] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ X6 )
% 5.41/5.73 => ( P @ X6 @ ( power_8256067586552552935nteger @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.73 => ( P @ ( abs_abs_Code_integer @ X ) @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_sqrt_wlog
% 5.41/5.73 thf(fact_6151_abs__sqrt__wlog,axiom,
% 5.41/5.73 ! [P: real > real > $o,X: real] :
% 5.41/5.73 ( ! [X6: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 5.41/5.73 => ( P @ X6 @ ( power_power_real @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.73 => ( P @ ( abs_abs_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_sqrt_wlog
% 5.41/5.73 thf(fact_6152_abs__sqrt__wlog,axiom,
% 5.41/5.73 ! [P: rat > rat > $o,X: rat] :
% 5.41/5.73 ( ! [X6: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ zero_zero_rat @ X6 )
% 5.41/5.73 => ( P @ X6 @ ( power_power_rat @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.73 => ( P @ ( abs_abs_rat @ X ) @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_sqrt_wlog
% 5.41/5.73 thf(fact_6153_abs__sqrt__wlog,axiom,
% 5.41/5.73 ! [P: int > int > $o,X: int] :
% 5.41/5.73 ( ! [X6: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ zero_zero_int @ X6 )
% 5.41/5.73 => ( P @ X6 @ ( power_power_int @ X6 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.73 => ( P @ ( abs_abs_int @ X ) @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_sqrt_wlog
% 5.41/5.73 thf(fact_6154_power2__le__iff__abs__le,axiom,
% 5.41/5.73 ! [Y: code_integer,X: code_integer] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ Y )
% 5.41/5.73 => ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_8256067586552552935nteger @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ Y ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_le_iff_abs_le
% 5.41/5.73 thf(fact_6155_power2__le__iff__abs__le,axiom,
% 5.41/5.73 ! [Y: real,X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.73 => ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ Y ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_le_iff_abs_le
% 5.41/5.73 thf(fact_6156_power2__le__iff__abs__le,axiom,
% 5.41/5.73 ! [Y: rat,X: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ zero_zero_rat @ Y )
% 5.41/5.73 => ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_rat @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ Y ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_le_iff_abs_le
% 5.41/5.73 thf(fact_6157_power2__le__iff__abs__le,axiom,
% 5.41/5.73 ! [Y: int,X: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.73 => ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_int @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ Y ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power2_le_iff_abs_le
% 5.41/5.73 thf(fact_6158_abs__square__le__1,axiom,
% 5.41/5.73 ! [X: code_integer] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.41/5.73 = ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_le_1
% 5.41/5.73 thf(fact_6159_abs__square__le__1,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.41/5.73 = ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_le_1
% 5.41/5.73 thf(fact_6160_abs__square__le__1,axiom,
% 5.41/5.73 ! [X: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.41/5.73 = ( ord_less_eq_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_le_1
% 5.41/5.73 thf(fact_6161_abs__square__le__1,axiom,
% 5.41/5.73 ! [X: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.41/5.73 = ( ord_less_eq_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_le_1
% 5.41/5.73 thf(fact_6162_abs__square__less__1,axiom,
% 5.41/5.73 ! [X: code_integer] :
% 5.41/5.73 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer )
% 5.41/5.73 = ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ X ) @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_less_1
% 5.41/5.73 thf(fact_6163_abs__square__less__1,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real )
% 5.41/5.73 = ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_less_1
% 5.41/5.73 thf(fact_6164_abs__square__less__1,axiom,
% 5.41/5.73 ! [X: rat] :
% 5.41/5.73 ( ( ord_less_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat )
% 5.41/5.73 = ( ord_less_rat @ ( abs_abs_rat @ X ) @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_less_1
% 5.41/5.73 thf(fact_6165_abs__square__less__1,axiom,
% 5.41/5.73 ! [X: int] :
% 5.41/5.73 ( ( ord_less_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int )
% 5.41/5.73 = ( ord_less_int @ ( abs_abs_int @ X ) @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_square_less_1
% 5.41/5.73 thf(fact_6166_oddE,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ~ ! [B5: code_integer] :
% 5.41/5.73 ( A
% 5.41/5.73 != ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B5 ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % oddE
% 5.41/5.73 thf(fact_6167_oddE,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ~ ! [B5: nat] :
% 5.41/5.73 ( A
% 5.41/5.73 != ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B5 ) @ one_one_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % oddE
% 5.41/5.73 thf(fact_6168_oddE,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ~ ! [B5: int] :
% 5.41/5.73 ( A
% 5.41/5.73 != ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B5 ) @ one_one_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % oddE
% 5.41/5.73 thf(fact_6169_mod2__eq__if,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_zero_nat ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod2_eq_if
% 5.41/5.73 thf(fact_6170_mod2__eq__if,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_zero_int ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod2_eq_if
% 5.41/5.73 thf(fact_6171_mod2__eq__if,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_z3403309356797280102nteger ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = one_one_Code_integer ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % mod2_eq_if
% 5.41/5.73 thf(fact_6172_parity__cases,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 != zero_zero_nat ) )
% 5.41/5.73 => ~ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 != one_one_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % parity_cases
% 5.41/5.73 thf(fact_6173_parity__cases,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 != zero_zero_int ) )
% 5.41/5.73 => ~ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 != one_one_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % parity_cases
% 5.41/5.73 thf(fact_6174_parity__cases,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 != zero_z3403309356797280102nteger ) )
% 5.41/5.73 => ~ ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.73 => ( ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 != one_one_Code_integer ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % parity_cases
% 5.41/5.73 thf(fact_6175_le__divide__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [W: num,B: real,C: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ ( divide_divide_real @ B @ C ) )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_divide_eq_numeral(2)
% 5.41/5.73 thf(fact_6176_le__divide__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [W: num,B: rat,C: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ ( divide_divide_rat @ B @ C ) )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % le_divide_eq_numeral(2)
% 5.41/5.73 thf(fact_6177_divide__le__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [B: real,C: real,W: num] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( divide_divide_real @ B @ C ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.73 = ( ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ord_less_eq_real @ B @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.73 => ( ( ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_real @ C @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_le_eq_numeral(2)
% 5.41/5.73 thf(fact_6178_divide__le__eq__numeral_I2_J,axiom,
% 5.41/5.73 ! [B: rat,C: rat,W: num] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( divide_divide_rat @ B @ C ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) )
% 5.41/5.73 = ( ( ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ord_less_eq_rat @ B @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ zero_zero_rat @ C )
% 5.41/5.73 => ( ( ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ ( times_times_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) @ C ) @ B ) )
% 5.41/5.73 & ( ~ ( ord_less_rat @ C @ zero_zero_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ zero_zero_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % divide_le_eq_numeral(2)
% 5.41/5.73 thf(fact_6179_zero__le__power__eq,axiom,
% 5.41/5.73 ! [A: real,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.41/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_power_eq
% 5.41/5.73 thf(fact_6180_zero__le__power__eq,axiom,
% 5.41/5.73 ! [A: rat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.41/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_power_eq
% 5.41/5.73 thf(fact_6181_zero__le__power__eq,axiom,
% 5.41/5.73 ! [A: int,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.41/5.73 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_power_eq
% 5.41/5.73 thf(fact_6182_zero__le__odd__power,axiom,
% 5.41/5.73 ! [N: nat,A: real] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.41/5.73 = ( ord_less_eq_real @ zero_zero_real @ A ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_odd_power
% 5.41/5.73 thf(fact_6183_zero__le__odd__power,axiom,
% 5.41/5.73 ! [N: nat,A: rat] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.41/5.73 = ( ord_less_eq_rat @ zero_zero_rat @ A ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_odd_power
% 5.41/5.73 thf(fact_6184_zero__le__odd__power,axiom,
% 5.41/5.73 ! [N: nat,A: int] :
% 5.41/5.73 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.41/5.73 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_odd_power
% 5.41/5.73 thf(fact_6185_zero__le__even__power,axiom,
% 5.41/5.73 ! [N: nat,A: real] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ord_less_eq_real @ zero_zero_real @ ( power_power_real @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_even_power
% 5.41/5.73 thf(fact_6186_zero__le__even__power,axiom,
% 5.41/5.73 ! [N: nat,A: rat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ord_less_eq_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_even_power
% 5.41/5.73 thf(fact_6187_zero__le__even__power,axiom,
% 5.41/5.73 ! [N: nat,A: int] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 => ( ord_less_eq_int @ zero_zero_int @ ( power_power_int @ A @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_even_power
% 5.41/5.73 thf(fact_6188_abs__ln__one__plus__x__minus__x__bound__nonpos,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.73 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_ln_one_plus_x_minus_x_bound_nonpos
% 5.41/5.73 thf(fact_6189_square__le__1,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.73 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % square_le_1
% 5.41/5.73 thf(fact_6190_square__le__1,axiom,
% 5.41/5.73 ! [X: code_integer] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ X )
% 5.41/5.73 => ( ( ord_le3102999989581377725nteger @ X @ one_one_Code_integer )
% 5.41/5.73 => ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_Code_integer ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % square_le_1
% 5.41/5.73 thf(fact_6191_square__le__1,axiom,
% 5.41/5.73 ! [X: rat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( uminus_uminus_rat @ one_one_rat ) @ X )
% 5.41/5.73 => ( ( ord_less_eq_rat @ X @ one_one_rat )
% 5.41/5.73 => ( ord_less_eq_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_rat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % square_le_1
% 5.41/5.73 thf(fact_6192_square__le__1,axiom,
% 5.41/5.73 ! [X: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ one_one_int ) @ X )
% 5.41/5.73 => ( ( ord_less_eq_int @ X @ one_one_int )
% 5.41/5.73 => ( ord_less_eq_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % square_le_1
% 5.41/5.73 thf(fact_6193_minus__power__mult__self,axiom,
% 5.41/5.73 ! [A: real,N: nat] :
% 5.41/5.73 ( ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) @ ( power_power_real @ ( uminus_uminus_real @ A ) @ N ) )
% 5.41/5.73 = ( power_power_real @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_power_mult_self
% 5.41/5.73 thf(fact_6194_minus__power__mult__self,axiom,
% 5.41/5.73 ! [A: int,N: nat] :
% 5.41/5.73 ( ( times_times_int @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) @ ( power_power_int @ ( uminus_uminus_int @ A ) @ N ) )
% 5.41/5.73 = ( power_power_int @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_power_mult_self
% 5.41/5.73 thf(fact_6195_minus__power__mult__self,axiom,
% 5.41/5.73 ! [A: complex,N: nat] :
% 5.41/5.73 ( ( times_times_complex @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) @ ( power_power_complex @ ( uminus1482373934393186551omplex @ A ) @ N ) )
% 5.41/5.73 = ( power_power_complex @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_power_mult_self
% 5.41/5.73 thf(fact_6196_minus__power__mult__self,axiom,
% 5.41/5.73 ! [A: code_integer,N: nat] :
% 5.41/5.73 ( ( times_3573771949741848930nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ A ) @ N ) )
% 5.41/5.73 = ( power_8256067586552552935nteger @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_power_mult_self
% 5.41/5.73 thf(fact_6197_minus__power__mult__self,axiom,
% 5.41/5.73 ! [A: rat,N: nat] :
% 5.41/5.73 ( ( times_times_rat @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) @ ( power_power_rat @ ( uminus_uminus_rat @ A ) @ N ) )
% 5.41/5.73 = ( power_power_rat @ A @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_power_mult_self
% 5.41/5.73 thf(fact_6198_list__decode_Ocases,axiom,
% 5.41/5.73 ! [X: nat] :
% 5.41/5.73 ( ( X != zero_zero_nat )
% 5.41/5.73 => ~ ! [N3: nat] :
% 5.41/5.73 ( X
% 5.41/5.73 != ( suc @ N3 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % list_decode.cases
% 5.41/5.73 thf(fact_6199_zero__less__power__eq,axiom,
% 5.41/5.73 ! [A: real,N: nat] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ A @ N ) )
% 5.41/5.73 = ( ( N = zero_zero_nat )
% 5.41/5.73 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( A != zero_zero_real ) )
% 5.41/5.73 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_real @ zero_zero_real @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_power_eq
% 5.41/5.73 thf(fact_6200_zero__less__power__eq,axiom,
% 5.41/5.73 ! [A: rat,N: nat] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ A @ N ) )
% 5.41/5.73 = ( ( N = zero_zero_nat )
% 5.41/5.73 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( A != zero_zero_rat ) )
% 5.41/5.73 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_rat @ zero_zero_rat @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_power_eq
% 5.41/5.73 thf(fact_6201_zero__less__power__eq,axiom,
% 5.41/5.73 ! [A: int,N: nat] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ A @ N ) )
% 5.41/5.73 = ( ( N = zero_zero_nat )
% 5.41/5.73 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( A != zero_zero_int ) )
% 5.41/5.73 | ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_int @ zero_zero_int @ A ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_power_eq
% 5.41/5.73 thf(fact_6202_power__minus1__odd,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus1_odd
% 5.41/5.73 thf(fact_6203_power__minus1__odd,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( power_power_int @ ( uminus_uminus_int @ one_one_int ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus1_odd
% 5.41/5.73 thf(fact_6204_power__minus1__odd,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus1_odd
% 5.41/5.73 thf(fact_6205_power__minus1__odd,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus1_odd
% 5.41/5.73 thf(fact_6206_power__minus1__odd,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( power_power_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_minus1_odd
% 5.41/5.73 thf(fact_6207_eq__diff__eq_H,axiom,
% 5.41/5.73 ! [X: real,Y: real,Z: real] :
% 5.41/5.73 ( ( X
% 5.41/5.73 = ( minus_minus_real @ Y @ Z ) )
% 5.41/5.73 = ( Y
% 5.41/5.73 = ( plus_plus_real @ X @ Z ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % eq_diff_eq'
% 5.41/5.73 thf(fact_6208_even__mask__div__iff_H,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mask_div_iff'
% 5.41/5.73 thf(fact_6209_even__mask__div__iff_H,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mask_div_iff'
% 5.41/5.73 thf(fact_6210_even__mask__div__iff_H,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mask_div_iff'
% 5.41/5.73 thf(fact_6211_power__le__zero__eq,axiom,
% 5.41/5.73 ! [A: real,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( power_power_real @ A @ N ) @ zero_zero_real )
% 5.41/5.73 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_eq_real @ A @ zero_zero_real ) )
% 5.41/5.73 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( A = zero_zero_real ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_zero_eq
% 5.41/5.73 thf(fact_6212_power__le__zero__eq,axiom,
% 5.41/5.73 ! [A: rat,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( power_power_rat @ A @ N ) @ zero_zero_rat )
% 5.41/5.73 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_eq_rat @ A @ zero_zero_rat ) )
% 5.41/5.73 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( A = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_zero_eq
% 5.41/5.73 thf(fact_6213_power__le__zero__eq,axiom,
% 5.41/5.73 ! [A: int,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( power_power_int @ A @ N ) @ zero_zero_int )
% 5.41/5.73 = ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.73 & ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( ord_less_eq_int @ A @ zero_zero_int ) )
% 5.41/5.73 | ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 & ( A = zero_zero_int ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % power_le_zero_eq
% 5.41/5.73 thf(fact_6214_even__mod__4__div__2,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.73 = ( suc @ zero_zero_nat ) )
% 5.41/5.73 => ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mod_4_div_2
% 5.41/5.73 thf(fact_6215_even__mask__div__iff,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ one_one_Code_integer ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 = zero_z3403309356797280102nteger )
% 5.41/5.73 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mask_div_iff
% 5.41/5.73 thf(fact_6216_even__mask__div__iff,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 = zero_zero_nat )
% 5.41/5.73 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mask_div_iff
% 5.41/5.73 thf(fact_6217_even__mask__div__iff,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 | ( ord_less_eq_nat @ M @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mask_div_iff
% 5.41/5.73 thf(fact_6218_abs__ln__one__plus__x__minus__x__bound__nonneg,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.73 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.73 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ln_ln_real @ ( plus_plus_real @ one_one_real @ X ) ) @ X ) ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_ln_one_plus_x_minus_x_bound_nonneg
% 5.41/5.73 thf(fact_6219_even__mult__exp__div__exp__iff,axiom,
% 5.41/5.73 ! [A: code_integer,M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ ( times_3573771949741848930nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ( ord_less_nat @ N @ M )
% 5.41/5.73 | ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 = zero_z3403309356797280102nteger )
% 5.41/5.73 | ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 & ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mult_exp_div_exp_iff
% 5.41/5.73 thf(fact_6220_even__mult__exp__div__exp__iff,axiom,
% 5.41/5.73 ! [A: nat,M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( times_times_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ( ord_less_nat @ N @ M )
% 5.41/5.73 | ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 = zero_zero_nat )
% 5.41/5.73 | ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 & ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mult_exp_div_exp_iff
% 5.41/5.73 thf(fact_6221_even__mult__exp__div__exp__iff,axiom,
% 5.41/5.73 ! [A: int,M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ ( times_times_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 = ( ( ord_less_nat @ N @ M )
% 5.41/5.73 | ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 | ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 & ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ M ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_mult_exp_div_exp_iff
% 5.41/5.73 thf(fact_6222_compl__le__compl__iff,axiom,
% 5.41/5.73 ! [X: set_int,Y: set_int] :
% 5.41/5.73 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ ( uminus1532241313380277803et_int @ Y ) )
% 5.41/5.73 = ( ord_less_eq_set_int @ Y @ X ) ) ).
% 5.41/5.73
% 5.41/5.73 % compl_le_compl_iff
% 5.41/5.73 thf(fact_6223_signed__take__bit__rec,axiom,
% 5.41/5.73 ( bit_ri6519982836138164636nteger
% 5.41/5.73 = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_rec
% 5.41/5.73 thf(fact_6224_signed__take__bit__rec,axiom,
% 5.41/5.73 ( bit_ri631733984087533419it_int
% 5.41/5.73 = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ ( uminus_uminus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( plus_plus_int @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_rec
% 5.41/5.73 thf(fact_6225_triangle__def,axiom,
% 5.41/5.73 ( nat_triangle
% 5.41/5.73 = ( ^ [N2: nat] : ( divide_divide_nat @ ( times_times_nat @ N2 @ ( suc @ N2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % triangle_def
% 5.41/5.73 thf(fact_6226_arctan__double,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.73 => ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ X ) )
% 5.41/5.73 = ( arctan @ ( divide_divide_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % arctan_double
% 5.41/5.73 thf(fact_6227_vebt__buildup_Oelims,axiom,
% 5.41/5.73 ! [X: nat,Y: vEBT_VEBT] :
% 5.41/5.73 ( ( ( vEBT_vebt_buildup @ X )
% 5.41/5.73 = Y )
% 5.41/5.73 => ( ( ( X = zero_zero_nat )
% 5.41/5.73 => ( Y
% 5.41/5.73 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.41/5.73 => ( ( ( X
% 5.41/5.73 = ( suc @ zero_zero_nat ) )
% 5.41/5.73 => ( Y
% 5.41/5.73 != ( vEBT_Leaf @ $false @ $false ) ) )
% 5.41/5.73 => ~ ! [Va2: nat] :
% 5.41/5.73 ( ( X
% 5.41/5.73 = ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.73 => ~ ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.73 => ( Y
% 5.41/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.41/5.73 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.73 => ( Y
% 5.41/5.73 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % vebt_buildup.elims
% 5.41/5.73 thf(fact_6228_flip__bit__0,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( bit_se1345352211410354436nteger @ zero_zero_nat @ A )
% 5.41/5.73 = ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % flip_bit_0
% 5.41/5.73 thf(fact_6229_flip__bit__0,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( bit_se2159334234014336723it_int @ zero_zero_nat @ A )
% 5.41/5.73 = ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % flip_bit_0
% 5.41/5.73 thf(fact_6230_flip__bit__0,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( bit_se2161824704523386999it_nat @ zero_zero_nat @ A )
% 5.41/5.73 = ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % flip_bit_0
% 5.41/5.73 thf(fact_6231_intind,axiom,
% 5.41/5.73 ! [I: nat,N: nat,P: nat > $o,X: nat] :
% 5.41/5.73 ( ( ord_less_nat @ I @ N )
% 5.41/5.73 => ( ( P @ X )
% 5.41/5.73 => ( P @ ( nth_nat @ ( replicate_nat @ N @ X ) @ I ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % intind
% 5.41/5.73 thf(fact_6232_intind,axiom,
% 5.41/5.73 ! [I: nat,N: nat,P: int > $o,X: int] :
% 5.41/5.73 ( ( ord_less_nat @ I @ N )
% 5.41/5.73 => ( ( P @ X )
% 5.41/5.73 => ( P @ ( nth_int @ ( replicate_int @ N @ X ) @ I ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % intind
% 5.41/5.73 thf(fact_6233_intind,axiom,
% 5.41/5.73 ! [I: nat,N: nat,P: vEBT_VEBT > $o,X: vEBT_VEBT] :
% 5.41/5.73 ( ( ord_less_nat @ I @ N )
% 5.41/5.73 => ( ( P @ X )
% 5.41/5.73 => ( P @ ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % intind
% 5.41/5.73 thf(fact_6234_Compl__anti__mono,axiom,
% 5.41/5.73 ! [A2: set_int,B3: set_int] :
% 5.41/5.73 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.73 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ B3 ) @ ( uminus1532241313380277803et_int @ A2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Compl_anti_mono
% 5.41/5.73 thf(fact_6235_Compl__subset__Compl__iff,axiom,
% 5.41/5.73 ! [A2: set_int,B3: set_int] :
% 5.41/5.73 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( uminus1532241313380277803et_int @ B3 ) )
% 5.41/5.73 = ( ord_less_eq_set_int @ B3 @ A2 ) ) ).
% 5.41/5.73
% 5.41/5.73 % Compl_subset_Compl_iff
% 5.41/5.73 thf(fact_6236_of__bool__less__eq__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.41/5.73 = ( P
% 5.41/5.73 => Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_iff
% 5.41/5.73 thf(fact_6237_of__bool__less__eq__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.41/5.73 = ( P
% 5.41/5.73 => Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_iff
% 5.41/5.73 thf(fact_6238_of__bool__less__eq__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.41/5.73 = ( P
% 5.41/5.73 => Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_iff
% 5.41/5.73 thf(fact_6239_of__bool__less__eq__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.41/5.73 = ( P
% 5.41/5.73 => Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_iff
% 5.41/5.73 thf(fact_6240_of__bool__eq_I1_J,axiom,
% 5.41/5.73 ( ( zero_n1201886186963655149omplex @ $false )
% 5.41/5.73 = zero_zero_complex ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(1)
% 5.41/5.73 thf(fact_6241_of__bool__eq_I1_J,axiom,
% 5.41/5.73 ( ( zero_n3304061248610475627l_real @ $false )
% 5.41/5.73 = zero_zero_real ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(1)
% 5.41/5.73 thf(fact_6242_of__bool__eq_I1_J,axiom,
% 5.41/5.73 ( ( zero_n2052037380579107095ol_rat @ $false )
% 5.41/5.73 = zero_zero_rat ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(1)
% 5.41/5.73 thf(fact_6243_of__bool__eq_I1_J,axiom,
% 5.41/5.73 ( ( zero_n2687167440665602831ol_nat @ $false )
% 5.41/5.73 = zero_zero_nat ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(1)
% 5.41/5.73 thf(fact_6244_of__bool__eq_I1_J,axiom,
% 5.41/5.73 ( ( zero_n2684676970156552555ol_int @ $false )
% 5.41/5.73 = zero_zero_int ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(1)
% 5.41/5.73 thf(fact_6245_of__bool__eq_I1_J,axiom,
% 5.41/5.73 ( ( zero_n356916108424825756nteger @ $false )
% 5.41/5.73 = zero_z3403309356797280102nteger ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(1)
% 5.41/5.73 thf(fact_6246_of__bool__eq__0__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.41/5.73 = zero_zero_complex )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_0_iff
% 5.41/5.73 thf(fact_6247_of__bool__eq__0__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.41/5.73 = zero_zero_real )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_0_iff
% 5.41/5.73 thf(fact_6248_of__bool__eq__0__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.41/5.73 = zero_zero_rat )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_0_iff
% 5.41/5.73 thf(fact_6249_of__bool__eq__0__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.41/5.73 = zero_zero_nat )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_0_iff
% 5.41/5.73 thf(fact_6250_of__bool__eq__0__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_0_iff
% 5.41/5.73 thf(fact_6251_of__bool__eq__0__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n356916108424825756nteger @ P )
% 5.41/5.73 = zero_z3403309356797280102nteger )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_0_iff
% 5.41/5.73 thf(fact_6252_of__bool__less__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) )
% 5.41/5.73 = ( ~ P
% 5.41/5.73 & Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_iff
% 5.41/5.73 thf(fact_6253_of__bool__less__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) )
% 5.41/5.73 = ( ~ P
% 5.41/5.73 & Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_iff
% 5.41/5.73 thf(fact_6254_of__bool__less__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) )
% 5.41/5.73 = ( ~ P
% 5.41/5.73 & Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_iff
% 5.41/5.73 thf(fact_6255_of__bool__less__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) )
% 5.41/5.73 = ( ~ P
% 5.41/5.73 & Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_iff
% 5.41/5.73 thf(fact_6256_of__bool__less__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) )
% 5.41/5.73 = ( ~ P
% 5.41/5.73 & Q ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_iff
% 5.41/5.73 thf(fact_6257_of__bool__eq__1__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n1201886186963655149omplex @ P )
% 5.41/5.73 = one_one_complex )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_1_iff
% 5.41/5.73 thf(fact_6258_of__bool__eq__1__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n3304061248610475627l_real @ P )
% 5.41/5.73 = one_one_real )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_1_iff
% 5.41/5.73 thf(fact_6259_of__bool__eq__1__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n2052037380579107095ol_rat @ P )
% 5.41/5.73 = one_one_rat )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_1_iff
% 5.41/5.73 thf(fact_6260_of__bool__eq__1__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n2687167440665602831ol_nat @ P )
% 5.41/5.73 = one_one_nat )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_1_iff
% 5.41/5.73 thf(fact_6261_of__bool__eq__1__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n2684676970156552555ol_int @ P )
% 5.41/5.73 = one_one_int )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_1_iff
% 5.41/5.73 thf(fact_6262_of__bool__eq__1__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ( zero_n356916108424825756nteger @ P )
% 5.41/5.73 = one_one_Code_integer )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_1_iff
% 5.41/5.73 thf(fact_6263_of__bool__eq_I2_J,axiom,
% 5.41/5.73 ( ( zero_n1201886186963655149omplex @ $true )
% 5.41/5.73 = one_one_complex ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(2)
% 5.41/5.73 thf(fact_6264_of__bool__eq_I2_J,axiom,
% 5.41/5.73 ( ( zero_n3304061248610475627l_real @ $true )
% 5.41/5.73 = one_one_real ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(2)
% 5.41/5.73 thf(fact_6265_of__bool__eq_I2_J,axiom,
% 5.41/5.73 ( ( zero_n2052037380579107095ol_rat @ $true )
% 5.41/5.73 = one_one_rat ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(2)
% 5.41/5.73 thf(fact_6266_of__bool__eq_I2_J,axiom,
% 5.41/5.73 ( ( zero_n2687167440665602831ol_nat @ $true )
% 5.41/5.73 = one_one_nat ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(2)
% 5.41/5.73 thf(fact_6267_of__bool__eq_I2_J,axiom,
% 5.41/5.73 ( ( zero_n2684676970156552555ol_int @ $true )
% 5.41/5.73 = one_one_int ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(2)
% 5.41/5.73 thf(fact_6268_of__bool__eq_I2_J,axiom,
% 5.41/5.73 ( ( zero_n356916108424825756nteger @ $true )
% 5.41/5.73 = one_one_Code_integer ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq(2)
% 5.41/5.73 thf(fact_6269_signed__take__bit__of__0,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ N @ zero_zero_int )
% 5.41/5.73 = zero_zero_int ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_of_0
% 5.41/5.73 thf(fact_6270_replicate__eq__replicate,axiom,
% 5.41/5.73 ! [M: nat,X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.41/5.73 ( ( ( replicate_VEBT_VEBT @ M @ X )
% 5.41/5.73 = ( replicate_VEBT_VEBT @ N @ Y ) )
% 5.41/5.73 = ( ( M = N )
% 5.41/5.73 & ( ( M != zero_zero_nat )
% 5.41/5.73 => ( X = Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eq_replicate
% 5.41/5.73 thf(fact_6271_abs__bool__eq,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( abs_abs_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.41/5.73 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_bool_eq
% 5.41/5.73 thf(fact_6272_abs__bool__eq,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( abs_abs_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.41/5.73 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_bool_eq
% 5.41/5.73 thf(fact_6273_abs__bool__eq,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( abs_abs_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.41/5.73 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_bool_eq
% 5.41/5.73 thf(fact_6274_abs__bool__eq,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( abs_abs_Code_integer @ ( zero_n356916108424825756nteger @ P ) )
% 5.41/5.73 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_bool_eq
% 5.41/5.73 thf(fact_6275_zdvd1__eq,axiom,
% 5.41/5.73 ! [X: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ X @ one_one_int )
% 5.41/5.73 = ( ( abs_abs_int @ X )
% 5.41/5.73 = one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd1_eq
% 5.41/5.73 thf(fact_6276_length__replicate,axiom,
% 5.41/5.73 ! [N: nat,X: vEBT_VEBT] :
% 5.41/5.73 ( ( size_s6755466524823107622T_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.41/5.73 = N ) ).
% 5.41/5.73
% 5.41/5.73 % length_replicate
% 5.41/5.73 thf(fact_6277_length__replicate,axiom,
% 5.41/5.73 ! [N: nat,X: $o] :
% 5.41/5.73 ( ( size_size_list_o @ ( replicate_o @ N @ X ) )
% 5.41/5.73 = N ) ).
% 5.41/5.73
% 5.41/5.73 % length_replicate
% 5.41/5.73 thf(fact_6278_length__replicate,axiom,
% 5.41/5.73 ! [N: nat,X: nat] :
% 5.41/5.73 ( ( size_size_list_nat @ ( replicate_nat @ N @ X ) )
% 5.41/5.73 = N ) ).
% 5.41/5.73
% 5.41/5.73 % length_replicate
% 5.41/5.73 thf(fact_6279_length__replicate,axiom,
% 5.41/5.73 ! [N: nat,X: int] :
% 5.41/5.73 ( ( size_size_list_int @ ( replicate_int @ N @ X ) )
% 5.41/5.73 = N ) ).
% 5.41/5.73
% 5.41/5.73 % length_replicate
% 5.41/5.73 thf(fact_6280_arctan__eq__zero__iff,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ( arctan @ X )
% 5.41/5.73 = zero_zero_real )
% 5.41/5.73 = ( X = zero_zero_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % arctan_eq_zero_iff
% 5.41/5.73 thf(fact_6281_arctan__zero__zero,axiom,
% 5.41/5.73 ( ( arctan @ zero_zero_real )
% 5.41/5.73 = zero_zero_real ) ).
% 5.41/5.73
% 5.41/5.73 % arctan_zero_zero
% 5.41/5.73 thf(fact_6282_of__bool__or__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n2687167440665602831ol_nat
% 5.41/5.73 @ ( P
% 5.41/5.73 | Q ) )
% 5.41/5.73 = ( ord_max_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_or_iff
% 5.41/5.73 thf(fact_6283_of__bool__or__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n2684676970156552555ol_int
% 5.41/5.73 @ ( P
% 5.41/5.73 | Q ) )
% 5.41/5.73 = ( ord_max_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_or_iff
% 5.41/5.73 thf(fact_6284_of__bool__or__iff,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n356916108424825756nteger
% 5.41/5.73 @ ( P
% 5.41/5.73 | Q ) )
% 5.41/5.73 = ( ord_max_Code_integer @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_or_iff
% 5.41/5.73 thf(fact_6285_triangle__0,axiom,
% 5.41/5.73 ( ( nat_triangle @ zero_zero_nat )
% 5.41/5.73 = zero_zero_nat ) ).
% 5.41/5.73
% 5.41/5.73 % triangle_0
% 5.41/5.73 thf(fact_6286_zero__less__of__bool__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_of_bool_iff
% 5.41/5.73 thf(fact_6287_zero__less__of__bool__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_of_bool_iff
% 5.41/5.73 thf(fact_6288_zero__less__of__bool__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_of_bool_iff
% 5.41/5.73 thf(fact_6289_zero__less__of__bool__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_of_bool_iff
% 5.41/5.73 thf(fact_6290_zero__less__of__bool__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) )
% 5.41/5.73 = P ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_of_bool_iff
% 5.41/5.73 thf(fact_6291_of__bool__less__one__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_one_iff
% 5.41/5.73 thf(fact_6292_of__bool__less__one__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_one_iff
% 5.41/5.73 thf(fact_6293_of__bool__less__one__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_one_iff
% 5.41/5.73 thf(fact_6294_of__bool__less__one__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_less_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_one_iff
% 5.41/5.73 thf(fact_6295_of__bool__less__one__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( ord_le6747313008572928689nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer )
% 5.41/5.73 = ~ P ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_one_iff
% 5.41/5.73 thf(fact_6296_of__bool__not__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( zero_n1201886186963655149omplex @ ~ P )
% 5.41/5.73 = ( minus_minus_complex @ one_one_complex @ ( zero_n1201886186963655149omplex @ P ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_not_iff
% 5.41/5.73 thf(fact_6297_of__bool__not__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( zero_n3304061248610475627l_real @ ~ P )
% 5.41/5.73 = ( minus_minus_real @ one_one_real @ ( zero_n3304061248610475627l_real @ P ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_not_iff
% 5.41/5.73 thf(fact_6298_of__bool__not__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( zero_n2052037380579107095ol_rat @ ~ P )
% 5.41/5.73 = ( minus_minus_rat @ one_one_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_not_iff
% 5.41/5.73 thf(fact_6299_of__bool__not__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( zero_n2684676970156552555ol_int @ ~ P )
% 5.41/5.73 = ( minus_minus_int @ one_one_int @ ( zero_n2684676970156552555ol_int @ P ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_not_iff
% 5.41/5.73 thf(fact_6300_of__bool__not__iff,axiom,
% 5.41/5.73 ! [P: $o] :
% 5.41/5.73 ( ( zero_n356916108424825756nteger @ ~ P )
% 5.41/5.73 = ( minus_8373710615458151222nteger @ one_one_Code_integer @ ( zero_n356916108424825756nteger @ P ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_not_iff
% 5.41/5.73 thf(fact_6301_Suc__0__mod__eq,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.73 = ( zero_n2687167440665602831ol_nat
% 5.41/5.73 @ ( N
% 5.41/5.73 != ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Suc_0_mod_eq
% 5.41/5.73 thf(fact_6302_zabs__less__one__iff,axiom,
% 5.41/5.73 ! [Z: int] :
% 5.41/5.73 ( ( ord_less_int @ ( abs_abs_int @ Z ) @ one_one_int )
% 5.41/5.73 = ( Z = zero_zero_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % zabs_less_one_iff
% 5.41/5.73 thf(fact_6303_signed__take__bit__Suc__1,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ one_one_int )
% 5.41/5.73 = one_one_int ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_Suc_1
% 5.41/5.73 thf(fact_6304_signed__take__bit__of__minus__1,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( bit_ri6519982836138164636nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.73 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_of_minus_1
% 5.41/5.73 thf(fact_6305_signed__take__bit__of__minus__1,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_of_minus_1
% 5.41/5.73 thf(fact_6306_signed__take__bit__numeral__of__1,axiom,
% 5.41/5.73 ! [K: num] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ K ) @ one_one_int )
% 5.41/5.73 = one_one_int ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_numeral_of_1
% 5.41/5.73 thf(fact_6307_Ball__set__replicate,axiom,
% 5.41/5.73 ! [N: nat,A: int,P: int > $o] :
% 5.41/5.73 ( ( ! [X3: int] :
% 5.41/5.73 ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.41/5.73 => ( P @ X3 ) ) )
% 5.41/5.73 = ( ( P @ A )
% 5.41/5.73 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Ball_set_replicate
% 5.41/5.73 thf(fact_6308_Ball__set__replicate,axiom,
% 5.41/5.73 ! [N: nat,A: nat,P: nat > $o] :
% 5.41/5.73 ( ( ! [X3: nat] :
% 5.41/5.73 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.41/5.73 => ( P @ X3 ) ) )
% 5.41/5.73 = ( ( P @ A )
% 5.41/5.73 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Ball_set_replicate
% 5.41/5.73 thf(fact_6309_Ball__set__replicate,axiom,
% 5.41/5.73 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.41/5.73 ( ( ! [X3: vEBT_VEBT] :
% 5.41/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.41/5.73 => ( P @ X3 ) ) )
% 5.41/5.73 = ( ( P @ A )
% 5.41/5.73 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Ball_set_replicate
% 5.41/5.73 thf(fact_6310_Bex__set__replicate,axiom,
% 5.41/5.73 ! [N: nat,A: int,P: int > $o] :
% 5.41/5.73 ( ( ? [X3: int] :
% 5.41/5.73 ( ( member_int @ X3 @ ( set_int2 @ ( replicate_int @ N @ A ) ) )
% 5.41/5.73 & ( P @ X3 ) ) )
% 5.41/5.73 = ( ( P @ A )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Bex_set_replicate
% 5.41/5.73 thf(fact_6311_Bex__set__replicate,axiom,
% 5.41/5.73 ! [N: nat,A: nat,P: nat > $o] :
% 5.41/5.73 ( ( ? [X3: nat] :
% 5.41/5.73 ( ( member_nat @ X3 @ ( set_nat2 @ ( replicate_nat @ N @ A ) ) )
% 5.41/5.73 & ( P @ X3 ) ) )
% 5.41/5.73 = ( ( P @ A )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Bex_set_replicate
% 5.41/5.73 thf(fact_6312_Bex__set__replicate,axiom,
% 5.41/5.73 ! [N: nat,A: vEBT_VEBT,P: vEBT_VEBT > $o] :
% 5.41/5.73 ( ( ? [X3: vEBT_VEBT] :
% 5.41/5.73 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ A ) ) )
% 5.41/5.73 & ( P @ X3 ) ) )
% 5.41/5.73 = ( ( P @ A )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % Bex_set_replicate
% 5.41/5.73 thf(fact_6313_in__set__replicate,axiom,
% 5.41/5.73 ! [X: complex,N: nat,Y: complex] :
% 5.41/5.73 ( ( member_complex @ X @ ( set_complex2 @ ( replicate_complex @ N @ Y ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % in_set_replicate
% 5.41/5.73 thf(fact_6314_in__set__replicate,axiom,
% 5.41/5.73 ! [X: real,N: nat,Y: real] :
% 5.41/5.73 ( ( member_real @ X @ ( set_real2 @ ( replicate_real @ N @ Y ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % in_set_replicate
% 5.41/5.73 thf(fact_6315_in__set__replicate,axiom,
% 5.41/5.73 ! [X: set_nat,N: nat,Y: set_nat] :
% 5.41/5.73 ( ( member_set_nat @ X @ ( set_set_nat2 @ ( replicate_set_nat @ N @ Y ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % in_set_replicate
% 5.41/5.73 thf(fact_6316_in__set__replicate,axiom,
% 5.41/5.73 ! [X: int,N: nat,Y: int] :
% 5.41/5.73 ( ( member_int @ X @ ( set_int2 @ ( replicate_int @ N @ Y ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % in_set_replicate
% 5.41/5.73 thf(fact_6317_in__set__replicate,axiom,
% 5.41/5.73 ! [X: nat,N: nat,Y: nat] :
% 5.41/5.73 ( ( member_nat @ X @ ( set_nat2 @ ( replicate_nat @ N @ Y ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % in_set_replicate
% 5.41/5.73 thf(fact_6318_in__set__replicate,axiom,
% 5.41/5.73 ! [X: vEBT_VEBT,N: nat,Y: vEBT_VEBT] :
% 5.41/5.73 ( ( member_VEBT_VEBT @ X @ ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ Y ) ) )
% 5.41/5.73 = ( ( X = Y )
% 5.41/5.73 & ( N != zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % in_set_replicate
% 5.41/5.73 thf(fact_6319_zero__less__arctan__iff,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_real @ zero_zero_real @ ( arctan @ X ) )
% 5.41/5.73 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_arctan_iff
% 5.41/5.73 thf(fact_6320_arctan__less__zero__iff,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_real @ ( arctan @ X ) @ zero_zero_real )
% 5.41/5.73 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % arctan_less_zero_iff
% 5.41/5.73 thf(fact_6321_nth__replicate,axiom,
% 5.41/5.73 ! [I: nat,N: nat,X: nat] :
% 5.41/5.73 ( ( ord_less_nat @ I @ N )
% 5.41/5.73 => ( ( nth_nat @ ( replicate_nat @ N @ X ) @ I )
% 5.41/5.73 = X ) ) ).
% 5.41/5.73
% 5.41/5.73 % nth_replicate
% 5.41/5.73 thf(fact_6322_nth__replicate,axiom,
% 5.41/5.73 ! [I: nat,N: nat,X: int] :
% 5.41/5.73 ( ( ord_less_nat @ I @ N )
% 5.41/5.73 => ( ( nth_int @ ( replicate_int @ N @ X ) @ I )
% 5.41/5.73 = X ) ) ).
% 5.41/5.73
% 5.41/5.73 % nth_replicate
% 5.41/5.73 thf(fact_6323_nth__replicate,axiom,
% 5.41/5.73 ! [I: nat,N: nat,X: vEBT_VEBT] :
% 5.41/5.73 ( ( ord_less_nat @ I @ N )
% 5.41/5.73 => ( ( nth_VEBT_VEBT @ ( replicate_VEBT_VEBT @ N @ X ) @ I )
% 5.41/5.73 = X ) ) ).
% 5.41/5.73
% 5.41/5.73 % nth_replicate
% 5.41/5.73 thf(fact_6324_arctan__le__zero__iff,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( arctan @ X ) @ zero_zero_real )
% 5.41/5.73 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % arctan_le_zero_iff
% 5.41/5.73 thf(fact_6325_zero__le__arctan__iff,axiom,
% 5.41/5.73 ! [X: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ zero_zero_real @ ( arctan @ X ) )
% 5.41/5.73 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_le_arctan_iff
% 5.41/5.73 thf(fact_6326_triangle__Suc,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( nat_triangle @ ( suc @ N ) )
% 5.41/5.73 = ( plus_plus_nat @ ( nat_triangle @ N ) @ ( suc @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % triangle_Suc
% 5.41/5.73 thf(fact_6327_signed__take__bit__Suc__minus__bit0,axiom,
% 5.41/5.73 ! [N: nat,K: num] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.41/5.73 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_Suc_minus_bit0
% 5.41/5.73 thf(fact_6328_signed__take__bit__Suc__bit0,axiom,
% 5.41/5.73 ! [N: nat,K: num] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.41/5.73 = ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_Suc_bit0
% 5.41/5.73 thf(fact_6329_odd__of__bool__self,axiom,
% 5.41/5.73 ! [P5: $o] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( zero_n2687167440665602831ol_nat @ P5 ) ) )
% 5.41/5.73 = P5 ) ).
% 5.41/5.73
% 5.41/5.73 % odd_of_bool_self
% 5.41/5.73 thf(fact_6330_odd__of__bool__self,axiom,
% 5.41/5.73 ! [P5: $o] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( zero_n2684676970156552555ol_int @ P5 ) ) )
% 5.41/5.73 = P5 ) ).
% 5.41/5.73
% 5.41/5.73 % odd_of_bool_self
% 5.41/5.73 thf(fact_6331_odd__of__bool__self,axiom,
% 5.41/5.73 ! [P5: $o] :
% 5.41/5.73 ( ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( zero_n356916108424825756nteger @ P5 ) ) )
% 5.41/5.73 = P5 ) ).
% 5.41/5.73
% 5.41/5.73 % odd_of_bool_self
% 5.41/5.73 thf(fact_6332_of__bool__half__eq__0,axiom,
% 5.41/5.73 ! [B: $o] :
% 5.41/5.73 ( ( divide_divide_nat @ ( zero_n2687167440665602831ol_nat @ B ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_zero_nat ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_half_eq_0
% 5.41/5.73 thf(fact_6333_of__bool__half__eq__0,axiom,
% 5.41/5.73 ! [B: $o] :
% 5.41/5.73 ( ( divide_divide_int @ ( zero_n2684676970156552555ol_int @ B ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_zero_int ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_half_eq_0
% 5.41/5.73 thf(fact_6334_of__bool__half__eq__0,axiom,
% 5.41/5.73 ! [B: $o] :
% 5.41/5.73 ( ( divide6298287555418463151nteger @ ( zero_n356916108424825756nteger @ B ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = zero_z3403309356797280102nteger ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_half_eq_0
% 5.41/5.73 thf(fact_6335_signed__take__bit__0,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( bit_ri6519982836138164636nteger @ zero_zero_nat @ A )
% 5.41/5.73 = ( uminus1351360451143612070nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_0
% 5.41/5.73 thf(fact_6336_signed__take__bit__0,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ zero_zero_nat @ A )
% 5.41/5.73 = ( uminus_uminus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_0
% 5.41/5.73 thf(fact_6337_one__div__2__pow__eq,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % one_div_2_pow_eq
% 5.41/5.73 thf(fact_6338_one__div__2__pow__eq,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % one_div_2_pow_eq
% 5.41/5.73 thf(fact_6339_one__div__2__pow__eq,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % one_div_2_pow_eq
% 5.41/5.73 thf(fact_6340_bits__1__div__exp,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( divide_divide_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bits_1_div_exp
% 5.41/5.73 thf(fact_6341_bits__1__div__exp,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( divide_divide_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n2684676970156552555ol_int @ ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bits_1_div_exp
% 5.41/5.73 thf(fact_6342_bits__1__div__exp,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( divide6298287555418463151nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n356916108424825756nteger @ ( N = zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bits_1_div_exp
% 5.41/5.73 thf(fact_6343_one__mod__2__pow__eq,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( modulo_modulo_nat @ one_one_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % one_mod_2_pow_eq
% 5.41/5.73 thf(fact_6344_one__mod__2__pow__eq,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( modulo_modulo_int @ one_one_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % one_mod_2_pow_eq
% 5.41/5.73 thf(fact_6345_one__mod__2__pow__eq,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( modulo364778990260209775nteger @ one_one_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % one_mod_2_pow_eq
% 5.41/5.73 thf(fact_6346_dvd__antisym,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( dvd_dvd_nat @ M @ N )
% 5.41/5.73 => ( ( dvd_dvd_nat @ N @ M )
% 5.41/5.73 => ( M = N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_antisym
% 5.41/5.73 thf(fact_6347_of__bool__eq__iff,axiom,
% 5.41/5.73 ! [P5: $o,Q2: $o] :
% 5.41/5.73 ( ( ( zero_n2687167440665602831ol_nat @ P5 )
% 5.41/5.73 = ( zero_n2687167440665602831ol_nat @ Q2 ) )
% 5.41/5.73 = ( P5 = Q2 ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_iff
% 5.41/5.73 thf(fact_6348_of__bool__eq__iff,axiom,
% 5.41/5.73 ! [P5: $o,Q2: $o] :
% 5.41/5.73 ( ( ( zero_n2684676970156552555ol_int @ P5 )
% 5.41/5.73 = ( zero_n2684676970156552555ol_int @ Q2 ) )
% 5.41/5.73 = ( P5 = Q2 ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_iff
% 5.41/5.73 thf(fact_6349_of__bool__eq__iff,axiom,
% 5.41/5.73 ! [P5: $o,Q2: $o] :
% 5.41/5.73 ( ( ( zero_n356916108424825756nteger @ P5 )
% 5.41/5.73 = ( zero_n356916108424825756nteger @ Q2 ) )
% 5.41/5.73 = ( P5 = Q2 ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_eq_iff
% 5.41/5.73 thf(fact_6350_zabs__def,axiom,
% 5.41/5.73 ( abs_abs_int
% 5.41/5.73 = ( ^ [I5: int] : ( if_int @ ( ord_less_int @ I5 @ zero_zero_int ) @ ( uminus_uminus_int @ I5 ) @ I5 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zabs_def
% 5.41/5.73 thf(fact_6351_of__bool__conj,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n3304061248610475627l_real
% 5.41/5.73 @ ( P
% 5.41/5.73 & Q ) )
% 5.41/5.73 = ( times_times_real @ ( zero_n3304061248610475627l_real @ P ) @ ( zero_n3304061248610475627l_real @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_conj
% 5.41/5.73 thf(fact_6352_of__bool__conj,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n2052037380579107095ol_rat
% 5.41/5.73 @ ( P
% 5.41/5.73 & Q ) )
% 5.41/5.73 = ( times_times_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ ( zero_n2052037380579107095ol_rat @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_conj
% 5.41/5.73 thf(fact_6353_of__bool__conj,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n2687167440665602831ol_nat
% 5.41/5.73 @ ( P
% 5.41/5.73 & Q ) )
% 5.41/5.73 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ ( zero_n2687167440665602831ol_nat @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_conj
% 5.41/5.73 thf(fact_6354_of__bool__conj,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n2684676970156552555ol_int
% 5.41/5.73 @ ( P
% 5.41/5.73 & Q ) )
% 5.41/5.73 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ P ) @ ( zero_n2684676970156552555ol_int @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_conj
% 5.41/5.73 thf(fact_6355_of__bool__conj,axiom,
% 5.41/5.73 ! [P: $o,Q: $o] :
% 5.41/5.73 ( ( zero_n356916108424825756nteger
% 5.41/5.73 @ ( P
% 5.41/5.73 & Q ) )
% 5.41/5.73 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ P ) @ ( zero_n356916108424825756nteger @ Q ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_conj
% 5.41/5.73 thf(fact_6356_signed__take__bit__mult,axiom,
% 5.41/5.73 ! [N: nat,K: int,L2: int] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.41/5.73 = ( bit_ri631733984087533419it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_mult
% 5.41/5.73 thf(fact_6357_signed__take__bit__add,axiom,
% 5.41/5.73 ! [N: nat,K: int,L2: int] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.41/5.73 = ( bit_ri631733984087533419it_int @ N @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_add
% 5.41/5.73 thf(fact_6358_uminus__int__code_I1_J,axiom,
% 5.41/5.73 ( ( uminus_uminus_int @ zero_zero_int )
% 5.41/5.73 = zero_zero_int ) ).
% 5.41/5.73
% 5.41/5.73 % uminus_int_code(1)
% 5.41/5.73 thf(fact_6359_abs__div,axiom,
% 5.41/5.73 ! [Y: int,X: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ Y @ X )
% 5.41/5.73 => ( ( abs_abs_int @ ( divide_divide_int @ X @ Y ) )
% 5.41/5.73 = ( divide_divide_int @ ( abs_abs_int @ X ) @ ( abs_abs_int @ Y ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_div
% 5.41/5.73 thf(fact_6360_signed__take__bit__diff,axiom,
% 5.41/5.73 ! [N: nat,K: int,L2: int] :
% 5.41/5.73 ( ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( bit_ri631733984087533419it_int @ N @ L2 ) ) )
% 5.41/5.73 = ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_diff
% 5.41/5.73 thf(fact_6361_arctan__monotone_H,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.73 => ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % arctan_monotone'
% 5.41/5.73 thf(fact_6362_arctan__le__iff,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.41/5.73 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.73
% 5.41/5.73 % arctan_le_iff
% 5.41/5.73 thf(fact_6363_zero__less__eq__of__bool,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_real @ zero_zero_real @ ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_eq_of_bool
% 5.41/5.73 thf(fact_6364_zero__less__eq__of__bool,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_rat @ zero_zero_rat @ ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_eq_of_bool
% 5.41/5.73 thf(fact_6365_zero__less__eq__of__bool,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_nat @ zero_zero_nat @ ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_eq_of_bool
% 5.41/5.73 thf(fact_6366_zero__less__eq__of__bool,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_int @ zero_zero_int @ ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_eq_of_bool
% 5.41/5.73 thf(fact_6367_zero__less__eq__of__bool,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( zero_n356916108424825756nteger @ P ) ) ).
% 5.41/5.73
% 5.41/5.73 % zero_less_eq_of_bool
% 5.41/5.73 thf(fact_6368_of__bool__less__eq__one,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_real @ ( zero_n3304061248610475627l_real @ P ) @ one_one_real ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_one
% 5.41/5.73 thf(fact_6369_of__bool__less__eq__one,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_rat @ ( zero_n2052037380579107095ol_rat @ P ) @ one_one_rat ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_one
% 5.41/5.73 thf(fact_6370_of__bool__less__eq__one,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_nat @ ( zero_n2687167440665602831ol_nat @ P ) @ one_one_nat ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_one
% 5.41/5.73 thf(fact_6371_of__bool__less__eq__one,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_less_eq_int @ ( zero_n2684676970156552555ol_int @ P ) @ one_one_int ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_one
% 5.41/5.73 thf(fact_6372_of__bool__less__eq__one,axiom,
% 5.41/5.73 ! [P: $o] : ( ord_le3102999989581377725nteger @ ( zero_n356916108424825756nteger @ P ) @ one_one_Code_integer ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_less_eq_one
% 5.41/5.73 thf(fact_6373_of__bool__def,axiom,
% 5.41/5.73 ( zero_n1201886186963655149omplex
% 5.41/5.73 = ( ^ [P2: $o] : ( if_complex @ P2 @ one_one_complex @ zero_zero_complex ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_def
% 5.41/5.73 thf(fact_6374_of__bool__def,axiom,
% 5.41/5.73 ( zero_n3304061248610475627l_real
% 5.41/5.73 = ( ^ [P2: $o] : ( if_real @ P2 @ one_one_real @ zero_zero_real ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_def
% 5.41/5.73 thf(fact_6375_of__bool__def,axiom,
% 5.41/5.73 ( zero_n2052037380579107095ol_rat
% 5.41/5.73 = ( ^ [P2: $o] : ( if_rat @ P2 @ one_one_rat @ zero_zero_rat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_def
% 5.41/5.73 thf(fact_6376_of__bool__def,axiom,
% 5.41/5.73 ( zero_n2687167440665602831ol_nat
% 5.41/5.73 = ( ^ [P2: $o] : ( if_nat @ P2 @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_def
% 5.41/5.73 thf(fact_6377_of__bool__def,axiom,
% 5.41/5.73 ( zero_n2684676970156552555ol_int
% 5.41/5.73 = ( ^ [P2: $o] : ( if_int @ P2 @ one_one_int @ zero_zero_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_def
% 5.41/5.73 thf(fact_6378_of__bool__def,axiom,
% 5.41/5.73 ( zero_n356916108424825756nteger
% 5.41/5.73 = ( ^ [P2: $o] : ( if_Code_integer @ P2 @ one_one_Code_integer @ zero_z3403309356797280102nteger ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_def
% 5.41/5.73 thf(fact_6379_split__of__bool,axiom,
% 5.41/5.73 ! [P: complex > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 5.41/5.73 = ( ( P5
% 5.41/5.73 => ( P @ one_one_complex ) )
% 5.41/5.73 & ( ~ P5
% 5.41/5.73 => ( P @ zero_zero_complex ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool
% 5.41/5.73 thf(fact_6380_split__of__bool,axiom,
% 5.41/5.73 ! [P: real > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 5.41/5.73 = ( ( P5
% 5.41/5.73 => ( P @ one_one_real ) )
% 5.41/5.73 & ( ~ P5
% 5.41/5.73 => ( P @ zero_zero_real ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool
% 5.41/5.73 thf(fact_6381_split__of__bool,axiom,
% 5.41/5.73 ! [P: rat > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 5.41/5.73 = ( ( P5
% 5.41/5.73 => ( P @ one_one_rat ) )
% 5.41/5.73 & ( ~ P5
% 5.41/5.73 => ( P @ zero_zero_rat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool
% 5.41/5.73 thf(fact_6382_split__of__bool,axiom,
% 5.41/5.73 ! [P: nat > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 5.41/5.73 = ( ( P5
% 5.41/5.73 => ( P @ one_one_nat ) )
% 5.41/5.73 & ( ~ P5
% 5.41/5.73 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool
% 5.41/5.73 thf(fact_6383_split__of__bool,axiom,
% 5.41/5.73 ! [P: int > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 5.41/5.73 = ( ( P5
% 5.41/5.73 => ( P @ one_one_int ) )
% 5.41/5.73 & ( ~ P5
% 5.41/5.73 => ( P @ zero_zero_int ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool
% 5.41/5.73 thf(fact_6384_split__of__bool,axiom,
% 5.41/5.73 ! [P: code_integer > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 5.41/5.73 = ( ( P5
% 5.41/5.73 => ( P @ one_one_Code_integer ) )
% 5.41/5.73 & ( ~ P5
% 5.41/5.73 => ( P @ zero_z3403309356797280102nteger ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool
% 5.41/5.73 thf(fact_6385_split__of__bool__asm,axiom,
% 5.41/5.73 ! [P: complex > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n1201886186963655149omplex @ P5 ) )
% 5.41/5.73 = ( ~ ( ( P5
% 5.41/5.73 & ~ ( P @ one_one_complex ) )
% 5.41/5.73 | ( ~ P5
% 5.41/5.73 & ~ ( P @ zero_zero_complex ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool_asm
% 5.41/5.73 thf(fact_6386_split__of__bool__asm,axiom,
% 5.41/5.73 ! [P: real > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n3304061248610475627l_real @ P5 ) )
% 5.41/5.73 = ( ~ ( ( P5
% 5.41/5.73 & ~ ( P @ one_one_real ) )
% 5.41/5.73 | ( ~ P5
% 5.41/5.73 & ~ ( P @ zero_zero_real ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool_asm
% 5.41/5.73 thf(fact_6387_split__of__bool__asm,axiom,
% 5.41/5.73 ! [P: rat > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n2052037380579107095ol_rat @ P5 ) )
% 5.41/5.73 = ( ~ ( ( P5
% 5.41/5.73 & ~ ( P @ one_one_rat ) )
% 5.41/5.73 | ( ~ P5
% 5.41/5.73 & ~ ( P @ zero_zero_rat ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool_asm
% 5.41/5.73 thf(fact_6388_split__of__bool__asm,axiom,
% 5.41/5.73 ! [P: nat > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n2687167440665602831ol_nat @ P5 ) )
% 5.41/5.73 = ( ~ ( ( P5
% 5.41/5.73 & ~ ( P @ one_one_nat ) )
% 5.41/5.73 | ( ~ P5
% 5.41/5.73 & ~ ( P @ zero_zero_nat ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool_asm
% 5.41/5.73 thf(fact_6389_split__of__bool__asm,axiom,
% 5.41/5.73 ! [P: int > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n2684676970156552555ol_int @ P5 ) )
% 5.41/5.73 = ( ~ ( ( P5
% 5.41/5.73 & ~ ( P @ one_one_int ) )
% 5.41/5.73 | ( ~ P5
% 5.41/5.73 & ~ ( P @ zero_zero_int ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool_asm
% 5.41/5.73 thf(fact_6390_split__of__bool__asm,axiom,
% 5.41/5.73 ! [P: code_integer > $o,P5: $o] :
% 5.41/5.73 ( ( P @ ( zero_n356916108424825756nteger @ P5 ) )
% 5.41/5.73 = ( ~ ( ( P5
% 5.41/5.73 & ~ ( P @ one_one_Code_integer ) )
% 5.41/5.73 | ( ~ P5
% 5.41/5.73 & ~ ( P @ zero_z3403309356797280102nteger ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % split_of_bool_asm
% 5.41/5.73 thf(fact_6391_dvd__imp__le__int,axiom,
% 5.41/5.73 ! [I: int,D: int] :
% 5.41/5.73 ( ( I != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ D @ I )
% 5.41/5.73 => ( ord_less_eq_int @ ( abs_abs_int @ D ) @ ( abs_abs_int @ I ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % dvd_imp_le_int
% 5.41/5.73 thf(fact_6392_replicate__length__same,axiom,
% 5.41/5.73 ! [Xs: list_VEBT_VEBT,X: vEBT_VEBT] :
% 5.41/5.73 ( ! [X6: vEBT_VEBT] :
% 5.41/5.73 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.73 => ( X6 = X ) )
% 5.41/5.73 => ( ( replicate_VEBT_VEBT @ ( size_s6755466524823107622T_VEBT @ Xs ) @ X )
% 5.41/5.73 = Xs ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_length_same
% 5.41/5.73 thf(fact_6393_replicate__length__same,axiom,
% 5.41/5.73 ! [Xs: list_o,X: $o] :
% 5.41/5.73 ( ! [X6: $o] :
% 5.41/5.73 ( ( member_o @ X6 @ ( set_o2 @ Xs ) )
% 5.41/5.73 => ( X6 = X ) )
% 5.41/5.73 => ( ( replicate_o @ ( size_size_list_o @ Xs ) @ X )
% 5.41/5.73 = Xs ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_length_same
% 5.41/5.73 thf(fact_6394_replicate__length__same,axiom,
% 5.41/5.73 ! [Xs: list_nat,X: nat] :
% 5.41/5.73 ( ! [X6: nat] :
% 5.41/5.73 ( ( member_nat @ X6 @ ( set_nat2 @ Xs ) )
% 5.41/5.73 => ( X6 = X ) )
% 5.41/5.73 => ( ( replicate_nat @ ( size_size_list_nat @ Xs ) @ X )
% 5.41/5.73 = Xs ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_length_same
% 5.41/5.73 thf(fact_6395_replicate__length__same,axiom,
% 5.41/5.73 ! [Xs: list_int,X: int] :
% 5.41/5.73 ( ! [X6: int] :
% 5.41/5.73 ( ( member_int @ X6 @ ( set_int2 @ Xs ) )
% 5.41/5.73 => ( X6 = X ) )
% 5.41/5.73 => ( ( replicate_int @ ( size_size_list_int @ Xs ) @ X )
% 5.41/5.73 = Xs ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_length_same
% 5.41/5.73 thf(fact_6396_replicate__eqI,axiom,
% 5.41/5.73 ! [Xs: list_complex,N: nat,X: complex] :
% 5.41/5.73 ( ( ( size_s3451745648224563538omplex @ Xs )
% 5.41/5.73 = N )
% 5.41/5.73 => ( ! [Y5: complex] :
% 5.41/5.73 ( ( member_complex @ Y5 @ ( set_complex2 @ Xs ) )
% 5.41/5.73 => ( Y5 = X ) )
% 5.41/5.73 => ( Xs
% 5.41/5.73 = ( replicate_complex @ N @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eqI
% 5.41/5.73 thf(fact_6397_replicate__eqI,axiom,
% 5.41/5.73 ! [Xs: list_real,N: nat,X: real] :
% 5.41/5.73 ( ( ( size_size_list_real @ Xs )
% 5.41/5.73 = N )
% 5.41/5.73 => ( ! [Y5: real] :
% 5.41/5.73 ( ( member_real @ Y5 @ ( set_real2 @ Xs ) )
% 5.41/5.73 => ( Y5 = X ) )
% 5.41/5.73 => ( Xs
% 5.41/5.73 = ( replicate_real @ N @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eqI
% 5.41/5.73 thf(fact_6398_replicate__eqI,axiom,
% 5.41/5.73 ! [Xs: list_set_nat,N: nat,X: set_nat] :
% 5.41/5.73 ( ( ( size_s3254054031482475050et_nat @ Xs )
% 5.41/5.73 = N )
% 5.41/5.73 => ( ! [Y5: set_nat] :
% 5.41/5.73 ( ( member_set_nat @ Y5 @ ( set_set_nat2 @ Xs ) )
% 5.41/5.73 => ( Y5 = X ) )
% 5.41/5.73 => ( Xs
% 5.41/5.73 = ( replicate_set_nat @ N @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eqI
% 5.41/5.73 thf(fact_6399_replicate__eqI,axiom,
% 5.41/5.73 ! [Xs: list_VEBT_VEBT,N: nat,X: vEBT_VEBT] :
% 5.41/5.73 ( ( ( size_s6755466524823107622T_VEBT @ Xs )
% 5.41/5.73 = N )
% 5.41/5.73 => ( ! [Y5: vEBT_VEBT] :
% 5.41/5.73 ( ( member_VEBT_VEBT @ Y5 @ ( set_VEBT_VEBT2 @ Xs ) )
% 5.41/5.73 => ( Y5 = X ) )
% 5.41/5.73 => ( Xs
% 5.41/5.73 = ( replicate_VEBT_VEBT @ N @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eqI
% 5.41/5.73 thf(fact_6400_replicate__eqI,axiom,
% 5.41/5.73 ! [Xs: list_o,N: nat,X: $o] :
% 5.41/5.73 ( ( ( size_size_list_o @ Xs )
% 5.41/5.73 = N )
% 5.41/5.73 => ( ! [Y5: $o] :
% 5.41/5.73 ( ( member_o @ Y5 @ ( set_o2 @ Xs ) )
% 5.41/5.73 => ( Y5 = X ) )
% 5.41/5.73 => ( Xs
% 5.41/5.73 = ( replicate_o @ N @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eqI
% 5.41/5.73 thf(fact_6401_replicate__eqI,axiom,
% 5.41/5.73 ! [Xs: list_nat,N: nat,X: nat] :
% 5.41/5.73 ( ( ( size_size_list_nat @ Xs )
% 5.41/5.73 = N )
% 5.41/5.73 => ( ! [Y5: nat] :
% 5.41/5.73 ( ( member_nat @ Y5 @ ( set_nat2 @ Xs ) )
% 5.41/5.73 => ( Y5 = X ) )
% 5.41/5.73 => ( Xs
% 5.41/5.73 = ( replicate_nat @ N @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eqI
% 5.41/5.73 thf(fact_6402_replicate__eqI,axiom,
% 5.41/5.73 ! [Xs: list_int,N: nat,X: int] :
% 5.41/5.73 ( ( ( size_size_list_int @ Xs )
% 5.41/5.73 = N )
% 5.41/5.73 => ( ! [Y5: int] :
% 5.41/5.73 ( ( member_int @ Y5 @ ( set_int2 @ Xs ) )
% 5.41/5.73 => ( Y5 = X ) )
% 5.41/5.73 => ( Xs
% 5.41/5.73 = ( replicate_int @ N @ X ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % replicate_eqI
% 5.41/5.73 thf(fact_6403_abs__zmult__eq__1,axiom,
% 5.41/5.73 ! [M: int,N: int] :
% 5.41/5.73 ( ( ( abs_abs_int @ ( times_times_int @ M @ N ) )
% 5.41/5.73 = one_one_int )
% 5.41/5.73 => ( ( abs_abs_int @ M )
% 5.41/5.73 = one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_zmult_eq_1
% 5.41/5.73 thf(fact_6404_subset__Compl__self__eq,axiom,
% 5.41/5.73 ! [A2: set_nat] :
% 5.41/5.73 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ A2 ) )
% 5.41/5.73 = ( A2 = bot_bot_set_nat ) ) ).
% 5.41/5.73
% 5.41/5.73 % subset_Compl_self_eq
% 5.41/5.73 thf(fact_6405_subset__Compl__self__eq,axiom,
% 5.41/5.73 ! [A2: set_real] :
% 5.41/5.73 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ A2 ) )
% 5.41/5.73 = ( A2 = bot_bot_set_real ) ) ).
% 5.41/5.73
% 5.41/5.73 % subset_Compl_self_eq
% 5.41/5.73 thf(fact_6406_subset__Compl__self__eq,axiom,
% 5.41/5.73 ! [A2: set_int] :
% 5.41/5.73 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ A2 ) )
% 5.41/5.73 = ( A2 = bot_bot_set_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % subset_Compl_self_eq
% 5.41/5.73 thf(fact_6407_zmult__eq__1__iff,axiom,
% 5.41/5.73 ! [M: int,N: int] :
% 5.41/5.73 ( ( ( times_times_int @ M @ N )
% 5.41/5.73 = one_one_int )
% 5.41/5.73 = ( ( ( M = one_one_int )
% 5.41/5.73 & ( N = one_one_int ) )
% 5.41/5.73 | ( ( M
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.73 & ( N
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zmult_eq_1_iff
% 5.41/5.73 thf(fact_6408_pos__zmult__eq__1__iff__lemma,axiom,
% 5.41/5.73 ! [M: int,N: int] :
% 5.41/5.73 ( ( ( times_times_int @ M @ N )
% 5.41/5.73 = one_one_int )
% 5.41/5.73 => ( ( M = one_one_int )
% 5.41/5.73 | ( M
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % pos_zmult_eq_1_iff_lemma
% 5.41/5.73 thf(fact_6409_minus__int__code_I2_J,axiom,
% 5.41/5.73 ! [L2: int] :
% 5.41/5.73 ( ( minus_minus_int @ zero_zero_int @ L2 )
% 5.41/5.73 = ( uminus_uminus_int @ L2 ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_int_code(2)
% 5.41/5.73 thf(fact_6410_zmod__zminus1__not__zero,axiom,
% 5.41/5.73 ! [K: int,L2: int] :
% 5.41/5.73 ( ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.41/5.73 != zero_zero_int )
% 5.41/5.73 => ( ( modulo_modulo_int @ K @ L2 )
% 5.41/5.73 != zero_zero_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % zmod_zminus1_not_zero
% 5.41/5.73 thf(fact_6411_zmod__zminus2__not__zero,axiom,
% 5.41/5.73 ! [K: int,L2: int] :
% 5.41/5.73 ( ( ( modulo_modulo_int @ K @ ( uminus_uminus_int @ L2 ) )
% 5.41/5.73 != zero_zero_int )
% 5.41/5.73 => ( ( modulo_modulo_int @ K @ L2 )
% 5.41/5.73 != zero_zero_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % zmod_zminus2_not_zero
% 5.41/5.73 thf(fact_6412_signed__take__bit__int__less__eq__self__iff,axiom,
% 5.41/5.73 ! [N: nat,K: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.41/5.73 = ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_less_eq_self_iff
% 5.41/5.73 thf(fact_6413_signed__take__bit__int__greater__eq__minus__exp,axiom,
% 5.41/5.73 ! [N: nat,K: int] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_greater_eq_minus_exp
% 5.41/5.73 thf(fact_6414_signed__take__bit__int__greater__self__iff,axiom,
% 5.41/5.73 ! [K: int,N: nat] :
% 5.41/5.73 ( ( ord_less_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.41/5.73 = ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_greater_self_iff
% 5.41/5.73 thf(fact_6415_signed__take__bit__int__eq__self,axiom,
% 5.41/5.73 ! [N: nat,K: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.41/5.73 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 => ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.41/5.73 = K ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_eq_self
% 5.41/5.73 thf(fact_6416_signed__take__bit__int__eq__self__iff,axiom,
% 5.41/5.73 ! [N: nat,K: int] :
% 5.41/5.73 ( ( ( bit_ri631733984087533419it_int @ N @ K )
% 5.41/5.73 = K )
% 5.41/5.73 = ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ K )
% 5.41/5.73 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_eq_self_iff
% 5.41/5.73 thf(fact_6417_zdvd__mult__cancel1,axiom,
% 5.41/5.73 ! [M: int,N: int] :
% 5.41/5.73 ( ( M != zero_zero_int )
% 5.41/5.73 => ( ( dvd_dvd_int @ ( times_times_int @ M @ N ) @ M )
% 5.41/5.73 = ( ( abs_abs_int @ N )
% 5.41/5.73 = one_one_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdvd_mult_cancel1
% 5.41/5.73 thf(fact_6418_abs__mod__less,axiom,
% 5.41/5.73 ! [L2: int,K: int] :
% 5.41/5.73 ( ( L2 != zero_zero_int )
% 5.41/5.73 => ( ord_less_int @ ( abs_abs_int @ ( modulo_modulo_int @ K @ L2 ) ) @ ( abs_abs_int @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % abs_mod_less
% 5.41/5.73 thf(fact_6419_zmod__zminus1__eq__if,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.73 = zero_zero_int ) )
% 5.41/5.73 & ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 != zero_zero_int )
% 5.41/5.73 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.73 = ( minus_minus_int @ B @ ( modulo_modulo_int @ A @ B ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zmod_zminus1_eq_if
% 5.41/5.73 thf(fact_6420_zmod__zminus2__eq__if,axiom,
% 5.41/5.73 ! [A: int,B: int] :
% 5.41/5.73 ( ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.73 = zero_zero_int ) )
% 5.41/5.73 & ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 != zero_zero_int )
% 5.41/5.73 => ( ( modulo_modulo_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.73 = ( minus_minus_int @ ( modulo_modulo_int @ A @ B ) @ B ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zmod_zminus2_eq_if
% 5.41/5.73 thf(fact_6421_even__abs__add__iff,axiom,
% 5.41/5.73 ! [K: int,L2: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ ( abs_abs_int @ K ) @ L2 ) )
% 5.41/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_abs_add_iff
% 5.41/5.73 thf(fact_6422_even__add__abs__iff,axiom,
% 5.41/5.73 ! [K: int,L2: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ ( abs_abs_int @ L2 ) ) )
% 5.41/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( plus_plus_int @ K @ L2 ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_add_abs_iff
% 5.41/5.73 thf(fact_6423_signed__take__bit__int__greater__eq,axiom,
% 5.41/5.73 ! [K: int,N: nat] :
% 5.41/5.73 ( ( ord_less_int @ K @ ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.73 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) @ ( bit_ri631733984087533419it_int @ N @ K ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_greater_eq
% 5.41/5.73 thf(fact_6424_verit__less__mono__div__int2,axiom,
% 5.41/5.73 ! [A2: int,B3: int,N: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ A2 @ B3 )
% 5.41/5.73 => ( ( ord_less_int @ zero_zero_int @ ( uminus_uminus_int @ N ) )
% 5.41/5.73 => ( ord_less_eq_int @ ( divide_divide_int @ B3 @ N ) @ ( divide_divide_int @ A2 @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % verit_less_mono_div_int2
% 5.41/5.73 thf(fact_6425_div__eq__minus1,axiom,
% 5.41/5.73 ! [B: int] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.73 => ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_eq_minus1
% 5.41/5.73 thf(fact_6426_of__bool__odd__eq__mod__2,axiom,
% 5.41/5.73 ! [A: nat] :
% 5.41/5.73 ( ( zero_n2687167440665602831ol_nat
% 5.41/5.73 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.73 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_odd_eq_mod_2
% 5.41/5.73 thf(fact_6427_of__bool__odd__eq__mod__2,axiom,
% 5.41/5.73 ! [A: int] :
% 5.41/5.73 ( ( zero_n2684676970156552555ol_int
% 5.41/5.73 @ ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.73 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_odd_eq_mod_2
% 5.41/5.73 thf(fact_6428_of__bool__odd__eq__mod__2,axiom,
% 5.41/5.73 ! [A: code_integer] :
% 5.41/5.73 ( ( zero_n356916108424825756nteger
% 5.41/5.73 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) )
% 5.41/5.73 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % of_bool_odd_eq_mod_2
% 5.41/5.73 thf(fact_6429_signed__take__bit__int__less__exp,axiom,
% 5.41/5.73 ! [N: nat,K: int] : ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_less_exp
% 5.41/5.73 thf(fact_6430_even__signed__take__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: code_integer] :
% 5.41/5.73 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ M @ A ) )
% 5.41/5.73 = ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_signed_take_bit_iff
% 5.41/5.73 thf(fact_6431_even__signed__take__bit__iff,axiom,
% 5.41/5.73 ! [M: nat,A: int] :
% 5.41/5.73 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ M @ A ) )
% 5.41/5.73 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ).
% 5.41/5.73
% 5.41/5.73 % even_signed_take_bit_iff
% 5.41/5.73 thf(fact_6432_minus__mod__int__eq,axiom,
% 5.41/5.73 ! [L2: int,K: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.41/5.73 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ K ) @ L2 )
% 5.41/5.73 = ( minus_minus_int @ ( minus_minus_int @ L2 @ one_one_int ) @ ( modulo_modulo_int @ ( minus_minus_int @ K @ one_one_int ) @ L2 ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_mod_int_eq
% 5.41/5.73 thf(fact_6433_zmod__minus1,axiom,
% 5.41/5.73 ! [B: int] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.73 => ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ B )
% 5.41/5.73 = ( minus_minus_int @ B @ one_one_int ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zmod_minus1
% 5.41/5.73 thf(fact_6434_zdiv__zminus1__eq__if,axiom,
% 5.41/5.73 ! [B: int,A: int] :
% 5.41/5.73 ( ( B != zero_zero_int )
% 5.41/5.73 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.73 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.41/5.73 & ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 != zero_zero_int )
% 5.41/5.73 => ( ( divide_divide_int @ ( uminus_uminus_int @ A ) @ B )
% 5.41/5.73 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdiv_zminus1_eq_if
% 5.41/5.73 thf(fact_6435_zdiv__zminus2__eq__if,axiom,
% 5.41/5.73 ! [B: int,A: int] :
% 5.41/5.73 ( ( B != zero_zero_int )
% 5.41/5.73 => ( ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 = zero_zero_int )
% 5.41/5.73 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.73 = ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) ) )
% 5.41/5.73 & ( ( ( modulo_modulo_int @ A @ B )
% 5.41/5.73 != zero_zero_int )
% 5.41/5.73 => ( ( divide_divide_int @ A @ ( uminus_uminus_int @ B ) )
% 5.41/5.73 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ A @ B ) ) @ one_one_int ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zdiv_zminus2_eq_if
% 5.41/5.73 thf(fact_6436_zminus1__lemma,axiom,
% 5.41/5.73 ! [A: int,B: int,Q2: int,R: int] :
% 5.41/5.73 ( ( eucl_rel_int @ A @ B @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.73 => ( ( B != zero_zero_int )
% 5.41/5.73 => ( eucl_rel_int @ ( uminus_uminus_int @ A ) @ B @ ( product_Pair_int_int @ ( if_int @ ( R = zero_zero_int ) @ ( uminus_uminus_int @ Q2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ Q2 ) @ one_one_int ) ) @ ( if_int @ ( R = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ B @ R ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % zminus1_lemma
% 5.41/5.73 thf(fact_6437_bits__induct,axiom,
% 5.41/5.73 ! [P: nat > $o,A: nat] :
% 5.41/5.73 ( ! [A5: nat] :
% 5.41/5.73 ( ( ( divide_divide_nat @ A5 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = A5 )
% 5.41/5.73 => ( P @ A5 ) )
% 5.41/5.73 => ( ! [A5: nat,B5: $o] :
% 5.41/5.73 ( ( P @ A5 )
% 5.41/5.73 => ( ( ( divide_divide_nat @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.73 = A5 )
% 5.41/5.73 => ( P @ ( plus_plus_nat @ ( zero_n2687167440665602831ol_nat @ B5 ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.41/5.73 => ( P @ A ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bits_induct
% 5.41/5.73 thf(fact_6438_bits__induct,axiom,
% 5.41/5.73 ! [P: int > $o,A: int] :
% 5.41/5.73 ( ! [A5: int] :
% 5.41/5.73 ( ( ( divide_divide_int @ A5 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = A5 )
% 5.41/5.73 => ( P @ A5 ) )
% 5.41/5.73 => ( ! [A5: int,B5: $o] :
% 5.41/5.73 ( ( P @ A5 )
% 5.41/5.73 => ( ( ( divide_divide_int @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.73 = A5 )
% 5.41/5.73 => ( P @ ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ B5 ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.41/5.73 => ( P @ A ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bits_induct
% 5.41/5.73 thf(fact_6439_bits__induct,axiom,
% 5.41/5.73 ! [P: code_integer > $o,A: code_integer] :
% 5.41/5.73 ( ! [A5: code_integer] :
% 5.41/5.73 ( ( ( divide6298287555418463151nteger @ A5 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = A5 )
% 5.41/5.73 => ( P @ A5 ) )
% 5.41/5.73 => ( ! [A5: code_integer,B5: $o] :
% 5.41/5.73 ( ( P @ A5 )
% 5.41/5.73 => ( ( ( divide6298287555418463151nteger @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.73 = A5 )
% 5.41/5.73 => ( P @ ( plus_p5714425477246183910nteger @ ( zero_n356916108424825756nteger @ B5 ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A5 ) ) ) ) )
% 5.41/5.73 => ( P @ A ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % bits_induct
% 5.41/5.73 thf(fact_6440_nat__intermed__int__val,axiom,
% 5.41/5.73 ! [M: nat,N: nat,F: nat > int,K: int] :
% 5.41/5.73 ( ! [I4: nat] :
% 5.41/5.73 ( ( ( ord_less_eq_nat @ M @ I4 )
% 5.41/5.73 & ( ord_less_nat @ I4 @ N ) )
% 5.41/5.73 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.41/5.73 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.73 => ( ( ord_less_eq_int @ ( F @ M ) @ K )
% 5.41/5.73 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.41/5.73 => ? [I4: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ M @ I4 )
% 5.41/5.73 & ( ord_less_eq_nat @ I4 @ N )
% 5.41/5.73 & ( ( F @ I4 )
% 5.41/5.73 = K ) ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nat_intermed_int_val
% 5.41/5.73 thf(fact_6441_decr__lemma,axiom,
% 5.41/5.73 ! [D: int,X: int,Z: int] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ D )
% 5.41/5.73 => ( ord_less_int @ ( minus_minus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) @ Z ) ) ).
% 5.41/5.73
% 5.41/5.73 % decr_lemma
% 5.41/5.73 thf(fact_6442_incr__lemma,axiom,
% 5.41/5.73 ! [D: int,Z: int,X: int] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ D )
% 5.41/5.73 => ( ord_less_int @ Z @ ( plus_plus_int @ X @ ( times_times_int @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ X @ Z ) ) @ one_one_int ) @ D ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % incr_lemma
% 5.41/5.73 thf(fact_6443_signed__take__bit__int__less__self__iff,axiom,
% 5.41/5.73 ! [N: nat,K: int] :
% 5.41/5.73 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ K )
% 5.41/5.73 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_less_self_iff
% 5.41/5.73 thf(fact_6444_signed__take__bit__int__greater__eq__self__iff,axiom,
% 5.41/5.73 ! [K: int,N: nat] :
% 5.41/5.73 ( ( ord_less_eq_int @ K @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.41/5.73 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_greater_eq_self_iff
% 5.41/5.73 thf(fact_6445_minus__1__div__exp__eq__int,axiom,
% 5.41/5.73 ! [N: nat] :
% 5.41/5.73 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.73
% 5.41/5.73 % minus_1_div_exp_eq_int
% 5.41/5.73 thf(fact_6446_div__pos__neg__trivial,axiom,
% 5.41/5.73 ! [K: int,L2: int] :
% 5.41/5.73 ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.73 => ( ( ord_less_eq_int @ ( plus_plus_int @ K @ L2 ) @ zero_zero_int )
% 5.41/5.73 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.73 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % div_pos_neg_trivial
% 5.41/5.73 thf(fact_6447_compl__mono,axiom,
% 5.41/5.73 ! [X: set_int,Y: set_int] :
% 5.41/5.73 ( ( ord_less_eq_set_int @ X @ Y )
% 5.41/5.73 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ ( uminus1532241313380277803et_int @ X ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % compl_mono
% 5.41/5.73 thf(fact_6448_compl__le__swap1,axiom,
% 5.41/5.73 ! [Y: set_int,X: set_int] :
% 5.41/5.73 ( ( ord_less_eq_set_int @ Y @ ( uminus1532241313380277803et_int @ X ) )
% 5.41/5.73 => ( ord_less_eq_set_int @ X @ ( uminus1532241313380277803et_int @ Y ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % compl_le_swap1
% 5.41/5.73 thf(fact_6449_compl__le__swap2,axiom,
% 5.41/5.73 ! [Y: set_int,X: set_int] :
% 5.41/5.73 ( ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ Y ) @ X )
% 5.41/5.73 => ( ord_less_eq_set_int @ ( uminus1532241313380277803et_int @ X ) @ Y ) ) ).
% 5.41/5.73
% 5.41/5.73 % compl_le_swap2
% 5.41/5.73 thf(fact_6450_exp__mod__exp,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( modulo_modulo_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ M @ N ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % exp_mod_exp
% 5.41/5.73 thf(fact_6451_exp__mod__exp,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( modulo_modulo_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ M @ N ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % exp_mod_exp
% 5.41/5.73 thf(fact_6452_exp__mod__exp,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( modulo364778990260209775nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ M @ N ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % exp_mod_exp
% 5.41/5.73 thf(fact_6453_nat__ivt__aux,axiom,
% 5.41/5.73 ! [N: nat,F: nat > int,K: int] :
% 5.41/5.73 ( ! [I4: nat] :
% 5.41/5.73 ( ( ord_less_nat @ I4 @ N )
% 5.41/5.73 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( suc @ I4 ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.41/5.73 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.41/5.73 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.41/5.73 => ? [I4: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ I4 @ N )
% 5.41/5.73 & ( ( F @ I4 )
% 5.41/5.73 = K ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nat_ivt_aux
% 5.41/5.73 thf(fact_6454_signed__take__bit__int__less__eq,axiom,
% 5.41/5.73 ! [N: nat,K: int] :
% 5.41/5.73 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.41/5.73 => ( ord_less_eq_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % signed_take_bit_int_less_eq
% 5.41/5.73 thf(fact_6455_int__bit__induct,axiom,
% 5.41/5.73 ! [P: int > $o,K: int] :
% 5.41/5.73 ( ( P @ zero_zero_int )
% 5.41/5.73 => ( ( P @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.73 => ( ! [K3: int] :
% 5.41/5.73 ( ( P @ K3 )
% 5.41/5.73 => ( ( K3 != zero_zero_int )
% 5.41/5.73 => ( P @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.73 => ( ! [K3: int] :
% 5.41/5.73 ( ( P @ K3 )
% 5.41/5.73 => ( ( K3
% 5.41/5.73 != ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.73 => ( P @ ( plus_plus_int @ one_one_int @ ( times_times_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) )
% 5.41/5.73 => ( P @ K ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % int_bit_induct
% 5.41/5.73 thf(fact_6456_nat0__intermed__int__val,axiom,
% 5.41/5.73 ! [N: nat,F: nat > int,K: int] :
% 5.41/5.73 ( ! [I4: nat] :
% 5.41/5.73 ( ( ord_less_nat @ I4 @ N )
% 5.41/5.73 => ( ord_less_eq_int @ ( abs_abs_int @ ( minus_minus_int @ ( F @ ( plus_plus_nat @ I4 @ one_one_nat ) ) @ ( F @ I4 ) ) ) @ one_one_int ) )
% 5.41/5.73 => ( ( ord_less_eq_int @ ( F @ zero_zero_nat ) @ K )
% 5.41/5.73 => ( ( ord_less_eq_int @ K @ ( F @ N ) )
% 5.41/5.73 => ? [I4: nat] :
% 5.41/5.73 ( ( ord_less_eq_nat @ I4 @ N )
% 5.41/5.73 & ( ( F @ I4 )
% 5.41/5.73 = K ) ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % nat0_intermed_int_val
% 5.41/5.73 thf(fact_6457_exp__div__exp__eq,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( divide_divide_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( times_times_nat
% 5.41/5.73 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.73 @ ( ( ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M )
% 5.41/5.73 != zero_zero_nat )
% 5.41/5.73 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.41/5.73 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % exp_div_exp_eq
% 5.41/5.73 thf(fact_6458_exp__div__exp__eq,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( divide_divide_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( times_times_int
% 5.41/5.73 @ ( zero_n2684676970156552555ol_int
% 5.41/5.73 @ ( ( ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ M )
% 5.41/5.73 != zero_zero_int )
% 5.41/5.73 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.41/5.73 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % exp_div_exp_eq
% 5.41/5.73 thf(fact_6459_exp__div__exp__eq,axiom,
% 5.41/5.73 ! [M: nat,N: nat] :
% 5.41/5.73 ( ( divide6298287555418463151nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.73 = ( times_3573771949741848930nteger
% 5.41/5.73 @ ( zero_n356916108424825756nteger
% 5.41/5.73 @ ( ( ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ M )
% 5.41/5.73 != zero_z3403309356797280102nteger )
% 5.41/5.73 & ( ord_less_eq_nat @ N @ M ) ) )
% 5.41/5.73 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( minus_minus_nat @ M @ N ) ) ) ) ).
% 5.41/5.73
% 5.41/5.73 % exp_div_exp_eq
% 5.41/5.73 thf(fact_6460_arctan__add,axiom,
% 5.41/5.73 ! [X: real,Y: real] :
% 5.41/5.73 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.73 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.73 => ( ( plus_plus_real @ ( arctan @ X ) @ ( arctan @ Y ) )
% 5.41/5.73 = ( arctan @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( minus_minus_real @ one_one_real @ ( times_times_real @ X @ Y ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % arctan_add
% 5.41/5.74 thf(fact_6461_vebt__buildup_Osimps_I3_J,axiom,
% 5.41/5.74 ! [Va: nat] :
% 5.41/5.74 ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.41/5.74 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.41/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.41/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va ) ) )
% 5.41/5.74 => ( ( vEBT_vebt_buildup @ ( suc @ ( suc @ Va ) ) )
% 5.41/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % vebt_buildup.simps(3)
% 5.41/5.74 thf(fact_6462_diff__shunt__var,axiom,
% 5.41/5.74 ! [X: set_real,Y: set_real] :
% 5.41/5.74 ( ( ( minus_minus_set_real @ X @ Y )
% 5.41/5.74 = bot_bot_set_real )
% 5.41/5.74 = ( ord_less_eq_set_real @ X @ Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % diff_shunt_var
% 5.41/5.74 thf(fact_6463_diff__shunt__var,axiom,
% 5.41/5.74 ! [X: set_nat,Y: set_nat] :
% 5.41/5.74 ( ( ( minus_minus_set_nat @ X @ Y )
% 5.41/5.74 = bot_bot_set_nat )
% 5.41/5.74 = ( ord_less_eq_set_nat @ X @ Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % diff_shunt_var
% 5.41/5.74 thf(fact_6464_diff__shunt__var,axiom,
% 5.41/5.74 ! [X: set_int,Y: set_int] :
% 5.41/5.74 ( ( ( minus_minus_set_int @ X @ Y )
% 5.41/5.74 = bot_bot_set_int )
% 5.41/5.74 = ( ord_less_eq_set_int @ X @ Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % diff_shunt_var
% 5.41/5.74 thf(fact_6465_signed__take__bit__Suc,axiom,
% 5.41/5.74 ! [N: nat,A: code_integer] :
% 5.41/5.74 ( ( bit_ri6519982836138164636nteger @ ( suc @ N ) @ A )
% 5.41/5.74 = ( plus_p5714425477246183910nteger @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_ri6519982836138164636nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_Suc
% 5.41/5.74 thf(fact_6466_signed__take__bit__Suc,axiom,
% 5.41/5.74 ! [N: nat,A: int] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ A )
% 5.41/5.74 = ( plus_plus_int @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri631733984087533419it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_Suc
% 5.41/5.74 thf(fact_6467_Divides_Oadjust__div__eq,axiom,
% 5.41/5.74 ! [Q2: int,R: int] :
% 5.41/5.74 ( ( adjust_div @ ( product_Pair_int_int @ Q2 @ R ) )
% 5.41/5.74 = ( plus_plus_int @ Q2 @ ( zero_n2684676970156552555ol_int @ ( R != zero_zero_int ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % Divides.adjust_div_eq
% 5.41/5.74 thf(fact_6468_vebt__buildup_Opelims,axiom,
% 5.41/5.74 ! [X: nat,Y: vEBT_VEBT] :
% 5.41/5.74 ( ( ( vEBT_vebt_buildup @ X )
% 5.41/5.74 = Y )
% 5.41/5.74 => ( ( accp_nat @ vEBT_v4011308405150292612up_rel @ X )
% 5.41/5.74 => ( ( ( X = zero_zero_nat )
% 5.41/5.74 => ( ( Y
% 5.41/5.74 = ( vEBT_Leaf @ $false @ $false ) )
% 5.41/5.74 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ zero_zero_nat ) ) )
% 5.41/5.74 => ( ( ( X
% 5.41/5.74 = ( suc @ zero_zero_nat ) )
% 5.41/5.74 => ( ( Y
% 5.41/5.74 = ( vEBT_Leaf @ $false @ $false ) )
% 5.41/5.74 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ zero_zero_nat ) ) ) )
% 5.41/5.74 => ~ ! [Va2: nat] :
% 5.41/5.74 ( ( X
% 5.41/5.74 = ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.74 => ( ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.74 => ( Y
% 5.41/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) )
% 5.41/5.74 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( suc @ Va2 ) ) )
% 5.41/5.74 => ( Y
% 5.41/5.74 = ( vEBT_Node @ none_P5556105721700978146at_nat @ ( suc @ ( suc @ Va2 ) ) @ ( replicate_VEBT_VEBT @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( vEBT_vebt_buildup @ ( suc @ ( divide_divide_nat @ ( suc @ ( suc @ Va2 ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.41/5.74 => ~ ( accp_nat @ vEBT_v4011308405150292612up_rel @ ( suc @ ( suc @ Va2 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % vebt_buildup.pelims
% 5.41/5.74 thf(fact_6469_option_Osize__gen_I2_J,axiom,
% 5.41/5.74 ! [X: nat > nat,X22: nat] :
% 5.41/5.74 ( ( size_option_nat @ X @ ( some_nat @ X22 ) )
% 5.41/5.74 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % option.size_gen(2)
% 5.41/5.74 thf(fact_6470_option_Osize__gen_I2_J,axiom,
% 5.41/5.74 ! [X: product_prod_nat_nat > nat,X22: product_prod_nat_nat] :
% 5.41/5.74 ( ( size_o8335143837870341156at_nat @ X @ ( some_P7363390416028606310at_nat @ X22 ) )
% 5.41/5.74 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % option.size_gen(2)
% 5.41/5.74 thf(fact_6471_option_Osize__gen_I2_J,axiom,
% 5.41/5.74 ! [X: num > nat,X22: num] :
% 5.41/5.74 ( ( size_option_num @ X @ ( some_num @ X22 ) )
% 5.41/5.74 = ( plus_plus_nat @ ( X @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % option.size_gen(2)
% 5.41/5.74 thf(fact_6472_set__decode__0,axiom,
% 5.41/5.74 ! [X: nat] :
% 5.41/5.74 ( ( member_nat @ zero_zero_nat @ ( nat_set_decode @ X ) )
% 5.41/5.74 = ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % set_decode_0
% 5.41/5.74 thf(fact_6473_set__decode__Suc,axiom,
% 5.41/5.74 ! [N: nat,X: nat] :
% 5.41/5.74 ( ( member_nat @ ( suc @ N ) @ ( nat_set_decode @ X ) )
% 5.41/5.74 = ( member_nat @ N @ ( nat_set_decode @ ( divide_divide_nat @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % set_decode_Suc
% 5.41/5.74 thf(fact_6474_add__scale__eq__noteq,axiom,
% 5.41/5.74 ! [R: complex,A: complex,B: complex,C: complex,D: complex] :
% 5.41/5.74 ( ( R != zero_zero_complex )
% 5.41/5.74 => ( ( ( A = B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 => ( ( plus_plus_complex @ A @ ( times_times_complex @ R @ C ) )
% 5.41/5.74 != ( plus_plus_complex @ B @ ( times_times_complex @ R @ D ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_scale_eq_noteq
% 5.41/5.74 thf(fact_6475_add__scale__eq__noteq,axiom,
% 5.41/5.74 ! [R: real,A: real,B: real,C: real,D: real] :
% 5.41/5.74 ( ( R != zero_zero_real )
% 5.41/5.74 => ( ( ( A = B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 => ( ( plus_plus_real @ A @ ( times_times_real @ R @ C ) )
% 5.41/5.74 != ( plus_plus_real @ B @ ( times_times_real @ R @ D ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_scale_eq_noteq
% 5.41/5.74 thf(fact_6476_add__scale__eq__noteq,axiom,
% 5.41/5.74 ! [R: rat,A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.74 ( ( R != zero_zero_rat )
% 5.41/5.74 => ( ( ( A = B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 => ( ( plus_plus_rat @ A @ ( times_times_rat @ R @ C ) )
% 5.41/5.74 != ( plus_plus_rat @ B @ ( times_times_rat @ R @ D ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_scale_eq_noteq
% 5.41/5.74 thf(fact_6477_add__scale__eq__noteq,axiom,
% 5.41/5.74 ! [R: nat,A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.74 ( ( R != zero_zero_nat )
% 5.41/5.74 => ( ( ( A = B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 => ( ( plus_plus_nat @ A @ ( times_times_nat @ R @ C ) )
% 5.41/5.74 != ( plus_plus_nat @ B @ ( times_times_nat @ R @ D ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_scale_eq_noteq
% 5.41/5.74 thf(fact_6478_add__scale__eq__noteq,axiom,
% 5.41/5.74 ! [R: int,A: int,B: int,C: int,D: int] :
% 5.41/5.74 ( ( R != zero_zero_int )
% 5.41/5.74 => ( ( ( A = B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 => ( ( plus_plus_int @ A @ ( times_times_int @ R @ C ) )
% 5.41/5.74 != ( plus_plus_int @ B @ ( times_times_int @ R @ D ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_scale_eq_noteq
% 5.41/5.74 thf(fact_6479_set__decode__zero,axiom,
% 5.41/5.74 ( ( nat_set_decode @ zero_zero_nat )
% 5.41/5.74 = bot_bot_set_nat ) ).
% 5.41/5.74
% 5.41/5.74 % set_decode_zero
% 5.41/5.74 thf(fact_6480_signed__take__bit__minus,axiom,
% 5.41/5.74 ! [N: nat,K: int] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ ( bit_ri631733984087533419it_int @ N @ K ) ) )
% 5.41/5.74 = ( bit_ri631733984087533419it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_minus
% 5.41/5.74 thf(fact_6481_subset__decode__imp__le,axiom,
% 5.41/5.74 ! [M: nat,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_set_nat @ ( nat_set_decode @ M ) @ ( nat_set_decode @ N ) )
% 5.41/5.74 => ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % subset_decode_imp_le
% 5.41/5.74 thf(fact_6482_add__0__iff,axiom,
% 5.41/5.74 ! [B: complex,A: complex] :
% 5.41/5.74 ( ( B
% 5.41/5.74 = ( plus_plus_complex @ B @ A ) )
% 5.41/5.74 = ( A = zero_zero_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_0_iff
% 5.41/5.74 thf(fact_6483_add__0__iff,axiom,
% 5.41/5.74 ! [B: real,A: real] :
% 5.41/5.74 ( ( B
% 5.41/5.74 = ( plus_plus_real @ B @ A ) )
% 5.41/5.74 = ( A = zero_zero_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_0_iff
% 5.41/5.74 thf(fact_6484_add__0__iff,axiom,
% 5.41/5.74 ! [B: rat,A: rat] :
% 5.41/5.74 ( ( B
% 5.41/5.74 = ( plus_plus_rat @ B @ A ) )
% 5.41/5.74 = ( A = zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_0_iff
% 5.41/5.74 thf(fact_6485_add__0__iff,axiom,
% 5.41/5.74 ! [B: nat,A: nat] :
% 5.41/5.74 ( ( B
% 5.41/5.74 = ( plus_plus_nat @ B @ A ) )
% 5.41/5.74 = ( A = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_0_iff
% 5.41/5.74 thf(fact_6486_add__0__iff,axiom,
% 5.41/5.74 ! [B: int,A: int] :
% 5.41/5.74 ( ( B
% 5.41/5.74 = ( plus_plus_int @ B @ A ) )
% 5.41/5.74 = ( A = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % add_0_iff
% 5.41/5.74 thf(fact_6487_crossproduct__eq,axiom,
% 5.41/5.74 ! [W: real,Y: real,X: real,Z: real] :
% 5.41/5.74 ( ( ( plus_plus_real @ ( times_times_real @ W @ Y ) @ ( times_times_real @ X @ Z ) )
% 5.41/5.74 = ( plus_plus_real @ ( times_times_real @ W @ Z ) @ ( times_times_real @ X @ Y ) ) )
% 5.41/5.74 = ( ( W = X )
% 5.41/5.74 | ( Y = Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_eq
% 5.41/5.74 thf(fact_6488_crossproduct__eq,axiom,
% 5.41/5.74 ! [W: rat,Y: rat,X: rat,Z: rat] :
% 5.41/5.74 ( ( ( plus_plus_rat @ ( times_times_rat @ W @ Y ) @ ( times_times_rat @ X @ Z ) )
% 5.41/5.74 = ( plus_plus_rat @ ( times_times_rat @ W @ Z ) @ ( times_times_rat @ X @ Y ) ) )
% 5.41/5.74 = ( ( W = X )
% 5.41/5.74 | ( Y = Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_eq
% 5.41/5.74 thf(fact_6489_crossproduct__eq,axiom,
% 5.41/5.74 ! [W: nat,Y: nat,X: nat,Z: nat] :
% 5.41/5.74 ( ( ( plus_plus_nat @ ( times_times_nat @ W @ Y ) @ ( times_times_nat @ X @ Z ) )
% 5.41/5.74 = ( plus_plus_nat @ ( times_times_nat @ W @ Z ) @ ( times_times_nat @ X @ Y ) ) )
% 5.41/5.74 = ( ( W = X )
% 5.41/5.74 | ( Y = Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_eq
% 5.41/5.74 thf(fact_6490_crossproduct__eq,axiom,
% 5.41/5.74 ! [W: int,Y: int,X: int,Z: int] :
% 5.41/5.74 ( ( ( plus_plus_int @ ( times_times_int @ W @ Y ) @ ( times_times_int @ X @ Z ) )
% 5.41/5.74 = ( plus_plus_int @ ( times_times_int @ W @ Z ) @ ( times_times_int @ X @ Y ) ) )
% 5.41/5.74 = ( ( W = X )
% 5.41/5.74 | ( Y = Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_eq
% 5.41/5.74 thf(fact_6491_crossproduct__noteq,axiom,
% 5.41/5.74 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.74 ( ( ( A != B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 = ( ( plus_plus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) )
% 5.41/5.74 != ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_noteq
% 5.41/5.74 thf(fact_6492_crossproduct__noteq,axiom,
% 5.41/5.74 ! [A: rat,B: rat,C: rat,D: rat] :
% 5.41/5.74 ( ( ( A != B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 = ( ( plus_plus_rat @ ( times_times_rat @ A @ C ) @ ( times_times_rat @ B @ D ) )
% 5.41/5.74 != ( plus_plus_rat @ ( times_times_rat @ A @ D ) @ ( times_times_rat @ B @ C ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_noteq
% 5.41/5.74 thf(fact_6493_crossproduct__noteq,axiom,
% 5.41/5.74 ! [A: nat,B: nat,C: nat,D: nat] :
% 5.41/5.74 ( ( ( A != B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 = ( ( plus_plus_nat @ ( times_times_nat @ A @ C ) @ ( times_times_nat @ B @ D ) )
% 5.41/5.74 != ( plus_plus_nat @ ( times_times_nat @ A @ D ) @ ( times_times_nat @ B @ C ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_noteq
% 5.41/5.74 thf(fact_6494_crossproduct__noteq,axiom,
% 5.41/5.74 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.74 ( ( ( A != B )
% 5.41/5.74 & ( C != D ) )
% 5.41/5.74 = ( ( plus_plus_int @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) )
% 5.41/5.74 != ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % crossproduct_noteq
% 5.41/5.74 thf(fact_6495_option_Osize__gen_I1_J,axiom,
% 5.41/5.74 ! [X: nat > nat] :
% 5.41/5.74 ( ( size_option_nat @ X @ none_nat )
% 5.41/5.74 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % option.size_gen(1)
% 5.41/5.74 thf(fact_6496_option_Osize__gen_I1_J,axiom,
% 5.41/5.74 ! [X: product_prod_nat_nat > nat] :
% 5.41/5.74 ( ( size_o8335143837870341156at_nat @ X @ none_P5556105721700978146at_nat )
% 5.41/5.74 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % option.size_gen(1)
% 5.41/5.74 thf(fact_6497_option_Osize__gen_I1_J,axiom,
% 5.41/5.74 ! [X: num > nat] :
% 5.41/5.74 ( ( size_option_num @ X @ none_num )
% 5.41/5.74 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % option.size_gen(1)
% 5.41/5.74 thf(fact_6498_set__decode__def,axiom,
% 5.41/5.74 ( nat_set_decode
% 5.41/5.74 = ( ^ [X3: nat] :
% 5.41/5.74 ( collect_nat
% 5.41/5.74 @ ^ [N2: nat] :
% 5.41/5.74 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % set_decode_def
% 5.41/5.74 thf(fact_6499_signed__take__bit__Suc__minus__bit1,axiom,
% 5.41/5.74 ! [N: nat,K: num] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.41/5.74 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_Suc_minus_bit1
% 5.41/5.74 thf(fact_6500_infinite__int__iff__unbounded__le,axiom,
% 5.41/5.74 ! [S2: set_int] :
% 5.41/5.74 ( ( ~ ( finite_finite_int @ S2 ) )
% 5.41/5.74 = ( ! [M3: int] :
% 5.41/5.74 ? [N2: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ M3 @ ( abs_abs_int @ N2 ) )
% 5.41/5.74 & ( member_int @ N2 @ S2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % infinite_int_iff_unbounded_le
% 5.41/5.74 thf(fact_6501_of__int__code__if,axiom,
% 5.41/5.74 ( ring_1_of_int_real
% 5.41/5.74 = ( ^ [K2: int] :
% 5.41/5.74 ( if_real @ ( K2 = zero_zero_int ) @ zero_zero_real
% 5.41/5.74 @ ( if_real @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_real @ ( ring_1_of_int_real @ ( uminus_uminus_int @ K2 ) ) )
% 5.41/5.74 @ ( if_real
% 5.41/5.74 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.74 = zero_zero_int )
% 5.41/5.74 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.41/5.74 @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_code_if
% 5.41/5.74 thf(fact_6502_of__int__code__if,axiom,
% 5.41/5.74 ( ring_1_of_int_int
% 5.41/5.74 = ( ^ [K2: int] :
% 5.41/5.74 ( if_int @ ( K2 = zero_zero_int ) @ zero_zero_int
% 5.41/5.74 @ ( if_int @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_int @ ( ring_1_of_int_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.41/5.74 @ ( if_int
% 5.41/5.74 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.74 = zero_zero_int )
% 5.41/5.74 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.41/5.74 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_int ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_code_if
% 5.41/5.74 thf(fact_6503_of__int__code__if,axiom,
% 5.41/5.74 ( ring_17405671764205052669omplex
% 5.41/5.74 = ( ^ [K2: int] :
% 5.41/5.74 ( if_complex @ ( K2 = zero_zero_int ) @ zero_zero_complex
% 5.41/5.74 @ ( if_complex @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1482373934393186551omplex @ ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ K2 ) ) )
% 5.41/5.74 @ ( if_complex
% 5.41/5.74 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.74 = zero_zero_int )
% 5.41/5.74 @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.41/5.74 @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( ring_17405671764205052669omplex @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_complex ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_code_if
% 5.41/5.74 thf(fact_6504_of__int__code__if,axiom,
% 5.41/5.74 ( ring_18347121197199848620nteger
% 5.41/5.74 = ( ^ [K2: int] :
% 5.41/5.74 ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.41/5.74 @ ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ K2 ) ) )
% 5.41/5.74 @ ( if_Code_integer
% 5.41/5.74 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.74 = zero_zero_int )
% 5.41/5.74 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.41/5.74 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_code_if
% 5.41/5.74 thf(fact_6505_of__int__code__if,axiom,
% 5.41/5.74 ( ring_1_of_int_rat
% 5.41/5.74 = ( ^ [K2: int] :
% 5.41/5.74 ( if_rat @ ( K2 = zero_zero_int ) @ zero_zero_rat
% 5.41/5.74 @ ( if_rat @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus_uminus_rat @ ( ring_1_of_int_rat @ ( uminus_uminus_int @ K2 ) ) )
% 5.41/5.74 @ ( if_rat
% 5.41/5.74 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.74 = zero_zero_int )
% 5.41/5.74 @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.41/5.74 @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( ring_1_of_int_rat @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_rat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_code_if
% 5.41/5.74 thf(fact_6506_one__div__minus__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( divide_divide_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % one_div_minus_numeral
% 5.41/5.74 thf(fact_6507_minus__one__div__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % minus_one_div_numeral
% 5.41/5.74 thf(fact_6508_semiring__norm_I90_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ( bit1 @ M )
% 5.41/5.74 = ( bit1 @ N ) )
% 5.41/5.74 = ( M = N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(90)
% 5.41/5.74 thf(fact_6509_semiring__norm_I88_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( bit0 @ M )
% 5.41/5.74 != ( bit1 @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(88)
% 5.41/5.74 thf(fact_6510_semiring__norm_I89_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( bit1 @ M )
% 5.41/5.74 != ( bit0 @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(89)
% 5.41/5.74 thf(fact_6511_semiring__norm_I84_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( one
% 5.41/5.74 != ( bit1 @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(84)
% 5.41/5.74 thf(fact_6512_semiring__norm_I86_J,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ( ( bit1 @ M )
% 5.41/5.74 != one ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(86)
% 5.41/5.74 thf(fact_6513_semiring__norm_I80_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(80)
% 5.41/5.74 thf(fact_6514_semiring__norm_I73_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(73)
% 5.41/5.74 thf(fact_6515_of__int__eq__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_1_of_int_int @ Z )
% 5.41/5.74 = zero_zero_int )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_0_iff
% 5.41/5.74 thf(fact_6516_of__int__eq__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_1_of_int_real @ Z )
% 5.41/5.74 = zero_zero_real )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_0_iff
% 5.41/5.74 thf(fact_6517_of__int__eq__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.41/5.74 = zero_zero_complex )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_0_iff
% 5.41/5.74 thf(fact_6518_of__int__eq__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_1_of_int_rat @ Z )
% 5.41/5.74 = zero_zero_rat )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_0_iff
% 5.41/5.74 thf(fact_6519_of__int__0__eq__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( zero_zero_int
% 5.41/5.74 = ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_eq_iff
% 5.41/5.74 thf(fact_6520_of__int__0__eq__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( zero_zero_real
% 5.41/5.74 = ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_eq_iff
% 5.41/5.74 thf(fact_6521_of__int__0__eq__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( zero_zero_complex
% 5.41/5.74 = ( ring_17405671764205052669omplex @ Z ) )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_eq_iff
% 5.41/5.74 thf(fact_6522_of__int__0__eq__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( zero_zero_rat
% 5.41/5.74 = ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( Z = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_eq_iff
% 5.41/5.74 thf(fact_6523_of__int__0,axiom,
% 5.41/5.74 ( ( ring_1_of_int_int @ zero_zero_int )
% 5.41/5.74 = zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0
% 5.41/5.74 thf(fact_6524_of__int__0,axiom,
% 5.41/5.74 ( ( ring_1_of_int_real @ zero_zero_int )
% 5.41/5.74 = zero_zero_real ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0
% 5.41/5.74 thf(fact_6525_of__int__0,axiom,
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ zero_zero_int )
% 5.41/5.74 = zero_zero_complex ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0
% 5.41/5.74 thf(fact_6526_of__int__0,axiom,
% 5.41/5.74 ( ( ring_1_of_int_rat @ zero_zero_int )
% 5.41/5.74 = zero_zero_rat ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0
% 5.41/5.74 thf(fact_6527_of__int__eq__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.41/5.74 = ( numera6690914467698888265omplex @ N ) )
% 5.41/5.74 = ( Z
% 5.41/5.74 = ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_iff
% 5.41/5.74 thf(fact_6528_of__int__eq__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ( ring_1_of_int_real @ Z )
% 5.41/5.74 = ( numeral_numeral_real @ N ) )
% 5.41/5.74 = ( Z
% 5.41/5.74 = ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_iff
% 5.41/5.74 thf(fact_6529_of__int__eq__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ( ring_1_of_int_rat @ Z )
% 5.41/5.74 = ( numeral_numeral_rat @ N ) )
% 5.41/5.74 = ( Z
% 5.41/5.74 = ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_iff
% 5.41/5.74 thf(fact_6530_of__int__eq__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ( ring_1_of_int_int @ Z )
% 5.41/5.74 = ( numeral_numeral_int @ N ) )
% 5.41/5.74 = ( Z
% 5.41/5.74 = ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_iff
% 5.41/5.74 thf(fact_6531_of__int__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ ( numeral_numeral_int @ K ) )
% 5.41/5.74 = ( numera6690914467698888265omplex @ K ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral
% 5.41/5.74 thf(fact_6532_of__int__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_1_of_int_real @ ( numeral_numeral_int @ K ) )
% 5.41/5.74 = ( numeral_numeral_real @ K ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral
% 5.41/5.74 thf(fact_6533_of__int__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_1_of_int_rat @ ( numeral_numeral_int @ K ) )
% 5.41/5.74 = ( numeral_numeral_rat @ K ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral
% 5.41/5.74 thf(fact_6534_of__int__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_1_of_int_int @ ( numeral_numeral_int @ K ) )
% 5.41/5.74 = ( numeral_numeral_int @ K ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral
% 5.41/5.74 thf(fact_6535_of__int__le__iff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_iff
% 5.41/5.74 thf(fact_6536_of__int__le__iff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_iff
% 5.41/5.74 thf(fact_6537_of__int__le__iff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ W @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_iff
% 5.41/5.74 thf(fact_6538_of__int__less__iff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ord_less_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_int @ W @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_iff
% 5.41/5.74 thf(fact_6539_of__int__less__iff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_int @ W @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_iff
% 5.41/5.74 thf(fact_6540_of__int__less__iff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ord_less_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_int @ W @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_iff
% 5.41/5.74 thf(fact_6541_of__int__eq__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_1_of_int_int @ Z )
% 5.41/5.74 = one_one_int )
% 5.41/5.74 = ( Z = one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_1_iff
% 5.41/5.74 thf(fact_6542_of__int__eq__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_1_of_int_real @ Z )
% 5.41/5.74 = one_one_real )
% 5.41/5.74 = ( Z = one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_1_iff
% 5.41/5.74 thf(fact_6543_of__int__eq__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_17405671764205052669omplex @ Z )
% 5.41/5.74 = one_one_complex )
% 5.41/5.74 = ( Z = one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_1_iff
% 5.41/5.74 thf(fact_6544_of__int__eq__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ( ring_1_of_int_rat @ Z )
% 5.41/5.74 = one_one_rat )
% 5.41/5.74 = ( Z = one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_1_iff
% 5.41/5.74 thf(fact_6545_of__int__1,axiom,
% 5.41/5.74 ( ( ring_1_of_int_int @ one_one_int )
% 5.41/5.74 = one_one_int ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1
% 5.41/5.74 thf(fact_6546_of__int__1,axiom,
% 5.41/5.74 ( ( ring_1_of_int_real @ one_one_int )
% 5.41/5.74 = one_one_real ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1
% 5.41/5.74 thf(fact_6547_of__int__1,axiom,
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ one_one_int )
% 5.41/5.74 = one_one_complex ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1
% 5.41/5.74 thf(fact_6548_of__int__1,axiom,
% 5.41/5.74 ( ( ring_1_of_int_rat @ one_one_int )
% 5.41/5.74 = one_one_rat ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1
% 5.41/5.74 thf(fact_6549_of__int__mult,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ ( times_times_int @ W @ Z ) )
% 5.41/5.74 = ( times_times_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_mult
% 5.41/5.74 thf(fact_6550_of__int__mult,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_real @ ( times_times_int @ W @ Z ) )
% 5.41/5.74 = ( times_times_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_mult
% 5.41/5.74 thf(fact_6551_of__int__mult,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_rat @ ( times_times_int @ W @ Z ) )
% 5.41/5.74 = ( times_times_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_mult
% 5.41/5.74 thf(fact_6552_of__int__mult,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_int @ ( times_times_int @ W @ Z ) )
% 5.41/5.74 = ( times_times_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_mult
% 5.41/5.74 thf(fact_6553_of__int__add,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_int @ ( plus_plus_int @ W @ Z ) )
% 5.41/5.74 = ( plus_plus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_add
% 5.41/5.74 thf(fact_6554_of__int__add,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_real @ ( plus_plus_int @ W @ Z ) )
% 5.41/5.74 = ( plus_plus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_add
% 5.41/5.74 thf(fact_6555_of__int__add,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ ( plus_plus_int @ W @ Z ) )
% 5.41/5.74 = ( plus_plus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_add
% 5.41/5.74 thf(fact_6556_of__int__add,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_rat @ ( plus_plus_int @ W @ Z ) )
% 5.41/5.74 = ( plus_plus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_add
% 5.41/5.74 thf(fact_6557_of__int__diff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ ( minus_minus_int @ W @ Z ) )
% 5.41/5.74 = ( minus_minus_complex @ ( ring_17405671764205052669omplex @ W ) @ ( ring_17405671764205052669omplex @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_diff
% 5.41/5.74 thf(fact_6558_of__int__diff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_real @ ( minus_minus_int @ W @ Z ) )
% 5.41/5.74 = ( minus_minus_real @ ( ring_1_of_int_real @ W ) @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_diff
% 5.41/5.74 thf(fact_6559_of__int__diff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_rat @ ( minus_minus_int @ W @ Z ) )
% 5.41/5.74 = ( minus_minus_rat @ ( ring_1_of_int_rat @ W ) @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_diff
% 5.41/5.74 thf(fact_6560_of__int__diff,axiom,
% 5.41/5.74 ! [W: int,Z: int] :
% 5.41/5.74 ( ( ring_1_of_int_int @ ( minus_minus_int @ W @ Z ) )
% 5.41/5.74 = ( minus_minus_int @ ( ring_1_of_int_int @ W ) @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_diff
% 5.41/5.74 thf(fact_6561_semiring__norm_I9_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(9)
% 5.41/5.74 thf(fact_6562_semiring__norm_I7_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( plus_plus_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( bit1 @ ( plus_plus_num @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(7)
% 5.41/5.74 thf(fact_6563_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_rat @ X )
% 5.41/5.74 = ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.41/5.74 = ( X
% 5.41/5.74 = ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6564_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_real @ X )
% 5.41/5.74 = ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.41/5.74 = ( X
% 5.41/5.74 = ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6565_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_int @ X )
% 5.41/5.74 = ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.41/5.74 = ( X
% 5.41/5.74 = ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6566_of__int__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ( ring_17405671764205052669omplex @ X )
% 5.41/5.74 = ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W ) )
% 5.41/5.74 = ( X
% 5.41/5.74 = ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6567_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W )
% 5.41/5.74 = ( ring_1_of_int_rat @ X ) )
% 5.41/5.74 = ( ( power_power_int @ B @ W )
% 5.41/5.74 = X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6568_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ( power_power_real @ ( ring_1_of_int_real @ B ) @ W )
% 5.41/5.74 = ( ring_1_of_int_real @ X ) )
% 5.41/5.74 = ( ( power_power_int @ B @ W )
% 5.41/5.74 = X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6569_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ( power_power_int @ ( ring_1_of_int_int @ B ) @ W )
% 5.41/5.74 = ( ring_1_of_int_int @ X ) )
% 5.41/5.74 = ( ( power_power_int @ B @ W )
% 5.41/5.74 = X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6570_of__int__eq__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ( power_power_complex @ ( ring_17405671764205052669omplex @ B ) @ W )
% 5.41/5.74 = ( ring_17405671764205052669omplex @ X ) )
% 5.41/5.74 = ( ( power_power_int @ B @ W )
% 5.41/5.74 = X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6571_of__int__power,axiom,
% 5.41/5.74 ! [Z: int,N: nat] :
% 5.41/5.74 ( ( ring_1_of_int_rat @ ( power_power_int @ Z @ N ) )
% 5.41/5.74 = ( power_power_rat @ ( ring_1_of_int_rat @ Z ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power
% 5.41/5.74 thf(fact_6572_of__int__power,axiom,
% 5.41/5.74 ! [Z: int,N: nat] :
% 5.41/5.74 ( ( ring_1_of_int_real @ ( power_power_int @ Z @ N ) )
% 5.41/5.74 = ( power_power_real @ ( ring_1_of_int_real @ Z ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power
% 5.41/5.74 thf(fact_6573_of__int__power,axiom,
% 5.41/5.74 ! [Z: int,N: nat] :
% 5.41/5.74 ( ( ring_1_of_int_int @ ( power_power_int @ Z @ N ) )
% 5.41/5.74 = ( power_power_int @ ( ring_1_of_int_int @ Z ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power
% 5.41/5.74 thf(fact_6574_of__int__power,axiom,
% 5.41/5.74 ! [Z: int,N: nat] :
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ ( power_power_int @ Z @ N ) )
% 5.41/5.74 = ( power_power_complex @ ( ring_17405671764205052669omplex @ Z ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power
% 5.41/5.74 thf(fact_6575_semiring__norm_I15_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( times_times_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( bit0 @ ( times_times_num @ ( bit1 @ M ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(15)
% 5.41/5.74 thf(fact_6576_semiring__norm_I14_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( times_times_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( bit0 @ ( times_times_num @ M @ ( bit1 @ N ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(14)
% 5.41/5.74 thf(fact_6577_semiring__norm_I81_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ord_less_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(81)
% 5.41/5.74 thf(fact_6578_semiring__norm_I72_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ord_less_eq_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(72)
% 5.41/5.74 thf(fact_6579_semiring__norm_I77_J,axiom,
% 5.41/5.74 ! [N: num] : ( ord_less_num @ one @ ( bit1 @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(77)
% 5.41/5.74 thf(fact_6580_semiring__norm_I70_J,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ~ ( ord_less_eq_num @ ( bit1 @ M ) @ one ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(70)
% 5.41/5.74 thf(fact_6581_zdiv__numeral__Bit1,axiom,
% 5.41/5.74 ! [V: num,W: num] :
% 5.41/5.74 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.41/5.74 = ( divide_divide_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % zdiv_numeral_Bit1
% 5.41/5.74 thf(fact_6582_semiring__norm_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( plus_plus_num @ one @ ( bit0 @ N ) )
% 5.41/5.74 = ( bit1 @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(3)
% 5.41/5.74 thf(fact_6583_semiring__norm_I4_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( plus_plus_num @ one @ ( bit1 @ N ) )
% 5.41/5.74 = ( bit0 @ ( plus_plus_num @ N @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(4)
% 5.41/5.74 thf(fact_6584_semiring__norm_I5_J,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ( ( plus_plus_num @ ( bit0 @ M ) @ one )
% 5.41/5.74 = ( bit1 @ M ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(5)
% 5.41/5.74 thf(fact_6585_semiring__norm_I8_J,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ( ( plus_plus_num @ ( bit1 @ M ) @ one )
% 5.41/5.74 = ( bit0 @ ( plus_plus_num @ M @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(8)
% 5.41/5.74 thf(fact_6586_semiring__norm_I10_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( plus_plus_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( bit0 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(10)
% 5.41/5.74 thf(fact_6587_semiring__norm_I16_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( times_times_num @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( bit1 @ ( plus_plus_num @ ( plus_plus_num @ M @ N ) @ ( bit0 @ ( times_times_num @ M @ N ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(16)
% 5.41/5.74 thf(fact_6588_semiring__norm_I79_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ord_less_num @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( ord_less_eq_num @ M @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(79)
% 5.41/5.74 thf(fact_6589_semiring__norm_I74_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ord_less_eq_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(74)
% 5.41/5.74 thf(fact_6590_of__int__0__le__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_le_iff
% 5.41/5.74 thf(fact_6591_of__int__0__le__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_le_iff
% 5.41/5.74 thf(fact_6592_of__int__0__le__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_le_iff
% 5.41/5.74 thf(fact_6593_of__int__le__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_0_iff
% 5.41/5.74 thf(fact_6594_of__int__le__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_0_iff
% 5.41/5.74 thf(fact_6595_of__int__le__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_0_iff
% 5.41/5.74 thf(fact_6596_of__int__0__less__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_less_iff
% 5.41/5.74 thf(fact_6597_of__int__0__less__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_less_iff
% 5.41/5.74 thf(fact_6598_of__int__0__less__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_0_less_iff
% 5.41/5.74 thf(fact_6599_of__int__less__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ zero_zero_real )
% 5.41/5.74 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_0_iff
% 5.41/5.74 thf(fact_6600_of__int__less__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ zero_zero_rat )
% 5.41/5.74 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_0_iff
% 5.41/5.74 thf(fact_6601_of__int__less__0__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ zero_zero_int )
% 5.41/5.74 = ( ord_less_int @ Z @ zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_0_iff
% 5.41/5.74 thf(fact_6602_of__int__le__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_numeral_iff
% 5.41/5.74 thf(fact_6603_of__int__le__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_numeral_iff
% 5.41/5.74 thf(fact_6604_of__int__le__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_numeral_iff
% 5.41/5.74 thf(fact_6605_of__int__numeral__le__iff,axiom,
% 5.41/5.74 ! [N: num,Z: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral_le_iff
% 5.41/5.74 thf(fact_6606_of__int__numeral__le__iff,axiom,
% 5.41/5.74 ! [N: num,Z: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral_le_iff
% 5.41/5.74 thf(fact_6607_of__int__numeral__le__iff,axiom,
% 5.41/5.74 ! [N: num,Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral_le_iff
% 5.41/5.74 thf(fact_6608_of__int__numeral__less__iff,axiom,
% 5.41/5.74 ! [N: num,Z: int] :
% 5.41/5.74 ( ( ord_less_real @ ( numeral_numeral_real @ N ) @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral_less_iff
% 5.41/5.74 thf(fact_6609_of__int__numeral__less__iff,axiom,
% 5.41/5.74 ! [N: num,Z: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( numeral_numeral_rat @ N ) @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral_less_iff
% 5.41/5.74 thf(fact_6610_of__int__numeral__less__iff,axiom,
% 5.41/5.74 ! [N: num,Z: int] :
% 5.41/5.74 ( ( ord_less_int @ ( numeral_numeral_int @ N ) @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_int @ ( numeral_numeral_int @ N ) @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_numeral_less_iff
% 5.41/5.74 thf(fact_6611_of__int__less__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.74 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_numeral_iff
% 5.41/5.74 thf(fact_6612_of__int__less__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.74 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_numeral_iff
% 5.41/5.74 thf(fact_6613_of__int__less__numeral__iff,axiom,
% 5.41/5.74 ! [Z: int,N: num] :
% 5.41/5.74 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.74 = ( ord_less_int @ Z @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_numeral_iff
% 5.41/5.74 thf(fact_6614_of__int__1__le__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1_le_iff
% 5.41/5.74 thf(fact_6615_of__int__1__le__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1_le_iff
% 5.41/5.74 thf(fact_6616_of__int__1__le__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_eq_int @ one_one_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1_le_iff
% 5.41/5.74 thf(fact_6617_of__int__le__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_1_iff
% 5.41/5.74 thf(fact_6618_of__int__le__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_1_iff
% 5.41/5.74 thf(fact_6619_of__int__le__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.41/5.74 = ( ord_less_eq_int @ Z @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_1_iff
% 5.41/5.74 thf(fact_6620_of__int__less__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_real @ ( ring_1_of_int_real @ Z ) @ one_one_real )
% 5.41/5.74 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_1_iff
% 5.41/5.74 thf(fact_6621_of__int__less__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( ring_1_of_int_rat @ Z ) @ one_one_rat )
% 5.41/5.74 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_1_iff
% 5.41/5.74 thf(fact_6622_of__int__less__1__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_int @ ( ring_1_of_int_int @ Z ) @ one_one_int )
% 5.41/5.74 = ( ord_less_int @ Z @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_1_iff
% 5.41/5.74 thf(fact_6623_of__int__1__less__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_real @ one_one_real @ ( ring_1_of_int_real @ Z ) )
% 5.41/5.74 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1_less_iff
% 5.41/5.74 thf(fact_6624_of__int__1__less__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_rat @ one_one_rat @ ( ring_1_of_int_rat @ Z ) )
% 5.41/5.74 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1_less_iff
% 5.41/5.74 thf(fact_6625_of__int__1__less__iff,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_int @ one_one_int @ ( ring_1_of_int_int @ Z ) )
% 5.41/5.74 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_1_less_iff
% 5.41/5.74 thf(fact_6626_dvd__numeral__simp,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( dvd_dvd_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.74 = ( unique6319869463603278526ux_int @ ( unique5052692396658037445od_int @ N @ M ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dvd_numeral_simp
% 5.41/5.74 thf(fact_6627_dvd__numeral__simp,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.74 = ( unique6322359934112328802ux_nat @ ( unique5055182867167087721od_nat @ N @ M ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dvd_numeral_simp
% 5.41/5.74 thf(fact_6628_dvd__numeral__simp,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ N ) )
% 5.41/5.74 = ( unique5706413561485394159nteger @ ( unique3479559517661332726nteger @ N @ M ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dvd_numeral_simp
% 5.41/5.74 thf(fact_6629_divmod__algorithm__code_I2_J,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ( ( unique5052692396658037445od_int @ M @ one )
% 5.41/5.74 = ( product_Pair_int_int @ ( numeral_numeral_int @ M ) @ zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(2)
% 5.41/5.74 thf(fact_6630_divmod__algorithm__code_I2_J,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ( ( unique5055182867167087721od_nat @ M @ one )
% 5.41/5.74 = ( product_Pair_nat_nat @ ( numeral_numeral_nat @ M ) @ zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(2)
% 5.41/5.74 thf(fact_6631_divmod__algorithm__code_I2_J,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ( ( unique3479559517661332726nteger @ M @ one )
% 5.41/5.74 = ( produc1086072967326762835nteger @ ( numera6620942414471956472nteger @ M ) @ zero_z3403309356797280102nteger ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(2)
% 5.41/5.74 thf(fact_6632_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.41/5.74 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6633_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_real @ Y )
% 5.41/5.74 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6634_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_rat @ Y )
% 5.41/5.74 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6635_of__int__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_int @ Y )
% 5.41/5.74 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6636_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.41/5.74 = ( ring_17405671764205052669omplex @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6637_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.41/5.74 = ( ring_1_of_int_real @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6638_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.41/5.74 = ( ring_1_of_int_rat @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6639_numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.41/5.74 = ( ring_1_of_int_int @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6640_of__int__le__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6641_of__int__le__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6642_of__int__le__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6643_of__int__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.41/5.74 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6644_of__int__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.41/5.74 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6645_of__int__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.41/5.74 = ( ord_less_eq_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6646_of__int__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ord_less_real @ ( ring_1_of_int_real @ X ) @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) )
% 5.41/5.74 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6647_of__int__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ord_less_rat @ ( ring_1_of_int_rat @ X ) @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) )
% 5.41/5.74 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6648_of__int__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: int,B: int,W: nat] :
% 5.41/5.74 ( ( ord_less_int @ ( ring_1_of_int_int @ X ) @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) )
% 5.41/5.74 = ( ord_less_int @ X @ ( power_power_int @ B @ W ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6649_of__int__less__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ord_less_real @ ( power_power_real @ ( ring_1_of_int_real @ B ) @ W ) @ ( ring_1_of_int_real @ X ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6650_of__int__less__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( power_power_rat @ ( ring_1_of_int_rat @ B ) @ W ) @ ( ring_1_of_int_rat @ X ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6651_of__int__less__of__int__power__cancel__iff,axiom,
% 5.41/5.74 ! [B: int,W: nat,X: int] :
% 5.41/5.74 ( ( ord_less_int @ ( power_power_int @ ( ring_1_of_int_int @ B ) @ W ) @ ( ring_1_of_int_int @ X ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ B @ W ) @ X ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_of_int_power_cancel_iff
% 5.41/5.74 thf(fact_6652_div__Suc__eq__div__add3,axiom,
% 5.41/5.74 ! [M: nat,N: nat] :
% 5.41/5.74 ( ( divide_divide_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.41/5.74 = ( divide_divide_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % div_Suc_eq_div_add3
% 5.41/5.74 thf(fact_6653_Suc__div__eq__add3__div__numeral,axiom,
% 5.41/5.74 ! [M: nat,V: num] :
% 5.41/5.74 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.74 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % Suc_div_eq_add3_div_numeral
% 5.41/5.74 thf(fact_6654_divmod__algorithm__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( unique5052692396658037445od_int @ one @ ( bit0 @ N ) )
% 5.41/5.74 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(3)
% 5.41/5.74 thf(fact_6655_divmod__algorithm__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( unique5055182867167087721od_nat @ one @ ( bit0 @ N ) )
% 5.41/5.74 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(3)
% 5.41/5.74 thf(fact_6656_divmod__algorithm__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( unique3479559517661332726nteger @ one @ ( bit0 @ N ) )
% 5.41/5.74 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(3)
% 5.41/5.74 thf(fact_6657_mod__Suc__eq__mod__add3,axiom,
% 5.41/5.74 ! [M: nat,N: nat] :
% 5.41/5.74 ( ( modulo_modulo_nat @ M @ ( suc @ ( suc @ ( suc @ N ) ) ) )
% 5.41/5.74 = ( modulo_modulo_nat @ M @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mod_Suc_eq_mod_add3
% 5.41/5.74 thf(fact_6658_Suc__mod__eq__add3__mod__numeral,axiom,
% 5.41/5.74 ! [M: nat,V: num] :
% 5.41/5.74 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ ( numeral_numeral_nat @ V ) )
% 5.41/5.74 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ ( numeral_numeral_nat @ V ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % Suc_mod_eq_add3_mod_numeral
% 5.41/5.74 thf(fact_6659_divmod__algorithm__code_I4_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( unique5052692396658037445od_int @ one @ ( bit1 @ N ) )
% 5.41/5.74 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(4)
% 5.41/5.74 thf(fact_6660_divmod__algorithm__code_I4_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( unique5055182867167087721od_nat @ one @ ( bit1 @ N ) )
% 5.41/5.74 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(4)
% 5.41/5.74 thf(fact_6661_divmod__algorithm__code_I4_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( unique3479559517661332726nteger @ one @ ( bit1 @ N ) )
% 5.41/5.74 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(4)
% 5.41/5.74 thf(fact_6662_minus__numeral__div__numeral,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % minus_numeral_div_numeral
% 5.41/5.74 thf(fact_6663_numeral__div__minus__numeral,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( divide_divide_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( adjust_div @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_div_minus_numeral
% 5.41/5.74 thf(fact_6664_of__int__le__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6665_of__int__le__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6666_of__int__le__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6667_numeral__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6668_numeral__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6669_numeral__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6670_of__int__less__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.41/5.74 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6671_of__int__less__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.41/5.74 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6672_of__int__less__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.41/5.74 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6673_numeral__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6674_numeral__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6675_numeral__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6676_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_real @ Y )
% 5.41/5.74 = ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6677_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_int @ Y )
% 5.41/5.74 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6678_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_17405671764205052669omplex @ Y )
% 5.41/5.74 = ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6679_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_18347121197199848620nteger @ Y )
% 5.41/5.74 = ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6680_of__int__eq__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [Y: int,X: num,N: nat] :
% 5.41/5.74 ( ( ( ring_1_of_int_rat @ Y )
% 5.41/5.74 = ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.41/5.74 = ( Y
% 5.41/5.74 = ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_eq_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6681_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N )
% 5.41/5.74 = ( ring_1_of_int_real @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6682_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.41/5.74 = ( ring_1_of_int_int @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6683_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ X ) ) @ N )
% 5.41/5.74 = ( ring_17405671764205052669omplex @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6684_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N )
% 5.41/5.74 = ( ring_18347121197199848620nteger @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6685_neg__numeral__power__eq__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,Y: int] :
% 5.41/5.74 ( ( ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N )
% 5.41/5.74 = ( ring_1_of_int_rat @ Y ) )
% 5.41/5.74 = ( ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N )
% 5.41/5.74 = Y ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_eq_of_int_cancel_iff
% 5.41/5.74 thf(fact_6686_zmod__numeral__Bit1,axiom,
% 5.41/5.74 ! [V: num,W: num] :
% 5.41/5.74 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ V ) ) @ ( numeral_numeral_int @ ( bit0 @ W ) ) )
% 5.41/5.74 = ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ W ) ) ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % zmod_numeral_Bit1
% 5.41/5.74 thf(fact_6687_divmod__algorithm__code_I8_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ( ord_less_num @ M @ N )
% 5.41/5.74 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) ) ) )
% 5.41/5.74 & ( ~ ( ord_less_num @ M @ N )
% 5.41/5.74 => ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(8)
% 5.41/5.74 thf(fact_6688_divmod__algorithm__code_I8_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ( ord_less_num @ M @ N )
% 5.41/5.74 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) ) ) )
% 5.41/5.74 & ( ~ ( ord_less_num @ M @ N )
% 5.41/5.74 => ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(8)
% 5.41/5.74 thf(fact_6689_divmod__algorithm__code_I8_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ( ord_less_num @ M @ N )
% 5.41/5.74 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) ) ) )
% 5.41/5.74 & ( ~ ( ord_less_num @ M @ N )
% 5.41/5.74 => ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(8)
% 5.41/5.74 thf(fact_6690_divmod__algorithm__code_I7_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ( ord_less_eq_num @ M @ N )
% 5.41/5.74 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) ) ) )
% 5.41/5.74 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.41/5.74 => ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( unique5026877609467782581ep_nat @ ( bit1 @ N ) @ ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(7)
% 5.41/5.74 thf(fact_6691_divmod__algorithm__code_I7_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ( ord_less_eq_num @ M @ N )
% 5.41/5.74 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) ) ) )
% 5.41/5.74 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.41/5.74 => ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( unique5024387138958732305ep_int @ ( bit1 @ N ) @ ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(7)
% 5.41/5.74 thf(fact_6692_divmod__algorithm__code_I7_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( ( ord_less_eq_num @ M @ N )
% 5.41/5.74 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) ) ) )
% 5.41/5.74 & ( ~ ( ord_less_eq_num @ M @ N )
% 5.41/5.74 => ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit1 @ N ) )
% 5.41/5.74 = ( unique4921790084139445826nteger @ ( bit1 @ N ) @ ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ ( bit1 @ N ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(7)
% 5.41/5.74 thf(fact_6693_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6694_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_le3102999989581377725nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6695_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6696_neg__numeral__power__le__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.41/5.74 = ( ord_less_eq_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_le_of_int_cancel_iff
% 5.41/5.74 thf(fact_6697_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6698_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_le3102999989581377725nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6699_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6700_of__int__le__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_eq_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_le_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6701_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_real @ ( ring_1_of_int_real @ A ) @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6702_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_int @ ( ring_1_of_int_int @ A ) @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6703_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_le6747313008572928689nteger @ ( ring_18347121197199848620nteger @ A ) @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6704_of__int__less__neg__numeral__power__cancel__iff,axiom,
% 5.41/5.74 ! [A: int,X: num,N: nat] :
% 5.41/5.74 ( ( ord_less_rat @ ( ring_1_of_int_rat @ A ) @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) )
% 5.41/5.74 = ( ord_less_int @ A @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_less_neg_numeral_power_cancel_iff
% 5.41/5.74 thf(fact_6705_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_real @ ( power_power_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ X ) ) @ N ) @ ( ring_1_of_int_real @ A ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6706_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ ( ring_1_of_int_int @ A ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6707_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_le6747313008572928689nteger @ ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ X ) ) @ N ) @ ( ring_18347121197199848620nteger @ A ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6708_neg__numeral__power__less__of__int__cancel__iff,axiom,
% 5.41/5.74 ! [X: num,N: nat,A: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( power_power_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ X ) ) @ N ) @ ( ring_1_of_int_rat @ A ) )
% 5.41/5.74 = ( ord_less_int @ ( power_power_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ X ) ) @ N ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % neg_numeral_power_less_of_int_cancel_iff
% 5.41/5.74 thf(fact_6709_signed__take__bit__Suc__bit1,axiom,
% 5.41/5.74 ! [N: nat,K: num] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.41/5.74 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_Suc_bit1
% 5.41/5.74 thf(fact_6710_mult__of__int__commute,axiom,
% 5.41/5.74 ! [X: int,Y: complex] :
% 5.41/5.74 ( ( times_times_complex @ ( ring_17405671764205052669omplex @ X ) @ Y )
% 5.41/5.74 = ( times_times_complex @ Y @ ( ring_17405671764205052669omplex @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mult_of_int_commute
% 5.41/5.74 thf(fact_6711_mult__of__int__commute,axiom,
% 5.41/5.74 ! [X: int,Y: real] :
% 5.41/5.74 ( ( times_times_real @ ( ring_1_of_int_real @ X ) @ Y )
% 5.41/5.74 = ( times_times_real @ Y @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mult_of_int_commute
% 5.41/5.74 thf(fact_6712_mult__of__int__commute,axiom,
% 5.41/5.74 ! [X: int,Y: rat] :
% 5.41/5.74 ( ( times_times_rat @ ( ring_1_of_int_rat @ X ) @ Y )
% 5.41/5.74 = ( times_times_rat @ Y @ ( ring_1_of_int_rat @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mult_of_int_commute
% 5.41/5.74 thf(fact_6713_mult__of__int__commute,axiom,
% 5.41/5.74 ! [X: int,Y: int] :
% 5.41/5.74 ( ( times_times_int @ ( ring_1_of_int_int @ X ) @ Y )
% 5.41/5.74 = ( times_times_int @ Y @ ( ring_1_of_int_int @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mult_of_int_commute
% 5.41/5.74 thf(fact_6714_verit__eq__simplify_I14_J,axiom,
% 5.41/5.74 ! [X22: num,X32: num] :
% 5.41/5.74 ( ( bit0 @ X22 )
% 5.41/5.74 != ( bit1 @ X32 ) ) ).
% 5.41/5.74
% 5.41/5.74 % verit_eq_simplify(14)
% 5.41/5.74 thf(fact_6715_verit__eq__simplify_I12_J,axiom,
% 5.41/5.74 ! [X32: num] :
% 5.41/5.74 ( one
% 5.41/5.74 != ( bit1 @ X32 ) ) ).
% 5.41/5.74
% 5.41/5.74 % verit_eq_simplify(12)
% 5.41/5.74 thf(fact_6716_num_Oexhaust,axiom,
% 5.41/5.74 ! [Y: num] :
% 5.41/5.74 ( ( Y != one )
% 5.41/5.74 => ( ! [X23: num] :
% 5.41/5.74 ( Y
% 5.41/5.74 != ( bit0 @ X23 ) )
% 5.41/5.74 => ~ ! [X33: num] :
% 5.41/5.74 ( Y
% 5.41/5.74 != ( bit1 @ X33 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % num.exhaust
% 5.41/5.74 thf(fact_6717_xor__num_Ocases,axiom,
% 5.41/5.74 ! [X: product_prod_num_num] :
% 5.41/5.74 ( ( X
% 5.41/5.74 != ( product_Pair_num_num @ one @ one ) )
% 5.41/5.74 => ( ! [N3: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ one @ ( bit0 @ N3 ) ) )
% 5.41/5.74 => ( ! [N3: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ one @ ( bit1 @ N3 ) ) )
% 5.41/5.74 => ( ! [M4: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ one ) )
% 5.41/5.74 => ( ! [M4: num,N3: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.41/5.74 => ( ! [M4: num,N3: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ ( bit0 @ M4 ) @ ( bit1 @ N3 ) ) )
% 5.41/5.74 => ( ! [M4: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ one ) )
% 5.41/5.74 => ( ! [M4: num,N3: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit0 @ N3 ) ) )
% 5.41/5.74 => ~ ! [M4: num,N3: num] :
% 5.41/5.74 ( X
% 5.41/5.74 != ( product_Pair_num_num @ ( bit1 @ M4 ) @ ( bit1 @ N3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % xor_num.cases
% 5.41/5.74 thf(fact_6718_numeral__Bit1,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_Bit1
% 5.41/5.74 thf(fact_6719_numeral__Bit1,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_Bit1
% 5.41/5.74 thf(fact_6720_numeral__Bit1,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_Bit1
% 5.41/5.74 thf(fact_6721_numeral__Bit1,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_Bit1
% 5.41/5.74 thf(fact_6722_numeral__Bit1,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_Bit1
% 5.41/5.74 thf(fact_6723_eval__nat__numeral_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.41/5.74 = ( suc @ ( numeral_numeral_nat @ ( bit0 @ N ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % eval_nat_numeral(3)
% 5.41/5.74 thf(fact_6724_cong__exp__iff__simps_I10_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(10)
% 5.41/5.74 thf(fact_6725_cong__exp__iff__simps_I10_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(10)
% 5.41/5.74 thf(fact_6726_cong__exp__iff__simps_I10_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(10)
% 5.41/5.74 thf(fact_6727_cong__exp__iff__simps_I12_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit0 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(12)
% 5.41/5.74 thf(fact_6728_cong__exp__iff__simps_I12_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(12)
% 5.41/5.74 thf(fact_6729_cong__exp__iff__simps_I12_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit0 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(12)
% 5.41/5.74 thf(fact_6730_cong__exp__iff__simps_I13_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.41/5.74 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(13)
% 5.41/5.74 thf(fact_6731_cong__exp__iff__simps_I13_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.41/5.74 = ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(13)
% 5.41/5.74 thf(fact_6732_cong__exp__iff__simps_I13_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num,N: num] :
% 5.41/5.74 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.41/5.74 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(13)
% 5.41/5.74 thf(fact_6733_power__minus__Bit1,axiom,
% 5.41/5.74 ! [X: real,K: num] :
% 5.41/5.74 ( ( power_power_real @ ( uminus_uminus_real @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_minus_Bit1
% 5.41/5.74 thf(fact_6734_power__minus__Bit1,axiom,
% 5.41/5.74 ! [X: int,K: num] :
% 5.41/5.74 ( ( power_power_int @ ( uminus_uminus_int @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( power_power_int @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_minus_Bit1
% 5.41/5.74 thf(fact_6735_power__minus__Bit1,axiom,
% 5.41/5.74 ! [X: complex,K: num] :
% 5.41/5.74 ( ( power_power_complex @ ( uminus1482373934393186551omplex @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.41/5.74 = ( uminus1482373934393186551omplex @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_minus_Bit1
% 5.41/5.74 thf(fact_6736_power__minus__Bit1,axiom,
% 5.41/5.74 ! [X: code_integer,K: num] :
% 5.41/5.74 ( ( power_8256067586552552935nteger @ ( uminus1351360451143612070nteger @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.41/5.74 = ( uminus1351360451143612070nteger @ ( power_8256067586552552935nteger @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_minus_Bit1
% 5.41/5.74 thf(fact_6737_power__minus__Bit1,axiom,
% 5.41/5.74 ! [X: rat,K: num] :
% 5.41/5.74 ( ( power_power_rat @ ( uminus_uminus_rat @ X ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_rat @ ( power_power_rat @ X @ ( numeral_numeral_nat @ ( bit1 @ K ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_minus_Bit1
% 5.41/5.74 thf(fact_6738_real__of__int__div4,axiom,
% 5.41/5.74 ! [N: int,X: int] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % real_of_int_div4
% 5.41/5.74 thf(fact_6739_real__of__int__div,axiom,
% 5.41/5.74 ! [D: int,N: int] :
% 5.41/5.74 ( ( dvd_dvd_int @ D @ N )
% 5.41/5.74 => ( ( ring_1_of_int_real @ ( divide_divide_int @ N @ D ) )
% 5.41/5.74 = ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % real_of_int_div
% 5.41/5.74 thf(fact_6740_numeral__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numera6690914467698888265omplex @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_complex @ ( plus_plus_complex @ ( numera6690914467698888265omplex @ N ) @ ( numera6690914467698888265omplex @ N ) ) @ one_one_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_code(3)
% 5.41/5.74 thf(fact_6741_numeral__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_real @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_real @ ( plus_plus_real @ ( numeral_numeral_real @ N ) @ ( numeral_numeral_real @ N ) ) @ one_one_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_code(3)
% 5.41/5.74 thf(fact_6742_numeral__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_rat @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_rat @ ( plus_plus_rat @ ( numeral_numeral_rat @ N ) @ ( numeral_numeral_rat @ N ) ) @ one_one_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_code(3)
% 5.41/5.74 thf(fact_6743_numeral__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_nat @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ N ) ) @ one_one_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_code(3)
% 5.41/5.74 thf(fact_6744_numeral__code_I3_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( numeral_numeral_int @ ( bit1 @ N ) )
% 5.41/5.74 = ( plus_plus_int @ ( plus_plus_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ N ) ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_code(3)
% 5.41/5.74 thf(fact_6745_power__numeral__odd,axiom,
% 5.41/5.74 ! [Z: complex,W: num] :
% 5.41/5.74 ( ( power_power_complex @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.41/5.74 = ( times_times_complex @ ( times_times_complex @ Z @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_complex @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_numeral_odd
% 5.41/5.74 thf(fact_6746_power__numeral__odd,axiom,
% 5.41/5.74 ! [Z: real,W: num] :
% 5.41/5.74 ( ( power_power_real @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.41/5.74 = ( times_times_real @ ( times_times_real @ Z @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_real @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_numeral_odd
% 5.41/5.74 thf(fact_6747_power__numeral__odd,axiom,
% 5.41/5.74 ! [Z: rat,W: num] :
% 5.41/5.74 ( ( power_power_rat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.41/5.74 = ( times_times_rat @ ( times_times_rat @ Z @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_rat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_numeral_odd
% 5.41/5.74 thf(fact_6748_power__numeral__odd,axiom,
% 5.41/5.74 ! [Z: nat,W: num] :
% 5.41/5.74 ( ( power_power_nat @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.41/5.74 = ( times_times_nat @ ( times_times_nat @ Z @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_nat @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_numeral_odd
% 5.41/5.74 thf(fact_6749_power__numeral__odd,axiom,
% 5.41/5.74 ! [Z: int,W: num] :
% 5.41/5.74 ( ( power_power_int @ Z @ ( numeral_numeral_nat @ ( bit1 @ W ) ) )
% 5.41/5.74 = ( times_times_int @ ( times_times_int @ Z @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) @ ( power_power_int @ Z @ ( numeral_numeral_nat @ W ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % power_numeral_odd
% 5.41/5.74 thf(fact_6750_of__int__nonneg,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_nonneg
% 5.41/5.74 thf(fact_6751_of__int__nonneg,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_nonneg
% 5.41/5.74 thf(fact_6752_of__int__nonneg,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.74 => ( ord_less_eq_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_nonneg
% 5.41/5.74 thf(fact_6753_of__int__leD,axiom,
% 5.41/5.74 ! [N: int,X: code_integer] :
% 5.41/5.74 ( ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_le3102999989581377725nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_leD
% 5.41/5.74 thf(fact_6754_of__int__leD,axiom,
% 5.41/5.74 ! [N: int,X: real] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_less_eq_real @ one_one_real @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_leD
% 5.41/5.74 thf(fact_6755_of__int__leD,axiom,
% 5.41/5.74 ! [N: int,X: rat] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_less_eq_rat @ one_one_rat @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_leD
% 5.41/5.74 thf(fact_6756_of__int__leD,axiom,
% 5.41/5.74 ! [N: int,X: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_less_eq_int @ one_one_int @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_leD
% 5.41/5.74 thf(fact_6757_of__int__pos,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.74 => ( ord_less_real @ zero_zero_real @ ( ring_1_of_int_real @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_pos
% 5.41/5.74 thf(fact_6758_of__int__pos,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.74 => ( ord_less_rat @ zero_zero_rat @ ( ring_1_of_int_rat @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_pos
% 5.41/5.74 thf(fact_6759_of__int__pos,axiom,
% 5.41/5.74 ! [Z: int] :
% 5.41/5.74 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.74 => ( ord_less_int @ zero_zero_int @ ( ring_1_of_int_int @ Z ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_pos
% 5.41/5.74 thf(fact_6760_of__int__lessD,axiom,
% 5.41/5.74 ! [N: int,X: code_integer] :
% 5.41/5.74 ( ( ord_le6747313008572928689nteger @ ( abs_abs_Code_integer @ ( ring_18347121197199848620nteger @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_le6747313008572928689nteger @ one_one_Code_integer @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_lessD
% 5.41/5.74 thf(fact_6761_of__int__lessD,axiom,
% 5.41/5.74 ! [N: int,X: real] :
% 5.41/5.74 ( ( ord_less_real @ ( abs_abs_real @ ( ring_1_of_int_real @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_less_real @ one_one_real @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_lessD
% 5.41/5.74 thf(fact_6762_of__int__lessD,axiom,
% 5.41/5.74 ! [N: int,X: rat] :
% 5.41/5.74 ( ( ord_less_rat @ ( abs_abs_rat @ ( ring_1_of_int_rat @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_less_rat @ one_one_rat @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_lessD
% 5.41/5.74 thf(fact_6763_of__int__lessD,axiom,
% 5.41/5.74 ! [N: int,X: int] :
% 5.41/5.74 ( ( ord_less_int @ ( abs_abs_int @ ( ring_1_of_int_int @ N ) ) @ X )
% 5.41/5.74 => ( ( N = zero_zero_int )
% 5.41/5.74 | ( ord_less_int @ one_one_int @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_lessD
% 5.41/5.74 thf(fact_6764_of__int__neg__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_1_of_int_real @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_neg_numeral
% 5.41/5.74 thf(fact_6765_of__int__neg__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_1_of_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_neg_numeral
% 5.41/5.74 thf(fact_6766_of__int__neg__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_17405671764205052669omplex @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.74 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_neg_numeral
% 5.41/5.74 thf(fact_6767_of__int__neg__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_18347121197199848620nteger @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.74 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_neg_numeral
% 5.41/5.74 thf(fact_6768_of__int__neg__numeral,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( ring_1_of_int_rat @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_neg_numeral
% 5.41/5.74 thf(fact_6769_numeral__Bit1__div__2,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( divide_divide_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.74 = ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_Bit1_div_2
% 5.41/5.74 thf(fact_6770_numeral__Bit1__div__2,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( divide_divide_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_Bit1_div_2
% 5.41/5.74 thf(fact_6771_odd__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % odd_numeral
% 5.41/5.74 thf(fact_6772_odd__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bit1 @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % odd_numeral
% 5.41/5.74 thf(fact_6773_odd__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % odd_numeral
% 5.41/5.74 thf(fact_6774_cong__exp__iff__simps_I3_J,axiom,
% 5.41/5.74 ! [N: num,Q2: num] :
% 5.41/5.74 ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != zero_zero_nat ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(3)
% 5.41/5.74 thf(fact_6775_cong__exp__iff__simps_I3_J,axiom,
% 5.41/5.74 ! [N: num,Q2: num] :
% 5.41/5.74 ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(3)
% 5.41/5.74 thf(fact_6776_cong__exp__iff__simps_I3_J,axiom,
% 5.41/5.74 ! [N: num,Q2: num] :
% 5.41/5.74 ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 != zero_z3403309356797280102nteger ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(3)
% 5.41/5.74 thf(fact_6777_power3__eq__cube,axiom,
% 5.41/5.74 ! [A: complex] :
% 5.41/5.74 ( ( power_power_complex @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.41/5.74 = ( times_times_complex @ ( times_times_complex @ A @ A ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % power3_eq_cube
% 5.41/5.74 thf(fact_6778_power3__eq__cube,axiom,
% 5.41/5.74 ! [A: real] :
% 5.41/5.74 ( ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.41/5.74 = ( times_times_real @ ( times_times_real @ A @ A ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % power3_eq_cube
% 5.41/5.74 thf(fact_6779_power3__eq__cube,axiom,
% 5.41/5.74 ! [A: rat] :
% 5.41/5.74 ( ( power_power_rat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.41/5.74 = ( times_times_rat @ ( times_times_rat @ A @ A ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % power3_eq_cube
% 5.41/5.74 thf(fact_6780_power3__eq__cube,axiom,
% 5.41/5.74 ! [A: nat] :
% 5.41/5.74 ( ( power_power_nat @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.41/5.74 = ( times_times_nat @ ( times_times_nat @ A @ A ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % power3_eq_cube
% 5.41/5.74 thf(fact_6781_power3__eq__cube,axiom,
% 5.41/5.74 ! [A: int] :
% 5.41/5.74 ( ( power_power_int @ A @ ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.41/5.74 = ( times_times_int @ ( times_times_int @ A @ A ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % power3_eq_cube
% 5.41/5.74 thf(fact_6782_numeral__3__eq__3,axiom,
% 5.41/5.74 ( ( numeral_numeral_nat @ ( bit1 @ one ) )
% 5.41/5.74 = ( suc @ ( suc @ ( suc @ zero_zero_nat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_3_eq_3
% 5.41/5.74 thf(fact_6783_Suc3__eq__add__3,axiom,
% 5.41/5.74 ! [N: nat] :
% 5.41/5.74 ( ( suc @ ( suc @ ( suc @ N ) ) )
% 5.41/5.74 = ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % Suc3_eq_add_3
% 5.41/5.74 thf(fact_6784_int__le__real__less,axiom,
% 5.41/5.74 ( ord_less_eq_int
% 5.41/5.74 = ( ^ [N2: int,M3: int] : ( ord_less_real @ ( ring_1_of_int_real @ N2 ) @ ( plus_plus_real @ ( ring_1_of_int_real @ M3 ) @ one_one_real ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % int_le_real_less
% 5.41/5.74 thf(fact_6785_int__less__real__le,axiom,
% 5.41/5.74 ( ord_less_int
% 5.41/5.74 = ( ^ [N2: int,M3: int] : ( ord_less_eq_real @ ( plus_plus_real @ ( ring_1_of_int_real @ N2 ) @ one_one_real ) @ ( ring_1_of_int_real @ M3 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % int_less_real_le
% 5.41/5.74 thf(fact_6786_real__of__int__div__aux,axiom,
% 5.41/5.74 ! [X: int,D: int] :
% 5.41/5.74 ( ( divide_divide_real @ ( ring_1_of_int_real @ X ) @ ( ring_1_of_int_real @ D ) )
% 5.41/5.74 = ( plus_plus_real @ ( ring_1_of_int_real @ ( divide_divide_int @ X @ D ) ) @ ( divide_divide_real @ ( ring_1_of_int_real @ ( modulo_modulo_int @ X @ D ) ) @ ( ring_1_of_int_real @ D ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % real_of_int_div_aux
% 5.41/5.74 thf(fact_6787_num_Osize_I6_J,axiom,
% 5.41/5.74 ! [X32: num] :
% 5.41/5.74 ( ( size_size_num @ ( bit1 @ X32 ) )
% 5.41/5.74 = ( plus_plus_nat @ ( size_size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % num.size(6)
% 5.41/5.74 thf(fact_6788_cong__exp__iff__simps_I7_J,axiom,
% 5.41/5.74 ! [Q2: num,N: num] :
% 5.41/5.74 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ N ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.41/5.74 = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(7)
% 5.41/5.74 thf(fact_6789_cong__exp__iff__simps_I7_J,axiom,
% 5.41/5.74 ! [Q2: num,N: num] :
% 5.41/5.74 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ N ) @ ( numeral_numeral_int @ Q2 ) )
% 5.41/5.74 = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(7)
% 5.41/5.74 thf(fact_6790_cong__exp__iff__simps_I7_J,axiom,
% 5.41/5.74 ! [Q2: num,N: num] :
% 5.41/5.74 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ N ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.41/5.74 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(7)
% 5.41/5.74 thf(fact_6791_cong__exp__iff__simps_I11_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num] :
% 5.41/5.74 ( ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ ( bit1 @ M ) ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo_modulo_nat @ ( numeral_numeral_nat @ one ) @ ( numeral_numeral_nat @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo_modulo_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ Q2 ) )
% 5.41/5.74 = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(11)
% 5.41/5.74 thf(fact_6792_cong__exp__iff__simps_I11_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num] :
% 5.41/5.74 ( ( ( modulo_modulo_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo_modulo_int @ ( numeral_numeral_int @ one ) @ ( numeral_numeral_int @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ Q2 ) )
% 5.41/5.74 = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(11)
% 5.41/5.74 thf(fact_6793_cong__exp__iff__simps_I11_J,axiom,
% 5.41/5.74 ! [M: num,Q2: num] :
% 5.41/5.74 ( ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ ( bit1 @ M ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) )
% 5.41/5.74 = ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ one ) @ ( numera6620942414471956472nteger @ ( bit0 @ Q2 ) ) ) )
% 5.41/5.74 = ( ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M ) @ ( numera6620942414471956472nteger @ Q2 ) )
% 5.41/5.74 = zero_z3403309356797280102nteger ) ) ).
% 5.41/5.74
% 5.41/5.74 % cong_exp_iff_simps(11)
% 5.41/5.74 thf(fact_6794_Suc__div__eq__add3__div,axiom,
% 5.41/5.74 ! [M: nat,N: nat] :
% 5.41/5.74 ( ( divide_divide_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.41/5.74 = ( divide_divide_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % Suc_div_eq_add3_div
% 5.41/5.74 thf(fact_6795_real__of__int__div2,axiom,
% 5.41/5.74 ! [N: int,X: int] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % real_of_int_div2
% 5.41/5.74 thf(fact_6796_Suc__mod__eq__add3__mod,axiom,
% 5.41/5.74 ! [M: nat,N: nat] :
% 5.41/5.74 ( ( modulo_modulo_nat @ ( suc @ ( suc @ ( suc @ M ) ) ) @ N )
% 5.41/5.74 = ( modulo_modulo_nat @ ( plus_plus_nat @ ( numeral_numeral_nat @ ( bit1 @ one ) ) @ M ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % Suc_mod_eq_add3_mod
% 5.41/5.74 thf(fact_6797_real__of__int__div3,axiom,
% 5.41/5.74 ! [N: int,X: int] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( ring_1_of_int_real @ N ) @ ( ring_1_of_int_real @ X ) ) @ ( ring_1_of_int_real @ ( divide_divide_int @ N @ X ) ) ) @ one_one_real ) ).
% 5.41/5.74
% 5.41/5.74 % real_of_int_div3
% 5.41/5.74 thf(fact_6798_divmod__int__def,axiom,
% 5.41/5.74 ( unique5052692396658037445od_int
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_int_def
% 5.41/5.74 thf(fact_6799_divmod__def,axiom,
% 5.41/5.74 ( unique5052692396658037445od_int
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( product_Pair_int_int @ ( divide_divide_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) @ ( modulo_modulo_int @ ( numeral_numeral_int @ M3 ) @ ( numeral_numeral_int @ N2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_def
% 5.41/5.74 thf(fact_6800_divmod__def,axiom,
% 5.41/5.74 ( unique5055182867167087721od_nat
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_def
% 5.41/5.74 thf(fact_6801_divmod__def,axiom,
% 5.41/5.74 ( unique3479559517661332726nteger
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_def
% 5.41/5.74 thf(fact_6802_even__of__int__iff,axiom,
% 5.41/5.74 ! [K: int] :
% 5.41/5.74 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( ring_18347121197199848620nteger @ K ) )
% 5.41/5.74 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.41/5.74
% 5.41/5.74 % even_of_int_iff
% 5.41/5.74 thf(fact_6803_even__of__int__iff,axiom,
% 5.41/5.74 ! [K: int] :
% 5.41/5.74 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( ring_1_of_int_int @ K ) )
% 5.41/5.74 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ).
% 5.41/5.74
% 5.41/5.74 % even_of_int_iff
% 5.41/5.74 thf(fact_6804_mod__exhaust__less__4,axiom,
% 5.41/5.74 ! [M: nat] :
% 5.41/5.74 ( ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.74 = one_one_nat )
% 5.41/5.74 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.74 = ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.74 | ( ( modulo_modulo_nat @ M @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.74 = ( numeral_numeral_nat @ ( bit1 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mod_exhaust_less_4
% 5.41/5.74 thf(fact_6805_infinite__nat__iff__unbounded,axiom,
% 5.41/5.74 ! [S2: set_nat] :
% 5.41/5.74 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.41/5.74 = ( ! [M3: nat] :
% 5.41/5.74 ? [N2: nat] :
% 5.41/5.74 ( ( ord_less_nat @ M3 @ N2 )
% 5.41/5.74 & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % infinite_nat_iff_unbounded
% 5.41/5.74 thf(fact_6806_unbounded__k__infinite,axiom,
% 5.41/5.74 ! [K: nat,S2: set_nat] :
% 5.41/5.74 ( ! [M4: nat] :
% 5.41/5.74 ( ( ord_less_nat @ K @ M4 )
% 5.41/5.74 => ? [N7: nat] :
% 5.41/5.74 ( ( ord_less_nat @ M4 @ N7 )
% 5.41/5.74 & ( member_nat @ N7 @ S2 ) ) )
% 5.41/5.74 => ~ ( finite_finite_nat @ S2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % unbounded_k_infinite
% 5.41/5.74 thf(fact_6807_infinite__nat__iff__unbounded__le,axiom,
% 5.41/5.74 ! [S2: set_nat] :
% 5.41/5.74 ( ( ~ ( finite_finite_nat @ S2 ) )
% 5.41/5.74 = ( ! [M3: nat] :
% 5.41/5.74 ? [N2: nat] :
% 5.41/5.74 ( ( ord_less_eq_nat @ M3 @ N2 )
% 5.41/5.74 & ( member_nat @ N2 @ S2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % infinite_nat_iff_unbounded_le
% 5.41/5.74 thf(fact_6808_odd__mod__4__div__2,axiom,
% 5.41/5.74 ! [N: nat] :
% 5.41/5.74 ( ( ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.74 = ( numeral_numeral_nat @ ( bit1 @ one ) ) )
% 5.41/5.74 => ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % odd_mod_4_div_2
% 5.41/5.74 thf(fact_6809_divmod__divmod__step,axiom,
% 5.41/5.74 ( unique5055182867167087721od_nat
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( if_Pro6206227464963214023at_nat @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_nat_nat @ zero_zero_nat @ ( numeral_numeral_nat @ M3 ) ) @ ( unique5026877609467782581ep_nat @ N2 @ ( unique5055182867167087721od_nat @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_divmod_step
% 5.41/5.74 thf(fact_6810_divmod__divmod__step,axiom,
% 5.41/5.74 ( unique5052692396658037445od_int
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( if_Pro3027730157355071871nt_int @ ( ord_less_num @ M3 @ N2 ) @ ( product_Pair_int_int @ zero_zero_int @ ( numeral_numeral_int @ M3 ) ) @ ( unique5024387138958732305ep_int @ N2 @ ( unique5052692396658037445od_int @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_divmod_step
% 5.41/5.74 thf(fact_6811_divmod__divmod__step,axiom,
% 5.41/5.74 ( unique3479559517661332726nteger
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( if_Pro6119634080678213985nteger @ ( ord_less_num @ M3 @ N2 ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( numera6620942414471956472nteger @ M3 ) ) @ ( unique4921790084139445826nteger @ N2 @ ( unique3479559517661332726nteger @ M3 @ ( bit0 @ N2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_divmod_step
% 5.41/5.74 thf(fact_6812_floor__exists,axiom,
% 5.41/5.74 ! [X: real] :
% 5.41/5.74 ? [Z5: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z5 ) @ X )
% 5.41/5.74 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % floor_exists
% 5.41/5.74 thf(fact_6813_floor__exists,axiom,
% 5.41/5.74 ! [X: rat] :
% 5.41/5.74 ? [Z5: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z5 ) @ X )
% 5.41/5.74 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z5 @ one_one_int ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % floor_exists
% 5.41/5.74 thf(fact_6814_floor__exists1,axiom,
% 5.41/5.74 ! [X: real] :
% 5.41/5.74 ? [X6: int] :
% 5.41/5.74 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ X6 ) @ X )
% 5.41/5.74 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ X6 @ one_one_int ) ) )
% 5.41/5.74 & ! [Y2: int] :
% 5.41/5.74 ( ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y2 ) @ X )
% 5.41/5.74 & ( ord_less_real @ X @ ( ring_1_of_int_real @ ( plus_plus_int @ Y2 @ one_one_int ) ) ) )
% 5.41/5.74 => ( Y2 = X6 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % floor_exists1
% 5.41/5.74 thf(fact_6815_floor__exists1,axiom,
% 5.41/5.74 ! [X: rat] :
% 5.41/5.74 ? [X6: int] :
% 5.41/5.74 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ X6 ) @ X )
% 5.41/5.74 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ X6 @ one_one_int ) ) )
% 5.41/5.74 & ! [Y2: int] :
% 5.41/5.74 ( ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y2 ) @ X )
% 5.41/5.74 & ( ord_less_rat @ X @ ( ring_1_of_int_rat @ ( plus_plus_int @ Y2 @ one_one_int ) ) ) )
% 5.41/5.74 => ( Y2 = X6 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % floor_exists1
% 5.41/5.74 thf(fact_6816_signed__take__bit__numeral__minus__bit1,axiom,
% 5.41/5.74 ! [L2: num,K: num] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.41/5.74 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( minus_minus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_numeral_minus_bit1
% 5.41/5.74 thf(fact_6817_dbl__dec__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.74 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(4)
% 5.41/5.74 thf(fact_6818_dbl__dec__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(4)
% 5.41/5.74 thf(fact_6819_dbl__dec__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.74 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(4)
% 5.41/5.74 thf(fact_6820_dbl__dec__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.74 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( bit1 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(4)
% 5.41/5.74 thf(fact_6821_dbl__dec__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.74 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(4)
% 5.41/5.74 thf(fact_6822_signed__take__bit__numeral__bit1,axiom,
% 5.41/5.74 ! [L2: num,K: num] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.41/5.74 = ( plus_plus_int @ ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_numeral_bit1
% 5.41/5.74 thf(fact_6823_dbl__inc__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu8557863876264182079omplex @ one_one_complex )
% 5.41/5.74 = ( numera6690914467698888265omplex @ ( bit1 @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(3)
% 5.41/5.74 thf(fact_6824_dbl__inc__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu8295874005876285629c_real @ one_one_real )
% 5.41/5.74 = ( numeral_numeral_real @ ( bit1 @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(3)
% 5.41/5.74 thf(fact_6825_dbl__inc__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu5219082963157363817nc_rat @ one_one_rat )
% 5.41/5.74 = ( numeral_numeral_rat @ ( bit1 @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(3)
% 5.41/5.74 thf(fact_6826_dbl__inc__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu5851722552734809277nc_int @ one_one_int )
% 5.41/5.74 = ( numeral_numeral_int @ ( bit1 @ one ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(3)
% 5.41/5.74 thf(fact_6827_dbl__dec__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu6511756317524482435omplex @ one_one_complex )
% 5.41/5.74 = one_one_complex ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(3)
% 5.41/5.74 thf(fact_6828_dbl__dec__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu6075765906172075777c_real @ one_one_real )
% 5.41/5.74 = one_one_real ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(3)
% 5.41/5.74 thf(fact_6829_dbl__dec__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu3179335615603231917ec_rat @ one_one_rat )
% 5.41/5.74 = one_one_rat ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(3)
% 5.41/5.74 thf(fact_6830_dbl__dec__simps_I3_J,axiom,
% 5.41/5.74 ( ( neg_nu3811975205180677377ec_int @ one_one_int )
% 5.41/5.74 = one_one_int ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(3)
% 5.41/5.74 thf(fact_6831_pred__numeral__simps_I1_J,axiom,
% 5.41/5.74 ( ( pred_numeral @ one )
% 5.41/5.74 = zero_zero_nat ) ).
% 5.41/5.74
% 5.41/5.74 % pred_numeral_simps(1)
% 5.41/5.74 thf(fact_6832_Suc__eq__numeral,axiom,
% 5.41/5.74 ! [N: nat,K: num] :
% 5.41/5.74 ( ( ( suc @ N )
% 5.41/5.74 = ( numeral_numeral_nat @ K ) )
% 5.41/5.74 = ( N
% 5.41/5.74 = ( pred_numeral @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % Suc_eq_numeral
% 5.41/5.74 thf(fact_6833_eq__numeral__Suc,axiom,
% 5.41/5.74 ! [K: num,N: nat] :
% 5.41/5.74 ( ( ( numeral_numeral_nat @ K )
% 5.41/5.74 = ( suc @ N ) )
% 5.41/5.74 = ( ( pred_numeral @ K )
% 5.41/5.74 = N ) ) ).
% 5.41/5.74
% 5.41/5.74 % eq_numeral_Suc
% 5.41/5.74 thf(fact_6834_dbl__inc__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu8557863876264182079omplex @ zero_zero_complex )
% 5.41/5.74 = one_one_complex ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(2)
% 5.41/5.74 thf(fact_6835_dbl__inc__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu8295874005876285629c_real @ zero_zero_real )
% 5.41/5.74 = one_one_real ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(2)
% 5.41/5.74 thf(fact_6836_dbl__inc__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu5219082963157363817nc_rat @ zero_zero_rat )
% 5.41/5.74 = one_one_rat ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(2)
% 5.41/5.74 thf(fact_6837_dbl__inc__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu5851722552734809277nc_int @ zero_zero_int )
% 5.41/5.74 = one_one_int ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(2)
% 5.41/5.74 thf(fact_6838_dbl__inc__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.74 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(4)
% 5.41/5.74 thf(fact_6839_dbl__inc__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.74 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(4)
% 5.41/5.74 thf(fact_6840_dbl__inc__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.74 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(4)
% 5.41/5.74 thf(fact_6841_dbl__inc__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.74 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(4)
% 5.41/5.74 thf(fact_6842_dbl__inc__simps_I4_J,axiom,
% 5.41/5.74 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.74 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(4)
% 5.41/5.74 thf(fact_6843_dbl__inc__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.41/5.74 = ( numera6690914467698888265omplex @ ( bit1 @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(5)
% 5.41/5.74 thf(fact_6844_dbl__inc__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) )
% 5.41/5.74 = ( numeral_numeral_real @ ( bit1 @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(5)
% 5.41/5.74 thf(fact_6845_dbl__inc__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) )
% 5.41/5.74 = ( numeral_numeral_rat @ ( bit1 @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(5)
% 5.41/5.74 thf(fact_6846_dbl__inc__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) )
% 5.41/5.74 = ( numeral_numeral_int @ ( bit1 @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(5)
% 5.41/5.74 thf(fact_6847_less__Suc__numeral,axiom,
% 5.41/5.74 ! [N: nat,K: num] :
% 5.41/5.74 ( ( ord_less_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.74 = ( ord_less_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % less_Suc_numeral
% 5.41/5.74 thf(fact_6848_less__numeral__Suc,axiom,
% 5.41/5.74 ! [K: num,N: nat] :
% 5.41/5.74 ( ( ord_less_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.41/5.74 = ( ord_less_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % less_numeral_Suc
% 5.41/5.74 thf(fact_6849_pred__numeral__simps_I3_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( pred_numeral @ ( bit1 @ K ) )
% 5.41/5.74 = ( numeral_numeral_nat @ ( bit0 @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % pred_numeral_simps(3)
% 5.41/5.74 thf(fact_6850_le__numeral__Suc,axiom,
% 5.41/5.74 ! [K: num,N: nat] :
% 5.41/5.74 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.41/5.74 = ( ord_less_eq_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % le_numeral_Suc
% 5.41/5.74 thf(fact_6851_le__Suc__numeral,axiom,
% 5.41/5.74 ! [N: nat,K: num] :
% 5.41/5.74 ( ( ord_less_eq_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.74 = ( ord_less_eq_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % le_Suc_numeral
% 5.41/5.74 thf(fact_6852_diff__numeral__Suc,axiom,
% 5.41/5.74 ! [K: num,N: nat] :
% 5.41/5.74 ( ( minus_minus_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.41/5.74 = ( minus_minus_nat @ ( pred_numeral @ K ) @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % diff_numeral_Suc
% 5.41/5.74 thf(fact_6853_diff__Suc__numeral,axiom,
% 5.41/5.74 ! [N: nat,K: num] :
% 5.41/5.74 ( ( minus_minus_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.74 = ( minus_minus_nat @ N @ ( pred_numeral @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % diff_Suc_numeral
% 5.41/5.74 thf(fact_6854_max__numeral__Suc,axiom,
% 5.41/5.74 ! [K: num,N: nat] :
% 5.41/5.74 ( ( ord_max_nat @ ( numeral_numeral_nat @ K ) @ ( suc @ N ) )
% 5.41/5.74 = ( suc @ ( ord_max_nat @ ( pred_numeral @ K ) @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % max_numeral_Suc
% 5.41/5.74 thf(fact_6855_max__Suc__numeral,axiom,
% 5.41/5.74 ! [N: nat,K: num] :
% 5.41/5.74 ( ( ord_max_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.74 = ( suc @ ( ord_max_nat @ N @ ( pred_numeral @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % max_Suc_numeral
% 5.41/5.74 thf(fact_6856_dbl__dec__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu6075765906172075777c_real @ zero_zero_real )
% 5.41/5.74 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(2)
% 5.41/5.74 thf(fact_6857_dbl__dec__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu3811975205180677377ec_int @ zero_zero_int )
% 5.41/5.74 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(2)
% 5.41/5.74 thf(fact_6858_dbl__dec__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu6511756317524482435omplex @ zero_zero_complex )
% 5.41/5.74 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(2)
% 5.41/5.74 thf(fact_6859_dbl__dec__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu7757733837767384882nteger @ zero_z3403309356797280102nteger )
% 5.41/5.74 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(2)
% 5.41/5.74 thf(fact_6860_dbl__dec__simps_I2_J,axiom,
% 5.41/5.74 ( ( neg_nu3179335615603231917ec_rat @ zero_zero_rat )
% 5.41/5.74 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(2)
% 5.41/5.74 thf(fact_6861_dbl__dec__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu6075765906172075777c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_real @ ( neg_nu8295874005876285629c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(1)
% 5.41/5.74 thf(fact_6862_dbl__dec__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu3811975205180677377ec_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( neg_nu5851722552734809277nc_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(1)
% 5.41/5.74 thf(fact_6863_dbl__dec__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu6511756317524482435omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.41/5.74 = ( uminus1482373934393186551omplex @ ( neg_nu8557863876264182079omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(1)
% 5.41/5.74 thf(fact_6864_dbl__dec__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu7757733837767384882nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.41/5.74 = ( uminus1351360451143612070nteger @ ( neg_nu5831290666863070958nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(1)
% 5.41/5.74 thf(fact_6865_dbl__dec__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu3179335615603231917ec_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_rat @ ( neg_nu5219082963157363817nc_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(1)
% 5.41/5.74 thf(fact_6866_dbl__inc__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu8295874005876285629c_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_real @ ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(1)
% 5.41/5.74 thf(fact_6867_dbl__inc__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu5851722552734809277nc_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(1)
% 5.41/5.74 thf(fact_6868_dbl__inc__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu8557863876264182079omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ K ) ) )
% 5.41/5.74 = ( uminus1482373934393186551omplex @ ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(1)
% 5.41/5.74 thf(fact_6869_dbl__inc__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu5831290666863070958nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ K ) ) )
% 5.41/5.74 = ( uminus1351360451143612070nteger @ ( neg_nu7757733837767384882nteger @ ( numera6620942414471956472nteger @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(1)
% 5.41/5.74 thf(fact_6870_dbl__inc__simps_I1_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu5219082963157363817nc_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.41/5.74 = ( uminus_uminus_rat @ ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_simps(1)
% 5.41/5.74 thf(fact_6871_signed__take__bit__numeral__bit0,axiom,
% 5.41/5.74 ! [L2: num,K: num] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.41/5.74 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_numeral_bit0
% 5.41/5.74 thf(fact_6872_signed__take__bit__numeral__minus__bit0,axiom,
% 5.41/5.74 ! [L2: num,K: num] :
% 5.41/5.74 ( ( bit_ri631733984087533419it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.41/5.74 = ( times_times_int @ ( bit_ri631733984087533419it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % signed_take_bit_numeral_minus_bit0
% 5.41/5.74 thf(fact_6873_numeral__eq__Suc,axiom,
% 5.41/5.74 ( numeral_numeral_nat
% 5.41/5.74 = ( ^ [K2: num] : ( suc @ ( pred_numeral @ K2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % numeral_eq_Suc
% 5.41/5.74 thf(fact_6874_pred__numeral__def,axiom,
% 5.41/5.74 ( pred_numeral
% 5.41/5.74 = ( ^ [K2: num] : ( minus_minus_nat @ ( numeral_numeral_nat @ K2 ) @ one_one_nat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % pred_numeral_def
% 5.41/5.74 thf(fact_6875_dbl__inc__def,axiom,
% 5.41/5.74 ( neg_nu8557863876264182079omplex
% 5.41/5.74 = ( ^ [X3: complex] : ( plus_plus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_def
% 5.41/5.74 thf(fact_6876_dbl__inc__def,axiom,
% 5.41/5.74 ( neg_nu8295874005876285629c_real
% 5.41/5.74 = ( ^ [X3: real] : ( plus_plus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_def
% 5.41/5.74 thf(fact_6877_dbl__inc__def,axiom,
% 5.41/5.74 ( neg_nu5219082963157363817nc_rat
% 5.41/5.74 = ( ^ [X3: rat] : ( plus_plus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_def
% 5.41/5.74 thf(fact_6878_dbl__inc__def,axiom,
% 5.41/5.74 ( neg_nu5851722552734809277nc_int
% 5.41/5.74 = ( ^ [X3: int] : ( plus_plus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_inc_def
% 5.41/5.74 thf(fact_6879_divmod_H__nat__def,axiom,
% 5.41/5.74 ( unique5055182867167087721od_nat
% 5.41/5.74 = ( ^ [M3: num,N2: num] : ( product_Pair_nat_nat @ ( divide_divide_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) @ ( modulo_modulo_nat @ ( numeral_numeral_nat @ M3 ) @ ( numeral_numeral_nat @ N2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod'_nat_def
% 5.41/5.74 thf(fact_6880_dbl__dec__def,axiom,
% 5.41/5.74 ( neg_nu6511756317524482435omplex
% 5.41/5.74 = ( ^ [X3: complex] : ( minus_minus_complex @ ( plus_plus_complex @ X3 @ X3 ) @ one_one_complex ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_def
% 5.41/5.74 thf(fact_6881_dbl__dec__def,axiom,
% 5.41/5.74 ( neg_nu6075765906172075777c_real
% 5.41/5.74 = ( ^ [X3: real] : ( minus_minus_real @ ( plus_plus_real @ X3 @ X3 ) @ one_one_real ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_def
% 5.41/5.74 thf(fact_6882_dbl__dec__def,axiom,
% 5.41/5.74 ( neg_nu3179335615603231917ec_rat
% 5.41/5.74 = ( ^ [X3: rat] : ( minus_minus_rat @ ( plus_plus_rat @ X3 @ X3 ) @ one_one_rat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_def
% 5.41/5.74 thf(fact_6883_dbl__dec__def,axiom,
% 5.41/5.74 ( neg_nu3811975205180677377ec_int
% 5.41/5.74 = ( ^ [X3: int] : ( minus_minus_int @ ( plus_plus_int @ X3 @ X3 ) @ one_one_int ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_def
% 5.41/5.74 thf(fact_6884_exists__least__lemma,axiom,
% 5.41/5.74 ! [P: nat > $o] :
% 5.41/5.74 ( ~ ( P @ zero_zero_nat )
% 5.41/5.74 => ( ? [X_12: nat] : ( P @ X_12 )
% 5.41/5.74 => ? [N3: nat] :
% 5.41/5.74 ( ~ ( P @ N3 )
% 5.41/5.74 & ( P @ ( suc @ N3 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % exists_least_lemma
% 5.41/5.74 thf(fact_6885_ex__le__of__int,axiom,
% 5.41/5.74 ! [X: real] :
% 5.41/5.74 ? [Z5: int] : ( ord_less_eq_real @ X @ ( ring_1_of_int_real @ Z5 ) ) ).
% 5.41/5.74
% 5.41/5.74 % ex_le_of_int
% 5.41/5.74 thf(fact_6886_ex__le__of__int,axiom,
% 5.41/5.74 ! [X: rat] :
% 5.41/5.74 ? [Z5: int] : ( ord_less_eq_rat @ X @ ( ring_1_of_int_rat @ Z5 ) ) ).
% 5.41/5.74
% 5.41/5.74 % ex_le_of_int
% 5.41/5.74 thf(fact_6887_ex__of__int__less,axiom,
% 5.41/5.74 ! [X: real] :
% 5.41/5.74 ? [Z5: int] : ( ord_less_real @ ( ring_1_of_int_real @ Z5 ) @ X ) ).
% 5.41/5.74
% 5.41/5.74 % ex_of_int_less
% 5.41/5.74 thf(fact_6888_ex__of__int__less,axiom,
% 5.41/5.74 ! [X: rat] :
% 5.41/5.74 ? [Z5: int] : ( ord_less_rat @ ( ring_1_of_int_rat @ Z5 ) @ X ) ).
% 5.41/5.74
% 5.41/5.74 % ex_of_int_less
% 5.41/5.74 thf(fact_6889_ex__less__of__int,axiom,
% 5.41/5.74 ! [X: real] :
% 5.41/5.74 ? [Z5: int] : ( ord_less_real @ X @ ( ring_1_of_int_real @ Z5 ) ) ).
% 5.41/5.74
% 5.41/5.74 % ex_less_of_int
% 5.41/5.74 thf(fact_6890_ex__less__of__int,axiom,
% 5.41/5.74 ! [X: rat] :
% 5.41/5.74 ? [Z5: int] : ( ord_less_rat @ X @ ( ring_1_of_int_rat @ Z5 ) ) ).
% 5.41/5.74
% 5.41/5.74 % ex_less_of_int
% 5.41/5.74 thf(fact_6891_round__unique,axiom,
% 5.41/5.74 ! [X: real,Y: int] :
% 5.41/5.74 ( ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ Y ) )
% 5.41/5.74 => ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Y ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.74 => ( ( archim8280529875227126926d_real @ X )
% 5.41/5.74 = Y ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_unique
% 5.41/5.74 thf(fact_6892_round__unique,axiom,
% 5.41/5.74 ! [X: rat,Y: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ Y ) )
% 5.41/5.74 => ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Y ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.74 => ( ( archim7778729529865785530nd_rat @ X )
% 5.41/5.74 = Y ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_unique
% 5.41/5.74 thf(fact_6893_round__unique_H,axiom,
% 5.41/5.74 ! [X: real,N: int] :
% 5.41/5.74 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ ( ring_1_of_int_real @ N ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.74 => ( ( archim8280529875227126926d_real @ X )
% 5.41/5.74 = N ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_unique'
% 5.41/5.74 thf(fact_6894_round__unique_H,axiom,
% 5.41/5.74 ! [X: rat,N: int] :
% 5.41/5.74 ( ( ord_less_rat @ ( abs_abs_rat @ ( minus_minus_rat @ X @ ( ring_1_of_int_rat @ N ) ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) )
% 5.41/5.74 => ( ( archim7778729529865785530nd_rat @ X )
% 5.41/5.74 = N ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_unique'
% 5.41/5.74 thf(fact_6895_of__int__round__abs__le,axiom,
% 5.41/5.74 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ X ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_abs_le
% 5.41/5.74 thf(fact_6896_of__int__round__abs__le,axiom,
% 5.41/5.74 ! [X: rat] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ X ) ) @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_abs_le
% 5.41/5.74 thf(fact_6897_of__int__round__gt,axiom,
% 5.41/5.74 ! [X: real] : ( ord_less_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_gt
% 5.41/5.74 thf(fact_6898_of__int__round__gt,axiom,
% 5.41/5.74 ! [X: rat] : ( ord_less_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_gt
% 5.41/5.74 thf(fact_6899_of__int__round__ge,axiom,
% 5.41/5.74 ! [X: real] : ( ord_less_eq_real @ ( minus_minus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_ge
% 5.41/5.74 thf(fact_6900_of__int__round__ge,axiom,
% 5.41/5.74 ! [X: rat] : ( ord_less_eq_rat @ ( minus_minus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_ge
% 5.41/5.74 thf(fact_6901_of__int__round__le,axiom,
% 5.41/5.74 ! [X: real] : ( ord_less_eq_real @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ X ) ) @ ( plus_plus_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_le
% 5.41/5.74 thf(fact_6902_of__int__round__le,axiom,
% 5.41/5.74 ! [X: rat] : ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ X ) ) @ ( plus_plus_rat @ X @ ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_round_le
% 5.41/5.74 thf(fact_6903_round__0,axiom,
% 5.41/5.74 ( ( archim8280529875227126926d_real @ zero_zero_real )
% 5.41/5.74 = zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % round_0
% 5.41/5.74 thf(fact_6904_round__0,axiom,
% 5.41/5.74 ( ( archim7778729529865785530nd_rat @ zero_zero_rat )
% 5.41/5.74 = zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % round_0
% 5.41/5.74 thf(fact_6905_round__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( archim8280529875227126926d_real @ ( numeral_numeral_real @ N ) )
% 5.41/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_numeral
% 5.41/5.74 thf(fact_6906_round__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( archim7778729529865785530nd_rat @ ( numeral_numeral_rat @ N ) )
% 5.41/5.74 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_numeral
% 5.41/5.74 thf(fact_6907_round__1,axiom,
% 5.41/5.74 ( ( archim8280529875227126926d_real @ one_one_real )
% 5.41/5.74 = one_one_int ) ).
% 5.41/5.74
% 5.41/5.74 % round_1
% 5.41/5.74 thf(fact_6908_round__1,axiom,
% 5.41/5.74 ( ( archim7778729529865785530nd_rat @ one_one_rat )
% 5.41/5.74 = one_one_int ) ).
% 5.41/5.74
% 5.41/5.74 % round_1
% 5.41/5.74 thf(fact_6909_round__neg__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( archim8280529875227126926d_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_neg_numeral
% 5.41/5.74 thf(fact_6910_round__neg__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( archim7778729529865785530nd_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.74 = ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_neg_numeral
% 5.41/5.74 thf(fact_6911_round__mono,axiom,
% 5.41/5.74 ! [X: rat,Y: rat] :
% 5.41/5.74 ( ( ord_less_eq_rat @ X @ Y )
% 5.41/5.74 => ( ord_less_eq_int @ ( archim7778729529865785530nd_rat @ X ) @ ( archim7778729529865785530nd_rat @ Y ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_mono
% 5.41/5.74 thf(fact_6912_round__diff__minimal,axiom,
% 5.41/5.74 ! [Z: real,M: int] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ ( archim8280529875227126926d_real @ Z ) ) ) ) @ ( abs_abs_real @ ( minus_minus_real @ Z @ ( ring_1_of_int_real @ M ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_diff_minimal
% 5.41/5.74 thf(fact_6913_round__diff__minimal,axiom,
% 5.41/5.74 ! [Z: rat,M: int] : ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ ( archim7778729529865785530nd_rat @ Z ) ) ) ) @ ( abs_abs_rat @ ( minus_minus_rat @ Z @ ( ring_1_of_int_rat @ M ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % round_diff_minimal
% 5.41/5.74 thf(fact_6914_divmod__BitM__2__eq,axiom,
% 5.41/5.74 ! [M: num] :
% 5.41/5.74 ( ( unique5052692396658037445od_int @ ( bitM @ M ) @ ( bit0 @ one ) )
% 5.41/5.74 = ( product_Pair_int_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ one_one_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_BitM_2_eq
% 5.41/5.74 thf(fact_6915_divmod__algorithm__code_I6_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( unique5052692396658037445od_int @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( produc4245557441103728435nt_int
% 5.41/5.74 @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) @ one_one_int ) )
% 5.41/5.74 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(6)
% 5.41/5.74 thf(fact_6916_divmod__algorithm__code_I6_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( unique5055182867167087721od_nat @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( produc2626176000494625587at_nat
% 5.41/5.74 @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) @ one_one_nat ) )
% 5.41/5.74 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(6)
% 5.41/5.74 thf(fact_6917_divmod__algorithm__code_I6_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( unique3479559517661332726nteger @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( produc6916734918728496179nteger
% 5.41/5.74 @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) @ one_one_Code_integer ) )
% 5.41/5.74 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(6)
% 5.41/5.74 thf(fact_6918_Sum__Icc__int,axiom,
% 5.41/5.74 ! [M: int,N: int] :
% 5.41/5.74 ( ( ord_less_eq_int @ M @ N )
% 5.41/5.74 => ( ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [X3: int] : X3
% 5.41/5.74 @ ( set_or1266510415728281911st_int @ M @ N ) )
% 5.41/5.74 = ( divide_divide_int @ ( minus_minus_int @ ( times_times_int @ N @ ( plus_plus_int @ N @ one_one_int ) ) @ ( times_times_int @ M @ ( minus_minus_int @ M @ one_one_int ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % Sum_Icc_int
% 5.41/5.74 thf(fact_6919_divmod__step__def,axiom,
% 5.41/5.74 ( unique5026877609467782581ep_nat
% 5.41/5.74 = ( ^ [L: num] :
% 5.41/5.74 ( produc2626176000494625587at_nat
% 5.41/5.74 @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_step_def
% 5.41/5.74 thf(fact_6920_divmod__step__def,axiom,
% 5.41/5.74 ( unique5024387138958732305ep_int
% 5.41/5.74 = ( ^ [L: num] :
% 5.41/5.74 ( produc4245557441103728435nt_int
% 5.41/5.74 @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_step_def
% 5.41/5.74 thf(fact_6921_divmod__step__def,axiom,
% 5.41/5.74 ( unique4921790084139445826nteger
% 5.41/5.74 = ( ^ [L: num] :
% 5.41/5.74 ( produc6916734918728496179nteger
% 5.41/5.74 @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_step_def
% 5.41/5.74 thf(fact_6922_even__set__encode__iff,axiom,
% 5.41/5.74 ! [A2: set_nat] :
% 5.41/5.74 ( ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat_set_encode @ A2 ) )
% 5.41/5.74 = ( ~ ( member_nat @ zero_zero_nat @ A2 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % even_set_encode_iff
% 5.41/5.74 thf(fact_6923_mask__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( bit_se2002935070580805687sk_nat @ ( numeral_numeral_nat @ N ) )
% 5.41/5.74 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mask_numeral
% 5.41/5.74 thf(fact_6924_mask__numeral,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( bit_se2000444600071755411sk_int @ ( numeral_numeral_nat @ N ) )
% 5.41/5.74 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ ( pred_numeral @ N ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % mask_numeral
% 5.41/5.74 thf(fact_6925_mask__nat__positive__iff,axiom,
% 5.41/5.74 ! [N: nat] :
% 5.41/5.74 ( ( ord_less_nat @ zero_zero_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.41/5.74 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % mask_nat_positive_iff
% 5.41/5.74 thf(fact_6926_sum_Oneutral__const,axiom,
% 5.41/5.74 ! [A2: set_int] :
% 5.41/5.74 ( ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [Uu3: int] : zero_zero_int
% 5.41/5.74 @ A2 )
% 5.41/5.74 = zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral_const
% 5.41/5.74 thf(fact_6927_sum_Oneutral__const,axiom,
% 5.41/5.74 ! [A2: set_complex] :
% 5.41/5.74 ( ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [Uu3: complex] : zero_zero_complex
% 5.41/5.74 @ A2 )
% 5.41/5.74 = zero_zero_complex ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral_const
% 5.41/5.74 thf(fact_6928_sum_Oneutral__const,axiom,
% 5.41/5.74 ! [A2: set_nat] :
% 5.41/5.74 ( ( groups3542108847815614940at_nat
% 5.41/5.74 @ ^ [Uu3: nat] : zero_zero_nat
% 5.41/5.74 @ A2 )
% 5.41/5.74 = zero_zero_nat ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral_const
% 5.41/5.74 thf(fact_6929_sum_Oneutral__const,axiom,
% 5.41/5.74 ! [A2: set_nat] :
% 5.41/5.74 ( ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [Uu3: nat] : zero_zero_real
% 5.41/5.74 @ A2 )
% 5.41/5.74 = zero_zero_real ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral_const
% 5.41/5.74 thf(fact_6930_case__prod__conv,axiom,
% 5.41/5.74 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,A: nat,B: nat] :
% 5.41/5.74 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.41/5.74 = ( F @ A @ B ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_conv
% 5.41/5.74 thf(fact_6931_case__prod__conv,axiom,
% 5.41/5.74 ! [F: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat] :
% 5.41/5.74 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ A @ B ) )
% 5.41/5.74 = ( F @ A @ B ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_conv
% 5.41/5.74 thf(fact_6932_case__prod__conv,axiom,
% 5.41/5.74 ! [F: int > int > product_prod_int_int,A: int,B: int] :
% 5.41/5.74 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.41/5.74 = ( F @ A @ B ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_conv
% 5.41/5.74 thf(fact_6933_case__prod__conv,axiom,
% 5.41/5.74 ! [F: int > int > $o,A: int,B: int] :
% 5.41/5.74 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.41/5.74 = ( F @ A @ B ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_conv
% 5.41/5.74 thf(fact_6934_case__prod__conv,axiom,
% 5.41/5.74 ! [F: int > int > int,A: int,B: int] :
% 5.41/5.74 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.41/5.74 = ( F @ A @ B ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_conv
% 5.41/5.74 thf(fact_6935_sum_Oempty,axiom,
% 5.41/5.74 ! [G: nat > complex] :
% 5.41/5.74 ( ( groups2073611262835488442omplex @ G @ bot_bot_set_nat )
% 5.41/5.74 = zero_zero_complex ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6936_sum_Oempty,axiom,
% 5.41/5.74 ! [G: nat > rat] :
% 5.41/5.74 ( ( groups2906978787729119204at_rat @ G @ bot_bot_set_nat )
% 5.41/5.74 = zero_zero_rat ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6937_sum_Oempty,axiom,
% 5.41/5.74 ! [G: nat > int] :
% 5.41/5.74 ( ( groups3539618377306564664at_int @ G @ bot_bot_set_nat )
% 5.41/5.74 = zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6938_sum_Oempty,axiom,
% 5.41/5.74 ! [G: int > complex] :
% 5.41/5.74 ( ( groups3049146728041665814omplex @ G @ bot_bot_set_int )
% 5.41/5.74 = zero_zero_complex ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6939_sum_Oempty,axiom,
% 5.41/5.74 ! [G: int > real] :
% 5.41/5.74 ( ( groups8778361861064173332t_real @ G @ bot_bot_set_int )
% 5.41/5.74 = zero_zero_real ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6940_sum_Oempty,axiom,
% 5.41/5.74 ! [G: int > rat] :
% 5.41/5.74 ( ( groups3906332499630173760nt_rat @ G @ bot_bot_set_int )
% 5.41/5.74 = zero_zero_rat ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6941_sum_Oempty,axiom,
% 5.41/5.74 ! [G: int > nat] :
% 5.41/5.74 ( ( groups4541462559716669496nt_nat @ G @ bot_bot_set_int )
% 5.41/5.74 = zero_zero_nat ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6942_sum_Oempty,axiom,
% 5.41/5.74 ! [G: real > complex] :
% 5.41/5.74 ( ( groups5754745047067104278omplex @ G @ bot_bot_set_real )
% 5.41/5.74 = zero_zero_complex ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6943_sum_Oempty,axiom,
% 5.41/5.74 ! [G: real > real] :
% 5.41/5.74 ( ( groups8097168146408367636l_real @ G @ bot_bot_set_real )
% 5.41/5.74 = zero_zero_real ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6944_sum_Oempty,axiom,
% 5.41/5.74 ! [G: real > rat] :
% 5.41/5.74 ( ( groups1300246762558778688al_rat @ G @ bot_bot_set_real )
% 5.41/5.74 = zero_zero_rat ) ).
% 5.41/5.74
% 5.41/5.74 % sum.empty
% 5.41/5.74 thf(fact_6945_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_nat,G: nat > complex] :
% 5.41/5.74 ( ~ ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.41/5.74 = zero_zero_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6946_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > complex] :
% 5.41/5.74 ( ~ ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.41/5.74 = zero_zero_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6947_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > real] :
% 5.41/5.74 ( ~ ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.41/5.74 = zero_zero_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6948_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_complex,G: complex > real] :
% 5.41/5.74 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.41/5.74 = zero_zero_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6949_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_nat,G: nat > rat] :
% 5.41/5.74 ( ~ ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.41/5.74 = zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6950_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > rat] :
% 5.41/5.74 ( ~ ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.41/5.74 = zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6951_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_complex,G: complex > rat] :
% 5.41/5.74 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.41/5.74 = zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6952_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > nat] :
% 5.41/5.74 ( ~ ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.41/5.74 = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6953_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_complex,G: complex > nat] :
% 5.41/5.74 ( ~ ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.41/5.74 = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6954_sum_Oinfinite,axiom,
% 5.41/5.74 ! [A2: set_nat,G: nat > int] :
% 5.41/5.74 ( ~ ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.41/5.74 = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.infinite
% 5.41/5.74 thf(fact_6955_sum__eq__0__iff,axiom,
% 5.41/5.74 ! [F3: set_int,F: int > nat] :
% 5.41/5.74 ( ( finite_finite_int @ F3 )
% 5.41/5.74 => ( ( ( groups4541462559716669496nt_nat @ F @ F3 )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 = ( ! [X3: int] :
% 5.41/5.74 ( ( member_int @ X3 @ F3 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_eq_0_iff
% 5.41/5.74 thf(fact_6956_sum__eq__0__iff,axiom,
% 5.41/5.74 ! [F3: set_complex,F: complex > nat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ F3 )
% 5.41/5.74 => ( ( ( groups5693394587270226106ex_nat @ F @ F3 )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 = ( ! [X3: complex] :
% 5.41/5.74 ( ( member_complex @ X3 @ F3 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_eq_0_iff
% 5.41/5.74 thf(fact_6957_sum__eq__0__iff,axiom,
% 5.41/5.74 ! [F3: set_nat,F: nat > nat] :
% 5.41/5.74 ( ( finite_finite_nat @ F3 )
% 5.41/5.74 => ( ( ( groups3542108847815614940at_nat @ F @ F3 )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 = ( ! [X3: nat] :
% 5.41/5.74 ( ( member_nat @ X3 @ F3 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_eq_0_iff
% 5.41/5.74 thf(fact_6958_mask__eq__0__iff,axiom,
% 5.41/5.74 ! [N: nat] :
% 5.41/5.74 ( ( ( bit_se2002935070580805687sk_nat @ N )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 = ( N = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % mask_eq_0_iff
% 5.41/5.74 thf(fact_6959_mask__eq__0__iff,axiom,
% 5.41/5.74 ! [N: nat] :
% 5.41/5.74 ( ( ( bit_se2000444600071755411sk_int @ N )
% 5.41/5.74 = zero_zero_int )
% 5.41/5.74 = ( N = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % mask_eq_0_iff
% 5.41/5.74 thf(fact_6960_mask__0,axiom,
% 5.41/5.74 ( ( bit_se2002935070580805687sk_nat @ zero_zero_nat )
% 5.41/5.74 = zero_zero_nat ) ).
% 5.41/5.74
% 5.41/5.74 % mask_0
% 5.41/5.74 thf(fact_6961_mask__0,axiom,
% 5.41/5.74 ( ( bit_se2000444600071755411sk_int @ zero_zero_nat )
% 5.41/5.74 = zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % mask_0
% 5.41/5.74 thf(fact_6962_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_real,A: real,B: real > complex] :
% 5.41/5.74 ( ( finite_finite_real @ S2 )
% 5.41/5.74 => ( ( ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups5754745047067104278omplex
% 5.41/5.74 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups5754745047067104278omplex
% 5.41/5.74 @ ^ [K2: real] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_complex ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6963_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_nat,A: nat,B: nat > complex] :
% 5.41/5.74 ( ( finite_finite_nat @ S2 )
% 5.41/5.74 => ( ( ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2073611262835488442omplex
% 5.41/5.74 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2073611262835488442omplex
% 5.41/5.74 @ ^ [K2: nat] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_complex ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6964_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_int,A: int,B: int > complex] :
% 5.41/5.74 ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ( ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3049146728041665814omplex
% 5.41/5.74 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3049146728041665814omplex
% 5.41/5.74 @ ^ [K2: int] : ( if_complex @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_complex ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6965_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_real,A: real,B: real > real] :
% 5.41/5.74 ( ( finite_finite_real @ S2 )
% 5.41/5.74 => ( ( ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups8097168146408367636l_real
% 5.41/5.74 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups8097168146408367636l_real
% 5.41/5.74 @ ^ [K2: real] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6966_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_int,A: int,B: int > real] :
% 5.41/5.74 ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ( ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups8778361861064173332t_real
% 5.41/5.74 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups8778361861064173332t_real
% 5.41/5.74 @ ^ [K2: int] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6967_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_complex,A: complex,B: complex > real] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.74 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5808333547571424918x_real
% 5.41/5.74 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5808333547571424918x_real
% 5.41/5.74 @ ^ [K2: complex] : ( if_real @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6968_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_real,A: real,B: real > rat] :
% 5.41/5.74 ( ( finite_finite_real @ S2 )
% 5.41/5.74 => ( ( ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups1300246762558778688al_rat
% 5.41/5.74 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups1300246762558778688al_rat
% 5.41/5.74 @ ^ [K2: real] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6969_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_nat,A: nat,B: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ S2 )
% 5.41/5.74 => ( ( ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2906978787729119204at_rat
% 5.41/5.74 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2906978787729119204at_rat
% 5.41/5.74 @ ^ [K2: nat] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6970_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_int,A: int,B: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ( ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3906332499630173760nt_rat
% 5.41/5.74 @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3906332499630173760nt_rat
% 5.41/5.74 @ ^ [K2: int] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6971_sum_Odelta_H,axiom,
% 5.41/5.74 ! [S2: set_complex,A: complex,B: complex > rat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.74 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5058264527183730370ex_rat
% 5.41/5.74 @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5058264527183730370ex_rat
% 5.41/5.74 @ ^ [K2: complex] : ( if_rat @ ( A = K2 ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta'
% 5.41/5.74 thf(fact_6972_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_real,A: real,B: real > complex] :
% 5.41/5.74 ( ( finite_finite_real @ S2 )
% 5.41/5.74 => ( ( ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups5754745047067104278omplex
% 5.41/5.74 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups5754745047067104278omplex
% 5.41/5.74 @ ^ [K2: real] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_complex ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6973_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_nat,A: nat,B: nat > complex] :
% 5.41/5.74 ( ( finite_finite_nat @ S2 )
% 5.41/5.74 => ( ( ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2073611262835488442omplex
% 5.41/5.74 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2073611262835488442omplex
% 5.41/5.74 @ ^ [K2: nat] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_complex ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6974_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_int,A: int,B: int > complex] :
% 5.41/5.74 ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ( ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3049146728041665814omplex
% 5.41/5.74 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3049146728041665814omplex
% 5.41/5.74 @ ^ [K2: int] : ( if_complex @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_complex )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_complex ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6975_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_real,A: real,B: real > real] :
% 5.41/5.74 ( ( finite_finite_real @ S2 )
% 5.41/5.74 => ( ( ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups8097168146408367636l_real
% 5.41/5.74 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups8097168146408367636l_real
% 5.41/5.74 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6976_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_int,A: int,B: int > real] :
% 5.41/5.74 ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ( ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups8778361861064173332t_real
% 5.41/5.74 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups8778361861064173332t_real
% 5.41/5.74 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6977_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_complex,A: complex,B: complex > real] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.74 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5808333547571424918x_real
% 5.41/5.74 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5808333547571424918x_real
% 5.41/5.74 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_real )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6978_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_real,A: real,B: real > rat] :
% 5.41/5.74 ( ( finite_finite_real @ S2 )
% 5.41/5.74 => ( ( ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups1300246762558778688al_rat
% 5.41/5.74 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.74 => ( ( groups1300246762558778688al_rat
% 5.41/5.74 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6979_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_nat,A: nat,B: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ S2 )
% 5.41/5.74 => ( ( ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2906978787729119204at_rat
% 5.41/5.74 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_nat @ A @ S2 )
% 5.41/5.74 => ( ( groups2906978787729119204at_rat
% 5.41/5.74 @ ^ [K2: nat] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6980_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_int,A: int,B: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ( ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3906332499630173760nt_rat
% 5.41/5.74 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.74 => ( ( groups3906332499630173760nt_rat
% 5.41/5.74 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6981_sum_Odelta,axiom,
% 5.41/5.74 ! [S2: set_complex,A: complex,B: complex > rat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.74 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5058264527183730370ex_rat
% 5.41/5.74 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = ( B @ A ) ) )
% 5.41/5.74 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.74 => ( ( groups5058264527183730370ex_rat
% 5.41/5.74 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ zero_zero_rat )
% 5.41/5.74 @ S2 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.delta
% 5.41/5.74 thf(fact_6982_sum__abs,axiom,
% 5.41/5.74 ! [F: int > int,A2: set_int] :
% 5.41/5.74 ( ord_less_eq_int @ ( abs_abs_int @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.41/5.74 @ ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_abs
% 5.41/5.74 thf(fact_6983_sum__abs,axiom,
% 5.41/5.74 ! [F: nat > real,A2: set_nat] :
% 5.41/5.74 ( ord_less_eq_real @ ( abs_abs_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.41/5.74 @ ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_abs
% 5.41/5.74 thf(fact_6984_set__encode__empty,axiom,
% 5.41/5.74 ( ( nat_set_encode @ bot_bot_set_nat )
% 5.41/5.74 = zero_zero_nat ) ).
% 5.41/5.74
% 5.41/5.74 % set_encode_empty
% 5.41/5.74 thf(fact_6985_dbl__dec__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu6511756317524482435omplex @ ( numera6690914467698888265omplex @ K ) )
% 5.41/5.74 = ( numera6690914467698888265omplex @ ( bitM @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(5)
% 5.41/5.74 thf(fact_6986_dbl__dec__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu6075765906172075777c_real @ ( numeral_numeral_real @ K ) )
% 5.41/5.74 = ( numeral_numeral_real @ ( bitM @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(5)
% 5.41/5.74 thf(fact_6987_dbl__dec__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu3179335615603231917ec_rat @ ( numeral_numeral_rat @ K ) )
% 5.41/5.74 = ( numeral_numeral_rat @ ( bitM @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(5)
% 5.41/5.74 thf(fact_6988_dbl__dec__simps_I5_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( neg_nu3811975205180677377ec_int @ ( numeral_numeral_int @ K ) )
% 5.41/5.74 = ( numeral_numeral_int @ ( bitM @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % dbl_dec_simps(5)
% 5.41/5.74 thf(fact_6989_mask__Suc__0,axiom,
% 5.41/5.74 ( ( bit_se2002935070580805687sk_nat @ ( suc @ zero_zero_nat ) )
% 5.41/5.74 = one_one_nat ) ).
% 5.41/5.74
% 5.41/5.74 % mask_Suc_0
% 5.41/5.74 thf(fact_6990_mask__Suc__0,axiom,
% 5.41/5.74 ( ( bit_se2000444600071755411sk_int @ ( suc @ zero_zero_nat ) )
% 5.41/5.74 = one_one_int ) ).
% 5.41/5.74
% 5.41/5.74 % mask_Suc_0
% 5.41/5.74 thf(fact_6991_sum__abs__ge__zero,axiom,
% 5.41/5.74 ! [F: int > int,A2: set_int] :
% 5.41/5.74 ( ord_less_eq_int @ zero_zero_int
% 5.41/5.74 @ ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [I5: int] : ( abs_abs_int @ ( F @ I5 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_abs_ge_zero
% 5.41/5.74 thf(fact_6992_sum__abs__ge__zero,axiom,
% 5.41/5.74 ! [F: nat > real,A2: set_nat] :
% 5.41/5.74 ( ord_less_eq_real @ zero_zero_real
% 5.41/5.74 @ ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [I5: nat] : ( abs_abs_real @ ( F @ I5 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_abs_ge_zero
% 5.41/5.74 thf(fact_6993_pred__numeral__simps_I2_J,axiom,
% 5.41/5.74 ! [K: num] :
% 5.41/5.74 ( ( pred_numeral @ ( bit0 @ K ) )
% 5.41/5.74 = ( numeral_numeral_nat @ ( bitM @ K ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % pred_numeral_simps(2)
% 5.41/5.74 thf(fact_6994_divmod__algorithm__code_I5_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( unique5052692396658037445od_int @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( produc4245557441103728435nt_int
% 5.41/5.74 @ ^ [Q5: int,R5: int] : ( product_Pair_int_int @ Q5 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ R5 ) )
% 5.41/5.74 @ ( unique5052692396658037445od_int @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(5)
% 5.41/5.74 thf(fact_6995_divmod__algorithm__code_I5_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( unique5055182867167087721od_nat @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( produc2626176000494625587at_nat
% 5.41/5.74 @ ^ [Q5: nat,R5: nat] : ( product_Pair_nat_nat @ Q5 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ R5 ) )
% 5.41/5.74 @ ( unique5055182867167087721od_nat @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(5)
% 5.41/5.74 thf(fact_6996_divmod__algorithm__code_I5_J,axiom,
% 5.41/5.74 ! [M: num,N: num] :
% 5.41/5.74 ( ( unique3479559517661332726nteger @ ( bit0 @ M ) @ ( bit0 @ N ) )
% 5.41/5.74 = ( produc6916734918728496179nteger
% 5.41/5.74 @ ^ [Q5: code_integer,R5: code_integer] : ( produc1086072967326762835nteger @ Q5 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ R5 ) )
% 5.41/5.74 @ ( unique3479559517661332726nteger @ M @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % divmod_algorithm_code(5)
% 5.41/5.74 thf(fact_6997_sum_Oneutral,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > int] :
% 5.41/5.74 ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ( G @ X6 )
% 5.41/5.74 = zero_zero_int ) )
% 5.41/5.74 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 5.41/5.74 = zero_zero_int ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral
% 5.41/5.74 thf(fact_6998_sum_Oneutral,axiom,
% 5.41/5.74 ! [A2: set_complex,G: complex > complex] :
% 5.41/5.74 ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ( G @ X6 )
% 5.41/5.74 = zero_zero_complex ) )
% 5.41/5.74 => ( ( groups7754918857620584856omplex @ G @ A2 )
% 5.41/5.74 = zero_zero_complex ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral
% 5.41/5.74 thf(fact_6999_sum_Oneutral,axiom,
% 5.41/5.74 ! [A2: set_nat,G: nat > nat] :
% 5.41/5.74 ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ( G @ X6 )
% 5.41/5.74 = zero_zero_nat ) )
% 5.41/5.74 => ( ( groups3542108847815614940at_nat @ G @ A2 )
% 5.41/5.74 = zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral
% 5.41/5.74 thf(fact_7000_sum_Oneutral,axiom,
% 5.41/5.74 ! [A2: set_nat,G: nat > real] :
% 5.41/5.74 ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ( G @ X6 )
% 5.41/5.74 = zero_zero_real ) )
% 5.41/5.74 => ( ( groups6591440286371151544t_real @ G @ A2 )
% 5.41/5.74 = zero_zero_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.neutral
% 5.41/5.74 thf(fact_7001_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: real > complex,A2: set_real] :
% 5.41/5.74 ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.41/5.74 != zero_zero_complex )
% 5.41/5.74 => ~ ! [A5: real] :
% 5.41/5.74 ( ( member_real @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_complex ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7002_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: nat > complex,A2: set_nat] :
% 5.41/5.74 ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.41/5.74 != zero_zero_complex )
% 5.41/5.74 => ~ ! [A5: nat] :
% 5.41/5.74 ( ( member_nat @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_complex ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7003_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: int > complex,A2: set_int] :
% 5.41/5.74 ( ( ( groups3049146728041665814omplex @ G @ A2 )
% 5.41/5.74 != zero_zero_complex )
% 5.41/5.74 => ~ ! [A5: int] :
% 5.41/5.74 ( ( member_int @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_complex ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7004_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: complex > real,A2: set_complex] :
% 5.41/5.74 ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.41/5.74 != zero_zero_real )
% 5.41/5.74 => ~ ! [A5: complex] :
% 5.41/5.74 ( ( member_complex @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_real ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7005_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: real > real,A2: set_real] :
% 5.41/5.74 ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.41/5.74 != zero_zero_real )
% 5.41/5.74 => ~ ! [A5: real] :
% 5.41/5.74 ( ( member_real @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_real ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7006_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: int > real,A2: set_int] :
% 5.41/5.74 ( ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.41/5.74 != zero_zero_real )
% 5.41/5.74 => ~ ! [A5: int] :
% 5.41/5.74 ( ( member_int @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_real ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7007_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: complex > rat,A2: set_complex] :
% 5.41/5.74 ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.41/5.74 != zero_zero_rat )
% 5.41/5.74 => ~ ! [A5: complex] :
% 5.41/5.74 ( ( member_complex @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_rat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7008_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: real > rat,A2: set_real] :
% 5.41/5.74 ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.41/5.74 != zero_zero_rat )
% 5.41/5.74 => ~ ! [A5: real] :
% 5.41/5.74 ( ( member_real @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_rat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7009_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: nat > rat,A2: set_nat] :
% 5.41/5.74 ( ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.41/5.74 != zero_zero_rat )
% 5.41/5.74 => ~ ! [A5: nat] :
% 5.41/5.74 ( ( member_nat @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_rat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7010_sum_Onot__neutral__contains__not__neutral,axiom,
% 5.41/5.74 ! [G: int > rat,A2: set_int] :
% 5.41/5.74 ( ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.41/5.74 != zero_zero_rat )
% 5.41/5.74 => ~ ! [A5: int] :
% 5.41/5.74 ( ( member_int @ A5 @ A2 )
% 5.41/5.74 => ( ( G @ A5 )
% 5.41/5.74 = zero_zero_rat ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.not_neutral_contains_not_neutral
% 5.41/5.74 thf(fact_7011_of__int__mask__eq,axiom,
% 5.41/5.74 ! [N: nat] :
% 5.41/5.74 ( ( ring_1_of_int_int @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.41/5.74 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % of_int_mask_eq
% 5.41/5.74 thf(fact_7012_old_Oprod_Ocase,axiom,
% 5.41/5.74 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,X1: nat,X22: nat] :
% 5.41/5.74 ( ( produc27273713700761075at_nat @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.41/5.74 = ( F @ X1 @ X22 ) ) ).
% 5.41/5.74
% 5.41/5.74 % old.prod.case
% 5.41/5.74 thf(fact_7013_old_Oprod_Ocase,axiom,
% 5.41/5.74 ! [F: nat > nat > product_prod_nat_nat > $o,X1: nat,X22: nat] :
% 5.41/5.74 ( ( produc8739625826339149834_nat_o @ F @ ( product_Pair_nat_nat @ X1 @ X22 ) )
% 5.41/5.74 = ( F @ X1 @ X22 ) ) ).
% 5.41/5.74
% 5.41/5.74 % old.prod.case
% 5.41/5.74 thf(fact_7014_old_Oprod_Ocase,axiom,
% 5.41/5.74 ! [F: int > int > product_prod_int_int,X1: int,X22: int] :
% 5.41/5.74 ( ( produc4245557441103728435nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.41/5.74 = ( F @ X1 @ X22 ) ) ).
% 5.41/5.74
% 5.41/5.74 % old.prod.case
% 5.41/5.74 thf(fact_7015_old_Oprod_Ocase,axiom,
% 5.41/5.74 ! [F: int > int > $o,X1: int,X22: int] :
% 5.41/5.74 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.41/5.74 = ( F @ X1 @ X22 ) ) ).
% 5.41/5.74
% 5.41/5.74 % old.prod.case
% 5.41/5.74 thf(fact_7016_old_Oprod_Ocase,axiom,
% 5.41/5.74 ! [F: int > int > int,X1: int,X22: int] :
% 5.41/5.74 ( ( produc8211389475949308722nt_int @ F @ ( product_Pair_int_int @ X1 @ X22 ) )
% 5.41/5.74 = ( F @ X1 @ X22 ) ) ).
% 5.41/5.74
% 5.41/5.74 % old.prod.case
% 5.41/5.74 thf(fact_7017_less__eq__mask,axiom,
% 5.41/5.74 ! [N: nat] : ( ord_less_eq_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % less_eq_mask
% 5.41/5.74 thf(fact_7018_semiring__norm_I26_J,axiom,
% 5.41/5.74 ( ( bitM @ one )
% 5.41/5.74 = one ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(26)
% 5.41/5.74 thf(fact_7019_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_complex,F: complex > rat,G: complex > rat] :
% 5.41/5.74 ( ! [I4: complex] :
% 5.41/5.74 ( ( member_complex @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ K5 ) @ ( groups5058264527183730370ex_rat @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7020_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_real,F: real > rat,G: real > rat] :
% 5.41/5.74 ( ! [I4: real] :
% 5.41/5.74 ( ( member_real @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ K5 ) @ ( groups1300246762558778688al_rat @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7021_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_nat,F: nat > rat,G: nat > rat] :
% 5.41/5.74 ( ! [I4: nat] :
% 5.41/5.74 ( ( member_nat @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ K5 ) @ ( groups2906978787729119204at_rat @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7022_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_int,F: int > rat,G: int > rat] :
% 5.41/5.74 ( ! [I4: int] :
% 5.41/5.74 ( ( member_int @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ K5 ) @ ( groups3906332499630173760nt_rat @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7023_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_complex,F: complex > nat,G: complex > nat] :
% 5.41/5.74 ( ! [I4: complex] :
% 5.41/5.74 ( ( member_complex @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ K5 ) @ ( groups5693394587270226106ex_nat @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7024_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_real,F: real > nat,G: real > nat] :
% 5.41/5.74 ( ! [I4: real] :
% 5.41/5.74 ( ( member_real @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ K5 ) @ ( groups1935376822645274424al_nat @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7025_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_int,F: int > nat,G: int > nat] :
% 5.41/5.74 ( ! [I4: int] :
% 5.41/5.74 ( ( member_int @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ K5 ) @ ( groups4541462559716669496nt_nat @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7026_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_complex,F: complex > int,G: complex > int] :
% 5.41/5.74 ( ! [I4: complex] :
% 5.41/5.74 ( ( member_complex @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ K5 ) @ ( groups5690904116761175830ex_int @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7027_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_real,F: real > int,G: real > int] :
% 5.41/5.74 ( ! [I4: real] :
% 5.41/5.74 ( ( member_real @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ K5 ) @ ( groups1932886352136224148al_int @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7028_sum__mono,axiom,
% 5.41/5.74 ! [K5: set_nat,F: nat > int,G: nat > int] :
% 5.41/5.74 ( ! [I4: nat] :
% 5.41/5.74 ( ( member_nat @ I4 @ K5 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ K5 ) @ ( groups3539618377306564664at_int @ G @ K5 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono
% 5.41/5.74 thf(fact_7029_sum__distrib__left,axiom,
% 5.41/5.74 ! [R: int,F: int > int,A2: set_int] :
% 5.41/5.74 ( ( times_times_int @ R @ ( groups4538972089207619220nt_int @ F @ A2 ) )
% 5.41/5.74 = ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [N2: int] : ( times_times_int @ R @ ( F @ N2 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_left
% 5.41/5.74 thf(fact_7030_sum__distrib__left,axiom,
% 5.41/5.74 ! [R: complex,F: complex > complex,A2: set_complex] :
% 5.41/5.74 ( ( times_times_complex @ R @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.41/5.74 = ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [N2: complex] : ( times_times_complex @ R @ ( F @ N2 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_left
% 5.41/5.74 thf(fact_7031_sum__distrib__left,axiom,
% 5.41/5.74 ! [R: nat,F: nat > nat,A2: set_nat] :
% 5.41/5.74 ( ( times_times_nat @ R @ ( groups3542108847815614940at_nat @ F @ A2 ) )
% 5.41/5.74 = ( groups3542108847815614940at_nat
% 5.41/5.74 @ ^ [N2: nat] : ( times_times_nat @ R @ ( F @ N2 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_left
% 5.41/5.74 thf(fact_7032_sum__distrib__left,axiom,
% 5.41/5.74 ! [R: real,F: nat > real,A2: set_nat] :
% 5.41/5.74 ( ( times_times_real @ R @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.41/5.74 = ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [N2: nat] : ( times_times_real @ R @ ( F @ N2 ) )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_left
% 5.41/5.74 thf(fact_7033_sum__distrib__right,axiom,
% 5.41/5.74 ! [F: int > int,A2: set_int,R: int] :
% 5.41/5.74 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ R )
% 5.41/5.74 = ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [N2: int] : ( times_times_int @ ( F @ N2 ) @ R )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_right
% 5.41/5.74 thf(fact_7034_sum__distrib__right,axiom,
% 5.41/5.74 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.41/5.74 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.41/5.74 = ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [N2: complex] : ( times_times_complex @ ( F @ N2 ) @ R )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_right
% 5.41/5.74 thf(fact_7035_sum__distrib__right,axiom,
% 5.41/5.74 ! [F: nat > nat,A2: set_nat,R: nat] :
% 5.41/5.74 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ R )
% 5.41/5.74 = ( groups3542108847815614940at_nat
% 5.41/5.74 @ ^ [N2: nat] : ( times_times_nat @ ( F @ N2 ) @ R )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_right
% 5.41/5.74 thf(fact_7036_sum__distrib__right,axiom,
% 5.41/5.74 ! [F: nat > real,A2: set_nat,R: real] :
% 5.41/5.74 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.41/5.74 = ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ R )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_distrib_right
% 5.41/5.74 thf(fact_7037_sum__product,axiom,
% 5.41/5.74 ! [F: int > int,A2: set_int,G: int > int,B3: set_int] :
% 5.41/5.74 ( ( times_times_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ B3 ) )
% 5.41/5.74 = ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [I5: int] :
% 5.41/5.74 ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [J3: int] : ( times_times_int @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.41/5.74 @ B3 )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_product
% 5.41/5.74 thf(fact_7038_sum__product,axiom,
% 5.41/5.74 ! [F: complex > complex,A2: set_complex,G: complex > complex,B3: set_complex] :
% 5.41/5.74 ( ( times_times_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ B3 ) )
% 5.41/5.74 = ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [I5: complex] :
% 5.41/5.74 ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [J3: complex] : ( times_times_complex @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.41/5.74 @ B3 )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_product
% 5.41/5.74 thf(fact_7039_sum__product,axiom,
% 5.41/5.74 ! [F: nat > nat,A2: set_nat,G: nat > nat,B3: set_nat] :
% 5.41/5.74 ( ( times_times_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ B3 ) )
% 5.41/5.74 = ( groups3542108847815614940at_nat
% 5.41/5.74 @ ^ [I5: nat] :
% 5.41/5.74 ( groups3542108847815614940at_nat
% 5.41/5.74 @ ^ [J3: nat] : ( times_times_nat @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.41/5.74 @ B3 )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_product
% 5.41/5.74 thf(fact_7040_sum__product,axiom,
% 5.41/5.74 ! [F: nat > real,A2: set_nat,G: nat > real,B3: set_nat] :
% 5.41/5.74 ( ( times_times_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ B3 ) )
% 5.41/5.74 = ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [I5: nat] :
% 5.41/5.74 ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [J3: nat] : ( times_times_real @ ( F @ I5 ) @ ( G @ J3 ) )
% 5.41/5.74 @ B3 )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_product
% 5.41/5.74 thf(fact_7041_sum_Odistrib,axiom,
% 5.41/5.74 ! [G: int > int,H2: int > int,A2: set_int] :
% 5.41/5.74 ( ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [X3: int] : ( plus_plus_int @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.41/5.74 @ A2 )
% 5.41/5.74 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ A2 ) @ ( groups4538972089207619220nt_int @ H2 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.distrib
% 5.41/5.74 thf(fact_7042_sum_Odistrib,axiom,
% 5.41/5.74 ! [G: complex > complex,H2: complex > complex,A2: set_complex] :
% 5.41/5.74 ( ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [X3: complex] : ( plus_plus_complex @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.41/5.74 @ A2 )
% 5.41/5.74 = ( plus_plus_complex @ ( groups7754918857620584856omplex @ G @ A2 ) @ ( groups7754918857620584856omplex @ H2 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.distrib
% 5.41/5.74 thf(fact_7043_sum_Odistrib,axiom,
% 5.41/5.74 ! [G: nat > nat,H2: nat > nat,A2: set_nat] :
% 5.41/5.74 ( ( groups3542108847815614940at_nat
% 5.41/5.74 @ ^ [X3: nat] : ( plus_plus_nat @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.41/5.74 @ A2 )
% 5.41/5.74 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ A2 ) @ ( groups3542108847815614940at_nat @ H2 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.distrib
% 5.41/5.74 thf(fact_7044_sum_Odistrib,axiom,
% 5.41/5.74 ! [G: nat > real,H2: nat > real,A2: set_nat] :
% 5.41/5.74 ( ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [X3: nat] : ( plus_plus_real @ ( G @ X3 ) @ ( H2 @ X3 ) )
% 5.41/5.74 @ A2 )
% 5.41/5.74 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ A2 ) @ ( groups6591440286371151544t_real @ H2 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.distrib
% 5.41/5.74 thf(fact_7045_sum__subtractf,axiom,
% 5.41/5.74 ! [F: int > int,G: int > int,A2: set_int] :
% 5.41/5.74 ( ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [X3: int] : ( minus_minus_int @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.74 @ A2 )
% 5.41/5.74 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_subtractf
% 5.41/5.74 thf(fact_7046_sum__subtractf,axiom,
% 5.41/5.74 ! [F: complex > complex,G: complex > complex,A2: set_complex] :
% 5.41/5.74 ( ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [X3: complex] : ( minus_minus_complex @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.74 @ A2 )
% 5.41/5.74 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ G @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_subtractf
% 5.41/5.74 thf(fact_7047_sum__subtractf,axiom,
% 5.41/5.74 ! [F: nat > real,G: nat > real,A2: set_nat] :
% 5.41/5.74 ( ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [X3: nat] : ( minus_minus_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.74 @ A2 )
% 5.41/5.74 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ G @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_subtractf
% 5.41/5.74 thf(fact_7048_sum__divide__distrib,axiom,
% 5.41/5.74 ! [F: complex > complex,A2: set_complex,R: complex] :
% 5.41/5.74 ( ( divide1717551699836669952omplex @ ( groups7754918857620584856omplex @ F @ A2 ) @ R )
% 5.41/5.74 = ( groups7754918857620584856omplex
% 5.41/5.74 @ ^ [N2: complex] : ( divide1717551699836669952omplex @ ( F @ N2 ) @ R )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_divide_distrib
% 5.41/5.74 thf(fact_7049_sum__divide__distrib,axiom,
% 5.41/5.74 ! [F: nat > real,A2: set_nat,R: real] :
% 5.41/5.74 ( ( divide_divide_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ R )
% 5.41/5.74 = ( groups6591440286371151544t_real
% 5.41/5.74 @ ^ [N2: nat] : ( divide_divide_real @ ( F @ N2 ) @ R )
% 5.41/5.74 @ A2 ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_divide_distrib
% 5.41/5.74 thf(fact_7050_mod__sum__eq,axiom,
% 5.41/5.74 ! [F: int > int,A: int,A2: set_int] :
% 5.41/5.74 ( ( modulo_modulo_int
% 5.41/5.74 @ ( groups4538972089207619220nt_int
% 5.41/5.74 @ ^ [I5: int] : ( modulo_modulo_int @ ( F @ I5 ) @ A )
% 5.41/5.74 @ A2 )
% 5.41/5.74 @ A )
% 5.41/5.74 = ( modulo_modulo_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % mod_sum_eq
% 5.41/5.74 thf(fact_7051_mod__sum__eq,axiom,
% 5.41/5.74 ! [F: nat > nat,A: nat,A2: set_nat] :
% 5.41/5.74 ( ( modulo_modulo_nat
% 5.41/5.74 @ ( groups3542108847815614940at_nat
% 5.41/5.74 @ ^ [I5: nat] : ( modulo_modulo_nat @ ( F @ I5 ) @ A )
% 5.41/5.74 @ A2 )
% 5.41/5.74 @ A )
% 5.41/5.74 = ( modulo_modulo_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ A ) ) ).
% 5.41/5.74
% 5.41/5.74 % mod_sum_eq
% 5.41/5.74 thf(fact_7052_case__prodE2,axiom,
% 5.41/5.74 ! [Q: ( product_prod_nat_nat > product_prod_nat_nat ) > $o,P: nat > nat > product_prod_nat_nat > product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.41/5.74 ( ( Q @ ( produc27273713700761075at_nat @ P @ Z ) )
% 5.41/5.74 => ~ ! [X6: nat,Y5: nat] :
% 5.41/5.74 ( ( Z
% 5.41/5.74 = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 5.41/5.74 => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prodE2
% 5.41/5.74 thf(fact_7053_case__prodE2,axiom,
% 5.41/5.74 ! [Q: ( product_prod_nat_nat > $o ) > $o,P: nat > nat > product_prod_nat_nat > $o,Z: product_prod_nat_nat] :
% 5.41/5.74 ( ( Q @ ( produc8739625826339149834_nat_o @ P @ Z ) )
% 5.41/5.74 => ~ ! [X6: nat,Y5: nat] :
% 5.41/5.74 ( ( Z
% 5.41/5.74 = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 5.41/5.74 => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prodE2
% 5.41/5.74 thf(fact_7054_case__prodE2,axiom,
% 5.41/5.74 ! [Q: product_prod_int_int > $o,P: int > int > product_prod_int_int,Z: product_prod_int_int] :
% 5.41/5.74 ( ( Q @ ( produc4245557441103728435nt_int @ P @ Z ) )
% 5.41/5.74 => ~ ! [X6: int,Y5: int] :
% 5.41/5.74 ( ( Z
% 5.41/5.74 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.74 => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prodE2
% 5.41/5.74 thf(fact_7055_case__prodE2,axiom,
% 5.41/5.74 ! [Q: $o > $o,P: int > int > $o,Z: product_prod_int_int] :
% 5.41/5.74 ( ( Q @ ( produc4947309494688390418_int_o @ P @ Z ) )
% 5.41/5.74 => ~ ! [X6: int,Y5: int] :
% 5.41/5.74 ( ( Z
% 5.41/5.74 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.74 => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prodE2
% 5.41/5.74 thf(fact_7056_case__prodE2,axiom,
% 5.41/5.74 ! [Q: int > $o,P: int > int > int,Z: product_prod_int_int] :
% 5.41/5.74 ( ( Q @ ( produc8211389475949308722nt_int @ P @ Z ) )
% 5.41/5.74 => ~ ! [X6: int,Y5: int] :
% 5.41/5.74 ( ( Z
% 5.41/5.74 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.74 => ~ ( Q @ ( P @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % case_prodE2
% 5.41/5.74 thf(fact_7057_case__prod__eta,axiom,
% 5.41/5.74 ! [F: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.41/5.74 ( ( produc27273713700761075at_nat
% 5.41/5.74 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.41/5.74 = F ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_eta
% 5.41/5.74 thf(fact_7058_case__prod__eta,axiom,
% 5.41/5.74 ! [F: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.41/5.74 ( ( produc8739625826339149834_nat_o
% 5.41/5.74 @ ^ [X3: nat,Y3: nat] : ( F @ ( product_Pair_nat_nat @ X3 @ Y3 ) ) )
% 5.41/5.74 = F ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_eta
% 5.41/5.74 thf(fact_7059_case__prod__eta,axiom,
% 5.41/5.74 ! [F: product_prod_int_int > product_prod_int_int] :
% 5.41/5.74 ( ( produc4245557441103728435nt_int
% 5.41/5.74 @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.41/5.74 = F ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_eta
% 5.41/5.74 thf(fact_7060_case__prod__eta,axiom,
% 5.41/5.74 ! [F: product_prod_int_int > $o] :
% 5.41/5.74 ( ( produc4947309494688390418_int_o
% 5.41/5.74 @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.41/5.74 = F ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_eta
% 5.41/5.74 thf(fact_7061_case__prod__eta,axiom,
% 5.41/5.74 ! [F: product_prod_int_int > int] :
% 5.41/5.74 ( ( produc8211389475949308722nt_int
% 5.41/5.74 @ ^ [X3: int,Y3: int] : ( F @ ( product_Pair_int_int @ X3 @ Y3 ) ) )
% 5.41/5.74 = F ) ).
% 5.41/5.74
% 5.41/5.74 % case_prod_eta
% 5.41/5.74 thf(fact_7062_cond__case__prod__eta,axiom,
% 5.41/5.74 ! [F: nat > nat > product_prod_nat_nat > product_prod_nat_nat,G: product_prod_nat_nat > product_prod_nat_nat > product_prod_nat_nat] :
% 5.41/5.74 ( ! [X6: nat,Y5: nat] :
% 5.41/5.74 ( ( F @ X6 @ Y5 )
% 5.41/5.74 = ( G @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) )
% 5.41/5.74 => ( ( produc27273713700761075at_nat @ F )
% 5.41/5.74 = G ) ) ).
% 5.41/5.74
% 5.41/5.74 % cond_case_prod_eta
% 5.41/5.74 thf(fact_7063_cond__case__prod__eta,axiom,
% 5.41/5.74 ! [F: nat > nat > product_prod_nat_nat > $o,G: product_prod_nat_nat > product_prod_nat_nat > $o] :
% 5.41/5.74 ( ! [X6: nat,Y5: nat] :
% 5.41/5.74 ( ( F @ X6 @ Y5 )
% 5.41/5.74 = ( G @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) )
% 5.41/5.74 => ( ( produc8739625826339149834_nat_o @ F )
% 5.41/5.74 = G ) ) ).
% 5.41/5.74
% 5.41/5.74 % cond_case_prod_eta
% 5.41/5.74 thf(fact_7064_cond__case__prod__eta,axiom,
% 5.41/5.74 ! [F: int > int > product_prod_int_int,G: product_prod_int_int > product_prod_int_int] :
% 5.41/5.74 ( ! [X6: int,Y5: int] :
% 5.41/5.74 ( ( F @ X6 @ Y5 )
% 5.41/5.74 = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 5.41/5.74 => ( ( produc4245557441103728435nt_int @ F )
% 5.41/5.74 = G ) ) ).
% 5.41/5.74
% 5.41/5.74 % cond_case_prod_eta
% 5.41/5.74 thf(fact_7065_cond__case__prod__eta,axiom,
% 5.41/5.74 ! [F: int > int > $o,G: product_prod_int_int > $o] :
% 5.41/5.74 ( ! [X6: int,Y5: int] :
% 5.41/5.74 ( ( F @ X6 @ Y5 )
% 5.41/5.74 = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 5.41/5.74 => ( ( produc4947309494688390418_int_o @ F )
% 5.41/5.74 = G ) ) ).
% 5.41/5.74
% 5.41/5.74 % cond_case_prod_eta
% 5.41/5.74 thf(fact_7066_cond__case__prod__eta,axiom,
% 5.41/5.74 ! [F: int > int > int,G: product_prod_int_int > int] :
% 5.41/5.74 ( ! [X6: int,Y5: int] :
% 5.41/5.74 ( ( F @ X6 @ Y5 )
% 5.41/5.74 = ( G @ ( product_Pair_int_int @ X6 @ Y5 ) ) )
% 5.41/5.74 => ( ( produc8211389475949308722nt_int @ F )
% 5.41/5.74 = G ) ) ).
% 5.41/5.74
% 5.41/5.74 % cond_case_prod_eta
% 5.41/5.74 thf(fact_7067_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > real] :
% 5.41/5.74 ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 5.41/5.74 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7068_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > real] :
% 5.41/5.74 ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 5.41/5.74 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7069_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > real] :
% 5.41/5.74 ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ ( F @ X6 ) @ zero_zero_real ) )
% 5.41/5.74 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ zero_zero_real ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7070_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > rat] :
% 5.41/5.74 ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7071_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > rat] :
% 5.41/5.74 ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7072_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_nat,F: nat > rat] :
% 5.41/5.74 ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7073_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > rat] :
% 5.41/5.74 ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ X6 ) @ zero_zero_rat ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ zero_zero_rat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7074_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > nat] :
% 5.41/5.74 ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 5.41/5.74 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7075_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > nat] :
% 5.41/5.74 ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 5.41/5.74 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7076_sum__nonpos,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > nat] :
% 5.41/5.74 ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ X6 ) @ zero_zero_nat ) )
% 5.41/5.74 => ( ord_less_eq_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ zero_zero_nat ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonpos
% 5.41/5.74 thf(fact_7077_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > real] :
% 5.41/5.74 ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7078_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > real] :
% 5.41/5.74 ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7079_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > real] :
% 5.41/5.74 ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7080_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > rat] :
% 5.41/5.74 ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7081_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > rat] :
% 5.41/5.74 ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7082_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_nat,F: nat > rat] :
% 5.41/5.74 ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7083_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > rat] :
% 5.41/5.74 ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7084_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > nat] :
% 5.41/5.74 ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7085_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > nat] :
% 5.41/5.74 ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7086_sum__nonneg,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > nat] :
% 5.41/5.74 ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg
% 5.41/5.74 thf(fact_7087_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: real > rat,I6: set_real,G: real > rat,I: real] :
% 5.41/5.74 ( ( ( groups1300246762558778688al_rat @ F @ I6 )
% 5.41/5.74 = ( groups1300246762558778688al_rat @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: real] :
% 5.41/5.74 ( ( member_real @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_real @ I @ I6 )
% 5.41/5.74 => ( ( finite_finite_real @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7088_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: nat > rat,I6: set_nat,G: nat > rat,I: nat] :
% 5.41/5.74 ( ( ( groups2906978787729119204at_rat @ F @ I6 )
% 5.41/5.74 = ( groups2906978787729119204at_rat @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: nat] :
% 5.41/5.74 ( ( member_nat @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_nat @ I @ I6 )
% 5.41/5.74 => ( ( finite_finite_nat @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7089_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: int > rat,I6: set_int,G: int > rat,I: int] :
% 5.41/5.74 ( ( ( groups3906332499630173760nt_rat @ F @ I6 )
% 5.41/5.74 = ( groups3906332499630173760nt_rat @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: int] :
% 5.41/5.74 ( ( member_int @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_int @ I @ I6 )
% 5.41/5.74 => ( ( finite_finite_int @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7090_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: complex > rat,I6: set_complex,G: complex > rat,I: complex] :
% 5.41/5.74 ( ( ( groups5058264527183730370ex_rat @ F @ I6 )
% 5.41/5.74 = ( groups5058264527183730370ex_rat @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: complex] :
% 5.41/5.74 ( ( member_complex @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_complex @ I @ I6 )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7091_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: real > nat,I6: set_real,G: real > nat,I: real] :
% 5.41/5.74 ( ( ( groups1935376822645274424al_nat @ F @ I6 )
% 5.41/5.74 = ( groups1935376822645274424al_nat @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: real] :
% 5.41/5.74 ( ( member_real @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_real @ I @ I6 )
% 5.41/5.74 => ( ( finite_finite_real @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7092_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: int > nat,I6: set_int,G: int > nat,I: int] :
% 5.41/5.74 ( ( ( groups4541462559716669496nt_nat @ F @ I6 )
% 5.41/5.74 = ( groups4541462559716669496nt_nat @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: int] :
% 5.41/5.74 ( ( member_int @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_int @ I @ I6 )
% 5.41/5.74 => ( ( finite_finite_int @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7093_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: complex > nat,I6: set_complex,G: complex > nat,I: complex] :
% 5.41/5.74 ( ( ( groups5693394587270226106ex_nat @ F @ I6 )
% 5.41/5.74 = ( groups5693394587270226106ex_nat @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: complex] :
% 5.41/5.74 ( ( member_complex @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_complex @ I @ I6 )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7094_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: real > int,I6: set_real,G: real > int,I: real] :
% 5.41/5.74 ( ( ( groups1932886352136224148al_int @ F @ I6 )
% 5.41/5.74 = ( groups1932886352136224148al_int @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: real] :
% 5.41/5.74 ( ( member_real @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_real @ I @ I6 )
% 5.41/5.74 => ( ( finite_finite_real @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7095_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: nat > int,I6: set_nat,G: nat > int,I: nat] :
% 5.41/5.74 ( ( ( groups3539618377306564664at_int @ F @ I6 )
% 5.41/5.74 = ( groups3539618377306564664at_int @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: nat] :
% 5.41/5.74 ( ( member_nat @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_nat @ I @ I6 )
% 5.41/5.74 => ( ( finite_finite_nat @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7096_sum__mono__inv,axiom,
% 5.41/5.74 ! [F: complex > int,I6: set_complex,G: complex > int,I: complex] :
% 5.41/5.74 ( ( ( groups5690904116761175830ex_int @ F @ I6 )
% 5.41/5.74 = ( groups5690904116761175830ex_int @ G @ I6 ) )
% 5.41/5.74 => ( ! [I4: complex] :
% 5.41/5.74 ( ( member_complex @ I4 @ I6 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ I4 ) @ ( G @ I4 ) ) )
% 5.41/5.74 => ( ( member_complex @ I @ I6 )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.74 => ( ( F @ I )
% 5.41/5.74 = ( G @ I ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_mono_inv
% 5.41/5.74 thf(fact_7097_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_real,G: real > complex,P: real > $o] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ( groups5754745047067104278omplex @ G
% 5.41/5.74 @ ( collect_real
% 5.41/5.74 @ ^ [X3: real] :
% 5.41/5.74 ( ( member_real @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups5754745047067104278omplex
% 5.41/5.74 @ ^ [X3: real] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7098_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_nat,G: nat > complex,P: nat > $o] :
% 5.41/5.74 ( ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ( groups2073611262835488442omplex @ G
% 5.41/5.74 @ ( collect_nat
% 5.41/5.74 @ ^ [X3: nat] :
% 5.41/5.74 ( ( member_nat @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups2073611262835488442omplex
% 5.41/5.74 @ ^ [X3: nat] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7099_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > complex,P: int > $o] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( groups3049146728041665814omplex @ G
% 5.41/5.74 @ ( collect_int
% 5.41/5.74 @ ^ [X3: int] :
% 5.41/5.74 ( ( member_int @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups3049146728041665814omplex
% 5.41/5.74 @ ^ [X3: int] : ( if_complex @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_complex )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7100_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_real,G: real > real,P: real > $o] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ( groups8097168146408367636l_real @ G
% 5.41/5.74 @ ( collect_real
% 5.41/5.74 @ ^ [X3: real] :
% 5.41/5.74 ( ( member_real @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups8097168146408367636l_real
% 5.41/5.74 @ ^ [X3: real] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7101_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > real,P: int > $o] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( groups8778361861064173332t_real @ G
% 5.41/5.74 @ ( collect_int
% 5.41/5.74 @ ^ [X3: int] :
% 5.41/5.74 ( ( member_int @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups8778361861064173332t_real
% 5.41/5.74 @ ^ [X3: int] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7102_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_complex,G: complex > real,P: complex > $o] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( groups5808333547571424918x_real @ G
% 5.41/5.74 @ ( collect_complex
% 5.41/5.74 @ ^ [X3: complex] :
% 5.41/5.74 ( ( member_complex @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups5808333547571424918x_real
% 5.41/5.74 @ ^ [X3: complex] : ( if_real @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_real )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7103_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_real,G: real > rat,P: real > $o] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ( groups1300246762558778688al_rat @ G
% 5.41/5.74 @ ( collect_real
% 5.41/5.74 @ ^ [X3: real] :
% 5.41/5.74 ( ( member_real @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups1300246762558778688al_rat
% 5.41/5.74 @ ^ [X3: real] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7104_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_nat,G: nat > rat,P: nat > $o] :
% 5.41/5.74 ( ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ( groups2906978787729119204at_rat @ G
% 5.41/5.74 @ ( collect_nat
% 5.41/5.74 @ ^ [X3: nat] :
% 5.41/5.74 ( ( member_nat @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups2906978787729119204at_rat
% 5.41/5.74 @ ^ [X3: nat] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7105_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_int,G: int > rat,P: int > $o] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( groups3906332499630173760nt_rat @ G
% 5.41/5.74 @ ( collect_int
% 5.41/5.74 @ ^ [X3: int] :
% 5.41/5.74 ( ( member_int @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups3906332499630173760nt_rat
% 5.41/5.74 @ ^ [X3: int] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7106_sum_Ointer__filter,axiom,
% 5.41/5.74 ! [A2: set_complex,G: complex > rat,P: complex > $o] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( groups5058264527183730370ex_rat @ G
% 5.41/5.74 @ ( collect_complex
% 5.41/5.74 @ ^ [X3: complex] :
% 5.41/5.74 ( ( member_complex @ X3 @ A2 )
% 5.41/5.74 & ( P @ X3 ) ) ) )
% 5.41/5.74 = ( groups5058264527183730370ex_rat
% 5.41/5.74 @ ^ [X3: complex] : ( if_rat @ ( P @ X3 ) @ ( G @ X3 ) @ zero_zero_rat )
% 5.41/5.74 @ A2 ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.inter_filter
% 5.41/5.74 thf(fact_7107_mask__nonnegative__int,axiom,
% 5.41/5.74 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.41/5.74
% 5.41/5.74 % mask_nonnegative_int
% 5.41/5.74 thf(fact_7108_not__mask__negative__int,axiom,
% 5.41/5.74 ! [N: nat] :
% 5.41/5.74 ~ ( ord_less_int @ ( bit_se2000444600071755411sk_int @ N ) @ zero_zero_int ) ).
% 5.41/5.74
% 5.41/5.74 % not_mask_negative_int
% 5.41/5.74 thf(fact_7109_semiring__norm_I28_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( bitM @ ( bit1 @ N ) )
% 5.41/5.74 = ( bit1 @ ( bit0 @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(28)
% 5.41/5.74 thf(fact_7110_semiring__norm_I27_J,axiom,
% 5.41/5.74 ! [N: num] :
% 5.41/5.74 ( ( bitM @ ( bit0 @ N ) )
% 5.41/5.74 = ( bit1 @ ( bitM @ N ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % semiring_norm(27)
% 5.41/5.74 thf(fact_7111_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > real] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups8097168146408367636l_real @ F @ A2 )
% 5.41/5.74 = zero_zero_real )
% 5.41/5.74 = ( ! [X3: real] :
% 5.41/5.74 ( ( member_real @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7112_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > real] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups8778361861064173332t_real @ F @ A2 )
% 5.41/5.74 = zero_zero_real )
% 5.41/5.74 = ( ! [X3: int] :
% 5.41/5.74 ( ( member_int @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7113_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > real] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups5808333547571424918x_real @ F @ A2 )
% 5.41/5.74 = zero_zero_real )
% 5.41/5.74 = ( ! [X3: complex] :
% 5.41/5.74 ( ( member_complex @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_real ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7114_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > rat] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups1300246762558778688al_rat @ F @ A2 )
% 5.41/5.74 = zero_zero_rat )
% 5.41/5.74 = ( ! [X3: real] :
% 5.41/5.74 ( ( member_real @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7115_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_nat,F: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups2906978787729119204at_rat @ F @ A2 )
% 5.41/5.74 = zero_zero_rat )
% 5.41/5.74 = ( ! [X3: nat] :
% 5.41/5.74 ( ( member_nat @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7116_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups3906332499630173760nt_rat @ F @ A2 )
% 5.41/5.74 = zero_zero_rat )
% 5.41/5.74 = ( ! [X3: int] :
% 5.41/5.74 ( ( member_int @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7117_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > rat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups5058264527183730370ex_rat @ F @ A2 )
% 5.41/5.74 = zero_zero_rat )
% 5.41/5.74 = ( ! [X3: complex] :
% 5.41/5.74 ( ( member_complex @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_rat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7118_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > nat] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups1935376822645274424al_nat @ F @ A2 )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 = ( ! [X3: real] :
% 5.41/5.74 ( ( member_real @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_nat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7119_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > nat] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 = ( ! [X3: int] :
% 5.41/5.74 ( ( member_int @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_nat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7120_sum__nonneg__eq__0__iff,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > nat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.74 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.41/5.74 = zero_zero_nat )
% 5.41/5.74 = ( ! [X3: complex] :
% 5.41/5.74 ( ( member_complex @ X3 @ A2 )
% 5.41/5.74 => ( ( F @ X3 )
% 5.41/5.74 = zero_zero_nat ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_nonneg_eq_0_iff
% 5.41/5.74 thf(fact_7121_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_int,T: set_int,G: int > real,I: int > int,F: int > real] :
% 5.41/5.74 ( ( finite_finite_int @ S )
% 5.41/5.74 => ( ( finite_finite_int @ T )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S )
% 5.41/5.74 => ? [Xa: int] :
% 5.41/5.74 ( ( member_int @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7122_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_int,T: set_complex,G: complex > real,I: complex > int,F: int > real] :
% 5.41/5.74 ( ( finite_finite_int @ S )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ T )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S )
% 5.41/5.74 => ? [Xa: complex] :
% 5.41/5.74 ( ( member_complex @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_real @ ( groups8778361861064173332t_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7123_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_complex,T: set_int,G: int > real,I: int > complex,F: complex > real] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.74 => ( ( finite_finite_int @ T )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ S )
% 5.41/5.74 => ? [Xa: int] :
% 5.41/5.74 ( ( member_int @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups8778361861064173332t_real @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7124_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_complex,T: set_complex,G: complex > real,I: complex > complex,F: complex > real] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ T )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_real @ zero_zero_real @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ S )
% 5.41/5.74 => ? [Xa: complex] :
% 5.41/5.74 ( ( member_complex @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ S ) @ ( groups5808333547571424918x_real @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7125_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_nat,T: set_nat,G: nat > rat,I: nat > nat,F: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ S )
% 5.41/5.74 => ( ( finite_finite_nat @ T )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ S )
% 5.41/5.74 => ? [Xa: nat] :
% 5.41/5.74 ( ( member_nat @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7126_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_nat,T: set_int,G: int > rat,I: int > nat,F: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ S )
% 5.41/5.74 => ( ( finite_finite_int @ T )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ S )
% 5.41/5.74 => ? [Xa: int] :
% 5.41/5.74 ( ( member_int @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7127_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_nat,T: set_complex,G: complex > rat,I: complex > nat,F: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ S )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ T )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ S )
% 5.41/5.74 => ? [Xa: complex] :
% 5.41/5.74 ( ( member_complex @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7128_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_int,T: set_nat,G: nat > rat,I: nat > int,F: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ S )
% 5.41/5.74 => ( ( finite_finite_nat @ T )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S )
% 5.41/5.74 => ? [Xa: nat] :
% 5.41/5.74 ( ( member_nat @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups2906978787729119204at_rat @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7129_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_int,T: set_int,G: int > rat,I: int > int,F: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ S )
% 5.41/5.74 => ( ( finite_finite_int @ T )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S )
% 5.41/5.74 => ? [Xa: int] :
% 5.41/5.74 ( ( member_int @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups3906332499630173760nt_rat @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7130_sum__le__included,axiom,
% 5.41/5.74 ! [S: set_int,T: set_complex,G: complex > rat,I: complex > int,F: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ S )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ T )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ T )
% 5.41/5.74 => ( ord_less_eq_rat @ zero_zero_rat @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S )
% 5.41/5.74 => ? [Xa: complex] :
% 5.41/5.74 ( ( member_complex @ Xa @ T )
% 5.41/5.74 & ( ( I @ Xa )
% 5.41/5.74 = X6 )
% 5.41/5.74 & ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ Xa ) ) ) )
% 5.41/5.74 => ( ord_less_eq_rat @ ( groups3906332499630173760nt_rat @ F @ S ) @ ( groups5058264527183730370ex_rat @ G @ T ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_le_included
% 5.41/5.74 thf(fact_7131_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > real,G: int > real] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: int] :
% 5.41/5.74 ( ( member_int @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7132_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: complex] :
% 5.41/5.74 ( ( member_complex @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_real @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7133_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: nat] :
% 5.41/5.74 ( ( member_nat @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7134_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: int] :
% 5.41/5.74 ( ( member_int @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7135_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: complex] :
% 5.41/5.74 ( ( member_complex @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_rat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7136_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: int] :
% 5.41/5.74 ( ( member_int @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7137_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: complex] :
% 5.41/5.74 ( ( member_complex @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_nat @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7138_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_nat,F: nat > int,G: nat > int] :
% 5.41/5.74 ( ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: nat] :
% 5.41/5.74 ( ( member_nat @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7139_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > int,G: complex > int] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: complex] :
% 5.41/5.74 ( ( member_complex @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7140_sum__strict__mono__ex1,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > int,G: int > int] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_eq_int @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ? [X4: int] :
% 5.41/5.74 ( ( member_int @ X4 @ A2 )
% 5.41/5.74 & ( ord_less_int @ ( F @ X4 ) @ ( G @ X4 ) ) )
% 5.41/5.74 => ( ord_less_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono_ex1
% 5.41/5.74 thf(fact_7141_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: complex > complex > $o,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 5.41/5.74 ( ( R4 @ zero_zero_complex @ zero_zero_complex )
% 5.41/5.74 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite_finite_nat @ S2 )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups2073611262835488442omplex @ H2 @ S2 ) @ ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7142_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: complex > complex > $o,S2: set_int,H2: int > complex,G: int > complex] :
% 5.41/5.74 ( ( R4 @ zero_zero_complex @ zero_zero_complex )
% 5.41/5.74 => ( ! [X15: complex,Y15: complex,X23: complex,Y23: complex] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_complex @ X15 @ Y15 ) @ ( plus_plus_complex @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups3049146728041665814omplex @ H2 @ S2 ) @ ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7143_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: real > real > $o,S2: set_int,H2: int > real,G: int > real] :
% 5.41/5.74 ( ( R4 @ zero_zero_real @ zero_zero_real )
% 5.41/5.74 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups8778361861064173332t_real @ H2 @ S2 ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7144_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: real > real > $o,S2: set_complex,H2: complex > real,G: complex > real] :
% 5.41/5.74 ( ( R4 @ zero_zero_real @ zero_zero_real )
% 5.41/5.74 => ( ! [X15: real,Y15: real,X23: real,Y23: real] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_real @ X15 @ Y15 ) @ ( plus_plus_real @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups5808333547571424918x_real @ H2 @ S2 ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7145_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: rat > rat > $o,S2: set_nat,H2: nat > rat,G: nat > rat] :
% 5.41/5.74 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 5.41/5.74 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite_finite_nat @ S2 )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups2906978787729119204at_rat @ H2 @ S2 ) @ ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7146_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: rat > rat > $o,S2: set_int,H2: int > rat,G: int > rat] :
% 5.41/5.74 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 5.41/5.74 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups3906332499630173760nt_rat @ H2 @ S2 ) @ ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7147_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: rat > rat > $o,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 5.41/5.74 ( ( R4 @ zero_zero_rat @ zero_zero_rat )
% 5.41/5.74 => ( ! [X15: rat,Y15: rat,X23: rat,Y23: rat] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_rat @ X15 @ Y15 ) @ ( plus_plus_rat @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups5058264527183730370ex_rat @ H2 @ S2 ) @ ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7148_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: nat > nat > $o,S2: set_int,H2: int > nat,G: int > nat] :
% 5.41/5.74 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 5.41/5.74 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite_finite_int @ S2 )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups4541462559716669496nt_nat @ H2 @ S2 ) @ ( groups4541462559716669496nt_nat @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7149_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: nat > nat > $o,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 5.41/5.74 ( ( R4 @ zero_zero_nat @ zero_zero_nat )
% 5.41/5.74 => ( ! [X15: nat,Y15: nat,X23: nat,Y23: nat] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_nat @ X15 @ Y15 ) @ ( plus_plus_nat @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups5693394587270226106ex_nat @ H2 @ S2 ) @ ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7150_sum_Orelated,axiom,
% 5.41/5.74 ! [R4: int > int > $o,S2: set_nat,H2: nat > int,G: nat > int] :
% 5.41/5.74 ( ( R4 @ zero_zero_int @ zero_zero_int )
% 5.41/5.74 => ( ! [X15: int,Y15: int,X23: int,Y23: int] :
% 5.41/5.74 ( ( ( R4 @ X15 @ X23 )
% 5.41/5.74 & ( R4 @ Y15 @ Y23 ) )
% 5.41/5.74 => ( R4 @ ( plus_plus_int @ X15 @ Y15 ) @ ( plus_plus_int @ X23 @ Y23 ) ) )
% 5.41/5.74 => ( ( finite_finite_nat @ S2 )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ S2 )
% 5.41/5.74 => ( R4 @ ( H2 @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( R4 @ ( groups3539618377306564664at_int @ H2 @ S2 ) @ ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum.related
% 5.41/5.74 thf(fact_7151_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > real,G: complex > real] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_complex )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7152_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > real,G: int > real] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_int )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7153_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > real,G: real > real] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_real )
% 5.41/5.74 => ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_real @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7154_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > rat,G: complex > rat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_complex )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7155_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_nat,F: nat > rat,G: nat > rat] :
% 5.41/5.74 ( ( finite_finite_nat @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_nat )
% 5.41/5.74 => ( ! [X6: nat] :
% 5.41/5.74 ( ( member_nat @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7156_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > rat,G: int > rat] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_int )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7157_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > rat,G: real > rat] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_real )
% 5.41/5.74 => ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_rat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7158_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_complex,F: complex > nat,G: complex > nat] :
% 5.41/5.74 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_complex )
% 5.41/5.74 => ( ! [X6: complex] :
% 5.41/5.74 ( ( member_complex @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7159_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_int,F: int > nat,G: int > nat] :
% 5.41/5.74 ( ( finite_finite_int @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_int )
% 5.41/5.74 => ( ! [X6: int] :
% 5.41/5.74 ( ( member_int @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7160_sum__strict__mono,axiom,
% 5.41/5.74 ! [A2: set_real,F: real > nat,G: real > nat] :
% 5.41/5.74 ( ( finite_finite_real @ A2 )
% 5.41/5.74 => ( ( A2 != bot_bot_set_real )
% 5.41/5.74 => ( ! [X6: real] :
% 5.41/5.74 ( ( member_real @ X6 @ A2 )
% 5.41/5.74 => ( ord_less_nat @ ( F @ X6 ) @ ( G @ X6 ) ) )
% 5.41/5.74 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.74
% 5.41/5.74 % sum_strict_mono
% 5.41/5.74 thf(fact_7161_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.74 ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > complex,H2: real > complex] :
% 5.41/5.74 ( ( finite_finite_real @ S4 )
% 5.41/5.74 => ( ( finite_finite_real @ T4 )
% 5.41/5.74 => ( ! [A5: real] :
% 5.41/5.74 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.74 => ( ( I @ ( J @ A5 ) )
% 5.41/5.74 = A5 ) )
% 5.41/5.74 => ( ! [A5: real] :
% 5.41/5.74 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.74 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.41/5.74 => ( ! [B5: real] :
% 5.41/5.74 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups5754745047067104278omplex @ G @ S2 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7162_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > complex,H2: int > complex] :
% 5.41/5.75 ( ( finite_finite_real @ S4 )
% 5.41/5.75 => ( ( finite_finite_int @ T4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups5754745047067104278omplex @ G @ S2 )
% 5.41/5.75 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7163_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > complex,H2: real > complex] :
% 5.41/5.75 ( ( finite_finite_int @ S4 )
% 5.41/5.75 => ( ( finite_finite_real @ T4 )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups3049146728041665814omplex @ G @ S2 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7164_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > complex,H2: int > complex] :
% 5.41/5.75 ( ( finite_finite_int @ S4 )
% 5.41/5.75 => ( ( finite_finite_int @ T4 )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups3049146728041665814omplex @ G @ S2 )
% 5.41/5.75 = ( groups3049146728041665814omplex @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7165_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_real,T4: set_real,S2: set_real,I: real > real,J: real > real,T3: set_real,G: real > real,H2: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ S4 )
% 5.41/5.75 => ( ( finite_finite_real @ T4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7166_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_real,T4: set_int,S2: set_real,I: int > real,J: real > int,T3: set_int,G: real > real,H2: int > real] :
% 5.41/5.75 ( ( finite_finite_real @ S4 )
% 5.41/5.75 => ( ( finite_finite_int @ T4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.41/5.75 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7167_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_real,T4: set_complex,S2: set_real,I: complex > real,J: real > complex,T3: set_complex,G: real > real,H2: complex > real] :
% 5.41/5.75 ( ( finite_finite_real @ S4 )
% 5.41/5.75 => ( ( finite3207457112153483333omplex @ T4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ S2 @ S4 ) )
% 5.41/5.75 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.41/5.75 => ( member_real @ ( I @ B5 ) @ ( minus_minus_set_real @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7168_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_int,T4: set_real,S2: set_int,I: real > int,J: int > real,T3: set_real,G: int > real,H2: real > real] :
% 5.41/5.75 ( ( finite_finite_int @ S4 )
% 5.41/5.75 => ( ( finite_finite_real @ T4 )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( member_real @ ( J @ A5 ) @ ( minus_minus_set_real @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ T3 @ T4 ) )
% 5.41/5.75 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7169_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_int,T4: set_int,S2: set_int,I: int > int,J: int > int,T3: set_int,G: int > real,H2: int > real] :
% 5.41/5.75 ( ( finite_finite_int @ S4 )
% 5.41/5.75 => ( ( finite_finite_int @ T4 )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( member_int @ ( J @ A5 ) @ ( minus_minus_set_int @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ ( minus_minus_set_int @ T3 @ T4 ) )
% 5.41/5.75 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: int] :
% 5.41/5.75 ( ( member_int @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.41/5.75 = ( groups8778361861064173332t_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7170_sum_Oreindex__bij__witness__not__neutral,axiom,
% 5.41/5.75 ! [S4: set_int,T4: set_complex,S2: set_int,I: complex > int,J: int > complex,T3: set_complex,G: int > real,H2: complex > real] :
% 5.41/5.75 ( ( finite_finite_int @ S4 )
% 5.41/5.75 => ( ( finite3207457112153483333omplex @ T4 )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( ( I @ ( J @ A5 ) )
% 5.41/5.75 = A5 ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ ( minus_minus_set_int @ S2 @ S4 ) )
% 5.41/5.75 => ( member_complex @ ( J @ A5 ) @ ( minus_811609699411566653omplex @ T3 @ T4 ) ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.41/5.75 => ( ( J @ ( I @ B5 ) )
% 5.41/5.75 = B5 ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ T3 @ T4 ) )
% 5.41/5.75 => ( member_int @ ( I @ B5 ) @ ( minus_minus_set_int @ S2 @ S4 ) ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S4 )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ T4 )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [A5: int] :
% 5.41/5.75 ( ( member_int @ A5 @ S2 )
% 5.41/5.75 => ( ( H2 @ ( J @ A5 ) )
% 5.41/5.75 = ( G @ A5 ) ) )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.reindex_bij_witness_not_neutral
% 5.41/5.75 thf(fact_7171_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_real,F: real > real,B3: real,I: real] :
% 5.41/5.75 ( ( finite_finite_real @ S )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_real @ I @ S )
% 5.41/5.75 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7172_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_int,F: int > real,B3: real,I: int] :
% 5.41/5.75 ( ( finite_finite_int @ S )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_int @ I @ S )
% 5.41/5.75 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7173_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_complex,F: complex > real,B3: real,I: complex] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_complex @ I @ S )
% 5.41/5.75 => ( ord_less_eq_real @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7174_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_real,F: real > rat,B3: rat,I: real] :
% 5.41/5.75 ( ( finite_finite_real @ S )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_real @ I @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7175_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_nat,F: nat > rat,B3: rat,I: nat] :
% 5.41/5.75 ( ( finite_finite_nat @ S )
% 5.41/5.75 => ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_nat @ I @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7176_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_int,F: int > rat,B3: rat,I: int] :
% 5.41/5.75 ( ( finite_finite_int @ S )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_int @ I @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7177_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_complex,F: complex > rat,B3: rat,I: complex] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_complex @ I @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7178_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_real,F: real > nat,B3: nat,I: real] :
% 5.41/5.75 ( ( finite_finite_real @ S )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_real @ I @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7179_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_int,F: int > nat,B3: nat,I: int] :
% 5.41/5.75 ( ( finite_finite_int @ S )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_int @ I @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7180_sum__nonneg__leq__bound,axiom,
% 5.41/5.75 ! [S: set_complex,F: complex > nat,B3: nat,I: complex] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 5.41/5.75 = B3 )
% 5.41/5.75 => ( ( member_complex @ I @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ ( F @ I ) @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_leq_bound
% 5.41/5.75 thf(fact_7181_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_real,F: real > real,I: real] :
% 5.41/5.75 ( ( finite_finite_real @ S )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups8097168146408367636l_real @ F @ S )
% 5.41/5.75 = zero_zero_real )
% 5.41/5.75 => ( ( member_real @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_real ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7182_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_int,F: int > real,I: int] :
% 5.41/5.75 ( ( finite_finite_int @ S )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups8778361861064173332t_real @ F @ S )
% 5.41/5.75 = zero_zero_real )
% 5.41/5.75 => ( ( member_int @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_real ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7183_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_complex,F: complex > real,I: complex] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5808333547571424918x_real @ F @ S )
% 5.41/5.75 = zero_zero_real )
% 5.41/5.75 => ( ( member_complex @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_real ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7184_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_real,F: real > rat,I: real] :
% 5.41/5.75 ( ( finite_finite_real @ S )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups1300246762558778688al_rat @ F @ S )
% 5.41/5.75 = zero_zero_rat )
% 5.41/5.75 => ( ( member_real @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7185_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_nat,F: nat > rat,I: nat] :
% 5.41/5.75 ( ( finite_finite_nat @ S )
% 5.41/5.75 => ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups2906978787729119204at_rat @ F @ S )
% 5.41/5.75 = zero_zero_rat )
% 5.41/5.75 => ( ( member_nat @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7186_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_int,F: int > rat,I: int] :
% 5.41/5.75 ( ( finite_finite_int @ S )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups3906332499630173760nt_rat @ F @ S )
% 5.41/5.75 = zero_zero_rat )
% 5.41/5.75 => ( ( member_int @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7187_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_complex,F: complex > rat,I: complex] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5058264527183730370ex_rat @ F @ S )
% 5.41/5.75 = zero_zero_rat )
% 5.41/5.75 => ( ( member_complex @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_rat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7188_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_real,F: real > nat,I: real] :
% 5.41/5.75 ( ( finite_finite_real @ S )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups1935376822645274424al_nat @ F @ S )
% 5.41/5.75 = zero_zero_nat )
% 5.41/5.75 => ( ( member_real @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7189_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_int,F: int > nat,I: int] :
% 5.41/5.75 ( ( finite_finite_int @ S )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups4541462559716669496nt_nat @ F @ S )
% 5.41/5.75 = zero_zero_nat )
% 5.41/5.75 => ( ( member_int @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7190_sum__nonneg__0,axiom,
% 5.41/5.75 ! [S: set_complex,F: complex > nat,I: complex] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ S )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ S )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5693394587270226106ex_nat @ F @ S )
% 5.41/5.75 = zero_zero_nat )
% 5.41/5.75 => ( ( member_complex @ I @ S )
% 5.41/5.75 => ( ( F @ I )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nonneg_0
% 5.41/5.75 thf(fact_7191_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_int,G: int > complex] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups3049146728041665814omplex @ G
% 5.41/5.75 @ ( minus_minus_set_int @ A2
% 5.41/5.75 @ ( collect_int
% 5.41/5.75 @ ^ [X3: int] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_complex ) ) ) )
% 5.41/5.75 = ( groups3049146728041665814omplex @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7192_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_int,G: int > real] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ G
% 5.41/5.75 @ ( minus_minus_set_int @ A2
% 5.41/5.75 @ ( collect_int
% 5.41/5.75 @ ^ [X3: int] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_real ) ) ) )
% 5.41/5.75 = ( groups8778361861064173332t_real @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7193_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_complex,G: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ G
% 5.41/5.75 @ ( minus_811609699411566653omplex @ A2
% 5.41/5.75 @ ( collect_complex
% 5.41/5.75 @ ^ [X3: complex] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_real ) ) ) )
% 5.41/5.75 = ( groups5808333547571424918x_real @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7194_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_int,G: int > rat] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups3906332499630173760nt_rat @ G
% 5.41/5.75 @ ( minus_minus_set_int @ A2
% 5.41/5.75 @ ( collect_int
% 5.41/5.75 @ ^ [X3: int] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_rat ) ) ) )
% 5.41/5.75 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7195_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_complex,G: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ G
% 5.41/5.75 @ ( minus_811609699411566653omplex @ A2
% 5.41/5.75 @ ( collect_complex
% 5.41/5.75 @ ^ [X3: complex] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_rat ) ) ) )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7196_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_int,G: int > nat] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups4541462559716669496nt_nat @ G
% 5.41/5.75 @ ( minus_minus_set_int @ A2
% 5.41/5.75 @ ( collect_int
% 5.41/5.75 @ ^ [X3: int] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_nat ) ) ) )
% 5.41/5.75 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7197_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_complex,G: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ G
% 5.41/5.75 @ ( minus_811609699411566653omplex @ A2
% 5.41/5.75 @ ( collect_complex
% 5.41/5.75 @ ^ [X3: complex] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_nat ) ) ) )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7198_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_complex,G: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ G
% 5.41/5.75 @ ( minus_811609699411566653omplex @ A2
% 5.41/5.75 @ ( collect_complex
% 5.41/5.75 @ ^ [X3: complex] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_int ) ) ) )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7199_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_nat,G: nat > complex] :
% 5.41/5.75 ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G
% 5.41/5.75 @ ( minus_minus_set_nat @ A2
% 5.41/5.75 @ ( collect_nat
% 5.41/5.75 @ ^ [X3: nat] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_complex ) ) ) )
% 5.41/5.75 = ( groups2073611262835488442omplex @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7200_sum_Osetdiff__irrelevant,axiom,
% 5.41/5.75 ! [A2: set_nat,G: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G
% 5.41/5.75 @ ( minus_minus_set_nat @ A2
% 5.41/5.75 @ ( collect_nat
% 5.41/5.75 @ ^ [X3: nat] :
% 5.41/5.75 ( ( G @ X3 )
% 5.41/5.75 = zero_zero_rat ) ) ) )
% 5.41/5.75 = ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.setdiff_irrelevant
% 5.41/5.75 thf(fact_7201_less__mask,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.75 => ( ord_less_nat @ N @ ( bit_se2002935070580805687sk_nat @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % less_mask
% 5.41/5.75 thf(fact_7202_eval__nat__numeral_I2_J,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( numeral_numeral_nat @ ( bit0 @ N ) )
% 5.41/5.75 = ( suc @ ( numeral_numeral_nat @ ( bitM @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % eval_nat_numeral(2)
% 5.41/5.75 thf(fact_7203_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_real,I: real,F: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ I6 )
% 5.41/5.75 => ( ( member_real @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7204_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_int,I: int,F: int > real] :
% 5.41/5.75 ( ( finite_finite_int @ I6 )
% 5.41/5.75 => ( ( member_int @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7205_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_complex,I: complex,F: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.75 => ( ( member_complex @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7206_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_real,I: real,F: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ I6 )
% 5.41/5.75 => ( ( member_real @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7207_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_nat,I: nat,F: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ I6 )
% 5.41/5.75 => ( ( member_nat @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7208_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_int,I: int,F: int > rat] :
% 5.41/5.75 ( ( finite_finite_int @ I6 )
% 5.41/5.75 => ( ( member_int @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7209_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_complex,I: complex,F: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.75 => ( ( member_complex @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7210_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_real,I: real,F: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ I6 )
% 5.41/5.75 => ( ( member_real @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7211_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_int,I: int,F: int > nat] :
% 5.41/5.75 ( ( finite_finite_int @ I6 )
% 5.41/5.75 => ( ( member_int @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7212_sum__pos2,axiom,
% 5.41/5.75 ! [I6: set_complex,I: complex,F: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.75 => ( ( member_complex @ I @ I6 )
% 5.41/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ I ) )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos2
% 5.41/5.75 thf(fact_7213_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_complex,F: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_complex )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( groups5808333547571424918x_real @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7214_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_int,F: int > real] :
% 5.41/5.75 ( ( finite_finite_int @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_int )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( groups8778361861064173332t_real @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7215_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_real,F: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_real )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_real @ zero_zero_real @ ( groups8097168146408367636l_real @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7216_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_complex,F: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_complex )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups5058264527183730370ex_rat @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7217_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_nat,F: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_nat )
% 5.41/5.75 => ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups2906978787729119204at_rat @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7218_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_int,F: int > rat] :
% 5.41/5.75 ( ( finite_finite_int @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_int )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups3906332499630173760nt_rat @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7219_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_real,F: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_real )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_rat @ zero_zero_rat @ ( groups1300246762558778688al_rat @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7220_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_complex,F: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_complex )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( groups5693394587270226106ex_nat @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7221_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_int,F: int > nat] :
% 5.41/5.75 ( ( finite_finite_int @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_int )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( groups4541462559716669496nt_nat @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7222_sum__pos,axiom,
% 5.41/5.75 ! [I6: set_real,F: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ I6 )
% 5.41/5.75 => ( ( I6 != bot_bot_set_real )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( F @ I4 ) ) )
% 5.41/5.75 => ( ord_less_nat @ zero_zero_nat @ ( groups1935376822645274424al_nat @ F @ I6 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_pos
% 5.41/5.75 thf(fact_7223_set__encode__inf,axiom,
% 5.41/5.75 ! [A2: set_nat] :
% 5.41/5.75 ( ~ ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( nat_set_encode @ A2 )
% 5.41/5.75 = zero_zero_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % set_encode_inf
% 5.41/5.75 thf(fact_7224_BitM__plus__one,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( plus_plus_num @ ( bitM @ N ) @ one )
% 5.41/5.75 = ( bit0 @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % BitM_plus_one
% 5.41/5.75 thf(fact_7225_one__plus__BitM,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( plus_plus_num @ one @ ( bitM @ N ) )
% 5.41/5.75 = ( bit0 @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % one_plus_BitM
% 5.41/5.75 thf(fact_7226_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,G: real > complex,H2: real > complex] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5754745047067104278omplex @ G @ T3 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7227_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,G: real > real,H2: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups8097168146408367636l_real @ G @ T3 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7228_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > real,H2: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7229_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,G: real > rat,H2: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups1300246762558778688al_rat @ G @ T3 )
% 5.41/5.75 = ( groups1300246762558778688al_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7230_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > rat,H2: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7231_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,G: real > nat,H2: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups1935376822645274424al_nat @ G @ T3 )
% 5.41/5.75 = ( groups1935376822645274424al_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7232_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > nat,H2: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7233_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,G: real > int,H2: real > int] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups1932886352136224148al_int @ G @ T3 )
% 5.41/5.75 = ( groups1932886352136224148al_int @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7234_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > int,H2: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7235_sum_Omono__neutral__cong__right,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,G: nat > complex,H2: nat > complex] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G @ T3 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ H2 @ S2 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_right
% 5.41/5.75 thf(fact_7236_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,H2: real > complex,G: real > complex] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5754745047067104278omplex @ G @ S2 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7237_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,H2: real > real,G: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups8097168146408367636l_real @ G @ S2 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7238_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,H2: complex > real,G: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ G @ S2 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7239_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,H2: real > rat,G: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups1300246762558778688al_rat @ G @ S2 )
% 5.41/5.75 = ( groups1300246762558778688al_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7240_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,H2: complex > rat,G: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7241_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,H2: real > nat,G: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups1935376822645274424al_nat @ G @ S2 )
% 5.41/5.75 = ( groups1935376822645274424al_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7242_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,H2: complex > nat,G: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7243_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_real,S2: set_real,H2: real > int,G: real > int] :
% 5.41/5.75 ( ( finite_finite_real @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ ( minus_minus_set_real @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups1932886352136224148al_int @ G @ S2 )
% 5.41/5.75 = ( groups1932886352136224148al_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7244_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,H2: complex > int,G: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7245_sum_Omono__neutral__cong__left,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,H2: nat > complex,G: nat > complex] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( H2 @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ S2 )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = ( H2 @ X6 ) ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G @ S2 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ H2 @ T3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_cong_left
% 5.41/5.75 thf(fact_7246_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ G @ T3 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7247_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ G @ T3 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7248_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ G @ T3 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7249_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ G @ T3 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7250_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G @ T3 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7251_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ T3 )
% 5.41/5.75 = ( groups2906978787729119204at_rat @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7252_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ T3 )
% 5.41/5.75 = ( groups3539618377306564664at_int @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7253_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_int,S2: set_int,G: int > complex] :
% 5.41/5.75 ( ( finite_finite_int @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: int] :
% 5.41/5.75 ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( groups3049146728041665814omplex @ G @ T3 )
% 5.41/5.75 = ( groups3049146728041665814omplex @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7254_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_int,S2: set_int,G: int > real] :
% 5.41/5.75 ( ( finite_finite_int @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: int] :
% 5.41/5.75 ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ G @ T3 )
% 5.41/5.75 = ( groups8778361861064173332t_real @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7255_sum_Omono__neutral__right,axiom,
% 5.41/5.75 ! [T3: set_int,S2: set_int,G: int > rat] :
% 5.41/5.75 ( ( finite_finite_int @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: int] :
% 5.41/5.75 ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( groups3906332499630173760nt_rat @ G @ T3 )
% 5.41/5.75 = ( groups3906332499630173760nt_rat @ G @ S2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_right
% 5.41/5.75 thf(fact_7256_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ G @ S2 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7257_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ G @ S2 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7258_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ G @ S2 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7259_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_complex,S2: set_complex,G: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ T3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ G @ S2 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7260_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,G: nat > complex] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G @ S2 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7261_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,G: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ S2 )
% 5.41/5.75 = ( groups2906978787729119204at_rat @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7262_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_nat,S2: set_nat,G: nat > int] :
% 5.41/5.75 ( ( finite_finite_nat @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ S2 )
% 5.41/5.75 = ( groups3539618377306564664at_int @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7263_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_int,S2: set_int,G: int > complex] :
% 5.41/5.75 ( ( finite_finite_int @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: int] :
% 5.41/5.75 ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( groups3049146728041665814omplex @ G @ S2 )
% 5.41/5.75 = ( groups3049146728041665814omplex @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7264_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_int,S2: set_int,G: int > real] :
% 5.41/5.75 ( ( finite_finite_int @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: int] :
% 5.41/5.75 ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ G @ S2 )
% 5.41/5.75 = ( groups8778361861064173332t_real @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7265_sum_Omono__neutral__left,axiom,
% 5.41/5.75 ! [T3: set_int,S2: set_int,G: int > rat] :
% 5.41/5.75 ( ( finite_finite_int @ T3 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ S2 @ T3 )
% 5.41/5.75 => ( ! [X6: int] :
% 5.41/5.75 ( ( member_int @ X6 @ ( minus_minus_set_int @ T3 @ S2 ) )
% 5.41/5.75 => ( ( G @ X6 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( groups3906332499630173760nt_rat @ G @ S2 )
% 5.41/5.75 = ( groups3906332499630173760nt_rat @ G @ T3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.mono_neutral_left
% 5.41/5.75 thf(fact_7266_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7267_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( ( groups8097168146408367636l_real @ G @ C4 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7268_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7269_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( ( groups1300246762558778688al_rat @ G @ C4 )
% 5.41/5.75 = ( groups1300246762558778688al_rat @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.41/5.75 = ( groups1300246762558778688al_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7270_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7271_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ( ( groups1935376822645274424al_nat @ G @ C4 )
% 5.41/5.75 = ( groups1935376822645274424al_nat @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.41/5.75 = ( groups1935376822645274424al_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7272_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7273_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( ( groups1932886352136224148al_int @ G @ C4 )
% 5.41/5.75 = ( groups1932886352136224148al_int @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.41/5.75 = ( groups1932886352136224148al_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7274_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( ( groups5690904116761175830ex_int @ G @ C4 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7275_sum_Osame__carrierI,axiom,
% 5.41/5.75 ! [C4: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 5.41/5.75 ( ( finite_finite_nat @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: nat] :
% 5.41/5.75 ( ( member_nat @ A5 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: nat] :
% 5.41/5.75 ( ( member_nat @ B5 @ ( minus_minus_set_nat @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( ( groups2073611262835488442omplex @ G @ C4 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ H2 @ C4 ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ H2 @ B3 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrierI
% 5.41/5.75 thf(fact_7276_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > complex,H2: real > complex] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( ( groups5754745047067104278omplex @ G @ A2 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups5754745047067104278omplex @ G @ C4 )
% 5.41/5.75 = ( groups5754745047067104278omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7277_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > real,H2: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups8097168146408367636l_real @ G @ C4 )
% 5.41/5.75 = ( groups8097168146408367636l_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7278_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > real,H2: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 => ( ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups5808333547571424918x_real @ G @ C4 )
% 5.41/5.75 = ( groups5808333547571424918x_real @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7279_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > rat,H2: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.41/5.75 = ( groups1300246762558778688al_rat @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups1300246762558778688al_rat @ G @ C4 )
% 5.41/5.75 = ( groups1300246762558778688al_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7280_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > rat,H2: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 => ( ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups5058264527183730370ex_rat @ G @ C4 )
% 5.41/5.75 = ( groups5058264527183730370ex_rat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7281_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > nat,H2: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.41/5.75 = ( groups1935376822645274424al_nat @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups1935376822645274424al_nat @ G @ C4 )
% 5.41/5.75 = ( groups1935376822645274424al_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7282_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > nat,H2: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 => ( ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups5693394587270226106ex_nat @ G @ C4 )
% 5.41/5.75 = ( groups5693394587270226106ex_nat @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7283_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_real,A2: set_real,B3: set_real,G: real > int,H2: real > int] :
% 5.41/5.75 ( ( finite_finite_real @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: real] :
% 5.41/5.75 ( ( member_real @ A5 @ ( minus_minus_set_real @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( ( groups1932886352136224148al_int @ G @ A2 )
% 5.41/5.75 = ( groups1932886352136224148al_int @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups1932886352136224148al_int @ G @ C4 )
% 5.41/5.75 = ( groups1932886352136224148al_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7284_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_complex,A2: set_complex,B3: set_complex,G: complex > int,H2: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: complex] :
% 5.41/5.75 ( ( member_complex @ A5 @ ( minus_811609699411566653omplex @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 => ( ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups5690904116761175830ex_int @ G @ C4 )
% 5.41/5.75 = ( groups5690904116761175830ex_int @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7285_sum_Osame__carrier,axiom,
% 5.41/5.75 ! [C4: set_nat,A2: set_nat,B3: set_nat,G: nat > complex,H2: nat > complex] :
% 5.41/5.75 ( ( finite_finite_nat @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ A2 @ C4 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ B3 @ C4 )
% 5.41/5.75 => ( ! [A5: nat] :
% 5.41/5.75 ( ( member_nat @ A5 @ ( minus_minus_set_nat @ C4 @ A2 ) )
% 5.41/5.75 => ( ( G @ A5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ! [B5: nat] :
% 5.41/5.75 ( ( member_nat @ B5 @ ( minus_minus_set_nat @ C4 @ B3 ) )
% 5.41/5.75 => ( ( H2 @ B5 )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 => ( ( ( groups2073611262835488442omplex @ G @ A2 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ H2 @ B3 ) )
% 5.41/5.75 = ( ( groups2073611262835488442omplex @ G @ C4 )
% 5.41/5.75 = ( groups2073611262835488442omplex @ H2 @ C4 ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.same_carrier
% 5.41/5.75 thf(fact_7286_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,G: complex > real] :
% 5.41/5.75 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.41/5.75 = ( plus_plus_real @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5808333547571424918x_real @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7287_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,G: complex > rat] :
% 5.41/5.75 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.41/5.75 = ( plus_plus_rat @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5058264527183730370ex_rat @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7288_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,G: complex > nat] :
% 5.41/5.75 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.41/5.75 = ( plus_plus_nat @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5693394587270226106ex_nat @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7289_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,G: complex > int] :
% 5.41/5.75 ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.41/5.75 = ( plus_plus_int @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) @ ( groups5690904116761175830ex_int @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7290_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_nat,A2: set_nat,G: nat > rat] :
% 5.41/5.75 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.41/5.75 => ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ A2 )
% 5.41/5.75 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups2906978787729119204at_rat @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7291_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_nat,A2: set_nat,G: nat > int] :
% 5.41/5.75 ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.41/5.75 => ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ A2 )
% 5.41/5.75 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( minus_minus_set_nat @ A2 @ B3 ) ) @ ( groups3539618377306564664at_int @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7292_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_int,A2: set_int,G: int > real] :
% 5.41/5.75 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.41/5.75 = ( plus_plus_real @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups8778361861064173332t_real @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7293_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_int,A2: set_int,G: int > rat] :
% 5.41/5.75 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.41/5.75 = ( plus_plus_rat @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups3906332499630173760nt_rat @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7294_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_int,A2: set_int,G: int > nat] :
% 5.41/5.75 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.41/5.75 = ( plus_plus_nat @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4541462559716669496nt_nat @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7295_sum_Osubset__diff,axiom,
% 5.41/5.75 ! [B3: set_int,A2: set_int,G: int > int] :
% 5.41/5.75 ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( groups4538972089207619220nt_int @ G @ A2 )
% 5.41/5.75 = ( plus_plus_int @ ( groups4538972089207619220nt_int @ G @ ( minus_minus_set_int @ A2 @ B3 ) ) @ ( groups4538972089207619220nt_int @ G @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.subset_diff
% 5.41/5.75 thf(fact_7296_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_complex,B3: set_complex,F: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7297_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_complex,B3: set_complex,F: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7298_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_complex,B3: set_complex,F: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7299_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_nat,B3: set_nat,F: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7300_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_nat,B3: set_nat,F: nat > int] :
% 5.41/5.75 ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7301_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_int,B3: set_int,F: int > real] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( groups8778361861064173332t_real @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7302_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_int,B3: set_int,F: int > rat] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( groups3906332499630173760nt_rat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7303_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_int,B3: set_int,F: int > int] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( groups4538972089207619220nt_int @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_int @ ( groups4538972089207619220nt_int @ F @ A2 ) @ ( groups4538972089207619220nt_int @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7304_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_complex,B3: set_complex,F: complex > complex] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( groups7754918857620584856omplex @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_complex @ ( groups7754918857620584856omplex @ F @ A2 ) @ ( groups7754918857620584856omplex @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7305_sum__diff,axiom,
% 5.41/5.75 ! [A2: set_nat,B3: set_nat,F: nat > real] :
% 5.41/5.75 ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ A2 ) @ ( groups6591440286371151544t_real @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff
% 5.41/5.75 thf(fact_7306_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,F: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7307_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,F: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7308_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,F: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7309_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,F: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7310_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_nat,A2: set_nat,F: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: nat] :
% 5.41/5.75 ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7311_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,F: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7312_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7313_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,F: real > int] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: real] :
% 5.41/5.75 ( ( member_real @ B5 @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7314_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,F: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: complex] :
% 5.41/5.75 ( ( member_complex @ B5 @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7315_sum__mono2,axiom,
% 5.41/5.75 ! [B3: set_nat,A2: set_nat,F: nat > int] :
% 5.41/5.75 ( ( finite_finite_nat @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.75 => ( ! [B5: nat] :
% 5.41/5.75 ( ( member_nat @ B5 @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.41/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ B5 ) ) )
% 5.41/5.75 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_mono2
% 5.41/5.75 thf(fact_7316_numeral__BitM,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( numera6690914467698888265omplex @ ( bitM @ N ) )
% 5.41/5.75 = ( minus_minus_complex @ ( numera6690914467698888265omplex @ ( bit0 @ N ) ) @ one_one_complex ) ) ).
% 5.41/5.75
% 5.41/5.75 % numeral_BitM
% 5.41/5.75 thf(fact_7317_numeral__BitM,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( numeral_numeral_real @ ( bitM @ N ) )
% 5.41/5.75 = ( minus_minus_real @ ( numeral_numeral_real @ ( bit0 @ N ) ) @ one_one_real ) ) ).
% 5.41/5.75
% 5.41/5.75 % numeral_BitM
% 5.41/5.75 thf(fact_7318_numeral__BitM,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( numeral_numeral_rat @ ( bitM @ N ) )
% 5.41/5.75 = ( minus_minus_rat @ ( numeral_numeral_rat @ ( bit0 @ N ) ) @ one_one_rat ) ) ).
% 5.41/5.75
% 5.41/5.75 % numeral_BitM
% 5.41/5.75 thf(fact_7319_numeral__BitM,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( numeral_numeral_int @ ( bitM @ N ) )
% 5.41/5.75 = ( minus_minus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) @ one_one_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % numeral_BitM
% 5.41/5.75 thf(fact_7320_odd__numeral__BitM,axiom,
% 5.41/5.75 ! [W: num] :
% 5.41/5.75 ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numera6620942414471956472nteger @ ( bitM @ W ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % odd_numeral_BitM
% 5.41/5.75 thf(fact_7321_odd__numeral__BitM,axiom,
% 5.41/5.75 ! [W: num] :
% 5.41/5.75 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ ( bitM @ W ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % odd_numeral_BitM
% 5.41/5.75 thf(fact_7322_odd__numeral__BitM,axiom,
% 5.41/5.75 ! [W: num] :
% 5.41/5.75 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_int @ ( bitM @ W ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % odd_numeral_BitM
% 5.41/5.75 thf(fact_7323_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,B: real,F: real > real] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( groups8097168146408367636l_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7324_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > real] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_real @ zero_zero_real @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( groups5808333547571424918x_real @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7325_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,B: real,F: real > rat] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( groups1300246762558778688al_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7326_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > rat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( groups5058264527183730370ex_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7327_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_nat,A2: set_nat,B: nat,F: nat > rat] :
% 5.41/5.75 ( ( finite_finite_nat @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.75 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_rat @ zero_zero_rat @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( groups2906978787729119204at_rat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7328_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,B: real,F: real > nat] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7329_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_nat @ zero_zero_nat @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7330_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_real,A2: set_real,B: real,F: real > int] :
% 5.41/5.75 ( ( finite_finite_real @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.75 => ( ( member_real @ B @ ( minus_minus_set_real @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( groups1932886352136224148al_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7331_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,B: complex,F: complex > int] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ A2 @ B3 )
% 5.41/5.75 => ( ( member_complex @ B @ ( minus_811609699411566653omplex @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( groups5690904116761175830ex_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7332_sum__strict__mono2,axiom,
% 5.41/5.75 ! [B3: set_nat,A2: set_nat,B: nat,F: nat > int] :
% 5.41/5.75 ( ( finite_finite_nat @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.75 => ( ( member_nat @ B @ ( minus_minus_set_nat @ B3 @ A2 ) )
% 5.41/5.75 => ( ( ord_less_int @ zero_zero_int @ ( F @ B ) )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ B3 )
% 5.41/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ord_less_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( groups3539618377306564664at_int @ F @ B3 ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_strict_mono2
% 5.41/5.75 thf(fact_7333_Suc__mask__eq__exp,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( suc @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.41/5.75 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % Suc_mask_eq_exp
% 5.41/5.75 thf(fact_7334_mask__nat__less__exp,axiom,
% 5.41/5.75 ! [N: nat] : ( ord_less_nat @ ( bit_se2002935070580805687sk_nat @ N ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_nat_less_exp
% 5.41/5.75 thf(fact_7335_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_complex,X: complex > code_integer,A: complex > code_integer,B: code_integer,Delta: code_integer] :
% 5.41/5.75 ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups6621422865394947399nteger @ X @ I6 )
% 5.41/5.75 = one_one_Code_integer )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_le3102999989581377725nteger
% 5.41/5.75 @ ( abs_abs_Code_integer
% 5.41/5.75 @ ( minus_8373710615458151222nteger
% 5.41/5.75 @ ( groups6621422865394947399nteger
% 5.41/5.75 @ ^ [I5: complex] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7336_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_real,X: real > code_integer,A: real > code_integer,B: code_integer,Delta: code_integer] :
% 5.41/5.75 ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups7713935264441627589nteger @ X @ I6 )
% 5.41/5.75 = one_one_Code_integer )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_le3102999989581377725nteger
% 5.41/5.75 @ ( abs_abs_Code_integer
% 5.41/5.75 @ ( minus_8373710615458151222nteger
% 5.41/5.75 @ ( groups7713935264441627589nteger
% 5.41/5.75 @ ^ [I5: real] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7337_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_nat,X: nat > code_integer,A: nat > code_integer,B: code_integer,Delta: code_integer] :
% 5.41/5.75 ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups7501900531339628137nteger @ X @ I6 )
% 5.41/5.75 = one_one_Code_integer )
% 5.41/5.75 => ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_le3102999989581377725nteger
% 5.41/5.75 @ ( abs_abs_Code_integer
% 5.41/5.75 @ ( minus_8373710615458151222nteger
% 5.41/5.75 @ ( groups7501900531339628137nteger
% 5.41/5.75 @ ^ [I5: nat] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7338_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_int,X: int > code_integer,A: int > code_integer,B: code_integer,Delta: code_integer] :
% 5.41/5.75 ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups7873554091576472773nteger @ X @ I6 )
% 5.41/5.75 = one_one_Code_integer )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_le3102999989581377725nteger @ ( abs_abs_Code_integer @ ( minus_8373710615458151222nteger @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_le3102999989581377725nteger
% 5.41/5.75 @ ( abs_abs_Code_integer
% 5.41/5.75 @ ( minus_8373710615458151222nteger
% 5.41/5.75 @ ( groups7873554091576472773nteger
% 5.41/5.75 @ ^ [I5: int] : ( times_3573771949741848930nteger @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7339_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_complex,X: complex > real,A: complex > real,B: real,Delta: real] :
% 5.41/5.75 ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5808333547571424918x_real @ X @ I6 )
% 5.41/5.75 = one_one_real )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_less_eq_real
% 5.41/5.75 @ ( abs_abs_real
% 5.41/5.75 @ ( minus_minus_real
% 5.41/5.75 @ ( groups5808333547571424918x_real
% 5.41/5.75 @ ^ [I5: complex] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7340_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_real,X: real > real,A: real > real,B: real,Delta: real] :
% 5.41/5.75 ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups8097168146408367636l_real @ X @ I6 )
% 5.41/5.75 = one_one_real )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_less_eq_real
% 5.41/5.75 @ ( abs_abs_real
% 5.41/5.75 @ ( minus_minus_real
% 5.41/5.75 @ ( groups8097168146408367636l_real
% 5.41/5.75 @ ^ [I5: real] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7341_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_int,X: int > real,A: int > real,B: real,Delta: real] :
% 5.41/5.75 ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ zero_zero_real @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups8778361861064173332t_real @ X @ I6 )
% 5.41/5.75 = one_one_real )
% 5.41/5.75 => ( ! [I4: int] :
% 5.41/5.75 ( ( member_int @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_less_eq_real
% 5.41/5.75 @ ( abs_abs_real
% 5.41/5.75 @ ( minus_minus_real
% 5.41/5.75 @ ( groups8778361861064173332t_real
% 5.41/5.75 @ ^ [I5: int] : ( times_times_real @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7342_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_complex,X: complex > rat,A: complex > rat,B: rat,Delta: rat] :
% 5.41/5.75 ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups5058264527183730370ex_rat @ X @ I6 )
% 5.41/5.75 = one_one_rat )
% 5.41/5.75 => ( ! [I4: complex] :
% 5.41/5.75 ( ( member_complex @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_less_eq_rat
% 5.41/5.75 @ ( abs_abs_rat
% 5.41/5.75 @ ( minus_minus_rat
% 5.41/5.75 @ ( groups5058264527183730370ex_rat
% 5.41/5.75 @ ^ [I5: complex] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7343_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_real,X: real > rat,A: real > rat,B: rat,Delta: rat] :
% 5.41/5.75 ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups1300246762558778688al_rat @ X @ I6 )
% 5.41/5.75 = one_one_rat )
% 5.41/5.75 => ( ! [I4: real] :
% 5.41/5.75 ( ( member_real @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_less_eq_rat
% 5.41/5.75 @ ( abs_abs_rat
% 5.41/5.75 @ ( minus_minus_rat
% 5.41/5.75 @ ( groups1300246762558778688al_rat
% 5.41/5.75 @ ^ [I5: real] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7344_convex__sum__bound__le,axiom,
% 5.41/5.75 ! [I6: set_nat,X: nat > rat,A: nat > rat,B: rat,Delta: rat] :
% 5.41/5.75 ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ zero_zero_rat @ ( X @ I4 ) ) )
% 5.41/5.75 => ( ( ( groups2906978787729119204at_rat @ X @ I6 )
% 5.41/5.75 = one_one_rat )
% 5.41/5.75 => ( ! [I4: nat] :
% 5.41/5.75 ( ( member_nat @ I4 @ I6 )
% 5.41/5.75 => ( ord_less_eq_rat @ ( abs_abs_rat @ ( minus_minus_rat @ ( A @ I4 ) @ B ) ) @ Delta ) )
% 5.41/5.75 => ( ord_less_eq_rat
% 5.41/5.75 @ ( abs_abs_rat
% 5.41/5.75 @ ( minus_minus_rat
% 5.41/5.75 @ ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( times_times_rat @ ( A @ I5 ) @ ( X @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 @ B ) )
% 5.41/5.75 @ Delta ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % convex_sum_bound_le
% 5.41/5.75 thf(fact_7345_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se2119862282449309892nteger @ N ) )
% 5.41/5.75 = ( N = zero_zero_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % semiring_bit_operations_class.even_mask_iff
% 5.41/5.75 thf(fact_7346_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.41/5.75 = ( N = zero_zero_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % semiring_bit_operations_class.even_mask_iff
% 5.41/5.75 thf(fact_7347_semiring__bit__operations__class_Oeven__mask__iff,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.41/5.75 = ( N = zero_zero_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % semiring_bit_operations_class.even_mask_iff
% 5.41/5.75 thf(fact_7348_mask__nat__def,axiom,
% 5.41/5.75 ( bit_se2002935070580805687sk_nat
% 5.41/5.75 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_nat_def
% 5.41/5.75 thf(fact_7349_mask__half__int,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( divide_divide_int @ ( bit_se2000444600071755411sk_int @ N ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.75 = ( bit_se2000444600071755411sk_int @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_half_int
% 5.41/5.75 thf(fact_7350_mask__int__def,axiom,
% 5.41/5.75 ( bit_se2000444600071755411sk_int
% 5.41/5.75 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_int_def
% 5.41/5.75 thf(fact_7351_mask__eq__exp__minus__1,axiom,
% 5.41/5.75 ( bit_se2002935070580805687sk_nat
% 5.41/5.75 = ( ^ [N2: nat] : ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_eq_exp_minus_1
% 5.41/5.75 thf(fact_7352_mask__eq__exp__minus__1,axiom,
% 5.41/5.75 ( bit_se2000444600071755411sk_int
% 5.41/5.75 = ( ^ [N2: nat] : ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) @ one_one_int ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_eq_exp_minus_1
% 5.41/5.75 thf(fact_7353_divmod__step__nat__def,axiom,
% 5.41/5.75 ( unique5026877609467782581ep_nat
% 5.41/5.75 = ( ^ [L: num] :
% 5.41/5.75 ( produc2626176000494625587at_nat
% 5.41/5.75 @ ^ [Q5: nat,R5: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ L ) @ R5 ) @ ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ one_one_nat ) @ ( minus_minus_nat @ R5 @ ( numeral_numeral_nat @ L ) ) ) @ ( product_Pair_nat_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % divmod_step_nat_def
% 5.41/5.75 thf(fact_7354_divmod__step__int__def,axiom,
% 5.41/5.75 ( unique5024387138958732305ep_int
% 5.41/5.75 = ( ^ [L: num] :
% 5.41/5.75 ( produc4245557441103728435nt_int
% 5.41/5.75 @ ^ [Q5: int,R5: int] : ( if_Pro3027730157355071871nt_int @ ( ord_less_eq_int @ ( numeral_numeral_int @ L ) @ R5 ) @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ one_one_int ) @ ( minus_minus_int @ R5 @ ( numeral_numeral_int @ L ) ) ) @ ( product_Pair_int_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % divmod_step_int_def
% 5.41/5.75 thf(fact_7355_divmod__nat__if,axiom,
% 5.41/5.75 ( divmod_nat
% 5.41/5.75 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.75 ( if_Pro6206227464963214023at_nat
% 5.41/5.75 @ ( ( N2 = zero_zero_nat )
% 5.41/5.75 | ( ord_less_nat @ M3 @ N2 ) )
% 5.41/5.75 @ ( product_Pair_nat_nat @ zero_zero_nat @ M3 )
% 5.41/5.75 @ ( produc2626176000494625587at_nat
% 5.41/5.75 @ ^ [Q5: nat] : ( product_Pair_nat_nat @ ( suc @ Q5 ) )
% 5.41/5.75 @ ( divmod_nat @ ( minus_minus_nat @ M3 @ N2 ) @ N2 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % divmod_nat_if
% 5.41/5.75 thf(fact_7356_num_Osize__gen_I3_J,axiom,
% 5.41/5.75 ! [X32: num] :
% 5.41/5.75 ( ( size_num @ ( bit1 @ X32 ) )
% 5.41/5.75 = ( plus_plus_nat @ ( size_num @ X32 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % num.size_gen(3)
% 5.41/5.75 thf(fact_7357_take__bit__rec,axiom,
% 5.41/5.75 ( bit_se1745604003318907178nteger
% 5.41/5.75 = ( ^ [N2: nat,A3: code_integer] : ( if_Code_integer @ ( N2 = zero_zero_nat ) @ zero_z3403309356797280102nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide6298287555418463151nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A3 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_rec
% 5.41/5.75 thf(fact_7358_take__bit__rec,axiom,
% 5.41/5.75 ( bit_se2923211474154528505it_int
% 5.41/5.75 = ( ^ [N2: nat,A3: int] : ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int @ ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_rec
% 5.41/5.75 thf(fact_7359_take__bit__rec,axiom,
% 5.41/5.75 ( bit_se2925701944663578781it_nat
% 5.41/5.75 = ( ^ [N2: nat,A3: nat] : ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat @ ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( divide_divide_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_rec
% 5.41/5.75 thf(fact_7360_num_Osize__gen_I2_J,axiom,
% 5.41/5.75 ! [X22: num] :
% 5.41/5.75 ( ( size_num @ ( bit0 @ X22 ) )
% 5.41/5.75 = ( plus_plus_nat @ ( size_num @ X22 ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % num.size_gen(2)
% 5.41/5.75 thf(fact_7361_tanh__real__altdef,axiom,
% 5.41/5.75 ( tanh_real
% 5.41/5.75 = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) @ ( plus_plus_real @ one_one_real @ ( exp_real @ ( times_times_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % tanh_real_altdef
% 5.41/5.75 thf(fact_7362_and__int__unfold,axiom,
% 5.41/5.75 ( bit_se725231765392027082nd_int
% 5.41/5.75 = ( ^ [K2: int,L: int] :
% 5.41/5.75 ( if_int
% 5.41/5.75 @ ( ( K2 = zero_zero_int )
% 5.41/5.75 | ( L = zero_zero_int ) )
% 5.41/5.75 @ zero_zero_int
% 5.41/5.75 @ ( if_int
% 5.41/5.75 @ ( K2
% 5.41/5.75 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 @ L
% 5.41/5.75 @ ( if_int
% 5.41/5.75 @ ( L
% 5.41/5.75 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 @ K2
% 5.41/5.75 @ ( plus_plus_int @ ( times_times_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_int_unfold
% 5.41/5.75 thf(fact_7363_and_Oidem,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ A @ A )
% 5.41/5.75 = A ) ).
% 5.41/5.75
% 5.41/5.75 % and.idem
% 5.41/5.75 thf(fact_7364_and_Oidem,axiom,
% 5.41/5.75 ! [A: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ A @ A )
% 5.41/5.75 = A ) ).
% 5.41/5.75
% 5.41/5.75 % and.idem
% 5.41/5.75 thf(fact_7365_and_Oleft__idem,axiom,
% 5.41/5.75 ! [A: int,B: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.41/5.75 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.left_idem
% 5.41/5.75 thf(fact_7366_and_Oleft__idem,axiom,
% 5.41/5.75 ! [A: nat,B: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.41/5.75 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.left_idem
% 5.41/5.75 thf(fact_7367_and_Oright__idem,axiom,
% 5.41/5.75 ! [A: int,B: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ B )
% 5.41/5.75 = ( bit_se725231765392027082nd_int @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.right_idem
% 5.41/5.75 thf(fact_7368_and_Oright__idem,axiom,
% 5.41/5.75 ! [A: nat,B: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ B )
% 5.41/5.75 = ( bit_se727722235901077358nd_nat @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.right_idem
% 5.41/5.75 thf(fact_7369_case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc8763457246119570046nteger,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 5.41/5.75 ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.41/5.75 => ( C @ A5 @ B5 ) )
% 5.41/5.75 => ( produc127349428274296955eger_o @ C @ P5 ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI2
% 5.41/5.75 thf(fact_7370_case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc1908205239877642774nteger,C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o] :
% 5.41/5.75 ( ! [A5: produc6241069584506657477e_term > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc8603105652947943368nteger @ A5 @ B5 ) )
% 5.41/5.75 => ( C @ A5 @ B5 ) )
% 5.41/5.75 => ( produc6253627499356882019eger_o @ C @ P5 ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI2
% 5.41/5.75 thf(fact_7371_case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc2285326912895808259nt_int,C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.41/5.75 ( ! [A5: produc8551481072490612790e_term > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc5700946648718959541nt_int @ A5 @ B5 ) )
% 5.41/5.75 => ( C @ A5 @ B5 ) )
% 5.41/5.75 => ( produc1573362020775583542_int_o @ C @ P5 ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI2
% 5.41/5.75 thf(fact_7372_case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc7773217078559923341nt_int,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o] :
% 5.41/5.75 ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 5.41/5.75 => ( C @ A5 @ B5 ) )
% 5.41/5.75 => ( produc2558449545302689196_int_o @ C @ P5 ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI2
% 5.41/5.75 thf(fact_7373_case__prodI2,axiom,
% 5.41/5.75 ! [P5: product_prod_int_int,C: int > int > $o] :
% 5.41/5.75 ( ! [A5: int,B5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.41/5.75 => ( C @ A5 @ B5 ) )
% 5.41/5.75 => ( produc4947309494688390418_int_o @ C @ P5 ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI2
% 5.41/5.75 thf(fact_7374_case__prodI,axiom,
% 5.41/5.75 ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( F @ A @ B )
% 5.41/5.75 => ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI
% 5.41/5.75 thf(fact_7375_case__prodI,axiom,
% 5.41/5.75 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( F @ A @ B )
% 5.41/5.75 => ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI
% 5.41/5.75 thf(fact_7376_case__prodI,axiom,
% 5.41/5.75 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.41/5.75 ( ( F @ A @ B )
% 5.41/5.75 => ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI
% 5.41/5.75 thf(fact_7377_case__prodI,axiom,
% 5.41/5.75 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.41/5.75 ( ( F @ A @ B )
% 5.41/5.75 => ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI
% 5.41/5.75 thf(fact_7378_case__prodI,axiom,
% 5.41/5.75 ! [F: int > int > $o,A: int,B: int] :
% 5.41/5.75 ( ( F @ A @ B )
% 5.41/5.75 => ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI
% 5.41/5.75 thf(fact_7379_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: product_prod_int_int,Z: complex,C: int > int > set_complex] :
% 5.41/5.75 ( ! [A5: int,B5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.41/5.75 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7380_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: product_prod_int_int,Z: real,C: int > int > set_real] :
% 5.41/5.75 ( ! [A5: int,B5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.41/5.75 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7381_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: product_prod_int_int,Z: nat,C: int > int > set_nat] :
% 5.41/5.75 ( ! [A5: int,B5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.41/5.75 => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7382_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: product_prod_int_int,Z: int,C: int > int > set_int] :
% 5.41/5.75 ( ! [A5: int,B5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.41/5.75 => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7383_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: product_prod_int_int,Z: set_nat,C: int > int > set_set_nat] :
% 5.41/5.75 ( ! [A5: int,B5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ A5 @ B5 ) )
% 5.41/5.75 => ( member_set_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7384_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc8763457246119570046nteger,Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex] :
% 5.41/5.75 ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.41/5.75 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7385_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc8763457246119570046nteger,Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real] :
% 5.41/5.75 ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.41/5.75 => ( member_real @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7386_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc8763457246119570046nteger,Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat] :
% 5.41/5.75 ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.41/5.75 => ( member_nat @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7387_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc8763457246119570046nteger,Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int] :
% 5.41/5.75 ( ! [A5: code_integer > option6357759511663192854e_term,B5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ A5 @ B5 ) )
% 5.41/5.75 => ( member_int @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7388_mem__case__prodI2,axiom,
% 5.41/5.75 ! [P5: produc7773217078559923341nt_int,Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex] :
% 5.41/5.75 ( ! [A5: int > option6357759511663192854e_term,B5: product_prod_int_int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc4305682042979456191nt_int @ A5 @ B5 ) )
% 5.41/5.75 => ( member_complex @ Z @ ( C @ A5 @ B5 ) ) )
% 5.41/5.75 => ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ P5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI2
% 5.41/5.75 thf(fact_7389_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: complex,C: int > int > set_complex,A: int,B: int] :
% 5.41/5.75 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7390_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: real,C: int > int > set_real,A: int,B: int] :
% 5.41/5.75 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7391_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: nat,C: int > int > set_nat,A: int,B: int] :
% 5.41/5.75 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7392_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: int,C: int > int > set_int,A: int,B: int] :
% 5.41/5.75 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_int @ Z @ ( produc73460835934605544et_int @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7393_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: set_nat,C: int > int > set_set_nat,A: int,B: int] :
% 5.41/5.75 ( ( member_set_nat @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7394_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7395_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( member_real @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_real @ Z @ ( produc815715089573277247t_real @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7396_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( member_nat @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7397_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( member_int @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ ( produc6137756002093451184nteger @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7398_mem__case__prodI,axiom,
% 5.41/5.75 ! [Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.41/5.75 ( ( member_complex @ Z @ ( C @ A @ B ) )
% 5.41/5.75 => ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ ( produc4305682042979456191nt_int @ A @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodI
% 5.41/5.75 thf(fact_7399_case__prodI2_H,axiom,
% 5.41/5.75 ! [P5: product_prod_nat_nat,C: nat > nat > product_prod_nat_nat > $o,X: product_prod_nat_nat] :
% 5.41/5.75 ( ! [A5: nat,B5: nat] :
% 5.41/5.75 ( ( ( product_Pair_nat_nat @ A5 @ B5 )
% 5.41/5.75 = P5 )
% 5.41/5.75 => ( C @ A5 @ B5 @ X ) )
% 5.41/5.75 => ( produc8739625826339149834_nat_o @ C @ P5 @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodI2'
% 5.41/5.75 thf(fact_7400_take__bit__of__0,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ zero_zero_int )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_0
% 5.41/5.75 thf(fact_7401_take__bit__of__0,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ N @ zero_zero_nat )
% 5.41/5.75 = zero_zero_nat ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_0
% 5.41/5.75 thf(fact_7402_and__zero__eq,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ A @ zero_zero_int )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_zero_eq
% 5.41/5.75 thf(fact_7403_and__zero__eq,axiom,
% 5.41/5.75 ! [A: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ A @ zero_zero_nat )
% 5.41/5.75 = zero_zero_nat ) ).
% 5.41/5.75
% 5.41/5.75 % and_zero_eq
% 5.41/5.75 thf(fact_7404_zero__and__eq,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ A )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % zero_and_eq
% 5.41/5.75 thf(fact_7405_zero__and__eq,axiom,
% 5.41/5.75 ! [A: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ zero_zero_nat @ A )
% 5.41/5.75 = zero_zero_nat ) ).
% 5.41/5.75
% 5.41/5.75 % zero_and_eq
% 5.41/5.75 thf(fact_7406_bit_Oconj__zero__left,axiom,
% 5.41/5.75 ! [X: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ zero_zero_int @ X )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % bit.conj_zero_left
% 5.41/5.75 thf(fact_7407_bit_Oconj__zero__right,axiom,
% 5.41/5.75 ! [X: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ X @ zero_zero_int )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % bit.conj_zero_right
% 5.41/5.75 thf(fact_7408_take__bit__and,axiom,
% 5.41/5.75 ! [N: nat,A: int,B: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.41/5.75 = ( bit_se725231765392027082nd_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_and
% 5.41/5.75 thf(fact_7409_take__bit__and,axiom,
% 5.41/5.75 ! [N: nat,A: nat,B: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.41/5.75 = ( bit_se727722235901077358nd_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_and
% 5.41/5.75 thf(fact_7410_exp__le__cancel__iff,axiom,
% 5.41/5.75 ! [X: real,Y: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.41/5.75 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_le_cancel_iff
% 5.41/5.75 thf(fact_7411_concat__bit__of__zero__2,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( bit_concat_bit @ N @ K @ zero_zero_int )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.41/5.75
% 5.41/5.75 % concat_bit_of_zero_2
% 5.41/5.75 thf(fact_7412_take__bit__0,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ zero_zero_nat @ A )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_0
% 5.41/5.75 thf(fact_7413_take__bit__0,axiom,
% 5.41/5.75 ! [A: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ zero_zero_nat @ A )
% 5.41/5.75 = zero_zero_nat ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_0
% 5.41/5.75 thf(fact_7414_exp__zero,axiom,
% 5.41/5.75 ( ( exp_complex @ zero_zero_complex )
% 5.41/5.75 = one_one_complex ) ).
% 5.41/5.75
% 5.41/5.75 % exp_zero
% 5.41/5.75 thf(fact_7415_exp__zero,axiom,
% 5.41/5.75 ( ( exp_real @ zero_zero_real )
% 5.41/5.75 = one_one_real ) ).
% 5.41/5.75
% 5.41/5.75 % exp_zero
% 5.41/5.75 thf(fact_7416_take__bit__Suc__1,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ one_one_int )
% 5.41/5.75 = one_one_int ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_1
% 5.41/5.75 thf(fact_7417_take__bit__Suc__1,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ one_one_nat )
% 5.41/5.75 = one_one_nat ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_1
% 5.41/5.75 thf(fact_7418_and_Oleft__neutral,axiom,
% 5.41/5.75 ! [A: code_integer] :
% 5.41/5.75 ( ( bit_se3949692690581998587nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ A )
% 5.41/5.75 = A ) ).
% 5.41/5.75
% 5.41/5.75 % and.left_neutral
% 5.41/5.75 thf(fact_7419_and_Oleft__neutral,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ one_one_int ) @ A )
% 5.41/5.75 = A ) ).
% 5.41/5.75
% 5.41/5.75 % and.left_neutral
% 5.41/5.75 thf(fact_7420_and_Oright__neutral,axiom,
% 5.41/5.75 ! [A: code_integer] :
% 5.41/5.75 ( ( bit_se3949692690581998587nteger @ A @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.75 = A ) ).
% 5.41/5.75
% 5.41/5.75 % and.right_neutral
% 5.41/5.75 thf(fact_7421_and_Oright__neutral,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ A @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 = A ) ).
% 5.41/5.75
% 5.41/5.75 % and.right_neutral
% 5.41/5.75 thf(fact_7422_bit_Oconj__one__right,axiom,
% 5.41/5.75 ! [X: code_integer] :
% 5.41/5.75 ( ( bit_se3949692690581998587nteger @ X @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.75 = X ) ).
% 5.41/5.75
% 5.41/5.75 % bit.conj_one_right
% 5.41/5.75 thf(fact_7423_bit_Oconj__one__right,axiom,
% 5.41/5.75 ! [X: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ X @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 = X ) ).
% 5.41/5.75
% 5.41/5.75 % bit.conj_one_right
% 5.41/5.75 thf(fact_7424_take__bit__numeral__1,axiom,
% 5.41/5.75 ! [L2: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ one_one_int )
% 5.41/5.75 = one_one_int ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_1
% 5.41/5.75 thf(fact_7425_take__bit__numeral__1,axiom,
% 5.41/5.75 ! [L2: num] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ one_one_nat )
% 5.41/5.75 = one_one_nat ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_1
% 5.41/5.75 thf(fact_7426_exp__eq__one__iff,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ( exp_real @ X )
% 5.41/5.75 = one_one_real )
% 5.41/5.75 = ( X = zero_zero_real ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_eq_one_iff
% 5.41/5.75 thf(fact_7427_and__nonnegative__int__iff,axiom,
% 5.41/5.75 ! [K: int,L2: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.41/5.75 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.75 | ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_nonnegative_int_iff
% 5.41/5.75 thf(fact_7428_and__negative__int__iff,axiom,
% 5.41/5.75 ! [K: int,L2: int] :
% 5.41/5.75 ( ( ord_less_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ zero_zero_int )
% 5.41/5.75 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.75 & ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_negative_int_iff
% 5.41/5.75 thf(fact_7429_take__bit__of__1__eq__0__iff,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.41/5.75 = zero_zero_int )
% 5.41/5.75 = ( N = zero_zero_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_1_eq_0_iff
% 5.41/5.75 thf(fact_7430_take__bit__of__1__eq__0__iff,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.41/5.75 = zero_zero_nat )
% 5.41/5.75 = ( N = zero_zero_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_1_eq_0_iff
% 5.41/5.75 thf(fact_7431_and__numerals_I2_J,axiom,
% 5.41/5.75 ! [Y: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.41/5.75 = one_one_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(2)
% 5.41/5.75 thf(fact_7432_and__numerals_I2_J,axiom,
% 5.41/5.75 ! [Y: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.41/5.75 = one_one_nat ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(2)
% 5.41/5.75 thf(fact_7433_and__numerals_I8_J,axiom,
% 5.41/5.75 ! [X: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ one_one_int )
% 5.41/5.75 = one_one_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(8)
% 5.41/5.75 thf(fact_7434_and__numerals_I8_J,axiom,
% 5.41/5.75 ! [X: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ one_one_nat )
% 5.41/5.75 = one_one_nat ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(8)
% 5.41/5.75 thf(fact_7435_one__less__exp__iff,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_real @ one_one_real @ ( exp_real @ X ) )
% 5.41/5.75 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % one_less_exp_iff
% 5.41/5.75 thf(fact_7436_exp__less__one__iff,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_real @ ( exp_real @ X ) @ one_one_real )
% 5.41/5.75 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_less_one_iff
% 5.41/5.75 thf(fact_7437_exp__le__one__iff,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ ( exp_real @ X ) @ one_one_real )
% 5.41/5.75 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_le_one_iff
% 5.41/5.75 thf(fact_7438_one__le__exp__iff,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ one_one_real @ ( exp_real @ X ) )
% 5.41/5.75 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % one_le_exp_iff
% 5.41/5.75 thf(fact_7439_take__bit__minus__one__eq__mask,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ N @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.75 = ( bit_se2119862282449309892nteger @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_minus_one_eq_mask
% 5.41/5.75 thf(fact_7440_take__bit__minus__one__eq__mask,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_minus_one_eq_mask
% 5.41/5.75 thf(fact_7441_exp__ln,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.75 => ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.41/5.75 = X ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_ln
% 5.41/5.75 thf(fact_7442_exp__ln__iff,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ( exp_real @ ( ln_ln_real @ X ) )
% 5.41/5.75 = X )
% 5.41/5.75 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_ln_iff
% 5.41/5.75 thf(fact_7443_take__bit__of__Suc__0,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.75 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_Suc_0
% 5.41/5.75 thf(fact_7444_and__numerals_I1_J,axiom,
% 5.41/5.75 ! [Y: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(1)
% 5.41/5.75 thf(fact_7445_and__numerals_I1_J,axiom,
% 5.41/5.75 ! [Y: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.41/5.75 = zero_zero_nat ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(1)
% 5.41/5.75 thf(fact_7446_and__numerals_I5_J,axiom,
% 5.41/5.75 ! [X: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ one_one_int )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(5)
% 5.41/5.75 thf(fact_7447_and__numerals_I5_J,axiom,
% 5.41/5.75 ! [X: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ one_one_nat )
% 5.41/5.75 = zero_zero_nat ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(5)
% 5.41/5.75 thf(fact_7448_and__numerals_I3_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.41/5.75 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(3)
% 5.41/5.75 thf(fact_7449_and__numerals_I3_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.41/5.75 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(3)
% 5.41/5.75 thf(fact_7450_sum_Ocl__ivl__Suc,axiom,
% 5.41/5.75 ! [N: nat,M: nat,G: nat > complex] :
% 5.41/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = zero_zero_complex ) )
% 5.41/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_complex @ ( groups2073611262835488442omplex @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.cl_ivl_Suc
% 5.41/5.75 thf(fact_7451_sum_Ocl__ivl__Suc,axiom,
% 5.41/5.75 ! [N: nat,M: nat,G: nat > rat] :
% 5.41/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = zero_zero_rat ) )
% 5.41/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.cl_ivl_Suc
% 5.41/5.75 thf(fact_7452_sum_Ocl__ivl__Suc,axiom,
% 5.41/5.75 ! [N: nat,M: nat,G: nat > int] :
% 5.41/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.cl_ivl_Suc
% 5.41/5.75 thf(fact_7453_sum_Ocl__ivl__Suc,axiom,
% 5.41/5.75 ! [N: nat,M: nat,G: nat > nat] :
% 5.41/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.cl_ivl_Suc
% 5.41/5.75 thf(fact_7454_sum_Ocl__ivl__Suc,axiom,
% 5.41/5.75 ! [N: nat,M: nat,G: nat > real] :
% 5.41/5.75 ( ( ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = zero_zero_real ) )
% 5.41/5.75 & ( ~ ( ord_less_nat @ ( suc @ N ) @ M )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.cl_ivl_Suc
% 5.41/5.75 thf(fact_7455_take__bit__of__1,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ N @ one_one_Code_integer )
% 5.41/5.75 = ( zero_n356916108424825756nteger @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_1
% 5.41/5.75 thf(fact_7456_take__bit__of__1,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ one_one_int )
% 5.41/5.75 = ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_1
% 5.41/5.75 thf(fact_7457_take__bit__of__1,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ N @ one_one_nat )
% 5.41/5.75 = ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_1
% 5.41/5.75 thf(fact_7458_and__minus__numerals_I6_J,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.41/5.75 = one_one_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_minus_numerals(6)
% 5.41/5.75 thf(fact_7459_and__minus__numerals_I2_J,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.75 = one_one_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_minus_numerals(2)
% 5.41/5.75 thf(fact_7460_sum__zero__power,axiom,
% 5.41/5.75 ! [A2: set_nat,C: nat > complex] :
% 5.41/5.75 ( ( ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex
% 5.41/5.75 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( C @ zero_zero_nat ) ) )
% 5.41/5.75 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex
% 5.41/5.75 @ ^ [I5: nat] : ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = zero_zero_complex ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_zero_power
% 5.41/5.75 thf(fact_7461_sum__zero__power,axiom,
% 5.41/5.75 ! [A2: set_nat,C: nat > rat] :
% 5.41/5.75 ( ( ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( C @ zero_zero_nat ) ) )
% 5.41/5.75 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = zero_zero_rat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_zero_power
% 5.41/5.75 thf(fact_7462_sum__zero__power,axiom,
% 5.41/5.75 ! [A2: set_nat,C: nat > real] :
% 5.41/5.75 ( ( ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( C @ zero_zero_nat ) ) )
% 5.41/5.75 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = zero_zero_real ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_zero_power
% 5.41/5.75 thf(fact_7463_and__numerals_I4_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.41/5.75 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(4)
% 5.41/5.75 thf(fact_7464_and__numerals_I4_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.41/5.75 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(4)
% 5.41/5.75 thf(fact_7465_and__numerals_I6_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit0 @ Y ) ) )
% 5.41/5.75 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(6)
% 5.41/5.75 thf(fact_7466_and__numerals_I6_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.41/5.75 = ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(6)
% 5.41/5.75 thf(fact_7467_even__take__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,A: code_integer] :
% 5.41/5.75 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se1745604003318907178nteger @ N @ A ) )
% 5.41/5.75 = ( ( N = zero_zero_nat )
% 5.41/5.75 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % even_take_bit_eq
% 5.41/5.75 thf(fact_7468_even__take__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,A: int] :
% 5.41/5.75 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.41/5.75 = ( ( N = zero_zero_nat )
% 5.41/5.75 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % even_take_bit_eq
% 5.41/5.75 thf(fact_7469_even__take__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,A: nat] :
% 5.41/5.75 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se2925701944663578781it_nat @ N @ A ) )
% 5.41/5.75 = ( ( N = zero_zero_nat )
% 5.41/5.75 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % even_take_bit_eq
% 5.41/5.75 thf(fact_7470_and__minus__numerals_I1_J,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_minus_numerals(1)
% 5.41/5.75 thf(fact_7471_and__minus__numerals_I5_J,axiom,
% 5.41/5.75 ! [N: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.41/5.75 = zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % and_minus_numerals(5)
% 5.41/5.75 thf(fact_7472_sum__zero__power_H,axiom,
% 5.41/5.75 ! [A2: set_nat,C: nat > complex,D: nat > complex] :
% 5.41/5.75 ( ( ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex
% 5.41/5.75 @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( divide1717551699836669952omplex @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.41/5.75 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2073611262835488442omplex
% 5.41/5.75 @ ^ [I5: nat] : ( divide1717551699836669952omplex @ ( times_times_complex @ ( C @ I5 ) @ ( power_power_complex @ zero_zero_complex @ I5 ) ) @ ( D @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = zero_zero_complex ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_zero_power'
% 5.41/5.75 thf(fact_7473_sum__zero__power_H,axiom,
% 5.41/5.75 ! [A2: set_nat,C: nat > rat,D: nat > rat] :
% 5.41/5.75 ( ( ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( divide_divide_rat @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.41/5.75 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( divide_divide_rat @ ( times_times_rat @ ( C @ I5 ) @ ( power_power_rat @ zero_zero_rat @ I5 ) ) @ ( D @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = zero_zero_rat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_zero_power'
% 5.41/5.75 thf(fact_7474_sum__zero__power_H,axiom,
% 5.41/5.75 ! [A2: set_nat,C: nat > real,D: nat > real] :
% 5.41/5.75 ( ( ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( divide_divide_real @ ( C @ zero_zero_nat ) @ ( D @ zero_zero_nat ) ) ) )
% 5.41/5.75 & ( ~ ( ( finite_finite_nat @ A2 )
% 5.41/5.75 & ( member_nat @ zero_zero_nat @ A2 ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( divide_divide_real @ ( times_times_real @ ( C @ I5 ) @ ( power_power_real @ zero_zero_real @ I5 ) ) @ ( D @ I5 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = zero_zero_real ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_zero_power'
% 5.41/5.75 thf(fact_7475_take__bit__Suc__0,axiom,
% 5.41/5.75 ! [A: code_integer] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ ( suc @ zero_zero_nat ) @ A )
% 5.41/5.75 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_0
% 5.41/5.75 thf(fact_7476_take__bit__Suc__0,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( suc @ zero_zero_nat ) @ A )
% 5.41/5.75 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_0
% 5.41/5.75 thf(fact_7477_take__bit__Suc__0,axiom,
% 5.41/5.75 ! [A: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( suc @ zero_zero_nat ) @ A )
% 5.41/5.75 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_0
% 5.41/5.75 thf(fact_7478_and__numerals_I7_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ X ) ) @ ( numeral_numeral_int @ ( bit1 @ Y ) ) )
% 5.41/5.75 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ X ) @ ( numeral_numeral_int @ Y ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(7)
% 5.41/5.75 thf(fact_7479_and__numerals_I7_J,axiom,
% 5.41/5.75 ! [X: num,Y: num] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.41/5.75 = ( plus_plus_nat @ one_one_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ X ) @ ( numeral_numeral_nat @ Y ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_numerals(7)
% 5.41/5.75 thf(fact_7480_take__bit__of__exp,axiom,
% 5.41/5.75 ! [M: nat,N: nat] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ M @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.75 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_nat @ N @ M ) ) @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_exp
% 5.41/5.75 thf(fact_7481_take__bit__of__exp,axiom,
% 5.41/5.75 ! [M: nat,N: nat] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ M @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.75 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_nat @ N @ M ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_exp
% 5.41/5.75 thf(fact_7482_take__bit__of__exp,axiom,
% 5.41/5.75 ! [M: nat,N: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.75 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_nat @ N @ M ) ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_exp
% 5.41/5.75 thf(fact_7483_take__bit__of__2,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ N @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.75 = ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_2
% 5.41/5.75 thf(fact_7484_take__bit__of__2,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.75 = ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_2
% 5.41/5.75 thf(fact_7485_take__bit__of__2,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.75 = ( times_times_nat @ ( zero_n2687167440665602831ol_nat @ ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_2
% 5.41/5.75 thf(fact_7486_take__bit__eq__mask,axiom,
% 5.41/5.75 ( bit_se2923211474154528505it_int
% 5.41/5.75 = ( ^ [N2: nat,A3: int] : ( bit_se725231765392027082nd_int @ A3 @ ( bit_se2000444600071755411sk_int @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_mask
% 5.41/5.75 thf(fact_7487_take__bit__eq__mask,axiom,
% 5.41/5.75 ( bit_se2925701944663578781it_nat
% 5.41/5.75 = ( ^ [N2: nat,A3: nat] : ( bit_se727722235901077358nd_nat @ A3 @ ( bit_se2002935070580805687sk_nat @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_mask
% 5.41/5.75 thf(fact_7488_of__int__and__eq,axiom,
% 5.41/5.75 ! [K: int,L2: int] :
% 5.41/5.75 ( ( ring_1_of_int_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.41/5.75 = ( bit_se725231765392027082nd_int @ ( ring_1_of_int_int @ K ) @ ( ring_1_of_int_int @ L2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % of_int_and_eq
% 5.41/5.75 thf(fact_7489_take__bit__of__int,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( ring_1_of_int_int @ K ) )
% 5.41/5.75 = ( ring_1_of_int_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_of_int
% 5.41/5.75 thf(fact_7490_and_Oassoc,axiom,
% 5.41/5.75 ! [A: int,B: int,C: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ ( bit_se725231765392027082nd_int @ A @ B ) @ C )
% 5.41/5.75 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.assoc
% 5.41/5.75 thf(fact_7491_and_Oassoc,axiom,
% 5.41/5.75 ! [A: nat,B: nat,C: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ ( bit_se727722235901077358nd_nat @ A @ B ) @ C )
% 5.41/5.75 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.assoc
% 5.41/5.75 thf(fact_7492_and_Ocommute,axiom,
% 5.41/5.75 ( bit_se725231765392027082nd_int
% 5.41/5.75 = ( ^ [A3: int,B2: int] : ( bit_se725231765392027082nd_int @ B2 @ A3 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.commute
% 5.41/5.75 thf(fact_7493_and_Ocommute,axiom,
% 5.41/5.75 ( bit_se727722235901077358nd_nat
% 5.41/5.75 = ( ^ [A3: nat,B2: nat] : ( bit_se727722235901077358nd_nat @ B2 @ A3 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.commute
% 5.41/5.75 thf(fact_7494_and_Oleft__commute,axiom,
% 5.41/5.75 ! [B: int,A: int,C: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ B @ ( bit_se725231765392027082nd_int @ A @ C ) )
% 5.41/5.75 = ( bit_se725231765392027082nd_int @ A @ ( bit_se725231765392027082nd_int @ B @ C ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.left_commute
% 5.41/5.75 thf(fact_7495_and_Oleft__commute,axiom,
% 5.41/5.75 ! [B: nat,A: nat,C: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ B @ ( bit_se727722235901077358nd_nat @ A @ C ) )
% 5.41/5.75 = ( bit_se727722235901077358nd_nat @ A @ ( bit_se727722235901077358nd_nat @ B @ C ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and.left_commute
% 5.41/5.75 thf(fact_7496_take__bit__add,axiom,
% 5.41/5.75 ! [N: nat,A: int,B: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N @ A ) @ ( bit_se2923211474154528505it_int @ N @ B ) ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ A @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_add
% 5.41/5.75 thf(fact_7497_take__bit__add,axiom,
% 5.41/5.75 ! [N: nat,A: nat,B: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ ( bit_se2925701944663578781it_nat @ N @ A ) @ ( bit_se2925701944663578781it_nat @ N @ B ) ) )
% 5.41/5.75 = ( bit_se2925701944663578781it_nat @ N @ ( plus_plus_nat @ A @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_add
% 5.41/5.75 thf(fact_7498_take__bit__tightened,axiom,
% 5.41/5.75 ! [N: nat,A: int,B: int,M: nat] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.41/5.75 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ M @ A )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ M @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_tightened
% 5.41/5.75 thf(fact_7499_take__bit__tightened,axiom,
% 5.41/5.75 ! [N: nat,A: nat,B: nat,M: nat] :
% 5.41/5.75 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.41/5.75 = ( bit_se2925701944663578781it_nat @ N @ B ) )
% 5.41/5.75 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ M @ A )
% 5.41/5.75 = ( bit_se2925701944663578781it_nat @ M @ B ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_tightened
% 5.41/5.75 thf(fact_7500_take__bit__tightened__less__eq__nat,axiom,
% 5.41/5.75 ! [M: nat,N: nat,Q2: nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ M @ Q2 ) @ ( bit_se2925701944663578781it_nat @ N @ Q2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_tightened_less_eq_nat
% 5.41/5.75 thf(fact_7501_take__bit__nat__less__eq__self,axiom,
% 5.41/5.75 ! [N: nat,M: nat] : ( ord_less_eq_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_nat_less_eq_self
% 5.41/5.75 thf(fact_7502_exp__not__eq__zero,axiom,
% 5.41/5.75 ! [X: complex] :
% 5.41/5.75 ( ( exp_complex @ X )
% 5.41/5.75 != zero_zero_complex ) ).
% 5.41/5.75
% 5.41/5.75 % exp_not_eq_zero
% 5.41/5.75 thf(fact_7503_exp__not__eq__zero,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( exp_real @ X )
% 5.41/5.75 != zero_zero_real ) ).
% 5.41/5.75
% 5.41/5.75 % exp_not_eq_zero
% 5.41/5.75 thf(fact_7504_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: complex,C: int > int > set_complex,P5: product_prod_int_int] :
% 5.41/5.75 ( ( member_complex @ Z @ ( produc8580519160106071146omplex @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: int,Y5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7505_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: real,C: int > int > set_real,P5: product_prod_int_int] :
% 5.41/5.75 ( ( member_real @ Z @ ( produc6452406959799940328t_real @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: int,Y5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_real @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7506_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: nat,C: int > int > set_nat,P5: product_prod_int_int] :
% 5.41/5.75 ( ( member_nat @ Z @ ( produc4251311855443802252et_nat @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: int,Y5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7507_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: int,C: int > int > set_int,P5: product_prod_int_int] :
% 5.41/5.75 ( ( member_int @ Z @ ( produc73460835934605544et_int @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: int,Y5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_int @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7508_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: set_nat,C: int > int > set_set_nat,P5: product_prod_int_int] :
% 5.41/5.75 ( ( member_set_nat @ Z @ ( produc5233655623923918146et_nat @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: int,Y5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_set_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7509_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: complex,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_complex,P5: produc8763457246119570046nteger] :
% 5.41/5.75 ( ( member_complex @ Z @ ( produc2592262431452330817omplex @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7510_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: real,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_real,P5: produc8763457246119570046nteger] :
% 5.41/5.75 ( ( member_real @ Z @ ( produc815715089573277247t_real @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_real @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7511_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: nat,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_nat,P5: produc8763457246119570046nteger] :
% 5.41/5.75 ( ( member_nat @ Z @ ( produc3558942015123893603et_nat @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_nat @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7512_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: int,C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > set_int,P5: produc8763457246119570046nteger] :
% 5.41/5.75 ( ( member_int @ Z @ ( produc8604463032469472703et_int @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_int @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7513_mem__case__prodE,axiom,
% 5.41/5.75 ! [Z: complex,C: ( int > option6357759511663192854e_term ) > product_prod_int_int > set_complex,P5: produc7773217078559923341nt_int] :
% 5.41/5.75 ( ( member_complex @ Z @ ( produc7959293469001253456omplex @ C @ P5 ) )
% 5.41/5.75 => ~ ! [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc4305682042979456191nt_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( member_complex @ Z @ ( C @ X6 @ Y5 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mem_case_prodE
% 5.41/5.75 thf(fact_7514_take__bit__minus,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_minus
% 5.41/5.75 thf(fact_7515_exp__times__arg__commute,axiom,
% 5.41/5.75 ! [A2: complex] :
% 5.41/5.75 ( ( times_times_complex @ ( exp_complex @ A2 ) @ A2 )
% 5.41/5.75 = ( times_times_complex @ A2 @ ( exp_complex @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_times_arg_commute
% 5.41/5.75 thf(fact_7516_exp__times__arg__commute,axiom,
% 5.41/5.75 ! [A2: real] :
% 5.41/5.75 ( ( times_times_real @ ( exp_real @ A2 ) @ A2 )
% 5.41/5.75 = ( times_times_real @ A2 @ ( exp_real @ A2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_times_arg_commute
% 5.41/5.75 thf(fact_7517_take__bit__mult,axiom,
% 5.41/5.75 ! [N: nat,K: int,L2: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ ( times_times_int @ K @ L2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_mult
% 5.41/5.75 thf(fact_7518_take__bit__diff,axiom,
% 5.41/5.75 ! [N: nat,K: int,L2: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( bit_se2923211474154528505it_int @ N @ L2 ) ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ L2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_diff
% 5.41/5.75 thf(fact_7519_concat__bit__eq__iff,axiom,
% 5.41/5.75 ! [N: nat,K: int,L2: int,R: int,S: int] :
% 5.41/5.75 ( ( ( bit_concat_bit @ N @ K @ L2 )
% 5.41/5.75 = ( bit_concat_bit @ N @ R @ S ) )
% 5.41/5.75 = ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ R ) )
% 5.41/5.75 & ( L2 = S ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % concat_bit_eq_iff
% 5.41/5.75 thf(fact_7520_concat__bit__take__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,B: int] :
% 5.41/5.75 ( ( bit_concat_bit @ N @ ( bit_se2923211474154528505it_int @ N @ B ) )
% 5.41/5.75 = ( bit_concat_bit @ N @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % concat_bit_take_bit_eq
% 5.41/5.75 thf(fact_7521_case__prodE,axiom,
% 5.41/5.75 ! [C: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P5: produc8763457246119570046nteger] :
% 5.41/5.75 ( ( produc127349428274296955eger_o @ C @ P5 )
% 5.41/5.75 => ~ ! [X6: code_integer > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc6137756002093451184nteger @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( C @ X6 @ Y5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodE
% 5.41/5.75 thf(fact_7522_case__prodE,axiom,
% 5.41/5.75 ! [C: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,P5: produc1908205239877642774nteger] :
% 5.41/5.75 ( ( produc6253627499356882019eger_o @ C @ P5 )
% 5.41/5.75 => ~ ! [X6: produc6241069584506657477e_term > option6357759511663192854e_term,Y5: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc8603105652947943368nteger @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( C @ X6 @ Y5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodE
% 5.41/5.75 thf(fact_7523_case__prodE,axiom,
% 5.41/5.75 ! [C: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,P5: produc2285326912895808259nt_int] :
% 5.41/5.75 ( ( produc1573362020775583542_int_o @ C @ P5 )
% 5.41/5.75 => ~ ! [X6: produc8551481072490612790e_term > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc5700946648718959541nt_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( C @ X6 @ Y5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodE
% 5.41/5.75 thf(fact_7524_case__prodE,axiom,
% 5.41/5.75 ! [C: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,P5: produc7773217078559923341nt_int] :
% 5.41/5.75 ( ( produc2558449545302689196_int_o @ C @ P5 )
% 5.41/5.75 => ~ ! [X6: int > option6357759511663192854e_term,Y5: product_prod_int_int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( produc4305682042979456191nt_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( C @ X6 @ Y5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodE
% 5.41/5.75 thf(fact_7525_case__prodE,axiom,
% 5.41/5.75 ! [C: int > int > $o,P5: product_prod_int_int] :
% 5.41/5.75 ( ( produc4947309494688390418_int_o @ C @ P5 )
% 5.41/5.75 => ~ ! [X6: int,Y5: int] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_int_int @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( C @ X6 @ Y5 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodE
% 5.41/5.75 thf(fact_7526_case__prodD,axiom,
% 5.41/5.75 ! [F: ( code_integer > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: code_integer > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( produc127349428274296955eger_o @ F @ ( produc6137756002093451184nteger @ A @ B ) )
% 5.41/5.75 => ( F @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodD
% 5.41/5.75 thf(fact_7527_case__prodD,axiom,
% 5.41/5.75 ! [F: ( produc6241069584506657477e_term > option6357759511663192854e_term ) > produc8923325533196201883nteger > $o,A: produc6241069584506657477e_term > option6357759511663192854e_term,B: produc8923325533196201883nteger] :
% 5.41/5.75 ( ( produc6253627499356882019eger_o @ F @ ( produc8603105652947943368nteger @ A @ B ) )
% 5.41/5.75 => ( F @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodD
% 5.41/5.75 thf(fact_7528_case__prodD,axiom,
% 5.41/5.75 ! [F: ( produc8551481072490612790e_term > option6357759511663192854e_term ) > product_prod_int_int > $o,A: produc8551481072490612790e_term > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.41/5.75 ( ( produc1573362020775583542_int_o @ F @ ( produc5700946648718959541nt_int @ A @ B ) )
% 5.41/5.75 => ( F @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodD
% 5.41/5.75 thf(fact_7529_case__prodD,axiom,
% 5.41/5.75 ! [F: ( int > option6357759511663192854e_term ) > product_prod_int_int > $o,A: int > option6357759511663192854e_term,B: product_prod_int_int] :
% 5.41/5.75 ( ( produc2558449545302689196_int_o @ F @ ( produc4305682042979456191nt_int @ A @ B ) )
% 5.41/5.75 => ( F @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodD
% 5.41/5.75 thf(fact_7530_case__prodD,axiom,
% 5.41/5.75 ! [F: int > int > $o,A: int,B: int] :
% 5.41/5.75 ( ( produc4947309494688390418_int_o @ F @ ( product_Pair_int_int @ A @ B ) )
% 5.41/5.75 => ( F @ A @ B ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodD
% 5.41/5.75 thf(fact_7531_case__prodE_H,axiom,
% 5.41/5.75 ! [C: nat > nat > product_prod_nat_nat > $o,P5: product_prod_nat_nat,Z: product_prod_nat_nat] :
% 5.41/5.75 ( ( produc8739625826339149834_nat_o @ C @ P5 @ Z )
% 5.41/5.75 => ~ ! [X6: nat,Y5: nat] :
% 5.41/5.75 ( ( P5
% 5.41/5.75 = ( product_Pair_nat_nat @ X6 @ Y5 ) )
% 5.41/5.75 => ~ ( C @ X6 @ Y5 @ Z ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodE'
% 5.41/5.75 thf(fact_7532_case__prodD_H,axiom,
% 5.41/5.75 ! [R4: nat > nat > product_prod_nat_nat > $o,A: nat,B: nat,C: product_prod_nat_nat] :
% 5.41/5.75 ( ( produc8739625826339149834_nat_o @ R4 @ ( product_Pair_nat_nat @ A @ B ) @ C )
% 5.41/5.75 => ( R4 @ A @ B @ C ) ) ).
% 5.41/5.75
% 5.41/5.75 % case_prodD'
% 5.41/5.75 thf(fact_7533_and__eq__minus__1__iff,axiom,
% 5.41/5.75 ! [A: code_integer,B: code_integer] :
% 5.41/5.75 ( ( ( bit_se3949692690581998587nteger @ A @ B )
% 5.41/5.75 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.75 = ( ( A
% 5.41/5.75 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.75 & ( B
% 5.41/5.75 = ( uminus1351360451143612070nteger @ one_one_Code_integer ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_eq_minus_1_iff
% 5.41/5.75 thf(fact_7534_and__eq__minus__1__iff,axiom,
% 5.41/5.75 ! [A: int,B: int] :
% 5.41/5.75 ( ( ( bit_se725231765392027082nd_int @ A @ B )
% 5.41/5.75 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 = ( ( A
% 5.41/5.75 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 & ( B
% 5.41/5.75 = ( uminus_uminus_int @ one_one_int ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_eq_minus_1_iff
% 5.41/5.75 thf(fact_7535_not__exp__less__zero,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ~ ( ord_less_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.41/5.75
% 5.41/5.75 % not_exp_less_zero
% 5.41/5.75 thf(fact_7536_exp__gt__zero,axiom,
% 5.41/5.75 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_gt_zero
% 5.41/5.75 thf(fact_7537_exp__total,axiom,
% 5.41/5.75 ! [Y: real] :
% 5.41/5.75 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.75 => ? [X6: real] :
% 5.41/5.75 ( ( exp_real @ X6 )
% 5.41/5.75 = Y ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_total
% 5.41/5.75 thf(fact_7538_exp__ge__zero,axiom,
% 5.41/5.75 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( exp_real @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_ge_zero
% 5.41/5.75 thf(fact_7539_not__exp__le__zero,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ~ ( ord_less_eq_real @ ( exp_real @ X ) @ zero_zero_real ) ).
% 5.41/5.75
% 5.41/5.75 % not_exp_le_zero
% 5.41/5.75 thf(fact_7540_sum__cong__Suc,axiom,
% 5.41/5.75 ! [A2: set_nat,F: nat > nat,G: nat > nat] :
% 5.41/5.75 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ ( suc @ X6 ) @ A2 )
% 5.41/5.75 => ( ( F @ ( suc @ X6 ) )
% 5.41/5.75 = ( G @ ( suc @ X6 ) ) ) )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.41/5.75 = ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_cong_Suc
% 5.41/5.75 thf(fact_7541_sum__cong__Suc,axiom,
% 5.41/5.75 ! [A2: set_nat,F: nat > real,G: nat > real] :
% 5.41/5.75 ( ~ ( member_nat @ zero_zero_nat @ A2 )
% 5.41/5.75 => ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ ( suc @ X6 ) @ A2 )
% 5.41/5.75 => ( ( F @ ( suc @ X6 ) )
% 5.41/5.75 = ( G @ ( suc @ X6 ) ) ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ F @ A2 )
% 5.41/5.75 = ( groups6591440286371151544t_real @ G @ A2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_cong_Suc
% 5.41/5.75 thf(fact_7542_take__bit__tightened__less__eq__int,axiom,
% 5.41/5.75 ! [M: nat,N: nat,K: int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ M @ K ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_tightened_less_eq_int
% 5.41/5.75 thf(fact_7543_AND__upper2_H,axiom,
% 5.41/5.75 ! [Y: int,Z: int,X: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.75 => ( ( ord_less_eq_int @ Y @ Z )
% 5.41/5.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % AND_upper2'
% 5.41/5.75 thf(fact_7544_AND__upper1_H,axiom,
% 5.41/5.75 ! [Y: int,Z: int,Ya: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.75 => ( ( ord_less_eq_int @ Y @ Z )
% 5.41/5.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % AND_upper1'
% 5.41/5.75 thf(fact_7545_AND__upper2,axiom,
% 5.41/5.75 ! [Y: int,X: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Y ) ) ).
% 5.41/5.75
% 5.41/5.75 % AND_upper2
% 5.41/5.75 thf(fact_7546_AND__upper1,axiom,
% 5.41/5.75 ! [X: int,Y: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % AND_upper1
% 5.41/5.75 thf(fact_7547_AND__lower,axiom,
% 5.41/5.75 ! [X: int,Y: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.75 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se725231765392027082nd_int @ X @ Y ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % AND_lower
% 5.41/5.75 thf(fact_7548_signed__take__bit__eq__iff__take__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,A: int,B: int] :
% 5.41/5.75 ( ( ( bit_ri631733984087533419it_int @ N @ A )
% 5.41/5.75 = ( bit_ri631733984087533419it_int @ N @ B ) )
% 5.41/5.75 = ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ ( suc @ N ) @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % signed_take_bit_eq_iff_take_bit_eq
% 5.41/5.75 thf(fact_7549_take__bit__int__less__eq__self__iff,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.41/5.75 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_less_eq_self_iff
% 5.41/5.75 thf(fact_7550_take__bit__nonnegative,axiom,
% 5.41/5.75 ! [N: nat,K: int] : ( ord_less_eq_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_nonnegative
% 5.41/5.75 thf(fact_7551_not__take__bit__negative,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ~ ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ zero_zero_int ) ).
% 5.41/5.75
% 5.41/5.75 % not_take_bit_negative
% 5.41/5.75 thf(fact_7552_take__bit__int__greater__self__iff,axiom,
% 5.41/5.75 ! [K: int,N: nat] :
% 5.41/5.75 ( ( ord_less_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.41/5.75 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_greater_self_iff
% 5.41/5.75 thf(fact_7553_signed__take__bit__take__bit,axiom,
% 5.41/5.75 ! [M: nat,N: nat,A: int] :
% 5.41/5.75 ( ( bit_ri631733984087533419it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) )
% 5.41/5.75 = ( if_int_int @ ( ord_less_eq_nat @ N @ M ) @ ( bit_se2923211474154528505it_int @ N ) @ ( bit_ri631733984087533419it_int @ M ) @ A ) ) ).
% 5.41/5.75
% 5.41/5.75 % signed_take_bit_take_bit
% 5.41/5.75 thf(fact_7554_mult__exp__exp,axiom,
% 5.41/5.75 ! [X: complex,Y: complex] :
% 5.41/5.75 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) )
% 5.41/5.75 = ( exp_complex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mult_exp_exp
% 5.41/5.75 thf(fact_7555_mult__exp__exp,axiom,
% 5.41/5.75 ! [X: real,Y: real] :
% 5.41/5.75 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) )
% 5.41/5.75 = ( exp_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mult_exp_exp
% 5.41/5.75 thf(fact_7556_exp__add__commuting,axiom,
% 5.41/5.75 ! [X: complex,Y: complex] :
% 5.41/5.75 ( ( ( times_times_complex @ X @ Y )
% 5.41/5.75 = ( times_times_complex @ Y @ X ) )
% 5.41/5.75 => ( ( exp_complex @ ( plus_plus_complex @ X @ Y ) )
% 5.41/5.75 = ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_add_commuting
% 5.41/5.75 thf(fact_7557_exp__add__commuting,axiom,
% 5.41/5.75 ! [X: real,Y: real] :
% 5.41/5.75 ( ( ( times_times_real @ X @ Y )
% 5.41/5.75 = ( times_times_real @ Y @ X ) )
% 5.41/5.75 => ( ( exp_real @ ( plus_plus_real @ X @ Y ) )
% 5.41/5.75 = ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_add_commuting
% 5.41/5.75 thf(fact_7558_exp__diff,axiom,
% 5.41/5.75 ! [X: complex,Y: complex] :
% 5.41/5.75 ( ( exp_complex @ ( minus_minus_complex @ X @ Y ) )
% 5.41/5.75 = ( divide1717551699836669952omplex @ ( exp_complex @ X ) @ ( exp_complex @ Y ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_diff
% 5.41/5.75 thf(fact_7559_exp__diff,axiom,
% 5.41/5.75 ! [X: real,Y: real] :
% 5.41/5.75 ( ( exp_real @ ( minus_minus_real @ X @ Y ) )
% 5.41/5.75 = ( divide_divide_real @ ( exp_real @ X ) @ ( exp_real @ Y ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_diff
% 5.41/5.75 thf(fact_7560_take__bit__unset__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,M: nat,A: int] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se4203085406695923979it_int @ M @ A ) )
% 5.41/5.75 = ( bit_se4203085406695923979it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_unset_bit_eq
% 5.41/5.75 thf(fact_7561_take__bit__unset__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,M: nat,A: nat] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.41/5.75 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se4205575877204974255it_nat @ M @ A ) )
% 5.41/5.75 = ( bit_se4205575877204974255it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_unset_bit_eq
% 5.41/5.75 thf(fact_7562_take__bit__set__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,M: nat,A: int] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se7879613467334960850it_int @ M @ A ) )
% 5.41/5.75 = ( bit_se7879613467334960850it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_set_bit_eq
% 5.41/5.75 thf(fact_7563_take__bit__set__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,M: nat,A: nat] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.41/5.75 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se7882103937844011126it_nat @ M @ A ) )
% 5.41/5.75 = ( bit_se7882103937844011126it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_set_bit_eq
% 5.41/5.75 thf(fact_7564_take__bit__flip__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,M: nat,A: int] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ N @ A ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( bit_se2159334234014336723it_int @ M @ A ) )
% 5.41/5.75 = ( bit_se2159334234014336723it_int @ M @ ( bit_se2923211474154528505it_int @ N @ A ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_flip_bit_eq
% 5.41/5.75 thf(fact_7565_take__bit__flip__bit__eq,axiom,
% 5.41/5.75 ! [N: nat,M: nat,A: nat] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.41/5.75 = ( bit_se2925701944663578781it_nat @ N @ A ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ N @ M )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ ( bit_se2161824704523386999it_nat @ M @ A ) )
% 5.41/5.75 = ( bit_se2161824704523386999it_nat @ M @ ( bit_se2925701944663578781it_nat @ N @ A ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_flip_bit_eq
% 5.41/5.75 thf(fact_7566_sum__subtractf__nat,axiom,
% 5.41/5.75 ! [A2: set_complex,G: complex > nat,F: complex > nat] :
% 5.41/5.75 ( ! [X6: complex] :
% 5.41/5.75 ( ( member_complex @ X6 @ A2 )
% 5.41/5.75 => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat
% 5.41/5.75 @ ^ [X3: complex] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_subtractf_nat
% 5.41/5.75 thf(fact_7567_sum__subtractf__nat,axiom,
% 5.41/5.75 ! [A2: set_real,G: real > nat,F: real > nat] :
% 5.41/5.75 ( ! [X6: real] :
% 5.41/5.75 ( ( member_real @ X6 @ A2 )
% 5.41/5.75 => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ( groups1935376822645274424al_nat
% 5.41/5.75 @ ^ [X3: real] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_subtractf_nat
% 5.41/5.75 thf(fact_7568_sum__subtractf__nat,axiom,
% 5.41/5.75 ! [A2: set_set_nat,G: set_nat > nat,F: set_nat > nat] :
% 5.41/5.75 ( ! [X6: set_nat] :
% 5.41/5.75 ( ( member_set_nat @ X6 @ A2 )
% 5.41/5.75 => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ( groups8294997508430121362at_nat
% 5.41/5.75 @ ^ [X3: set_nat] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( groups8294997508430121362at_nat @ G @ A2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_subtractf_nat
% 5.41/5.75 thf(fact_7569_sum__subtractf__nat,axiom,
% 5.41/5.75 ! [A2: set_int,G: int > nat,F: int > nat] :
% 5.41/5.75 ( ! [X6: int] :
% 5.41/5.75 ( ( member_int @ X6 @ A2 )
% 5.41/5.75 => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ( groups4541462559716669496nt_nat
% 5.41/5.75 @ ^ [X3: int] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_subtractf_nat
% 5.41/5.75 thf(fact_7570_sum__subtractf__nat,axiom,
% 5.41/5.75 ! [A2: set_nat,G: nat > nat,F: nat > nat] :
% 5.41/5.75 ( ! [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ A2 )
% 5.41/5.75 => ( ord_less_eq_nat @ ( G @ X6 ) @ ( F @ X6 ) ) )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [X3: nat] : ( minus_minus_nat @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.75 @ A2 )
% 5.41/5.75 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ G @ A2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_subtractf_nat
% 5.41/5.75 thf(fact_7571_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.41/5.75 ! [G: nat > nat,M: nat,N: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.41/5.75 = ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.shift_bounds_cl_Suc_ivl
% 5.41/5.75 thf(fact_7572_sum_Oshift__bounds__cl__Suc__ivl,axiom,
% 5.41/5.75 ! [G: nat > real,M: nat,N: nat] :
% 5.41/5.75 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.41/5.75 = ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.shift_bounds_cl_Suc_ivl
% 5.41/5.75 thf(fact_7573_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.41/5.75 ! [G: nat > nat,M: nat,K: nat,N: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.41/5.75 = ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.shift_bounds_cl_nat_ivl
% 5.41/5.75 thf(fact_7574_sum_Oshift__bounds__cl__nat__ivl,axiom,
% 5.41/5.75 ! [G: nat > real,M: nat,K: nat,N: nat] :
% 5.41/5.75 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ M @ K ) @ ( plus_plus_nat @ N @ K ) ) )
% 5.41/5.75 = ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ I5 @ K ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.shift_bounds_cl_nat_ivl
% 5.41/5.75 thf(fact_7575_sum__eq__Suc0__iff,axiom,
% 5.41/5.75 ! [A2: set_int,F: int > nat] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.41/5.75 = ( suc @ zero_zero_nat ) )
% 5.41/5.75 = ( ? [X3: int] :
% 5.41/5.75 ( ( member_int @ X3 @ A2 )
% 5.41/5.75 & ( ( F @ X3 )
% 5.41/5.75 = ( suc @ zero_zero_nat ) )
% 5.41/5.75 & ! [Y3: int] :
% 5.41/5.75 ( ( member_int @ Y3 @ A2 )
% 5.41/5.75 => ( ( X3 != Y3 )
% 5.41/5.75 => ( ( F @ Y3 )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_eq_Suc0_iff
% 5.41/5.75 thf(fact_7576_sum__eq__Suc0__iff,axiom,
% 5.41/5.75 ! [A2: set_complex,F: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.41/5.75 = ( suc @ zero_zero_nat ) )
% 5.41/5.75 = ( ? [X3: complex] :
% 5.41/5.75 ( ( member_complex @ X3 @ A2 )
% 5.41/5.75 & ( ( F @ X3 )
% 5.41/5.75 = ( suc @ zero_zero_nat ) )
% 5.41/5.75 & ! [Y3: complex] :
% 5.41/5.75 ( ( member_complex @ Y3 @ A2 )
% 5.41/5.75 => ( ( X3 != Y3 )
% 5.41/5.75 => ( ( F @ Y3 )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_eq_Suc0_iff
% 5.41/5.75 thf(fact_7577_sum__eq__Suc0__iff,axiom,
% 5.41/5.75 ! [A2: set_nat,F: nat > nat] :
% 5.41/5.75 ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.41/5.75 = ( suc @ zero_zero_nat ) )
% 5.41/5.75 = ( ? [X3: nat] :
% 5.41/5.75 ( ( member_nat @ X3 @ A2 )
% 5.41/5.75 & ( ( F @ X3 )
% 5.41/5.75 = ( suc @ zero_zero_nat ) )
% 5.41/5.75 & ! [Y3: nat] :
% 5.41/5.75 ( ( member_nat @ Y3 @ A2 )
% 5.41/5.75 => ( ( X3 != Y3 )
% 5.41/5.75 => ( ( F @ Y3 )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_eq_Suc0_iff
% 5.41/5.75 thf(fact_7578_sum__SucD,axiom,
% 5.41/5.75 ! [F: nat > nat,A2: set_nat,N: nat] :
% 5.41/5.75 ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.41/5.75 = ( suc @ N ) )
% 5.41/5.75 => ? [X6: nat] :
% 5.41/5.75 ( ( member_nat @ X6 @ A2 )
% 5.41/5.75 & ( ord_less_nat @ zero_zero_nat @ ( F @ X6 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_SucD
% 5.41/5.75 thf(fact_7579_exp__gt__one,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.75 => ( ord_less_real @ one_one_real @ ( exp_real @ X ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_gt_one
% 5.41/5.75 thf(fact_7580_sum__eq__1__iff,axiom,
% 5.41/5.75 ! [A2: set_int,F: int > nat] :
% 5.41/5.75 ( ( finite_finite_int @ A2 )
% 5.41/5.75 => ( ( ( groups4541462559716669496nt_nat @ F @ A2 )
% 5.41/5.75 = one_one_nat )
% 5.41/5.75 = ( ? [X3: int] :
% 5.41/5.75 ( ( member_int @ X3 @ A2 )
% 5.41/5.75 & ( ( F @ X3 )
% 5.41/5.75 = one_one_nat )
% 5.41/5.75 & ! [Y3: int] :
% 5.41/5.75 ( ( member_int @ Y3 @ A2 )
% 5.41/5.75 => ( ( X3 != Y3 )
% 5.41/5.75 => ( ( F @ Y3 )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_eq_1_iff
% 5.41/5.75 thf(fact_7581_sum__eq__1__iff,axiom,
% 5.41/5.75 ! [A2: set_complex,F: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.75 => ( ( ( groups5693394587270226106ex_nat @ F @ A2 )
% 5.41/5.75 = one_one_nat )
% 5.41/5.75 = ( ? [X3: complex] :
% 5.41/5.75 ( ( member_complex @ X3 @ A2 )
% 5.41/5.75 & ( ( F @ X3 )
% 5.41/5.75 = one_one_nat )
% 5.41/5.75 & ! [Y3: complex] :
% 5.41/5.75 ( ( member_complex @ Y3 @ A2 )
% 5.41/5.75 => ( ( X3 != Y3 )
% 5.41/5.75 => ( ( F @ Y3 )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_eq_1_iff
% 5.41/5.75 thf(fact_7582_sum__eq__1__iff,axiom,
% 5.41/5.75 ! [A2: set_nat,F: nat > nat] :
% 5.41/5.75 ( ( finite_finite_nat @ A2 )
% 5.41/5.75 => ( ( ( groups3542108847815614940at_nat @ F @ A2 )
% 5.41/5.75 = one_one_nat )
% 5.41/5.75 = ( ? [X3: nat] :
% 5.41/5.75 ( ( member_nat @ X3 @ A2 )
% 5.41/5.75 & ( ( F @ X3 )
% 5.41/5.75 = one_one_nat )
% 5.41/5.75 & ! [Y3: nat] :
% 5.41/5.75 ( ( member_nat @ Y3 @ A2 )
% 5.41/5.75 => ( ( X3 != Y3 )
% 5.41/5.75 => ( ( F @ Y3 )
% 5.41/5.75 = zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_eq_1_iff
% 5.41/5.75 thf(fact_7583_take__bit__signed__take__bit,axiom,
% 5.41/5.75 ! [M: nat,N: nat,A: int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ M @ ( bit_ri631733984087533419it_int @ N @ A ) )
% 5.41/5.75 = ( bit_se2923211474154528505it_int @ M @ A ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_signed_take_bit
% 5.41/5.75 thf(fact_7584_exp__ge__add__one__self,axiom,
% 5.41/5.75 ! [X: real] : ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_ge_add_one_self
% 5.41/5.75 thf(fact_7585_and__less__eq,axiom,
% 5.41/5.75 ! [L2: int,K: int] :
% 5.41/5.75 ( ( ord_less_int @ L2 @ zero_zero_int )
% 5.41/5.75 => ( ord_less_eq_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ K ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_less_eq
% 5.41/5.75 thf(fact_7586_AND__upper1_H_H,axiom,
% 5.41/5.75 ! [Y: int,Z: int,Ya: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.75 => ( ( ord_less_int @ Y @ Z )
% 5.41/5.75 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ Y @ Ya ) @ Z ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % AND_upper1''
% 5.41/5.75 thf(fact_7587_AND__upper2_H_H,axiom,
% 5.41/5.75 ! [Y: int,Z: int,X: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.75 => ( ( ord_less_int @ Y @ Z )
% 5.41/5.75 => ( ord_less_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ Z ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % AND_upper2''
% 5.41/5.75 thf(fact_7588_take__bit__eq__mask__iff,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.41/5.75 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.41/5.75 = ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.41/5.75 = zero_zero_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_mask_iff
% 5.41/5.75 thf(fact_7589_exp__minus__inverse,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( times_times_real @ ( exp_real @ X ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) )
% 5.41/5.75 = one_one_real ) ).
% 5.41/5.75
% 5.41/5.75 % exp_minus_inverse
% 5.41/5.75 thf(fact_7590_exp__minus__inverse,axiom,
% 5.41/5.75 ! [X: complex] :
% 5.41/5.75 ( ( times_times_complex @ ( exp_complex @ X ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X ) ) )
% 5.41/5.75 = one_one_complex ) ).
% 5.41/5.75
% 5.41/5.75 % exp_minus_inverse
% 5.41/5.75 thf(fact_7591_take__bit__decr__eq,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.41/5.75 != zero_zero_int )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( minus_minus_int @ K @ one_one_int ) )
% 5.41/5.75 = ( minus_minus_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ one_one_int ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_decr_eq
% 5.41/5.75 thf(fact_7592_sum__power__add,axiom,
% 5.41/5.75 ! [X: complex,M: nat,I6: set_nat] :
% 5.41/5.75 ( ( groups2073611262835488442omplex
% 5.41/5.75 @ ^ [I5: nat] : ( power_power_complex @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 = ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ I6 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_power_add
% 5.41/5.75 thf(fact_7593_sum__power__add,axiom,
% 5.41/5.75 ! [X: rat,M: nat,I6: set_nat] :
% 5.41/5.75 ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( power_power_rat @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 = ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ I6 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_power_add
% 5.41/5.75 thf(fact_7594_sum__power__add,axiom,
% 5.41/5.75 ! [X: int,M: nat,I6: set_nat] :
% 5.41/5.75 ( ( groups3539618377306564664at_int
% 5.41/5.75 @ ^ [I5: nat] : ( power_power_int @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 = ( times_times_int @ ( power_power_int @ X @ M ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ I6 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_power_add
% 5.41/5.75 thf(fact_7595_sum__power__add,axiom,
% 5.41/5.75 ! [X: real,M: nat,I6: set_nat] :
% 5.41/5.75 ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( power_power_real @ X @ ( plus_plus_nat @ M @ I5 ) )
% 5.41/5.75 @ I6 )
% 5.41/5.75 = ( times_times_real @ ( power_power_real @ X @ M ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ I6 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_power_add
% 5.41/5.75 thf(fact_7596_sum_OatLeastAtMost__rev,axiom,
% 5.41/5.75 ! [G: nat > nat,N: nat,M: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.41/5.75 = ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeastAtMost_rev
% 5.41/5.75 thf(fact_7597_sum_OatLeastAtMost__rev,axiom,
% 5.41/5.75 ! [G: nat > real,N: nat,M: nat] :
% 5.41/5.75 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ N @ M ) )
% 5.41/5.75 = ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ ( plus_plus_nat @ M @ N ) @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ N @ M ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeastAtMost_rev
% 5.41/5.75 thf(fact_7598_sum__nth__roots,axiom,
% 5.41/5.75 ! [N: nat,C: complex] :
% 5.41/5.75 ( ( ord_less_nat @ one_one_nat @ N )
% 5.41/5.75 => ( ( groups7754918857620584856omplex
% 5.41/5.75 @ ^ [X3: complex] : X3
% 5.41/5.75 @ ( collect_complex
% 5.41/5.75 @ ^ [Z3: complex] :
% 5.41/5.75 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.75 = C ) ) )
% 5.41/5.75 = zero_zero_complex ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_nth_roots
% 5.41/5.75 thf(fact_7599_sum__roots__unity,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( ord_less_nat @ one_one_nat @ N )
% 5.41/5.75 => ( ( groups7754918857620584856omplex
% 5.41/5.75 @ ^ [X3: complex] : X3
% 5.41/5.75 @ ( collect_complex
% 5.41/5.75 @ ^ [Z3: complex] :
% 5.41/5.75 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.75 = one_one_complex ) ) )
% 5.41/5.75 = zero_zero_complex ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_roots_unity
% 5.41/5.75 thf(fact_7600_even__and__iff,axiom,
% 5.41/5.75 ! [A: code_integer,B: code_integer] :
% 5.41/5.75 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( bit_se3949692690581998587nteger @ A @ B ) )
% 5.41/5.75 = ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 | ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % even_and_iff
% 5.41/5.75 thf(fact_7601_even__and__iff,axiom,
% 5.41/5.75 ! [A: int,B: int] :
% 5.41/5.75 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ A @ B ) )
% 5.41/5.75 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % even_and_iff
% 5.41/5.75 thf(fact_7602_even__and__iff,axiom,
% 5.41/5.75 ! [A: nat,B: nat] :
% 5.41/5.75 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ A @ B ) )
% 5.41/5.75 = ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 | ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % even_and_iff
% 5.41/5.75 thf(fact_7603_sum__diff__nat,axiom,
% 5.41/5.75 ! [B3: set_complex,A2: set_complex,F: complex > nat] :
% 5.41/5.75 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.75 => ( ( ord_le211207098394363844omplex @ B3 @ A2 )
% 5.41/5.75 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( groups5693394587270226106ex_nat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff_nat
% 5.41/5.75 thf(fact_7604_sum__diff__nat,axiom,
% 5.41/5.75 ! [B3: set_int,A2: set_int,F: int > nat] :
% 5.41/5.75 ( ( finite_finite_int @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_int @ B3 @ A2 )
% 5.41/5.75 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( groups4541462559716669496nt_nat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff_nat
% 5.41/5.75 thf(fact_7605_sum__diff__nat,axiom,
% 5.41/5.75 ! [B3: set_nat,A2: set_nat,F: nat > nat] :
% 5.41/5.75 ( ( finite_finite_nat @ B3 )
% 5.41/5.75 => ( ( ord_less_eq_set_nat @ B3 @ A2 )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ B3 ) )
% 5.41/5.75 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( groups3542108847815614940at_nat @ F @ B3 ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_diff_nat
% 5.41/5.75 thf(fact_7606_exp__ge__add__one__self__aux,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.75 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ X ) @ ( exp_real @ X ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_ge_add_one_self_aux
% 5.41/5.75 thf(fact_7607_sum__shift__lb__Suc0__0,axiom,
% 5.41/5.75 ! [F: nat > complex,K: nat] :
% 5.41/5.75 ( ( ( F @ zero_zero_nat )
% 5.41/5.75 = zero_zero_complex )
% 5.41/5.75 => ( ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.41/5.75 = ( groups2073611262835488442omplex @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_shift_lb_Suc0_0
% 5.41/5.75 thf(fact_7608_sum__shift__lb__Suc0__0,axiom,
% 5.41/5.75 ! [F: nat > rat,K: nat] :
% 5.41/5.75 ( ( ( F @ zero_zero_nat )
% 5.41/5.75 = zero_zero_rat )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.41/5.75 = ( groups2906978787729119204at_rat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_shift_lb_Suc0_0
% 5.41/5.75 thf(fact_7609_sum__shift__lb__Suc0__0,axiom,
% 5.41/5.75 ! [F: nat > int,K: nat] :
% 5.41/5.75 ( ( ( F @ zero_zero_nat )
% 5.41/5.75 = zero_zero_int )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.41/5.75 = ( groups3539618377306564664at_int @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_shift_lb_Suc0_0
% 5.41/5.75 thf(fact_7610_sum__shift__lb__Suc0__0,axiom,
% 5.41/5.75 ! [F: nat > nat,K: nat] :
% 5.41/5.75 ( ( ( F @ zero_zero_nat )
% 5.41/5.75 = zero_zero_nat )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.41/5.75 = ( groups3542108847815614940at_nat @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_shift_lb_Suc0_0
% 5.41/5.75 thf(fact_7611_sum__shift__lb__Suc0__0,axiom,
% 5.41/5.75 ! [F: nat > real,K: nat] :
% 5.41/5.75 ( ( ( F @ zero_zero_nat )
% 5.41/5.75 = zero_zero_real )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ K ) )
% 5.41/5.75 = ( groups6591440286371151544t_real @ F @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ K ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_shift_lb_Suc0_0
% 5.41/5.75 thf(fact_7612_even__and__iff__int,axiom,
% 5.41/5.75 ! [K: int,L2: int] :
% 5.41/5.75 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ K @ L2 ) )
% 5.41/5.75 = ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.41/5.75 | ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % even_and_iff_int
% 5.41/5.75 thf(fact_7613_sum_OatLeast0__atMost__Suc,axiom,
% 5.41/5.75 ! [G: nat > rat,N: nat] :
% 5.41/5.75 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast0_atMost_Suc
% 5.41/5.75 thf(fact_7614_sum_OatLeast0__atMost__Suc,axiom,
% 5.41/5.75 ! [G: nat > int,N: nat] :
% 5.41/5.75 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast0_atMost_Suc
% 5.41/5.75 thf(fact_7615_sum_OatLeast0__atMost__Suc,axiom,
% 5.41/5.75 ! [G: nat > nat,N: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast0_atMost_Suc
% 5.41/5.75 thf(fact_7616_sum_OatLeast0__atMost__Suc,axiom,
% 5.41/5.75 ! [G: nat > real,N: nat] :
% 5.41/5.75 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) @ ( G @ ( suc @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast0_atMost_Suc
% 5.41/5.75 thf(fact_7617_lemma__exp__total,axiom,
% 5.41/5.75 ! [Y: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ one_one_real @ Y )
% 5.41/5.75 => ? [X6: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 5.41/5.75 & ( ord_less_eq_real @ X6 @ ( minus_minus_real @ Y @ one_one_real ) )
% 5.41/5.75 & ( ( exp_real @ X6 )
% 5.41/5.75 = Y ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % lemma_exp_total
% 5.41/5.75 thf(fact_7618_sum_OatLeast__Suc__atMost,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > rat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( plus_plus_rat @ ( G @ M ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast_Suc_atMost
% 5.41/5.75 thf(fact_7619_sum_OatLeast__Suc__atMost,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( plus_plus_int @ ( G @ M ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast_Suc_atMost
% 5.41/5.75 thf(fact_7620_sum_OatLeast__Suc__atMost,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( plus_plus_nat @ ( G @ M ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast_Suc_atMost
% 5.41/5.75 thf(fact_7621_sum_OatLeast__Suc__atMost,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > real] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( plus_plus_real @ ( G @ M ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.atLeast_Suc_atMost
% 5.41/5.75 thf(fact_7622_sum_Onat__ivl__Suc_H,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > rat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_rat @ ( G @ ( suc @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.nat_ivl_Suc'
% 5.41/5.75 thf(fact_7623_sum_Onat__ivl__Suc_H,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( G @ ( suc @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.nat_ivl_Suc'
% 5.41/5.75 thf(fact_7624_sum_Onat__ivl__Suc_H,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_nat @ ( G @ ( suc @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.nat_ivl_Suc'
% 5.41/5.75 thf(fact_7625_sum_Onat__ivl__Suc_H,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > real] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_real @ ( G @ ( suc @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.nat_ivl_Suc'
% 5.41/5.75 thf(fact_7626_ln__ge__iff,axiom,
% 5.41/5.75 ! [X: real,Y: real] :
% 5.41/5.75 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.75 => ( ( ord_less_eq_real @ Y @ ( ln_ln_real @ X ) )
% 5.41/5.75 = ( ord_less_eq_real @ ( exp_real @ Y ) @ X ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % ln_ge_iff
% 5.41/5.75 thf(fact_7627_ln__x__over__x__mono,axiom,
% 5.41/5.75 ! [X: real,Y: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ ( exp_real @ one_one_real ) @ X )
% 5.41/5.75 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.75 => ( ord_less_eq_real @ ( divide_divide_real @ ( ln_ln_real @ Y ) @ Y ) @ ( divide_divide_real @ ( ln_ln_real @ X ) @ X ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % ln_x_over_x_mono
% 5.41/5.75 thf(fact_7628_sum_OSuc__reindex__ivl,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > rat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_rat @ ( G @ M )
% 5.41/5.75 @ ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.Suc_reindex_ivl
% 5.41/5.75 thf(fact_7629_sum_OSuc__reindex__ivl,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( G @ M )
% 5.41/5.75 @ ( groups3539618377306564664at_int
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.Suc_reindex_ivl
% 5.41/5.75 thf(fact_7630_sum_OSuc__reindex__ivl,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_nat @ ( G @ M )
% 5.41/5.75 @ ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.Suc_reindex_ivl
% 5.41/5.75 thf(fact_7631_sum_OSuc__reindex__ivl,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > real] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( G @ ( suc @ N ) ) )
% 5.41/5.75 = ( plus_plus_real @ ( G @ M )
% 5.41/5.75 @ ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.Suc_reindex_ivl
% 5.41/5.75 thf(fact_7632_sum__Suc__diff,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > rat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( minus_minus_rat @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_Suc_diff
% 5.41/5.75 thf(fact_7633_sum__Suc__diff,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( groups3539618377306564664at_int
% 5.41/5.75 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( minus_minus_int @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_Suc_diff
% 5.41/5.75 thf(fact_7634_sum__Suc__diff,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > real] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ ( suc @ I5 ) ) @ ( F @ I5 ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( minus_minus_real @ ( F @ ( suc @ N ) ) @ ( F @ M ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_Suc_diff
% 5.41/5.75 thf(fact_7635_take__bit__Suc__bit0,axiom,
% 5.41/5.75 ! [N: nat,K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.41/5.75 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_bit0
% 5.41/5.75 thf(fact_7636_take__bit__Suc__bit0,axiom,
% 5.41/5.75 ! [N: nat,K: num] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.41/5.75 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_bit0
% 5.41/5.75 thf(fact_7637_take__bit__eq__mod,axiom,
% 5.41/5.75 ( bit_se1745604003318907178nteger
% 5.41/5.75 = ( ^ [N2: nat,A3: code_integer] : ( modulo364778990260209775nteger @ A3 @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_mod
% 5.41/5.75 thf(fact_7638_take__bit__eq__mod,axiom,
% 5.41/5.75 ( bit_se2923211474154528505it_int
% 5.41/5.75 = ( ^ [N2: nat,A3: int] : ( modulo_modulo_int @ A3 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_mod
% 5.41/5.75 thf(fact_7639_take__bit__eq__mod,axiom,
% 5.41/5.75 ( bit_se2925701944663578781it_nat
% 5.41/5.75 = ( ^ [N2: nat,A3: nat] : ( modulo_modulo_nat @ A3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_mod
% 5.41/5.75 thf(fact_7640_one__and__eq,axiom,
% 5.41/5.75 ! [A: code_integer] :
% 5.41/5.75 ( ( bit_se3949692690581998587nteger @ one_one_Code_integer @ A )
% 5.41/5.75 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % one_and_eq
% 5.41/5.75 thf(fact_7641_one__and__eq,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ one_one_int @ A )
% 5.41/5.75 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % one_and_eq
% 5.41/5.75 thf(fact_7642_one__and__eq,axiom,
% 5.41/5.75 ! [A: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ one_one_nat @ A )
% 5.41/5.75 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % one_and_eq
% 5.41/5.75 thf(fact_7643_and__one__eq,axiom,
% 5.41/5.75 ! [A: code_integer] :
% 5.41/5.75 ( ( bit_se3949692690581998587nteger @ A @ one_one_Code_integer )
% 5.41/5.75 = ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_one_eq
% 5.41/5.75 thf(fact_7644_and__one__eq,axiom,
% 5.41/5.75 ! [A: int] :
% 5.41/5.75 ( ( bit_se725231765392027082nd_int @ A @ one_one_int )
% 5.41/5.75 = ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_one_eq
% 5.41/5.75 thf(fact_7645_and__one__eq,axiom,
% 5.41/5.75 ! [A: nat] :
% 5.41/5.75 ( ( bit_se727722235901077358nd_nat @ A @ one_one_nat )
% 5.41/5.75 = ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_one_eq
% 5.41/5.75 thf(fact_7646_take__bit__nat__eq__self__iff,axiom,
% 5.41/5.75 ! [N: nat,M: nat] :
% 5.41/5.75 ( ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.41/5.75 = M )
% 5.41/5.75 = ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_nat_eq_self_iff
% 5.41/5.75 thf(fact_7647_take__bit__nat__less__exp,axiom,
% 5.41/5.75 ! [N: nat,M: nat] : ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_nat_less_exp
% 5.41/5.75 thf(fact_7648_take__bit__nat__eq__self,axiom,
% 5.41/5.75 ! [M: nat,N: nat] :
% 5.41/5.75 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ M )
% 5.41/5.75 = M ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_nat_eq_self
% 5.41/5.75 thf(fact_7649_take__bit__nat__def,axiom,
% 5.41/5.75 ( bit_se2925701944663578781it_nat
% 5.41/5.75 = ( ^ [N2: nat,M3: nat] : ( modulo_modulo_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_nat_def
% 5.41/5.75 thf(fact_7650_exp__le,axiom,
% 5.41/5.75 ord_less_eq_real @ ( exp_real @ one_one_real ) @ ( numeral_numeral_real @ ( bit1 @ one ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_le
% 5.41/5.75 thf(fact_7651_take__bit__int__less__exp,axiom,
% 5.41/5.75 ! [N: nat,K: int] : ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_less_exp
% 5.41/5.75 thf(fact_7652_sum_Oub__add__nat,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > rat,P5: nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 5.41/5.75 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.ub_add_nat
% 5.41/5.75 thf(fact_7653_sum_Oub__add__nat,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > int,P5: nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.41/5.75 => ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.ub_add_nat
% 5.41/5.75 thf(fact_7654_sum_Oub__add__nat,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > nat,P5: nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.41/5.75 => ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 5.41/5.75 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.ub_add_nat
% 5.41/5.75 thf(fact_7655_sum_Oub__add__nat,axiom,
% 5.41/5.75 ! [M: nat,N: nat,G: nat > real,P5: nat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ ( plus_plus_nat @ N @ one_one_nat ) )
% 5.41/5.75 => ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ N @ P5 ) ) )
% 5.41/5.75 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ M @ N ) ) @ ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ ( plus_plus_nat @ N @ P5 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.ub_add_nat
% 5.41/5.75 thf(fact_7656_take__bit__int__def,axiom,
% 5.41/5.75 ( bit_se2923211474154528505it_int
% 5.41/5.75 = ( ^ [N2: nat,K2: int] : ( modulo_modulo_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_def
% 5.41/5.75 thf(fact_7657_set__encode__def,axiom,
% 5.41/5.75 ( nat_set_encode
% 5.41/5.75 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % set_encode_def
% 5.41/5.75 thf(fact_7658_tanh__altdef,axiom,
% 5.41/5.75 ( tanh_real
% 5.41/5.75 = ( ^ [X3: real] : ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) @ ( plus_plus_real @ ( exp_real @ X3 ) @ ( exp_real @ ( uminus_uminus_real @ X3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % tanh_altdef
% 5.41/5.75 thf(fact_7659_tanh__altdef,axiom,
% 5.41/5.75 ( tanh_complex
% 5.41/5.75 = ( ^ [X3: complex] : ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) @ ( plus_plus_complex @ ( exp_complex @ X3 ) @ ( exp_complex @ ( uminus1482373934393186551omplex @ X3 ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % tanh_altdef
% 5.41/5.75 thf(fact_7660_num_Osize__gen_I1_J,axiom,
% 5.41/5.75 ( ( size_num @ one )
% 5.41/5.75 = zero_zero_nat ) ).
% 5.41/5.75
% 5.41/5.75 % num.size_gen(1)
% 5.41/5.75 thf(fact_7661_take__bit__eq__0__iff,axiom,
% 5.41/5.75 ! [N: nat,A: code_integer] :
% 5.41/5.75 ( ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.41/5.75 = zero_z3403309356797280102nteger )
% 5.41/5.75 = ( dvd_dvd_Code_integer @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_0_iff
% 5.41/5.75 thf(fact_7662_take__bit__eq__0__iff,axiom,
% 5.41/5.75 ! [N: nat,A: int] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.41/5.75 = zero_zero_int )
% 5.41/5.75 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_0_iff
% 5.41/5.75 thf(fact_7663_take__bit__eq__0__iff,axiom,
% 5.41/5.75 ! [N: nat,A: nat] :
% 5.41/5.75 ( ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.41/5.75 = zero_zero_nat )
% 5.41/5.75 = ( dvd_dvd_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ A ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_0_iff
% 5.41/5.75 thf(fact_7664_Divides_Oadjust__div__def,axiom,
% 5.41/5.75 ( adjust_div
% 5.41/5.75 = ( produc8211389475949308722nt_int
% 5.41/5.75 @ ^ [Q5: int,R5: int] : ( plus_plus_int @ Q5 @ ( zero_n2684676970156552555ol_int @ ( R5 != zero_zero_int ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % Divides.adjust_div_def
% 5.41/5.75 thf(fact_7665_take__bit__numeral__bit0,axiom,
% 5.41/5.75 ! [L2: num,K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit0 @ K ) ) )
% 5.41/5.75 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_bit0
% 5.41/5.75 thf(fact_7666_take__bit__numeral__bit0,axiom,
% 5.41/5.75 ! [L2: num,K: num] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit0 @ K ) ) )
% 5.41/5.75 = ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_bit0
% 5.41/5.75 thf(fact_7667_take__bit__nat__less__self__iff,axiom,
% 5.41/5.75 ! [N: nat,M: nat] :
% 5.41/5.75 ( ( ord_less_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) @ M )
% 5.41/5.75 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_nat_less_self_iff
% 5.41/5.75 thf(fact_7668_exp__half__le2,axiom,
% 5.41/5.75 ord_less_eq_real @ ( exp_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_half_le2
% 5.41/5.75 thf(fact_7669_take__bit__Suc__minus__bit0,axiom,
% 5.41/5.75 ! [N: nat,K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.41/5.75 = ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_minus_bit0
% 5.41/5.75 thf(fact_7670_take__bit__int__less__self__iff,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ord_less_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ K )
% 5.41/5.75 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_less_self_iff
% 5.41/5.75 thf(fact_7671_take__bit__int__greater__eq__self__iff,axiom,
% 5.41/5.75 ! [K: int,N: nat] :
% 5.41/5.75 ( ( ord_less_eq_int @ K @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.41/5.75 = ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_greater_eq_self_iff
% 5.41/5.75 thf(fact_7672_exp__double,axiom,
% 5.41/5.75 ! [Z: complex] :
% 5.41/5.75 ( ( exp_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ Z ) )
% 5.41/5.75 = ( power_power_complex @ ( exp_complex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_double
% 5.41/5.75 thf(fact_7673_exp__double,axiom,
% 5.41/5.75 ! [Z: real] :
% 5.41/5.75 ( ( exp_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ Z ) )
% 5.41/5.75 = ( power_power_real @ ( exp_real @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_double
% 5.41/5.75 thf(fact_7674_sum__natinterval__diff,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > complex] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups2073611262835488442omplex
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( minus_minus_complex @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups2073611262835488442omplex
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_complex @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = zero_zero_complex ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_natinterval_diff
% 5.41/5.75 thf(fact_7675_sum__natinterval__diff,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > rat] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( minus_minus_rat @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = zero_zero_rat ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_natinterval_diff
% 5.41/5.75 thf(fact_7676_sum__natinterval__diff,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > int] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups3539618377306564664at_int
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( minus_minus_int @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups3539618377306564664at_int
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = zero_zero_int ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_natinterval_diff
% 5.41/5.75 thf(fact_7677_sum__natinterval__diff,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > real] :
% 5.41/5.75 ( ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( minus_minus_real @ ( F @ M ) @ ( F @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) )
% 5.41/5.75 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( plus_plus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = zero_zero_real ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_natinterval_diff
% 5.41/5.75 thf(fact_7678_sum__telescope_H_H,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > rat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_rat @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.41/5.75 = ( minus_minus_rat @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_telescope''
% 5.41/5.75 thf(fact_7679_sum__telescope_H_H,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups3539618377306564664at_int
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_int @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.41/5.75 = ( minus_minus_int @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_telescope''
% 5.41/5.75 thf(fact_7680_sum__telescope_H_H,axiom,
% 5.41/5.75 ! [M: nat,N: nat,F: nat > real] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [K2: nat] : ( minus_minus_real @ ( F @ K2 ) @ ( F @ ( minus_minus_nat @ K2 @ one_one_nat ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.41/5.75 = ( minus_minus_real @ ( F @ N ) @ ( F @ M ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_telescope''
% 5.41/5.75 thf(fact_7681_take__bit__int__eq__self__iff,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.41/5.75 = K )
% 5.41/5.75 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.75 & ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_eq_self_iff
% 5.41/5.75 thf(fact_7682_take__bit__int__eq__self,axiom,
% 5.41/5.75 ! [K: int,N: nat] :
% 5.41/5.75 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.75 => ( ( ord_less_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.41/5.75 = K ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_eq_self
% 5.41/5.75 thf(fact_7683_take__bit__numeral__minus__bit0,axiom,
% 5.41/5.75 ! [L2: num,K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.41/5.75 = ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_minus_bit0
% 5.41/5.75 thf(fact_7684_take__bit__incr__eq,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.41/5.75 != ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( plus_plus_int @ K @ one_one_int ) )
% 5.41/5.75 = ( plus_plus_int @ one_one_int @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_incr_eq
% 5.41/5.75 thf(fact_7685_divmod__nat__def,axiom,
% 5.41/5.75 ( divmod_nat
% 5.41/5.75 = ( ^ [M3: nat,N2: nat] : ( product_Pair_nat_nat @ ( divide_divide_nat @ M3 @ N2 ) @ ( modulo_modulo_nat @ M3 @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % divmod_nat_def
% 5.41/5.75 thf(fact_7686_take__bit__eq__mask__iff__exp__dvd,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ( bit_se2923211474154528505it_int @ N @ K )
% 5.41/5.75 = ( bit_se2000444600071755411sk_int @ N ) )
% 5.41/5.75 = ( dvd_dvd_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( plus_plus_int @ K @ one_one_int ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_eq_mask_iff_exp_dvd
% 5.41/5.75 thf(fact_7687_mask__eq__sum__exp,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int )
% 5.41/5.75 = ( groups3539618377306564664at_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.75 @ ( collect_nat
% 5.41/5.75 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_eq_sum_exp
% 5.41/5.75 thf(fact_7688_mask__eq__sum__exp,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat )
% 5.41/5.75 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.75 @ ( collect_nat
% 5.41/5.75 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_eq_sum_exp
% 5.41/5.75 thf(fact_7689_sum__gp__multiplied,axiom,
% 5.41/5.75 ! [M: nat,N: nat,X: complex] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.41/5.75 = ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_gp_multiplied
% 5.41/5.75 thf(fact_7690_sum__gp__multiplied,axiom,
% 5.41/5.75 ! [M: nat,N: nat,X: rat] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.41/5.75 = ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_gp_multiplied
% 5.41/5.75 thf(fact_7691_sum__gp__multiplied,axiom,
% 5.41/5.75 ! [M: nat,N: nat,X: int] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.41/5.75 = ( minus_minus_int @ ( power_power_int @ X @ M ) @ ( power_power_int @ X @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_gp_multiplied
% 5.41/5.75 thf(fact_7692_sum__gp__multiplied,axiom,
% 5.41/5.75 ! [M: nat,N: nat,X: real] :
% 5.41/5.75 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.75 => ( ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) )
% 5.41/5.75 = ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum_gp_multiplied
% 5.41/5.75 thf(fact_7693_sum_Oin__pairs,axiom,
% 5.41/5.75 ! [G: nat > rat,M: nat,N: nat] :
% 5.41/5.75 ( ( groups2906978787729119204at_rat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.41/5.75 = ( groups2906978787729119204at_rat
% 5.41/5.75 @ ^ [I5: nat] : ( plus_plus_rat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.in_pairs
% 5.41/5.75 thf(fact_7694_sum_Oin__pairs,axiom,
% 5.41/5.75 ! [G: nat > int,M: nat,N: nat] :
% 5.41/5.75 ( ( groups3539618377306564664at_int @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.41/5.75 = ( groups3539618377306564664at_int
% 5.41/5.75 @ ^ [I5: nat] : ( plus_plus_int @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.in_pairs
% 5.41/5.75 thf(fact_7695_sum_Oin__pairs,axiom,
% 5.41/5.75 ! [G: nat > nat,M: nat,N: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.41/5.75 = ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [I5: nat] : ( plus_plus_nat @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.in_pairs
% 5.41/5.75 thf(fact_7696_sum_Oin__pairs,axiom,
% 5.41/5.75 ! [G: nat > real,M: nat,N: nat] :
% 5.41/5.75 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) )
% 5.41/5.75 = ( groups6591440286371151544t_real
% 5.41/5.75 @ ^ [I5: nat] : ( plus_plus_real @ ( G @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) @ ( G @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) ) ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % sum.in_pairs
% 5.41/5.75 thf(fact_7697_take__bit__Suc__minus__1__eq,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.75 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_Code_integer ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_minus_1_eq
% 5.41/5.75 thf(fact_7698_take__bit__Suc__minus__1__eq,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N ) ) @ one_one_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_minus_1_eq
% 5.41/5.75 thf(fact_7699_take__bit__Suc__bit1,axiom,
% 5.41/5.75 ! [N: nat,K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_bit1
% 5.41/5.75 thf(fact_7700_take__bit__Suc__bit1,axiom,
% 5.41/5.75 ! [N: nat,K: num] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.41/5.75 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc_bit1
% 5.41/5.75 thf(fact_7701_take__bit__numeral__minus__1__eq,axiom,
% 5.41/5.75 ! [K: num] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ ( numeral_numeral_nat @ K ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.75 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_Code_integer ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_minus_1_eq
% 5.41/5.75 thf(fact_7702_take__bit__numeral__minus__1__eq,axiom,
% 5.41/5.75 ! [K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ K ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.75 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ K ) ) @ one_one_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_minus_1_eq
% 5.41/5.75 thf(fact_7703_take__bit__Suc,axiom,
% 5.41/5.75 ! [N: nat,A: code_integer] :
% 5.41/5.75 ( ( bit_se1745604003318907178nteger @ ( suc @ N ) @ A )
% 5.41/5.75 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( bit_se1745604003318907178nteger @ N @ ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( modulo364778990260209775nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc
% 5.41/5.75 thf(fact_7704_take__bit__Suc,axiom,
% 5.41/5.75 ! [N: nat,A: int] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ A )
% 5.41/5.75 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc
% 5.41/5.75 thf(fact_7705_take__bit__Suc,axiom,
% 5.41/5.75 ! [N: nat,A: nat] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( suc @ N ) @ A )
% 5.41/5.75 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ N @ ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_Suc
% 5.41/5.75 thf(fact_7706_exp__bound,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.75 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.75 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_bound
% 5.41/5.75 thf(fact_7707_take__bit__int__less__eq,axiom,
% 5.41/5.75 ! [N: nat,K: int] :
% 5.41/5.75 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K )
% 5.41/5.75 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.75 => ( ord_less_eq_int @ ( bit_se2923211474154528505it_int @ N @ K ) @ ( minus_minus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_less_eq
% 5.41/5.75 thf(fact_7708_take__bit__int__greater__eq,axiom,
% 5.41/5.75 ! [K: int,N: nat] :
% 5.41/5.75 ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.75 => ( ord_less_eq_int @ ( plus_plus_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_int_greater_eq
% 5.41/5.75 thf(fact_7709_signed__take__bit__eq__take__bit__shift,axiom,
% 5.41/5.75 ( bit_ri631733984087533419it_int
% 5.41/5.75 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ ( plus_plus_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % signed_take_bit_eq_take_bit_shift
% 5.41/5.75 thf(fact_7710_mask__eq__sum__exp__nat,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.75 = ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.75 @ ( collect_nat
% 5.41/5.75 @ ^ [Q5: nat] : ( ord_less_nat @ Q5 @ N ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % mask_eq_sum_exp_nat
% 5.41/5.75 thf(fact_7711_and__int__rec,axiom,
% 5.41/5.75 ( bit_se725231765392027082nd_int
% 5.41/5.75 = ( ^ [K2: int,L: int] :
% 5.41/5.75 ( plus_plus_int
% 5.41/5.75 @ ( zero_n2684676970156552555ol_int
% 5.41/5.75 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.41/5.75 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.41/5.75 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_int_rec
% 5.41/5.75 thf(fact_7712_stable__imp__take__bit__eq,axiom,
% 5.41/5.75 ! [A: code_integer,N: nat] :
% 5.41/5.75 ( ( ( divide6298287555418463151nteger @ A @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.75 = A )
% 5.41/5.75 => ( ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.41/5.75 = zero_z3403309356797280102nteger ) )
% 5.41/5.75 & ( ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 => ( ( bit_se1745604003318907178nteger @ N @ A )
% 5.41/5.75 = ( minus_8373710615458151222nteger @ ( power_8256067586552552935nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ N ) @ one_one_Code_integer ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % stable_imp_take_bit_eq
% 5.41/5.75 thf(fact_7713_stable__imp__take__bit__eq,axiom,
% 5.41/5.75 ! [A: int,N: nat] :
% 5.41/5.75 ( ( ( divide_divide_int @ A @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.75 = A )
% 5.41/5.75 => ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.41/5.75 = zero_zero_int ) )
% 5.41/5.75 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ A )
% 5.41/5.75 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ one_one_int ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % stable_imp_take_bit_eq
% 5.41/5.75 thf(fact_7714_stable__imp__take__bit__eq,axiom,
% 5.41/5.75 ! [A: nat,N: nat] :
% 5.41/5.75 ( ( ( divide_divide_nat @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.75 = A )
% 5.41/5.75 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.41/5.75 = zero_zero_nat ) )
% 5.41/5.75 & ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A )
% 5.41/5.75 => ( ( bit_se2925701944663578781it_nat @ N @ A )
% 5.41/5.75 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % stable_imp_take_bit_eq
% 5.41/5.75 thf(fact_7715_gauss__sum__nat,axiom,
% 5.41/5.75 ! [N: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [X3: nat] : X3
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.75 = ( divide_divide_nat @ ( times_times_nat @ N @ ( suc @ N ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % gauss_sum_nat
% 5.41/5.75 thf(fact_7716_take__bit__numeral__bit1,axiom,
% 5.41/5.75 ! [L2: num,K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_int @ ( bit1 @ K ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( numeral_numeral_int @ K ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_bit1
% 5.41/5.75 thf(fact_7717_take__bit__numeral__bit1,axiom,
% 5.41/5.75 ! [L2: num,K: num] :
% 5.41/5.75 ( ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ L2 ) @ ( numeral_numeral_nat @ ( bit1 @ K ) ) )
% 5.41/5.75 = ( plus_plus_nat @ ( times_times_nat @ ( bit_se2925701944663578781it_nat @ ( pred_numeral @ L2 ) @ ( numeral_numeral_nat @ K ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_bit1
% 5.41/5.75 thf(fact_7718_real__exp__bound__lemma,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.75 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.75 => ( ord_less_eq_real @ ( exp_real @ X ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % real_exp_bound_lemma
% 5.41/5.75 thf(fact_7719_take__bit__minus__small__eq,axiom,
% 5.41/5.75 ! [K: int,N: nat] :
% 5.41/5.75 ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.75 => ( ( ord_less_eq_int @ K @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.75 => ( ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ K ) )
% 5.41/5.75 = ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ K ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_minus_small_eq
% 5.41/5.75 thf(fact_7720_arith__series__nat,axiom,
% 5.41/5.75 ! [A: nat,D: nat,N: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ I5 @ D ) )
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.75 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ N @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % arith_series_nat
% 5.41/5.75 thf(fact_7721_Sum__Icc__nat,axiom,
% 5.41/5.75 ! [M: nat,N: nat] :
% 5.41/5.75 ( ( groups3542108847815614940at_nat
% 5.41/5.75 @ ^ [X3: nat] : X3
% 5.41/5.75 @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.75 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( plus_plus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % Sum_Icc_nat
% 5.41/5.75 thf(fact_7722_exp__lower__Taylor__quadratic,axiom,
% 5.41/5.75 ! [X: real] :
% 5.41/5.75 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.75 => ( ord_less_eq_real @ ( plus_plus_real @ ( plus_plus_real @ one_one_real @ X ) @ ( divide_divide_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( exp_real @ X ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % exp_lower_Taylor_quadratic
% 5.41/5.75 thf(fact_7723_take__bit__numeral__minus__bit1,axiom,
% 5.41/5.75 ! [L2: num,K: num] :
% 5.41/5.75 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.41/5.75 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.75
% 5.41/5.75 % take_bit_numeral_minus_bit1
% 5.41/5.75 thf(fact_7724_and__int_Oelims,axiom,
% 5.41/5.75 ! [X: int,Xa2: int,Y: int] :
% 5.41/5.75 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.41/5.75 = Y )
% 5.41/5.75 => ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.75 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.75 => ( Y
% 5.41/5.75 = ( uminus_uminus_int
% 5.41/5.75 @ ( zero_n2684676970156552555ol_int
% 5.41/5.75 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.41/5.75 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.41/5.75 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.75 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.75 => ( Y
% 5.41/5.75 = ( plus_plus_int
% 5.41/5.75 @ ( zero_n2684676970156552555ol_int
% 5.41/5.75 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.41/5.75 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.41/5.75 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.75
% 5.41/5.75 % and_int.elims
% 5.41/5.75 thf(fact_7725_and__int_Osimps,axiom,
% 5.41/5.75 ( bit_se725231765392027082nd_int
% 5.41/5.75 = ( ^ [K2: int,L: int] :
% 5.41/5.75 ( if_int
% 5.41/5.75 @ ( ( member_int @ K2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.76 & ( member_int @ L @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.76 @ ( uminus_uminus_int
% 5.41/5.76 @ ( zero_n2684676970156552555ol_int
% 5.41/5.76 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.41/5.76 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.41/5.76 @ ( plus_plus_int
% 5.41/5.76 @ ( zero_n2684676970156552555ol_int
% 5.41/5.76 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.41/5.76 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.41/5.76 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % and_int.simps
% 5.41/5.76 thf(fact_7726_take__bit__Suc__minus__bit1,axiom,
% 5.41/5.76 ! [N: nat,K: num] :
% 5.41/5.76 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.41/5.76 = ( plus_plus_int @ ( times_times_int @ ( bit_se2923211474154528505it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ one_one_int ) ) ).
% 5.41/5.76
% 5.41/5.76 % take_bit_Suc_minus_bit1
% 5.41/5.76 thf(fact_7727_sum__gp,axiom,
% 5.41/5.76 ! [N: nat,M: nat,X: complex] :
% 5.41/5.76 ( ( ( ord_less_nat @ N @ M )
% 5.41/5.76 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = zero_zero_complex ) )
% 5.41/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 5.41/5.76 => ( ( ( X = one_one_complex )
% 5.41/5.76 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = ( semiri8010041392384452111omplex @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.41/5.76 & ( ( X != one_one_complex )
% 5.41/5.76 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ M ) @ ( power_power_complex @ X @ ( suc @ N ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_gp
% 5.41/5.76 thf(fact_7728_sum__gp,axiom,
% 5.41/5.76 ! [N: nat,M: nat,X: rat] :
% 5.41/5.76 ( ( ( ord_less_nat @ N @ M )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = zero_zero_rat ) )
% 5.41/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 5.41/5.76 => ( ( ( X = one_one_rat )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = ( semiri681578069525770553at_rat @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.41/5.76 & ( ( X != one_one_rat )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ M ) @ ( power_power_rat @ X @ ( suc @ N ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_gp
% 5.41/5.76 thf(fact_7729_sum__gp,axiom,
% 5.41/5.76 ! [N: nat,M: nat,X: real] :
% 5.41/5.76 ( ( ( ord_less_nat @ N @ M )
% 5.41/5.76 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = zero_zero_real ) )
% 5.41/5.76 & ( ~ ( ord_less_nat @ N @ M )
% 5.41/5.76 => ( ( ( X = one_one_real )
% 5.41/5.76 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = ( semiri5074537144036343181t_real @ ( minus_minus_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) )
% 5.41/5.76 & ( ( X != one_one_real )
% 5.41/5.76 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ N ) )
% 5.41/5.76 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ M ) @ ( power_power_real @ X @ ( suc @ N ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_gp
% 5.41/5.76 thf(fact_7730_log__base__10__eq1,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.76 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_base_10_eq1
% 5.41/5.76 thf(fact_7731_of__nat__eq__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ( semiri8010041392384452111omplex @ M )
% 5.41/5.76 = ( semiri8010041392384452111omplex @ N ) )
% 5.41/5.76 = ( M = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_iff
% 5.41/5.76 thf(fact_7732_of__nat__eq__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ( semiri5074537144036343181t_real @ M )
% 5.41/5.76 = ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( M = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_iff
% 5.41/5.76 thf(fact_7733_of__nat__eq__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ( semiri681578069525770553at_rat @ M )
% 5.41/5.76 = ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 = ( M = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_iff
% 5.41/5.76 thf(fact_7734_of__nat__eq__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.41/5.76 = ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( M = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_iff
% 5.41/5.76 thf(fact_7735_of__nat__eq__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ( semiri1314217659103216013at_int @ M )
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( M = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_iff
% 5.41/5.76 thf(fact_7736_insert__subset,axiom,
% 5.41/5.76 ! [X: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.76 ( ( ord_le211207098394363844omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( ( member_complex @ X @ B3 )
% 5.41/5.76 & ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_subset
% 5.41/5.76 thf(fact_7737_insert__subset,axiom,
% 5.41/5.76 ! [X: real,A2: set_real,B3: set_real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( ( member_real @ X @ B3 )
% 5.41/5.76 & ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_subset
% 5.41/5.76 thf(fact_7738_insert__subset,axiom,
% 5.41/5.76 ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.76 ( ( ord_le6893508408891458716et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( ( member_set_nat @ X @ B3 )
% 5.41/5.76 & ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_subset
% 5.41/5.76 thf(fact_7739_insert__subset,axiom,
% 5.41/5.76 ! [X: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( ( member_nat @ X @ B3 )
% 5.41/5.76 & ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_subset
% 5.41/5.76 thf(fact_7740_insert__subset,axiom,
% 5.41/5.76 ! [X: int,A2: set_int,B3: set_int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( ( member_int @ X @ B3 )
% 5.41/5.76 & ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_subset
% 5.41/5.76 thf(fact_7741_int__eq__iff__numeral,axiom,
% 5.41/5.76 ! [M: nat,V: num] :
% 5.41/5.76 ( ( ( semiri1314217659103216013at_int @ M )
% 5.41/5.76 = ( numeral_numeral_int @ V ) )
% 5.41/5.76 = ( M
% 5.41/5.76 = ( numeral_numeral_nat @ V ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_eq_iff_numeral
% 5.41/5.76 thf(fact_7742_abs__of__nat,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( abs_abs_Code_integer @ ( semiri4939895301339042750nteger @ N ) )
% 5.41/5.76 = ( semiri4939895301339042750nteger @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % abs_of_nat
% 5.41/5.76 thf(fact_7743_abs__of__nat,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( abs_abs_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( semiri5074537144036343181t_real @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % abs_of_nat
% 5.41/5.76 thf(fact_7744_abs__of__nat,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( abs_abs_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 = ( semiri681578069525770553at_rat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % abs_of_nat
% 5.41/5.76 thf(fact_7745_abs__of__nat,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( abs_abs_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % abs_of_nat
% 5.41/5.76 thf(fact_7746_negative__eq__positive,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( semiri1314217659103216013at_int @ M ) )
% 5.41/5.76 = ( ( N = zero_zero_nat )
% 5.41/5.76 & ( M = zero_zero_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % negative_eq_positive
% 5.41/5.76 thf(fact_7747_Diff__insert0,axiom,
% 5.41/5.76 ! [X: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.76 ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 5.41/5.76 = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert0
% 5.41/5.76 thf(fact_7748_Diff__insert0,axiom,
% 5.41/5.76 ! [X: real,A2: set_real,B3: set_real] :
% 5.41/5.76 ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( minus_minus_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert0
% 5.41/5.76 thf(fact_7749_Diff__insert0,axiom,
% 5.41/5.76 ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.76 ( ~ ( member_set_nat @ X @ A2 )
% 5.41/5.76 => ( ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 5.41/5.76 = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert0
% 5.41/5.76 thf(fact_7750_Diff__insert0,axiom,
% 5.41/5.76 ! [X: int,A2: set_int,B3: set_int] :
% 5.41/5.76 ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( minus_minus_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert0
% 5.41/5.76 thf(fact_7751_Diff__insert0,axiom,
% 5.41/5.76 ! [X: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.76 ( ~ ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert0
% 5.41/5.76 thf(fact_7752_insert__Diff1,axiom,
% 5.41/5.76 ! [X: complex,B3: set_complex,A2: set_complex] :
% 5.41/5.76 ( ( member_complex @ X @ B3 )
% 5.41/5.76 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff1
% 5.41/5.76 thf(fact_7753_insert__Diff1,axiom,
% 5.41/5.76 ! [X: real,B3: set_real,A2: set_real] :
% 5.41/5.76 ( ( member_real @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff1
% 5.41/5.76 thf(fact_7754_insert__Diff1,axiom,
% 5.41/5.76 ! [X: set_nat,B3: set_set_nat,A2: set_set_nat] :
% 5.41/5.76 ( ( member_set_nat @ X @ B3 )
% 5.41/5.76 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff1
% 5.41/5.76 thf(fact_7755_insert__Diff1,axiom,
% 5.41/5.76 ! [X: int,B3: set_int,A2: set_int] :
% 5.41/5.76 ( ( member_int @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff1
% 5.41/5.76 thf(fact_7756_insert__Diff1,axiom,
% 5.41/5.76 ! [X: nat,B3: set_nat,A2: set_nat] :
% 5.41/5.76 ( ( member_nat @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff1
% 5.41/5.76 thf(fact_7757_negative__zle,axiom,
% 5.41/5.76 ! [N: nat,M: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ ( semiri1314217659103216013at_int @ M ) ) ).
% 5.41/5.76
% 5.41/5.76 % negative_zle
% 5.41/5.76 thf(fact_7758_of__nat__eq__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ( semiri8010041392384452111omplex @ M )
% 5.41/5.76 = zero_zero_complex )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_0_iff
% 5.41/5.76 thf(fact_7759_of__nat__eq__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ( semiri5074537144036343181t_real @ M )
% 5.41/5.76 = zero_zero_real )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_0_iff
% 5.41/5.76 thf(fact_7760_of__nat__eq__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ( semiri681578069525770553at_rat @ M )
% 5.41/5.76 = zero_zero_rat )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_0_iff
% 5.41/5.76 thf(fact_7761_of__nat__eq__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ( semiri1316708129612266289at_nat @ M )
% 5.41/5.76 = zero_zero_nat )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_0_iff
% 5.41/5.76 thf(fact_7762_of__nat__eq__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ( semiri1314217659103216013at_int @ M )
% 5.41/5.76 = zero_zero_int )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_0_iff
% 5.41/5.76 thf(fact_7763_of__nat__0__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( zero_zero_complex
% 5.41/5.76 = ( semiri8010041392384452111omplex @ N ) )
% 5.41/5.76 = ( zero_zero_nat = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_eq_iff
% 5.41/5.76 thf(fact_7764_of__nat__0__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( zero_zero_real
% 5.41/5.76 = ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( zero_zero_nat = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_eq_iff
% 5.41/5.76 thf(fact_7765_of__nat__0__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( zero_zero_rat
% 5.41/5.76 = ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 = ( zero_zero_nat = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_eq_iff
% 5.41/5.76 thf(fact_7766_of__nat__0__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( zero_zero_nat
% 5.41/5.76 = ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( zero_zero_nat = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_eq_iff
% 5.41/5.76 thf(fact_7767_of__nat__0__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( zero_zero_int
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( zero_zero_nat = N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_eq_iff
% 5.41/5.76 thf(fact_7768_of__nat__0,axiom,
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ zero_zero_nat )
% 5.41/5.76 = zero_zero_complex ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0
% 5.41/5.76 thf(fact_7769_of__nat__0,axiom,
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ zero_zero_nat )
% 5.41/5.76 = zero_zero_real ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0
% 5.41/5.76 thf(fact_7770_of__nat__0,axiom,
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ zero_zero_nat )
% 5.41/5.76 = zero_zero_rat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0
% 5.41/5.76 thf(fact_7771_of__nat__0,axiom,
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ zero_zero_nat )
% 5.41/5.76 = zero_zero_nat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0
% 5.41/5.76 thf(fact_7772_of__nat__0,axiom,
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.41/5.76 = zero_zero_int ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0
% 5.41/5.76 thf(fact_7773_of__nat__less__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_iff
% 5.41/5.76 thf(fact_7774_of__nat__less__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_iff
% 5.41/5.76 thf(fact_7775_of__nat__less__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_iff
% 5.41/5.76 thf(fact_7776_of__nat__less__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_iff
% 5.41/5.76 thf(fact_7777_of__nat__numeral,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( numeral_numeral_nat @ N ) )
% 5.41/5.76 = ( numera6690914467698888265omplex @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_numeral
% 5.41/5.76 thf(fact_7778_of__nat__numeral,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( numeral_numeral_nat @ N ) )
% 5.41/5.76 = ( numeral_numeral_real @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_numeral
% 5.41/5.76 thf(fact_7779_of__nat__numeral,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( numeral_numeral_nat @ N ) )
% 5.41/5.76 = ( numeral_numeral_rat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_numeral
% 5.41/5.76 thf(fact_7780_of__nat__numeral,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( numeral_numeral_nat @ N ) )
% 5.41/5.76 = ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_numeral
% 5.41/5.76 thf(fact_7781_of__nat__numeral,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.41/5.76 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_numeral
% 5.41/5.76 thf(fact_7782_of__nat__le__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_iff
% 5.41/5.76 thf(fact_7783_of__nat__le__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_iff
% 5.41/5.76 thf(fact_7784_of__nat__le__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_iff
% 5.41/5.76 thf(fact_7785_of__nat__le__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_iff
% 5.41/5.76 thf(fact_7786_singleton__insert__inj__eq,axiom,
% 5.41/5.76 ! [B: nat,A: nat,A2: set_nat] :
% 5.41/5.76 ( ( ( insert_nat @ B @ bot_bot_set_nat )
% 5.41/5.76 = ( insert_nat @ A @ A2 ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % singleton_insert_inj_eq
% 5.41/5.76 thf(fact_7787_singleton__insert__inj__eq,axiom,
% 5.41/5.76 ! [B: real,A: real,A2: set_real] :
% 5.41/5.76 ( ( ( insert_real @ B @ bot_bot_set_real )
% 5.41/5.76 = ( insert_real @ A @ A2 ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % singleton_insert_inj_eq
% 5.41/5.76 thf(fact_7788_singleton__insert__inj__eq,axiom,
% 5.41/5.76 ! [B: int,A: int,A2: set_int] :
% 5.41/5.76 ( ( ( insert_int @ B @ bot_bot_set_int )
% 5.41/5.76 = ( insert_int @ A @ A2 ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % singleton_insert_inj_eq
% 5.41/5.76 thf(fact_7789_singleton__insert__inj__eq_H,axiom,
% 5.41/5.76 ! [A: nat,A2: set_nat,B: nat] :
% 5.41/5.76 ( ( ( insert_nat @ A @ A2 )
% 5.41/5.76 = ( insert_nat @ B @ bot_bot_set_nat ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ bot_bot_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % singleton_insert_inj_eq'
% 5.41/5.76 thf(fact_7790_singleton__insert__inj__eq_H,axiom,
% 5.41/5.76 ! [A: real,A2: set_real,B: real] :
% 5.41/5.76 ( ( ( insert_real @ A @ A2 )
% 5.41/5.76 = ( insert_real @ B @ bot_bot_set_real ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ bot_bot_set_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % singleton_insert_inj_eq'
% 5.41/5.76 thf(fact_7791_singleton__insert__inj__eq_H,axiom,
% 5.41/5.76 ! [A: int,A2: set_int,B: int] :
% 5.41/5.76 ( ( ( insert_int @ A @ A2 )
% 5.41/5.76 = ( insert_int @ B @ bot_bot_set_int ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ bot_bot_set_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % singleton_insert_inj_eq'
% 5.41/5.76 thf(fact_7792_of__nat__add,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.76 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_add
% 5.41/5.76 thf(fact_7793_of__nat__add,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.76 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_add
% 5.41/5.76 thf(fact_7794_of__nat__add,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.76 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_add
% 5.41/5.76 thf(fact_7795_of__nat__add,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.76 = ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_add
% 5.41/5.76 thf(fact_7796_of__nat__add,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.76 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_add
% 5.41/5.76 thf(fact_7797_of__nat__mult,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( times_times_nat @ M @ N ) )
% 5.41/5.76 = ( times_times_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mult
% 5.41/5.76 thf(fact_7798_of__nat__mult,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( times_times_nat @ M @ N ) )
% 5.41/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mult
% 5.41/5.76 thf(fact_7799_of__nat__mult,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( times_times_nat @ M @ N ) )
% 5.41/5.76 = ( times_times_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mult
% 5.41/5.76 thf(fact_7800_of__nat__mult,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( times_times_nat @ M @ N ) )
% 5.41/5.76 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mult
% 5.41/5.76 thf(fact_7801_of__nat__mult,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ M @ N ) )
% 5.41/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mult
% 5.41/5.76 thf(fact_7802_of__nat__1,axiom,
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ one_one_nat )
% 5.41/5.76 = one_one_complex ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1
% 5.41/5.76 thf(fact_7803_of__nat__1,axiom,
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ one_one_nat )
% 5.41/5.76 = one_one_real ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1
% 5.41/5.76 thf(fact_7804_of__nat__1,axiom,
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ one_one_nat )
% 5.41/5.76 = one_one_rat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1
% 5.41/5.76 thf(fact_7805_of__nat__1,axiom,
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ one_one_nat )
% 5.41/5.76 = one_one_nat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1
% 5.41/5.76 thf(fact_7806_of__nat__1,axiom,
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.41/5.76 = one_one_int ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1
% 5.41/5.76 thf(fact_7807_of__nat__1__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( one_one_complex
% 5.41/5.76 = ( semiri8010041392384452111omplex @ N ) )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1_eq_iff
% 5.41/5.76 thf(fact_7808_of__nat__1__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( one_one_real
% 5.41/5.76 = ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1_eq_iff
% 5.41/5.76 thf(fact_7809_of__nat__1__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( one_one_rat
% 5.41/5.76 = ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1_eq_iff
% 5.41/5.76 thf(fact_7810_of__nat__1__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( one_one_nat
% 5.41/5.76 = ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1_eq_iff
% 5.41/5.76 thf(fact_7811_of__nat__1__eq__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( one_one_int
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_1_eq_iff
% 5.41/5.76 thf(fact_7812_of__nat__eq__1__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ( semiri8010041392384452111omplex @ N )
% 5.41/5.76 = one_one_complex )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_1_iff
% 5.41/5.76 thf(fact_7813_of__nat__eq__1__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ( semiri5074537144036343181t_real @ N )
% 5.41/5.76 = one_one_real )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_1_iff
% 5.41/5.76 thf(fact_7814_of__nat__eq__1__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ( semiri681578069525770553at_rat @ N )
% 5.41/5.76 = one_one_rat )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_1_iff
% 5.41/5.76 thf(fact_7815_of__nat__eq__1__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ( semiri1316708129612266289at_nat @ N )
% 5.41/5.76 = one_one_nat )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_1_iff
% 5.41/5.76 thf(fact_7816_of__nat__eq__1__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ( semiri1314217659103216013at_int @ N )
% 5.41/5.76 = one_one_int )
% 5.41/5.76 = ( N = one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_1_iff
% 5.41/5.76 thf(fact_7817_atLeastAtMost__singleton,axiom,
% 5.41/5.76 ! [A: nat] :
% 5.41/5.76 ( ( set_or1269000886237332187st_nat @ A @ A )
% 5.41/5.76 = ( insert_nat @ A @ bot_bot_set_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton
% 5.41/5.76 thf(fact_7818_atLeastAtMost__singleton,axiom,
% 5.41/5.76 ! [A: int] :
% 5.41/5.76 ( ( set_or1266510415728281911st_int @ A @ A )
% 5.41/5.76 = ( insert_int @ A @ bot_bot_set_int ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton
% 5.41/5.76 thf(fact_7819_atLeastAtMost__singleton,axiom,
% 5.41/5.76 ! [A: real] :
% 5.41/5.76 ( ( set_or1222579329274155063t_real @ A @ A )
% 5.41/5.76 = ( insert_real @ A @ bot_bot_set_real ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton
% 5.41/5.76 thf(fact_7820_atLeastAtMost__singleton__iff,axiom,
% 5.41/5.76 ! [A: nat,B: nat,C: nat] :
% 5.41/5.76 ( ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.41/5.76 = ( insert_nat @ C @ bot_bot_set_nat ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( B = C ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton_iff
% 5.41/5.76 thf(fact_7821_atLeastAtMost__singleton__iff,axiom,
% 5.41/5.76 ! [A: int,B: int,C: int] :
% 5.41/5.76 ( ( ( set_or1266510415728281911st_int @ A @ B )
% 5.41/5.76 = ( insert_int @ C @ bot_bot_set_int ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( B = C ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton_iff
% 5.41/5.76 thf(fact_7822_atLeastAtMost__singleton__iff,axiom,
% 5.41/5.76 ! [A: real,B: real,C: real] :
% 5.41/5.76 ( ( ( set_or1222579329274155063t_real @ A @ B )
% 5.41/5.76 = ( insert_real @ C @ bot_bot_set_real ) )
% 5.41/5.76 = ( ( A = B )
% 5.41/5.76 & ( B = C ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton_iff
% 5.41/5.76 thf(fact_7823_insert__Diff__single,axiom,
% 5.41/5.76 ! [A: int,A2: set_int] :
% 5.41/5.76 ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( insert_int @ A @ A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_single
% 5.41/5.76 thf(fact_7824_insert__Diff__single,axiom,
% 5.41/5.76 ! [A: real,A2: set_real] :
% 5.41/5.76 ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( insert_real @ A @ A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_single
% 5.41/5.76 thf(fact_7825_insert__Diff__single,axiom,
% 5.41/5.76 ! [A: nat,A2: set_nat] :
% 5.41/5.76 ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( insert_nat @ A @ A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_single
% 5.41/5.76 thf(fact_7826_finite__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_real,A: real,B3: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) ) )
% 5.41/5.76 = ( finite_finite_real @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_Diff_insert
% 5.41/5.76 thf(fact_7827_finite__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_int,A: int,B3: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) ) )
% 5.41/5.76 = ( finite_finite_int @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_Diff_insert
% 5.41/5.76 thf(fact_7828_finite__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_complex,A: complex,B3: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ B3 ) ) )
% 5.41/5.76 = ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_Diff_insert
% 5.41/5.76 thf(fact_7829_finite__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_nat,A: nat,B3: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) ) )
% 5.41/5.76 = ( finite_finite_nat @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_Diff_insert
% 5.41/5.76 thf(fact_7830_of__nat__power,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( power_power_nat @ M @ N ) )
% 5.41/5.76 = ( power_power_complex @ ( semiri8010041392384452111omplex @ M ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power
% 5.41/5.76 thf(fact_7831_of__nat__power,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( power_power_nat @ M @ N ) )
% 5.41/5.76 = ( power_power_real @ ( semiri5074537144036343181t_real @ M ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power
% 5.41/5.76 thf(fact_7832_of__nat__power,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( power_power_nat @ M @ N ) )
% 5.41/5.76 = ( power_power_rat @ ( semiri681578069525770553at_rat @ M ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power
% 5.41/5.76 thf(fact_7833_of__nat__power,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( power_power_nat @ M @ N ) )
% 5.41/5.76 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ M ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power
% 5.41/5.76 thf(fact_7834_of__nat__power,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( power_power_nat @ M @ N ) )
% 5.41/5.76 = ( power_power_int @ ( semiri1314217659103216013at_int @ M ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power
% 5.41/5.76 thf(fact_7835_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W )
% 5.41/5.76 = ( semiri8010041392384452111omplex @ X ) )
% 5.41/5.76 = ( ( power_power_nat @ B @ W )
% 5.41/5.76 = X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7836_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W )
% 5.41/5.76 = ( semiri5074537144036343181t_real @ X ) )
% 5.41/5.76 = ( ( power_power_nat @ B @ W )
% 5.41/5.76 = X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7837_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W )
% 5.41/5.76 = ( semiri681578069525770553at_rat @ X ) )
% 5.41/5.76 = ( ( power_power_nat @ B @ W )
% 5.41/5.76 = X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7838_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W )
% 5.41/5.76 = ( semiri1316708129612266289at_nat @ X ) )
% 5.41/5.76 = ( ( power_power_nat @ B @ W )
% 5.41/5.76 = X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7839_of__nat__eq__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W )
% 5.41/5.76 = ( semiri1314217659103216013at_int @ X ) )
% 5.41/5.76 = ( ( power_power_nat @ B @ W )
% 5.41/5.76 = X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_eq_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7840_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ( semiri8010041392384452111omplex @ X )
% 5.41/5.76 = ( power_power_complex @ ( semiri8010041392384452111omplex @ B ) @ W ) )
% 5.41/5.76 = ( X
% 5.41/5.76 = ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7841_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ( semiri5074537144036343181t_real @ X )
% 5.41/5.76 = ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.41/5.76 = ( X
% 5.41/5.76 = ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7842_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ( semiri681578069525770553at_rat @ X )
% 5.41/5.76 = ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.41/5.76 = ( X
% 5.41/5.76 = ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7843_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ( semiri1316708129612266289at_nat @ X )
% 5.41/5.76 = ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.41/5.76 = ( X
% 5.41/5.76 = ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7844_of__nat__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ( semiri1314217659103216013at_int @ X )
% 5.41/5.76 = ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.41/5.76 = ( X
% 5.41/5.76 = ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7845_log__one,axiom,
% 5.41/5.76 ! [A: real] :
% 5.41/5.76 ( ( log @ A @ one_one_real )
% 5.41/5.76 = zero_zero_real ) ).
% 5.41/5.76
% 5.41/5.76 % log_one
% 5.41/5.76 thf(fact_7846_pred__numeral__inc,axiom,
% 5.41/5.76 ! [K: num] :
% 5.41/5.76 ( ( pred_numeral @ ( inc @ K ) )
% 5.41/5.76 = ( numeral_numeral_nat @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % pred_numeral_inc
% 5.41/5.76 thf(fact_7847_of__nat__of__bool,axiom,
% 5.41/5.76 ! [P: $o] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.41/5.76 = ( zero_n1201886186963655149omplex @ P ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_of_bool
% 5.41/5.76 thf(fact_7848_of__nat__of__bool,axiom,
% 5.41/5.76 ! [P: $o] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.41/5.76 = ( zero_n3304061248610475627l_real @ P ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_of_bool
% 5.41/5.76 thf(fact_7849_of__nat__of__bool,axiom,
% 5.41/5.76 ! [P: $o] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.41/5.76 = ( zero_n2052037380579107095ol_rat @ P ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_of_bool
% 5.41/5.76 thf(fact_7850_of__nat__of__bool,axiom,
% 5.41/5.76 ! [P: $o] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.41/5.76 = ( zero_n2687167440665602831ol_nat @ P ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_of_bool
% 5.41/5.76 thf(fact_7851_of__nat__of__bool,axiom,
% 5.41/5.76 ! [P: $o] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.41/5.76 = ( zero_n2684676970156552555ol_int @ P ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_of_bool
% 5.41/5.76 thf(fact_7852_of__nat__of__bool,axiom,
% 5.41/5.76 ! [P: $o] :
% 5.41/5.76 ( ( semiri4939895301339042750nteger @ ( zero_n2687167440665602831ol_nat @ P ) )
% 5.41/5.76 = ( zero_n356916108424825756nteger @ P ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_of_bool
% 5.41/5.76 thf(fact_7853_of__nat__le__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_0_iff
% 5.41/5.76 thf(fact_7854_of__nat__le__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_0_iff
% 5.41/5.76 thf(fact_7855_of__nat__le__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_0_iff
% 5.41/5.76 thf(fact_7856_of__nat__le__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int )
% 5.41/5.76 = ( M = zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_0_iff
% 5.41/5.76 thf(fact_7857_and__nat__numerals_I3_J,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.76 = zero_zero_nat ) ).
% 5.41/5.76
% 5.41/5.76 % and_nat_numerals(3)
% 5.41/5.76 thf(fact_7858_and__nat__numerals_I1_J,axiom,
% 5.41/5.76 ! [Y: num] :
% 5.41/5.76 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.41/5.76 = zero_zero_nat ) ).
% 5.41/5.76
% 5.41/5.76 % and_nat_numerals(1)
% 5.41/5.76 thf(fact_7859_of__nat__Suc,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( suc @ M ) )
% 5.41/5.76 = ( plus_plus_complex @ one_one_complex @ ( semiri8010041392384452111omplex @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_Suc
% 5.41/5.76 thf(fact_7860_of__nat__Suc,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( suc @ M ) )
% 5.41/5.76 = ( plus_plus_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_Suc
% 5.41/5.76 thf(fact_7861_of__nat__Suc,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( suc @ M ) )
% 5.41/5.76 = ( plus_plus_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_Suc
% 5.41/5.76 thf(fact_7862_of__nat__Suc,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( suc @ M ) )
% 5.41/5.76 = ( plus_plus_nat @ one_one_nat @ ( semiri1316708129612266289at_nat @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_Suc
% 5.41/5.76 thf(fact_7863_of__nat__Suc,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( suc @ M ) )
% 5.41/5.76 = ( plus_plus_int @ one_one_int @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_Suc
% 5.41/5.76 thf(fact_7864_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > real] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7865_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > real] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7866_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7867_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > rat] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7868_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_nat,X: nat,G: nat > rat] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ~ ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7869_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > rat] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7870_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > rat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7871_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > nat] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7872_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > nat] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7873_sum_Oinsert,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert
% 5.41/5.76 thf(fact_7874_numeral__less__real__of__nat__iff,axiom,
% 5.41/5.76 ! [W: num,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( numeral_numeral_real @ W ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( ord_less_nat @ ( numeral_numeral_nat @ W ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_less_real_of_nat_iff
% 5.41/5.76 thf(fact_7875_real__of__nat__less__numeral__iff,axiom,
% 5.41/5.76 ! [N: nat,W: num] :
% 5.41/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( numeral_numeral_real @ W ) )
% 5.41/5.76 = ( ord_less_nat @ N @ ( numeral_numeral_nat @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_less_numeral_iff
% 5.41/5.76 thf(fact_7876_numeral__le__real__of__nat__iff,axiom,
% 5.41/5.76 ! [N: num,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( numeral_numeral_real @ N ) @ ( semiri5074537144036343181t_real @ M ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( numeral_numeral_nat @ N ) @ M ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_le_real_of_nat_iff
% 5.41/5.76 thf(fact_7877_subset__Compl__singleton,axiom,
% 5.41/5.76 ! [A2: set_complex,B: complex] :
% 5.41/5.76 ( ( ord_le211207098394363844omplex @ A2 @ ( uminus8566677241136511917omplex @ ( insert_complex @ B @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( ~ ( member_complex @ B @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Compl_singleton
% 5.41/5.76 thf(fact_7878_subset__Compl__singleton,axiom,
% 5.41/5.76 ! [A2: set_set_nat,B: set_nat] :
% 5.41/5.76 ( ( ord_le6893508408891458716et_nat @ A2 @ ( uminus613421341184616069et_nat @ ( insert_set_nat @ B @ bot_bot_set_set_nat ) ) )
% 5.41/5.76 = ( ~ ( member_set_nat @ B @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Compl_singleton
% 5.41/5.76 thf(fact_7879_subset__Compl__singleton,axiom,
% 5.41/5.76 ! [A2: set_nat,B: nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ A2 @ ( uminus5710092332889474511et_nat @ ( insert_nat @ B @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( ~ ( member_nat @ B @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Compl_singleton
% 5.41/5.76 thf(fact_7880_subset__Compl__singleton,axiom,
% 5.41/5.76 ! [A2: set_real,B: real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ A2 @ ( uminus612125837232591019t_real @ ( insert_real @ B @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( ~ ( member_real @ B @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Compl_singleton
% 5.41/5.76 thf(fact_7881_subset__Compl__singleton,axiom,
% 5.41/5.76 ! [A2: set_int,B: int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ A2 @ ( uminus1532241313380277803et_int @ ( insert_int @ B @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( ~ ( member_int @ B @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Compl_singleton
% 5.41/5.76 thf(fact_7882_log__eq__one,axiom,
% 5.41/5.76 ! [A: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.76 => ( ( A != one_one_real )
% 5.41/5.76 => ( ( log @ A @ A )
% 5.41/5.76 = one_one_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_eq_one
% 5.41/5.76 thf(fact_7883_log__less__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real,Y: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.76 => ( ( ord_less_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 5.41/5.76 = ( ord_less_real @ X @ Y ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_less_cancel_iff
% 5.41/5.76 thf(fact_7884_log__less__one__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ ( log @ A @ X ) @ one_one_real )
% 5.41/5.76 = ( ord_less_real @ X @ A ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_less_one_cancel_iff
% 5.41/5.76 thf(fact_7885_one__less__log__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ one_one_real @ ( log @ A @ X ) )
% 5.41/5.76 = ( ord_less_real @ A @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % one_less_log_cancel_iff
% 5.41/5.76 thf(fact_7886_log__less__zero__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.41/5.76 = ( ord_less_real @ X @ one_one_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_less_zero_cancel_iff
% 5.41/5.76 thf(fact_7887_zero__less__log__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.41/5.76 = ( ord_less_real @ one_one_real @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zero_less_log_cancel_iff
% 5.41/5.76 thf(fact_7888_of__nat__0__less__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_less_iff
% 5.41/5.76 thf(fact_7889_of__nat__0__less__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_less_iff
% 5.41/5.76 thf(fact_7890_of__nat__0__less__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_less_iff
% 5.41/5.76 thf(fact_7891_of__nat__0__less__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ord_less_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( ord_less_nat @ zero_zero_nat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_less_iff
% 5.41/5.76 thf(fact_7892_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7893_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7894_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7895_of__nat__less__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7896_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7897_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7898_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7899_of__nat__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7900_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: num,N: nat,Y: nat] :
% 5.41/5.76 ( ( ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N )
% 5.41/5.76 = ( semiri8010041392384452111omplex @ Y ) )
% 5.41/5.76 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.41/5.76 = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7901_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: num,N: nat,Y: nat] :
% 5.41/5.76 ( ( ( power_power_real @ ( numeral_numeral_real @ X ) @ N )
% 5.41/5.76 = ( semiri5074537144036343181t_real @ Y ) )
% 5.41/5.76 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.41/5.76 = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7902_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: num,N: nat,Y: nat] :
% 5.41/5.76 ( ( ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N )
% 5.41/5.76 = ( semiri681578069525770553at_rat @ Y ) )
% 5.41/5.76 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.41/5.76 = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7903_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: num,N: nat,Y: nat] :
% 5.41/5.76 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.41/5.76 = ( semiri1316708129612266289at_nat @ Y ) )
% 5.41/5.76 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.41/5.76 = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7904_numeral__power__eq__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: num,N: nat,Y: nat] :
% 5.41/5.76 ( ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.41/5.76 = ( semiri1314217659103216013at_int @ Y ) )
% 5.41/5.76 = ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.41/5.76 = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_eq_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7905_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [Y: nat,X: num,N: nat] :
% 5.41/5.76 ( ( ( semiri8010041392384452111omplex @ Y )
% 5.41/5.76 = ( power_power_complex @ ( numera6690914467698888265omplex @ X ) @ N ) )
% 5.41/5.76 = ( Y
% 5.41/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_eq_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7906_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [Y: nat,X: num,N: nat] :
% 5.41/5.76 ( ( ( semiri5074537144036343181t_real @ Y )
% 5.41/5.76 = ( power_power_real @ ( numeral_numeral_real @ X ) @ N ) )
% 5.41/5.76 = ( Y
% 5.41/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_eq_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7907_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [Y: nat,X: num,N: nat] :
% 5.41/5.76 ( ( ( semiri681578069525770553at_rat @ Y )
% 5.41/5.76 = ( power_power_rat @ ( numeral_numeral_rat @ X ) @ N ) )
% 5.41/5.76 = ( Y
% 5.41/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_eq_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7908_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [Y: nat,X: num,N: nat] :
% 5.41/5.76 ( ( ( semiri1316708129612266289at_nat @ Y )
% 5.41/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.41/5.76 = ( Y
% 5.41/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_eq_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7909_real__of__nat__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [Y: nat,X: num,N: nat] :
% 5.41/5.76 ( ( ( semiri1314217659103216013at_int @ Y )
% 5.41/5.76 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) )
% 5.41/5.76 = ( Y
% 5.41/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_eq_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7910_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7911_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7912_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7913_of__nat__le__of__nat__power__cancel__iff,axiom,
% 5.41/5.76 ! [B: nat,W: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ B @ W ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_of_nat_power_cancel_iff
% 5.41/5.76 thf(fact_7914_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( semiri5074537144036343181t_real @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7915_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( semiri681578069525770553at_rat @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7916_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7917_of__nat__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,B: nat,W: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( semiri1314217659103216013at_int @ B ) @ W ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ B @ W ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7918_and__nat__numerals_I4_J,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( bit_se727722235901077358nd_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.76 = one_one_nat ) ).
% 5.41/5.76
% 5.41/5.76 % and_nat_numerals(4)
% 5.41/5.76 thf(fact_7919_and__nat__numerals_I2_J,axiom,
% 5.41/5.76 ! [Y: num] :
% 5.41/5.76 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.41/5.76 = one_one_nat ) ).
% 5.41/5.76
% 5.41/5.76 % and_nat_numerals(2)
% 5.41/5.76 thf(fact_7920_set__replicate,axiom,
% 5.41/5.76 ! [N: nat,X: vEBT_VEBT] :
% 5.41/5.76 ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.41/5.76 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate
% 5.41/5.76 thf(fact_7921_set__replicate,axiom,
% 5.41/5.76 ! [N: nat,X: nat] :
% 5.41/5.76 ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.41/5.76 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate
% 5.41/5.76 thf(fact_7922_set__replicate,axiom,
% 5.41/5.76 ! [N: nat,X: int] :
% 5.41/5.76 ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.41/5.76 = ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate
% 5.41/5.76 thf(fact_7923_set__replicate,axiom,
% 5.41/5.76 ! [N: nat,X: real] :
% 5.41/5.76 ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 5.41/5.76 = ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate
% 5.41/5.76 thf(fact_7924_log__le__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real,Y: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.76 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ ( log @ A @ Y ) )
% 5.41/5.76 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_le_cancel_iff
% 5.41/5.76 thf(fact_7925_log__le__one__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ one_one_real )
% 5.41/5.76 = ( ord_less_eq_real @ X @ A ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_le_one_cancel_iff
% 5.41/5.76 thf(fact_7926_one__le__log__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_eq_real @ one_one_real @ ( log @ A @ X ) )
% 5.41/5.76 = ( ord_less_eq_real @ A @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % one_le_log_cancel_iff
% 5.41/5.76 thf(fact_7927_log__le__zero__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_eq_real @ ( log @ A @ X ) @ zero_zero_real )
% 5.41/5.76 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_le_zero_cancel_iff
% 5.41/5.76 thf(fact_7928_zero__le__log__cancel__iff,axiom,
% 5.41/5.76 ! [A: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ ( log @ A @ X ) )
% 5.41/5.76 = ( ord_less_eq_real @ one_one_real @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zero_le_log_cancel_iff
% 5.41/5.76 thf(fact_7929_add__neg__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( plus_plus_real @ ( uminus_uminus_real @ one_one_real ) @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.76 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(5)
% 5.41/5.76 thf(fact_7930_add__neg__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( plus_plus_int @ ( uminus_uminus_int @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.76 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(5)
% 5.41/5.76 thf(fact_7931_add__neg__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ N ) ) )
% 5.41/5.76 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(5)
% 5.41/5.76 thf(fact_7932_add__neg__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ N ) ) )
% 5.41/5.76 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(5)
% 5.41/5.76 thf(fact_7933_add__neg__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( plus_plus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ N ) ) )
% 5.41/5.76 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(5)
% 5.41/5.76 thf(fact_7934_add__neg__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( plus_plus_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ M ) ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.76 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(6)
% 5.41/5.76 thf(fact_7935_add__neg__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.76 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(6)
% 5.41/5.76 thf(fact_7936_add__neg__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( plus_plus_complex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ M ) ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.76 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(6)
% 5.41/5.76 thf(fact_7937_add__neg__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( plus_p5714425477246183910nteger @ ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ M ) ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.76 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(6)
% 5.41/5.76 thf(fact_7938_add__neg__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( plus_plus_rat @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ M ) ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.76 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_neg_numeral_special(6)
% 5.41/5.76 thf(fact_7939_diff__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( minus_minus_real @ ( numeral_numeral_real @ M ) @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.76 = ( numeral_numeral_real @ ( inc @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(6)
% 5.41/5.76 thf(fact_7940_diff__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( minus_minus_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.76 = ( numeral_numeral_int @ ( inc @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(6)
% 5.41/5.76 thf(fact_7941_diff__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( minus_minus_complex @ ( numera6690914467698888265omplex @ M ) @ ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.76 = ( numera6690914467698888265omplex @ ( inc @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(6)
% 5.41/5.76 thf(fact_7942_diff__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( minus_8373710615458151222nteger @ ( numera6620942414471956472nteger @ M ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) )
% 5.41/5.76 = ( numera6620942414471956472nteger @ ( inc @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(6)
% 5.41/5.76 thf(fact_7943_diff__numeral__special_I6_J,axiom,
% 5.41/5.76 ! [M: num] :
% 5.41/5.76 ( ( minus_minus_rat @ ( numeral_numeral_rat @ M ) @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.76 = ( numeral_numeral_rat @ ( inc @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(6)
% 5.41/5.76 thf(fact_7944_diff__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( minus_minus_real @ ( uminus_uminus_real @ one_one_real ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.76 = ( uminus_uminus_real @ ( numeral_numeral_real @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(5)
% 5.41/5.76 thf(fact_7945_diff__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( minus_minus_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.76 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(5)
% 5.41/5.76 thf(fact_7946_diff__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( minus_minus_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ ( numera6690914467698888265omplex @ N ) )
% 5.41/5.76 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(5)
% 5.41/5.76 thf(fact_7947_diff__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ ( numera6620942414471956472nteger @ N ) )
% 5.41/5.76 = ( uminus1351360451143612070nteger @ ( numera6620942414471956472nteger @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(5)
% 5.41/5.76 thf(fact_7948_diff__numeral__special_I5_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( minus_minus_rat @ ( uminus_uminus_rat @ one_one_rat ) @ ( numeral_numeral_rat @ N ) )
% 5.41/5.76 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ ( inc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % diff_numeral_special(5)
% 5.41/5.76 thf(fact_7949_log__pow__cancel,axiom,
% 5.41/5.76 ! [A: real,B: nat] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.76 => ( ( A != one_one_real )
% 5.41/5.76 => ( ( log @ A @ ( power_power_real @ A @ B ) )
% 5.41/5.76 = ( semiri5074537144036343181t_real @ B ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_pow_cancel
% 5.41/5.76 thf(fact_7950_of__nat__zero__less__power__iff,axiom,
% 5.41/5.76 ! [X: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ ( power_power_real @ ( semiri5074537144036343181t_real @ X ) @ N ) )
% 5.41/5.76 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.41/5.76 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_zero_less_power_iff
% 5.41/5.76 thf(fact_7951_of__nat__zero__less__power__iff,axiom,
% 5.41/5.76 ! [X: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_rat @ zero_zero_rat @ ( power_power_rat @ ( semiri681578069525770553at_rat @ X ) @ N ) )
% 5.41/5.76 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.41/5.76 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_zero_less_power_iff
% 5.41/5.76 thf(fact_7952_of__nat__zero__less__power__iff,axiom,
% 5.41/5.76 ! [X: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ zero_zero_nat @ ( power_power_nat @ ( semiri1316708129612266289at_nat @ X ) @ N ) )
% 5.41/5.76 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.41/5.76 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_zero_less_power_iff
% 5.41/5.76 thf(fact_7953_of__nat__zero__less__power__iff,axiom,
% 5.41/5.76 ! [X: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_int @ zero_zero_int @ ( power_power_int @ ( semiri1314217659103216013at_int @ X ) @ N ) )
% 5.41/5.76 = ( ( ord_less_nat @ zero_zero_nat @ X )
% 5.41/5.76 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_zero_less_power_iff
% 5.41/5.76 thf(fact_7954_Suc__0__and__eq,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( bit_se727722235901077358nd_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.76 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Suc_0_and_eq
% 5.41/5.76 thf(fact_7955_and__Suc__0__eq,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( bit_se727722235901077358nd_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.76 = ( modulo_modulo_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % and_Suc_0_eq
% 5.41/5.76 thf(fact_7956_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7957_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7958_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7959_numeral__power__less__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.41/5.76 = ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_less_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7960_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7961_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7962_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7963_of__nat__less__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7964_even__of__nat,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.41/5.76 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % even_of_nat
% 5.41/5.76 thf(fact_7965_even__of__nat,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % even_of_nat
% 5.41/5.76 thf(fact_7966_even__of__nat,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % even_of_nat
% 5.41/5.76 thf(fact_7967_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) @ ( semiri5074537144036343181t_real @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7968_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_rat @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) @ ( semiri681578069525770553at_rat @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7969_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ ( semiri1316708129612266289at_nat @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7970_numeral__power__le__of__nat__cancel__iff,axiom,
% 5.41/5.76 ! [I: num,N: nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) @ ( semiri1314217659103216013at_int @ X ) )
% 5.41/5.76 = ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_power_le_of_nat_cancel_iff
% 5.41/5.76 thf(fact_7971_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ ( power_power_real @ ( numeral_numeral_real @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7972_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ X ) @ ( power_power_rat @ ( numeral_numeral_rat @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7973_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7974_of__nat__le__numeral__power__cancel__iff,axiom,
% 5.41/5.76 ! [X: nat,I: num,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ X ) @ ( power_power_int @ ( numeral_numeral_int @ I ) @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ ( power_power_nat @ ( numeral_numeral_nat @ I ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_le_numeral_power_cancel_iff
% 5.41/5.76 thf(fact_7975_Collect__case__prod__mono,axiom,
% 5.41/5.76 ! [A2: int > int > $o,B3: int > int > $o] :
% 5.41/5.76 ( ( ord_le6741204236512500942_int_o @ A2 @ B3 )
% 5.41/5.76 => ( ord_le2843351958646193337nt_int @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ A2 ) ) @ ( collec213857154873943460nt_int @ ( produc4947309494688390418_int_o @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Collect_case_prod_mono
% 5.41/5.76 thf(fact_7976_real__arch__simple,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ? [N3: nat] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_arch_simple
% 5.41/5.76 thf(fact_7977_real__arch__simple,axiom,
% 5.41/5.76 ! [X: rat] :
% 5.41/5.76 ? [N3: nat] : ( ord_less_eq_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_arch_simple
% 5.41/5.76 thf(fact_7978_reals__Archimedean2,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ? [N3: nat] : ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ N3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % reals_Archimedean2
% 5.41/5.76 thf(fact_7979_reals__Archimedean2,axiom,
% 5.41/5.76 ! [X: rat] :
% 5.41/5.76 ? [N3: nat] : ( ord_less_rat @ X @ ( semiri681578069525770553at_rat @ N3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % reals_Archimedean2
% 5.41/5.76 thf(fact_7980_mult__of__nat__commute,axiom,
% 5.41/5.76 ! [X: nat,Y: complex] :
% 5.41/5.76 ( ( times_times_complex @ ( semiri8010041392384452111omplex @ X ) @ Y )
% 5.41/5.76 = ( times_times_complex @ Y @ ( semiri8010041392384452111omplex @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mult_of_nat_commute
% 5.41/5.76 thf(fact_7981_mult__of__nat__commute,axiom,
% 5.41/5.76 ! [X: nat,Y: real] :
% 5.41/5.76 ( ( times_times_real @ ( semiri5074537144036343181t_real @ X ) @ Y )
% 5.41/5.76 = ( times_times_real @ Y @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mult_of_nat_commute
% 5.41/5.76 thf(fact_7982_mult__of__nat__commute,axiom,
% 5.41/5.76 ! [X: nat,Y: rat] :
% 5.41/5.76 ( ( times_times_rat @ ( semiri681578069525770553at_rat @ X ) @ Y )
% 5.41/5.76 = ( times_times_rat @ Y @ ( semiri681578069525770553at_rat @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mult_of_nat_commute
% 5.41/5.76 thf(fact_7983_mult__of__nat__commute,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( times_times_nat @ ( semiri1316708129612266289at_nat @ X ) @ Y )
% 5.41/5.76 = ( times_times_nat @ Y @ ( semiri1316708129612266289at_nat @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mult_of_nat_commute
% 5.41/5.76 thf(fact_7984_mult__of__nat__commute,axiom,
% 5.41/5.76 ! [X: nat,Y: int] :
% 5.41/5.76 ( ( times_times_int @ ( semiri1314217659103216013at_int @ X ) @ Y )
% 5.41/5.76 = ( times_times_int @ Y @ ( semiri1314217659103216013at_int @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mult_of_nat_commute
% 5.41/5.76 thf(fact_7985_insert__mono,axiom,
% 5.41/5.76 ! [C4: set_nat,D4: set_nat,A: nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ C4 @ D4 )
% 5.41/5.76 => ( ord_less_eq_set_nat @ ( insert_nat @ A @ C4 ) @ ( insert_nat @ A @ D4 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_mono
% 5.41/5.76 thf(fact_7986_insert__mono,axiom,
% 5.41/5.76 ! [C4: set_real,D4: set_real,A: real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ C4 @ D4 )
% 5.41/5.76 => ( ord_less_eq_set_real @ ( insert_real @ A @ C4 ) @ ( insert_real @ A @ D4 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_mono
% 5.41/5.76 thf(fact_7987_insert__mono,axiom,
% 5.41/5.76 ! [C4: set_int,D4: set_int,A: int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ C4 @ D4 )
% 5.41/5.76 => ( ord_less_eq_set_int @ ( insert_int @ A @ C4 ) @ ( insert_int @ A @ D4 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_mono
% 5.41/5.76 thf(fact_7988_subset__insert,axiom,
% 5.41/5.76 ! [X: complex,A2: set_complex,B3: set_complex] :
% 5.41/5.76 ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 5.41/5.76 = ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert
% 5.41/5.76 thf(fact_7989_subset__insert,axiom,
% 5.41/5.76 ! [X: real,A2: set_real,B3: set_real] :
% 5.41/5.76 ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 5.41/5.76 = ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert
% 5.41/5.76 thf(fact_7990_subset__insert,axiom,
% 5.41/5.76 ! [X: set_nat,A2: set_set_nat,B3: set_set_nat] :
% 5.41/5.76 ( ~ ( member_set_nat @ X @ A2 )
% 5.41/5.76 => ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 5.41/5.76 = ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert
% 5.41/5.76 thf(fact_7991_subset__insert,axiom,
% 5.41/5.76 ! [X: nat,A2: set_nat,B3: set_nat] :
% 5.41/5.76 ( ~ ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 5.41/5.76 = ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert
% 5.41/5.76 thf(fact_7992_subset__insert,axiom,
% 5.41/5.76 ! [X: int,A2: set_int,B3: set_int] :
% 5.41/5.76 ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 5.41/5.76 = ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert
% 5.41/5.76 thf(fact_7993_subset__insertI,axiom,
% 5.41/5.76 ! [B3: set_nat,A: nat] : ( ord_less_eq_set_nat @ B3 @ ( insert_nat @ A @ B3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insertI
% 5.41/5.76 thf(fact_7994_subset__insertI,axiom,
% 5.41/5.76 ! [B3: set_real,A: real] : ( ord_less_eq_set_real @ B3 @ ( insert_real @ A @ B3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insertI
% 5.41/5.76 thf(fact_7995_subset__insertI,axiom,
% 5.41/5.76 ! [B3: set_int,A: int] : ( ord_less_eq_set_int @ B3 @ ( insert_int @ A @ B3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insertI
% 5.41/5.76 thf(fact_7996_subset__insertI2,axiom,
% 5.41/5.76 ! [A2: set_nat,B3: set_nat,B: nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ A2 @ B3 )
% 5.41/5.76 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ B @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insertI2
% 5.41/5.76 thf(fact_7997_subset__insertI2,axiom,
% 5.41/5.76 ! [A2: set_real,B3: set_real,B: real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ A2 @ B3 )
% 5.41/5.76 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ B @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insertI2
% 5.41/5.76 thf(fact_7998_subset__insertI2,axiom,
% 5.41/5.76 ! [A2: set_int,B3: set_int,B: int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ A2 @ B3 )
% 5.41/5.76 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ B @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insertI2
% 5.41/5.76 thf(fact_7999_take__bit__of__nat,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( bit_se2923211474154528505it_int @ N @ ( semiri1314217659103216013at_int @ M ) )
% 5.41/5.76 = ( semiri1314217659103216013at_int @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % take_bit_of_nat
% 5.41/5.76 thf(fact_8000_take__bit__of__nat,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( bit_se2925701944663578781it_nat @ N @ ( semiri1316708129612266289at_nat @ M ) )
% 5.41/5.76 = ( semiri1316708129612266289at_nat @ ( bit_se2925701944663578781it_nat @ N @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % take_bit_of_nat
% 5.41/5.76 thf(fact_8001_of__nat__and__eq,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.41/5.76 = ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_and_eq
% 5.41/5.76 thf(fact_8002_of__nat__and__eq,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( bit_se727722235901077358nd_nat @ M @ N ) )
% 5.41/5.76 = ( bit_se727722235901077358nd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_and_eq
% 5.41/5.76 thf(fact_8003_insert__Diff__if,axiom,
% 5.41/5.76 ! [X: complex,B3: set_complex,A2: set_complex] :
% 5.41/5.76 ( ( ( member_complex @ X @ B3 )
% 5.41/5.76 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_811609699411566653omplex @ A2 @ B3 ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ X @ B3 )
% 5.41/5.76 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( insert_complex @ X @ ( minus_811609699411566653omplex @ A2 @ B3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_if
% 5.41/5.76 thf(fact_8004_insert__Diff__if,axiom,
% 5.41/5.76 ! [X: real,B3: set_real,A2: set_real] :
% 5.41/5.76 ( ( ( member_real @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_minus_set_real @ A2 @ B3 ) ) )
% 5.41/5.76 & ( ~ ( member_real @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( insert_real @ X @ ( minus_minus_set_real @ A2 @ B3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_if
% 5.41/5.76 thf(fact_8005_insert__Diff__if,axiom,
% 5.41/5.76 ! [X: set_nat,B3: set_set_nat,A2: set_set_nat] :
% 5.41/5.76 ( ( ( member_set_nat @ X @ B3 )
% 5.41/5.76 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) )
% 5.41/5.76 & ( ~ ( member_set_nat @ X @ B3 )
% 5.41/5.76 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( insert_set_nat @ X @ ( minus_2163939370556025621et_nat @ A2 @ B3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_if
% 5.41/5.76 thf(fact_8006_insert__Diff__if,axiom,
% 5.41/5.76 ! [X: int,B3: set_int,A2: set_int] :
% 5.41/5.76 ( ( ( member_int @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_minus_set_int @ A2 @ B3 ) ) )
% 5.41/5.76 & ( ~ ( member_int @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( insert_int @ X @ ( minus_minus_set_int @ A2 @ B3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_if
% 5.41/5.76 thf(fact_8007_insert__Diff__if,axiom,
% 5.41/5.76 ! [X: nat,B3: set_nat,A2: set_nat] :
% 5.41/5.76 ( ( ( member_nat @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( minus_minus_set_nat @ A2 @ B3 ) ) )
% 5.41/5.76 & ( ~ ( member_nat @ X @ B3 )
% 5.41/5.76 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ B3 )
% 5.41/5.76 = ( insert_nat @ X @ ( minus_minus_set_nat @ A2 @ B3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff_if
% 5.41/5.76 thf(fact_8008_int__diff__cases,axiom,
% 5.41/5.76 ! [Z: int] :
% 5.41/5.76 ~ ! [M4: nat,N3: nat] :
% 5.41/5.76 ( Z
% 5.41/5.76 != ( minus_minus_int @ ( semiri1314217659103216013at_int @ M4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_diff_cases
% 5.41/5.76 thf(fact_8009_log__of__power__eq,axiom,
% 5.41/5.76 ! [M: nat,B: real,N: nat] :
% 5.41/5.76 ( ( ( semiri5074537144036343181t_real @ M )
% 5.41/5.76 = ( power_power_real @ B @ N ) )
% 5.41/5.76 => ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.76 => ( ( semiri5074537144036343181t_real @ N )
% 5.41/5.76 = ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_of_power_eq
% 5.41/5.76 thf(fact_8010_less__log__of__power,axiom,
% 5.41/5.76 ! [B: real,N: nat,M: real] :
% 5.41/5.76 ( ( ord_less_real @ ( power_power_real @ B @ N ) @ M )
% 5.41/5.76 => ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.76 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % less_log_of_power
% 5.41/5.76 thf(fact_8011_of__nat__less__of__int__iff,axiom,
% 5.41/5.76 ! [N: nat,X: int] :
% 5.41/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( ring_1_of_int_real @ X ) )
% 5.41/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_of_int_iff
% 5.41/5.76 thf(fact_8012_of__nat__less__of__int__iff,axiom,
% 5.41/5.76 ! [N: nat,X: int] :
% 5.41/5.76 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( ring_1_of_int_rat @ X ) )
% 5.41/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_of_int_iff
% 5.41/5.76 thf(fact_8013_of__nat__less__of__int__iff,axiom,
% 5.41/5.76 ! [N: nat,X: int] :
% 5.41/5.76 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( ring_1_of_int_int @ X ) )
% 5.41/5.76 = ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_of_int_iff
% 5.41/5.76 thf(fact_8014_num__induct,axiom,
% 5.41/5.76 ! [P: num > $o,X: num] :
% 5.41/5.76 ( ( P @ one )
% 5.41/5.76 => ( ! [X6: num] :
% 5.41/5.76 ( ( P @ X6 )
% 5.41/5.76 => ( P @ ( inc @ X6 ) ) )
% 5.41/5.76 => ( P @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % num_induct
% 5.41/5.76 thf(fact_8015_add__inc,axiom,
% 5.41/5.76 ! [X: num,Y: num] :
% 5.41/5.76 ( ( plus_plus_num @ X @ ( inc @ Y ) )
% 5.41/5.76 = ( inc @ ( plus_plus_num @ X @ Y ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_inc
% 5.41/5.76 thf(fact_8016_le__log__of__power,axiom,
% 5.41/5.76 ! [B: real,N: nat,M: real] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( power_power_real @ B @ N ) @ M )
% 5.41/5.76 => ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.76 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % le_log_of_power
% 5.41/5.76 thf(fact_8017_log__base__pow,axiom,
% 5.41/5.76 ! [A: real,N: nat,X: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.76 => ( ( log @ ( power_power_real @ A @ N ) @ X )
% 5.41/5.76 = ( divide_divide_real @ ( log @ A @ X ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_base_pow
% 5.41/5.76 thf(fact_8018_log__nat__power,axiom,
% 5.41/5.76 ! [X: real,B: real,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( log @ B @ ( power_power_real @ X @ N ) )
% 5.41/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_nat_power
% 5.41/5.76 thf(fact_8019_of__nat__0__le__iff,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_eq_real @ zero_zero_real @ ( semiri5074537144036343181t_real @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_le_iff
% 5.41/5.76 thf(fact_8020_of__nat__0__le__iff,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_eq_rat @ zero_zero_rat @ ( semiri681578069525770553at_rat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_le_iff
% 5.41/5.76 thf(fact_8021_of__nat__0__le__iff,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_eq_nat @ zero_zero_nat @ ( semiri1316708129612266289at_nat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_le_iff
% 5.41/5.76 thf(fact_8022_of__nat__0__le__iff,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_eq_int @ zero_zero_int @ ( semiri1314217659103216013at_int @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_0_le_iff
% 5.41/5.76 thf(fact_8023_of__nat__less__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ~ ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ zero_zero_real ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_0_iff
% 5.41/5.76 thf(fact_8024_of__nat__less__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ~ ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ zero_zero_rat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_0_iff
% 5.41/5.76 thf(fact_8025_of__nat__less__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ~ ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ zero_zero_nat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_0_iff
% 5.41/5.76 thf(fact_8026_of__nat__less__0__iff,axiom,
% 5.41/5.76 ! [M: nat] :
% 5.41/5.76 ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ zero_zero_int ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_0_iff
% 5.41/5.76 thf(fact_8027_of__nat__neq__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( suc @ N ) )
% 5.41/5.76 != zero_zero_complex ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_neq_0
% 5.41/5.76 thf(fact_8028_of__nat__neq__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( suc @ N ) )
% 5.41/5.76 != zero_zero_real ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_neq_0
% 5.41/5.76 thf(fact_8029_of__nat__neq__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( suc @ N ) )
% 5.41/5.76 != zero_zero_rat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_neq_0
% 5.41/5.76 thf(fact_8030_of__nat__neq__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( suc @ N ) )
% 5.41/5.76 != zero_zero_nat ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_neq_0
% 5.41/5.76 thf(fact_8031_of__nat__neq__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.41/5.76 != zero_zero_int ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_neq_0
% 5.41/5.76 thf(fact_8032_div__mult2__eq_H,axiom,
% 5.41/5.76 ! [A: nat,M: nat,N: nat] :
% 5.41/5.76 ( ( divide_divide_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.41/5.76 = ( divide_divide_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % div_mult2_eq'
% 5.41/5.76 thf(fact_8033_div__mult2__eq_H,axiom,
% 5.41/5.76 ! [A: int,M: nat,N: nat] :
% 5.41/5.76 ( ( divide_divide_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.76 = ( divide_divide_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % div_mult2_eq'
% 5.41/5.76 thf(fact_8034_less__imp__of__nat__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ M @ N )
% 5.41/5.76 => ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % less_imp_of_nat_less
% 5.41/5.76 thf(fact_8035_less__imp__of__nat__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ M @ N )
% 5.41/5.76 => ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % less_imp_of_nat_less
% 5.41/5.76 thf(fact_8036_less__imp__of__nat__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ M @ N )
% 5.41/5.76 => ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % less_imp_of_nat_less
% 5.41/5.76 thf(fact_8037_less__imp__of__nat__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ M @ N )
% 5.41/5.76 => ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % less_imp_of_nat_less
% 5.41/5.76 thf(fact_8038_of__nat__less__imp__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_imp_less
% 5.41/5.76 thf(fact_8039_of__nat__less__imp__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) )
% 5.41/5.76 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_imp_less
% 5.41/5.76 thf(fact_8040_of__nat__less__imp__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_imp_less
% 5.41/5.76 thf(fact_8041_of__nat__less__imp__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 => ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_imp_less
% 5.41/5.76 thf(fact_8042_of__nat__mono,axiom,
% 5.41/5.76 ! [I: nat,J: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.76 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ I ) @ ( semiri5074537144036343181t_real @ J ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mono
% 5.41/5.76 thf(fact_8043_of__nat__mono,axiom,
% 5.41/5.76 ! [I: nat,J: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.76 => ( ord_less_eq_rat @ ( semiri681578069525770553at_rat @ I ) @ ( semiri681578069525770553at_rat @ J ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mono
% 5.41/5.76 thf(fact_8044_of__nat__mono,axiom,
% 5.41/5.76 ! [I: nat,J: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.76 => ( ord_less_eq_nat @ ( semiri1316708129612266289at_nat @ I ) @ ( semiri1316708129612266289at_nat @ J ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mono
% 5.41/5.76 thf(fact_8045_of__nat__mono,axiom,
% 5.41/5.76 ! [I: nat,J: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.76 => ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mono
% 5.41/5.76 thf(fact_8046_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.76 = ( divide_divide_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.41/5.76 thf(fact_8047_unique__euclidean__semiring__with__nat__class_Oof__nat__div,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.76 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % unique_euclidean_semiring_with_nat_class.of_nat_div
% 5.41/5.76 thf(fact_8048_of__nat__dvd__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( dvd_dvd_Code_integer @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) )
% 5.41/5.76 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_dvd_iff
% 5.41/5.76 thf(fact_8049_of__nat__dvd__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( dvd_dvd_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) )
% 5.41/5.76 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_dvd_iff
% 5.41/5.76 thf(fact_8050_of__nat__dvd__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( dvd_dvd_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( dvd_dvd_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_dvd_iff
% 5.41/5.76 thf(fact_8051_subset__singletonD,axiom,
% 5.41/5.76 ! [A2: set_nat,X: nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.41/5.76 => ( ( A2 = bot_bot_set_nat )
% 5.41/5.76 | ( A2
% 5.41/5.76 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_singletonD
% 5.41/5.76 thf(fact_8052_subset__singletonD,axiom,
% 5.41/5.76 ! [A2: set_real,X: real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) )
% 5.41/5.76 => ( ( A2 = bot_bot_set_real )
% 5.41/5.76 | ( A2
% 5.41/5.76 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_singletonD
% 5.41/5.76 thf(fact_8053_subset__singletonD,axiom,
% 5.41/5.76 ! [A2: set_int,X: int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) )
% 5.41/5.76 => ( ( A2 = bot_bot_set_int )
% 5.41/5.76 | ( A2
% 5.41/5.76 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_singletonD
% 5.41/5.76 thf(fact_8054_subset__singleton__iff,axiom,
% 5.41/5.76 ! [X8: set_nat,A: nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ X8 @ ( insert_nat @ A @ bot_bot_set_nat ) )
% 5.41/5.76 = ( ( X8 = bot_bot_set_nat )
% 5.41/5.76 | ( X8
% 5.41/5.76 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_singleton_iff
% 5.41/5.76 thf(fact_8055_subset__singleton__iff,axiom,
% 5.41/5.76 ! [X8: set_real,A: real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ X8 @ ( insert_real @ A @ bot_bot_set_real ) )
% 5.41/5.76 = ( ( X8 = bot_bot_set_real )
% 5.41/5.76 | ( X8
% 5.41/5.76 = ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_singleton_iff
% 5.41/5.76 thf(fact_8056_subset__singleton__iff,axiom,
% 5.41/5.76 ! [X8: set_int,A: int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ X8 @ ( insert_int @ A @ bot_bot_set_int ) )
% 5.41/5.76 = ( ( X8 = bot_bot_set_int )
% 5.41/5.76 | ( X8
% 5.41/5.76 = ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_singleton_iff
% 5.41/5.76 thf(fact_8057_int__ops_I1_J,axiom,
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ zero_zero_nat )
% 5.41/5.76 = zero_zero_int ) ).
% 5.41/5.76
% 5.41/5.76 % int_ops(1)
% 5.41/5.76 thf(fact_8058_int__ops_I3_J,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( numeral_numeral_nat @ N ) )
% 5.41/5.76 = ( numeral_numeral_int @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_ops(3)
% 5.41/5.76 thf(fact_8059_nat__int__comparison_I2_J,axiom,
% 5.41/5.76 ( ord_less_nat
% 5.41/5.76 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_int_comparison(2)
% 5.41/5.76 thf(fact_8060_atLeastAtMost__singleton_H,axiom,
% 5.41/5.76 ! [A: nat,B: nat] :
% 5.41/5.76 ( ( A = B )
% 5.41/5.76 => ( ( set_or1269000886237332187st_nat @ A @ B )
% 5.41/5.76 = ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton'
% 5.41/5.76 thf(fact_8061_atLeastAtMost__singleton_H,axiom,
% 5.41/5.76 ! [A: int,B: int] :
% 5.41/5.76 ( ( A = B )
% 5.41/5.76 => ( ( set_or1266510415728281911st_int @ A @ B )
% 5.41/5.76 = ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton'
% 5.41/5.76 thf(fact_8062_atLeastAtMost__singleton_H,axiom,
% 5.41/5.76 ! [A: real,B: real] :
% 5.41/5.76 ( ( A = B )
% 5.41/5.76 => ( ( set_or1222579329274155063t_real @ A @ B )
% 5.41/5.76 = ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMost_singleton'
% 5.41/5.76 thf(fact_8063_Diff__insert__absorb,axiom,
% 5.41/5.76 ! [X: complex,A2: set_complex] :
% 5.41/5.76 ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( minus_811609699411566653omplex @ ( insert_complex @ X @ A2 ) @ ( insert_complex @ X @ bot_bot_set_complex ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert_absorb
% 5.41/5.76 thf(fact_8064_Diff__insert__absorb,axiom,
% 5.41/5.76 ! [X: set_nat,A2: set_set_nat] :
% 5.41/5.76 ( ~ ( member_set_nat @ X @ A2 )
% 5.41/5.76 => ( ( minus_2163939370556025621et_nat @ ( insert_set_nat @ X @ A2 ) @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert_absorb
% 5.41/5.76 thf(fact_8065_Diff__insert__absorb,axiom,
% 5.41/5.76 ! [X: int,A2: set_int] :
% 5.41/5.76 ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( minus_minus_set_int @ ( insert_int @ X @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert_absorb
% 5.41/5.76 thf(fact_8066_Diff__insert__absorb,axiom,
% 5.41/5.76 ! [X: real,A2: set_real] :
% 5.41/5.76 ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( minus_minus_set_real @ ( insert_real @ X @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert_absorb
% 5.41/5.76 thf(fact_8067_Diff__insert__absorb,axiom,
% 5.41/5.76 ! [X: nat,A2: set_nat] :
% 5.41/5.76 ( ~ ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ( minus_minus_set_nat @ ( insert_nat @ X @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert_absorb
% 5.41/5.76 thf(fact_8068_Diff__insert2,axiom,
% 5.41/5.76 ! [A2: set_int,A: int,B3: set_int] :
% 5.41/5.76 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) @ B3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert2
% 5.41/5.76 thf(fact_8069_Diff__insert2,axiom,
% 5.41/5.76 ! [A2: set_real,A: real,B3: set_real] :
% 5.41/5.76 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) @ B3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert2
% 5.41/5.76 thf(fact_8070_Diff__insert2,axiom,
% 5.41/5.76 ! [A2: set_nat,A: nat,B3: set_nat] :
% 5.41/5.76 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) @ B3 ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert2
% 5.41/5.76 thf(fact_8071_insert__Diff,axiom,
% 5.41/5.76 ! [A: complex,A2: set_complex] :
% 5.41/5.76 ( ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( insert_complex @ A @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff
% 5.41/5.76 thf(fact_8072_insert__Diff,axiom,
% 5.41/5.76 ! [A: set_nat,A2: set_set_nat] :
% 5.41/5.76 ( ( member_set_nat @ A @ A2 )
% 5.41/5.76 => ( ( insert_set_nat @ A @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff
% 5.41/5.76 thf(fact_8073_insert__Diff,axiom,
% 5.41/5.76 ! [A: int,A2: set_int] :
% 5.41/5.76 ( ( member_int @ A @ A2 )
% 5.41/5.76 => ( ( insert_int @ A @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff
% 5.41/5.76 thf(fact_8074_insert__Diff,axiom,
% 5.41/5.76 ! [A: real,A2: set_real] :
% 5.41/5.76 ( ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( insert_real @ A @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff
% 5.41/5.76 thf(fact_8075_insert__Diff,axiom,
% 5.41/5.76 ! [A: nat,A2: set_nat] :
% 5.41/5.76 ( ( member_nat @ A @ A2 )
% 5.41/5.76 => ( ( insert_nat @ A @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = A2 ) ) ).
% 5.41/5.76
% 5.41/5.76 % insert_Diff
% 5.41/5.76 thf(fact_8076_Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_int,A: int,B3: set_int] :
% 5.41/5.76 ( ( minus_minus_set_int @ A2 @ ( insert_int @ A @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_int @ ( minus_minus_set_int @ A2 @ B3 ) @ ( insert_int @ A @ bot_bot_set_int ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert
% 5.41/5.76 thf(fact_8077_Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_real,A: real,B3: set_real] :
% 5.41/5.76 ( ( minus_minus_set_real @ A2 @ ( insert_real @ A @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_real @ ( minus_minus_set_real @ A2 @ B3 ) @ ( insert_real @ A @ bot_bot_set_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert
% 5.41/5.76 thf(fact_8078_Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_nat,A: nat,B3: set_nat] :
% 5.41/5.76 ( ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ B3 ) )
% 5.41/5.76 = ( minus_minus_set_nat @ ( minus_minus_set_nat @ A2 @ B3 ) @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_insert
% 5.41/5.76 thf(fact_8079_zle__int,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.76 = ( ord_less_eq_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % zle_int
% 5.41/5.76 thf(fact_8080_nat__int__comparison_I3_J,axiom,
% 5.41/5.76 ( ord_less_eq_nat
% 5.41/5.76 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_int_comparison(3)
% 5.41/5.76 thf(fact_8081_subset__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_complex,B3: set_complex,X: complex,C4: set_complex] :
% 5.41/5.76 ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ ( insert_complex @ X @ C4 ) ) )
% 5.41/5.76 = ( ( ord_le211207098394363844omplex @ A2 @ ( minus_811609699411566653omplex @ B3 @ C4 ) )
% 5.41/5.76 & ~ ( member_complex @ X @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Diff_insert
% 5.41/5.76 thf(fact_8082_subset__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_real,B3: set_real,X: real,C4: set_real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ ( insert_real @ X @ C4 ) ) )
% 5.41/5.76 = ( ( ord_less_eq_set_real @ A2 @ ( minus_minus_set_real @ B3 @ C4 ) )
% 5.41/5.76 & ~ ( member_real @ X @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Diff_insert
% 5.41/5.76 thf(fact_8083_subset__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_set_nat,B3: set_set_nat,X: set_nat,C4: set_set_nat] :
% 5.41/5.76 ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B3 @ ( insert_set_nat @ X @ C4 ) ) )
% 5.41/5.76 = ( ( ord_le6893508408891458716et_nat @ A2 @ ( minus_2163939370556025621et_nat @ B3 @ C4 ) )
% 5.41/5.76 & ~ ( member_set_nat @ X @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Diff_insert
% 5.41/5.76 thf(fact_8084_subset__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_nat,B3: set_nat,X: nat,C4: set_nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ ( insert_nat @ X @ C4 ) ) )
% 5.41/5.76 = ( ( ord_less_eq_set_nat @ A2 @ ( minus_minus_set_nat @ B3 @ C4 ) )
% 5.41/5.76 & ~ ( member_nat @ X @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Diff_insert
% 5.41/5.76 thf(fact_8085_subset__Diff__insert,axiom,
% 5.41/5.76 ! [A2: set_int,B3: set_int,X: int,C4: set_int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ ( insert_int @ X @ C4 ) ) )
% 5.41/5.76 = ( ( ord_less_eq_set_int @ A2 @ ( minus_minus_set_int @ B3 @ C4 ) )
% 5.41/5.76 & ~ ( member_int @ X @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_Diff_insert
% 5.41/5.76 thf(fact_8086_nonneg__int__cases,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ( K
% 5.41/5.76 != ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nonneg_int_cases
% 5.41/5.76 thf(fact_8087_zero__le__imp__eq__int,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.76 => ? [N3: nat] :
% 5.41/5.76 ( K
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zero_le_imp_eq_int
% 5.41/5.76 thf(fact_8088_of__nat__mod,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri4939895301339042750nteger @ ( modulo_modulo_nat @ M @ N ) )
% 5.41/5.76 = ( modulo364778990260209775nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mod
% 5.41/5.76 thf(fact_8089_of__nat__mod,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( modulo_modulo_nat @ M @ N ) )
% 5.41/5.76 = ( modulo_modulo_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mod
% 5.41/5.76 thf(fact_8090_of__nat__mod,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) )
% 5.41/5.76 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mod
% 5.41/5.76 thf(fact_8091_zadd__int__left,axiom,
% 5.41/5.76 ! [M: nat,N: nat,Z: int] :
% 5.41/5.76 ( ( plus_plus_int @ ( semiri1314217659103216013at_int @ M ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ Z ) )
% 5.41/5.76 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ M @ N ) ) @ Z ) ) ).
% 5.41/5.76
% 5.41/5.76 % zadd_int_left
% 5.41/5.76 thf(fact_8092_int__plus,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ N @ M ) )
% 5.41/5.76 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_plus
% 5.41/5.76 thf(fact_8093_int__ops_I5_J,axiom,
% 5.41/5.76 ! [A: nat,B: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( plus_plus_nat @ A @ B ) )
% 5.41/5.76 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_ops(5)
% 5.41/5.76 thf(fact_8094_int__ops_I7_J,axiom,
% 5.41/5.76 ! [A: nat,B: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( times_times_nat @ A @ B ) )
% 5.41/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_ops(7)
% 5.41/5.76 thf(fact_8095_int__ops_I2_J,axiom,
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ one_one_nat )
% 5.41/5.76 = one_one_int ) ).
% 5.41/5.76
% 5.41/5.76 % int_ops(2)
% 5.41/5.76 thf(fact_8096_zle__iff__zadd,axiom,
% 5.41/5.76 ( ord_less_eq_int
% 5.41/5.76 = ( ^ [W3: int,Z3: int] :
% 5.41/5.76 ? [N2: nat] :
% 5.41/5.76 ( Z3
% 5.41/5.76 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zle_iff_zadd
% 5.41/5.76 thf(fact_8097_zdiv__int,axiom,
% 5.41/5.76 ! [A: nat,B: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( divide_divide_nat @ A @ B ) )
% 5.41/5.76 = ( divide_divide_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zdiv_int
% 5.41/5.76 thf(fact_8098_of__nat__max,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( semiri4216267220026989637d_enat @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.76 = ( ord_ma741700101516333627d_enat @ ( semiri4216267220026989637d_enat @ X ) @ ( semiri4216267220026989637d_enat @ Y ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_max
% 5.41/5.76 thf(fact_8099_of__nat__max,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( semiri4939895301339042750nteger @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.76 = ( ord_max_Code_integer @ ( semiri4939895301339042750nteger @ X ) @ ( semiri4939895301339042750nteger @ Y ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_max
% 5.41/5.76 thf(fact_8100_of__nat__max,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.76 = ( ord_max_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ Y ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_max
% 5.41/5.76 thf(fact_8101_of__nat__max,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.76 = ( ord_max_rat @ ( semiri681578069525770553at_rat @ X ) @ ( semiri681578069525770553at_rat @ Y ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_max
% 5.41/5.76 thf(fact_8102_of__nat__max,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.76 = ( ord_max_nat @ ( semiri1316708129612266289at_nat @ X ) @ ( semiri1316708129612266289at_nat @ Y ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_max
% 5.41/5.76 thf(fact_8103_of__nat__max,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( ord_max_nat @ X @ Y ) )
% 5.41/5.76 = ( ord_max_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_max
% 5.41/5.76 thf(fact_8104_zmod__int,axiom,
% 5.41/5.76 ! [A: nat,B: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ A @ B ) )
% 5.41/5.76 = ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zmod_int
% 5.41/5.76 thf(fact_8105_log2__of__power__eq,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( M
% 5.41/5.76 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.76 => ( ( semiri5074537144036343181t_real @ N )
% 5.41/5.76 = ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log2_of_power_eq
% 5.41/5.76 thf(fact_8106_log__of__power__less,axiom,
% 5.41/5.76 ! [M: nat,B: real,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.41/5.76 => ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.76 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.76 => ( ord_less_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_of_power_less
% 5.41/5.76 thf(fact_8107_nat__less__as__int,axiom,
% 5.41/5.76 ( ord_less_nat
% 5.41/5.76 = ( ^ [A3: nat,B2: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_less_as_int
% 5.41/5.76 thf(fact_8108_nat__leq__as__int,axiom,
% 5.41/5.76 ( ord_less_eq_nat
% 5.41/5.76 = ( ^ [A3: nat,B2: nat] : ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_leq_as_int
% 5.41/5.76 thf(fact_8109_of__nat__mask__eq,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri1316708129612266289at_nat @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.41/5.76 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mask_eq
% 5.41/5.76 thf(fact_8110_of__nat__mask__eq,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( bit_se2002935070580805687sk_nat @ N ) )
% 5.41/5.76 = ( bit_se2000444600071755411sk_int @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_mask_eq
% 5.41/5.76 thf(fact_8111_inc_Osimps_I1_J,axiom,
% 5.41/5.76 ( ( inc @ one )
% 5.41/5.76 = ( bit0 @ one ) ) ).
% 5.41/5.76
% 5.41/5.76 % inc.simps(1)
% 5.41/5.76 thf(fact_8112_inc_Osimps_I3_J,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( inc @ ( bit1 @ X ) )
% 5.41/5.76 = ( bit0 @ ( inc @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % inc.simps(3)
% 5.41/5.76 thf(fact_8113_inc_Osimps_I2_J,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( inc @ ( bit0 @ X ) )
% 5.41/5.76 = ( bit1 @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % inc.simps(2)
% 5.41/5.76 thf(fact_8114_log__of__power__le,axiom,
% 5.41/5.76 ! [M: nat,B: real,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ M ) @ ( power_power_real @ B @ N ) )
% 5.41/5.76 => ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.76 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.76 => ( ord_less_eq_real @ ( log @ B @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_of_power_le
% 5.41/5.76 thf(fact_8115_ex__less__of__nat__mult,axiom,
% 5.41/5.76 ! [X: real,Y: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ? [N3: nat] : ( ord_less_real @ Y @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % ex_less_of_nat_mult
% 5.41/5.76 thf(fact_8116_ex__less__of__nat__mult,axiom,
% 5.41/5.76 ! [X: rat,Y: rat] :
% 5.41/5.76 ( ( ord_less_rat @ zero_zero_rat @ X )
% 5.41/5.76 => ? [N3: nat] : ( ord_less_rat @ Y @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N3 ) @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % ex_less_of_nat_mult
% 5.41/5.76 thf(fact_8117_add__One,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( plus_plus_num @ X @ one )
% 5.41/5.76 = ( inc @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % add_One
% 5.41/5.76 thf(fact_8118_inc__BitM__eq,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( inc @ ( bitM @ N ) )
% 5.41/5.76 = ( bit0 @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % inc_BitM_eq
% 5.41/5.76 thf(fact_8119_of__nat__diff,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.76 => ( ( semiri8010041392384452111omplex @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.76 = ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_diff
% 5.41/5.76 thf(fact_8120_of__nat__diff,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.76 => ( ( semiri5074537144036343181t_real @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.76 = ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_diff
% 5.41/5.76 thf(fact_8121_of__nat__diff,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.76 => ( ( semiri681578069525770553at_rat @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.76 = ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_diff
% 5.41/5.76 thf(fact_8122_of__nat__diff,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.76 => ( ( semiri1316708129612266289at_nat @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.76 = ( minus_minus_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_diff
% 5.41/5.76 thf(fact_8123_of__nat__diff,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.76 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ M @ N ) )
% 5.41/5.76 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_diff
% 5.41/5.76 thf(fact_8124_BitM__inc__eq,axiom,
% 5.41/5.76 ! [N: num] :
% 5.41/5.76 ( ( bitM @ ( inc @ N ) )
% 5.41/5.76 = ( bit1 @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % BitM_inc_eq
% 5.41/5.76 thf(fact_8125_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_complex,P: set_complex > $o,F: complex > rat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ! [X6: complex,S5: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S5 )
% 5.41/5.76 => ( ! [Y2: complex] :
% 5.41/5.76 ( ( member_complex @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8126_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_nat,P: set_nat > $o,F: nat > rat] :
% 5.41/5.76 ( ( finite_finite_nat @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [X6: nat,S5: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ S5 )
% 5.41/5.76 => ( ! [Y2: nat] :
% 5.41/5.76 ( ( member_nat @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8127_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_int,P: set_int > $o,F: int > rat] :
% 5.41/5.76 ( ( finite_finite_int @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [X6: int,S5: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ S5 )
% 5.41/5.76 => ( ! [Y2: int] :
% 5.41/5.76 ( ( member_int @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_int @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8128_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_real,P: set_real > $o,F: real > rat] :
% 5.41/5.76 ( ( finite_finite_real @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [X6: real,S5: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ S5 )
% 5.41/5.76 => ( ! [Y2: real] :
% 5.41/5.76 ( ( member_real @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_real @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8129_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_complex,P: set_complex > $o,F: complex > num] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ! [X6: complex,S5: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S5 )
% 5.41/5.76 => ( ! [Y2: complex] :
% 5.41/5.76 ( ( member_complex @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8130_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_nat,P: set_nat > $o,F: nat > num] :
% 5.41/5.76 ( ( finite_finite_nat @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [X6: nat,S5: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ S5 )
% 5.41/5.76 => ( ! [Y2: nat] :
% 5.41/5.76 ( ( member_nat @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8131_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_int,P: set_int > $o,F: int > num] :
% 5.41/5.76 ( ( finite_finite_int @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [X6: int,S5: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ S5 )
% 5.41/5.76 => ( ! [Y2: int] :
% 5.41/5.76 ( ( member_int @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_int @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8132_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_real,P: set_real > $o,F: real > num] :
% 5.41/5.76 ( ( finite_finite_real @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [X6: real,S5: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ S5 )
% 5.41/5.76 => ( ! [Y2: real] :
% 5.41/5.76 ( ( member_real @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_num @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_real @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8133_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_complex,P: set_complex > $o,F: complex > nat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ! [X6: complex,S5: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S5 )
% 5.41/5.76 => ( ! [Y2: complex] :
% 5.41/5.76 ( ( member_complex @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_complex @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8134_finite__ranking__induct,axiom,
% 5.41/5.76 ! [S2: set_nat,P: set_nat > $o,F: nat > nat] :
% 5.41/5.76 ( ( finite_finite_nat @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [X6: nat,S5: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ S5 )
% 5.41/5.76 => ( ! [Y2: nat] :
% 5.41/5.76 ( ( member_nat @ Y2 @ S5 )
% 5.41/5.76 => ( ord_less_eq_nat @ ( F @ Y2 ) @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( P @ S5 )
% 5.41/5.76 => ( P @ ( insert_nat @ X6 @ S5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_ranking_induct
% 5.41/5.76 thf(fact_8135_finite__linorder__max__induct,axiom,
% 5.41/5.76 ! [A2: set_real,P: set_real > $o] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [B5: real,A7: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ A7 )
% 5.41/5.76 => ( ! [X4: real] :
% 5.41/5.76 ( ( member_real @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_real @ X4 @ B5 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_max_induct
% 5.41/5.76 thf(fact_8136_finite__linorder__max__induct,axiom,
% 5.41/5.76 ! [A2: set_rat,P: set_rat > $o] :
% 5.41/5.76 ( ( finite_finite_rat @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_rat )
% 5.41/5.76 => ( ! [B5: rat,A7: set_rat] :
% 5.41/5.76 ( ( finite_finite_rat @ A7 )
% 5.41/5.76 => ( ! [X4: rat] :
% 5.41/5.76 ( ( member_rat @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_rat @ X4 @ B5 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_max_induct
% 5.41/5.76 thf(fact_8137_finite__linorder__max__induct,axiom,
% 5.41/5.76 ! [A2: set_num,P: set_num > $o] :
% 5.41/5.76 ( ( finite_finite_num @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_num )
% 5.41/5.76 => ( ! [B5: num,A7: set_num] :
% 5.41/5.76 ( ( finite_finite_num @ A7 )
% 5.41/5.76 => ( ! [X4: num] :
% 5.41/5.76 ( ( member_num @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_num @ X4 @ B5 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_max_induct
% 5.41/5.76 thf(fact_8138_finite__linorder__max__induct,axiom,
% 5.41/5.76 ! [A2: set_nat,P: set_nat > $o] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [B5: nat,A7: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ A7 )
% 5.41/5.76 => ( ! [X4: nat] :
% 5.41/5.76 ( ( member_nat @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_nat @ X4 @ B5 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_max_induct
% 5.41/5.76 thf(fact_8139_finite__linorder__max__induct,axiom,
% 5.41/5.76 ! [A2: set_int,P: set_int > $o] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [B5: int,A7: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ A7 )
% 5.41/5.76 => ( ! [X4: int] :
% 5.41/5.76 ( ( member_int @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_int @ X4 @ B5 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_max_induct
% 5.41/5.76 thf(fact_8140_finite__linorder__min__induct,axiom,
% 5.41/5.76 ! [A2: set_real,P: set_real > $o] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [B5: real,A7: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ A7 )
% 5.41/5.76 => ( ! [X4: real] :
% 5.41/5.76 ( ( member_real @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_real @ B5 @ X4 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_real @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_min_induct
% 5.41/5.76 thf(fact_8141_finite__linorder__min__induct,axiom,
% 5.41/5.76 ! [A2: set_rat,P: set_rat > $o] :
% 5.41/5.76 ( ( finite_finite_rat @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_rat )
% 5.41/5.76 => ( ! [B5: rat,A7: set_rat] :
% 5.41/5.76 ( ( finite_finite_rat @ A7 )
% 5.41/5.76 => ( ! [X4: rat] :
% 5.41/5.76 ( ( member_rat @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_rat @ B5 @ X4 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_rat @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_min_induct
% 5.41/5.76 thf(fact_8142_finite__linorder__min__induct,axiom,
% 5.41/5.76 ! [A2: set_num,P: set_num > $o] :
% 5.41/5.76 ( ( finite_finite_num @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_num )
% 5.41/5.76 => ( ! [B5: num,A7: set_num] :
% 5.41/5.76 ( ( finite_finite_num @ A7 )
% 5.41/5.76 => ( ! [X4: num] :
% 5.41/5.76 ( ( member_num @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_num @ B5 @ X4 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_num @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_min_induct
% 5.41/5.76 thf(fact_8143_finite__linorder__min__induct,axiom,
% 5.41/5.76 ! [A2: set_nat,P: set_nat > $o] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [B5: nat,A7: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ A7 )
% 5.41/5.76 => ( ! [X4: nat] :
% 5.41/5.76 ( ( member_nat @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_nat @ B5 @ X4 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_nat @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_min_induct
% 5.41/5.76 thf(fact_8144_finite__linorder__min__induct,axiom,
% 5.41/5.76 ! [A2: set_int,P: set_int > $o] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [B5: int,A7: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ A7 )
% 5.41/5.76 => ( ! [X4: int] :
% 5.41/5.76 ( ( member_int @ X4 @ A7 )
% 5.41/5.76 => ( ord_less_int @ B5 @ X4 ) )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( insert_int @ B5 @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_linorder_min_induct
% 5.41/5.76 thf(fact_8145_exp__of__nat2__mult,axiom,
% 5.41/5.76 ! [X: complex,N: nat] :
% 5.41/5.76 ( ( exp_complex @ ( times_times_complex @ X @ ( semiri8010041392384452111omplex @ N ) ) )
% 5.41/5.76 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_of_nat2_mult
% 5.41/5.76 thf(fact_8146_exp__of__nat2__mult,axiom,
% 5.41/5.76 ! [X: real,N: nat] :
% 5.41/5.76 ( ( exp_real @ ( times_times_real @ X @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.41/5.76 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_of_nat2_mult
% 5.41/5.76 thf(fact_8147_exp__of__nat__mult,axiom,
% 5.41/5.76 ! [N: nat,X: complex] :
% 5.41/5.76 ( ( exp_complex @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ X ) )
% 5.41/5.76 = ( power_power_complex @ ( exp_complex @ X ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_of_nat_mult
% 5.41/5.76 thf(fact_8148_exp__of__nat__mult,axiom,
% 5.41/5.76 ! [N: nat,X: real] :
% 5.41/5.76 ( ( exp_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) )
% 5.41/5.76 = ( power_power_real @ ( exp_real @ X ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_of_nat_mult
% 5.41/5.76 thf(fact_8149_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > real] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( groups8097168146408367636l_real @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8150_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > real] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( groups8778361861064173332t_real @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8151_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( groups5808333547571424918x_real @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8152_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > rat] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( groups1300246762558778688al_rat @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8153_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_nat,X: nat,G: nat > rat] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ( ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 5.41/5.76 = ( groups2906978787729119204at_rat @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ G @ ( insert_nat @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups2906978787729119204at_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8154_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > rat] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( groups3906332499630173760nt_rat @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8155_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > rat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( groups5058264527183730370ex_rat @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8156_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > nat] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( groups1935376822645274424al_nat @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8157_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > nat] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( groups4541462559716669496nt_nat @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8158_sum_Oinsert__if,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( groups5693394587270226106ex_nat @ G @ A2 ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ A2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_if
% 5.41/5.76 thf(fact_8159_finite__subset__induct,axiom,
% 5.41/5.76 ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ F3 )
% 5.41/5.76 => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_set_nat )
% 5.41/5.76 => ( ! [A5: set_nat,F4: set_set_nat] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ F4 )
% 5.41/5.76 => ( ( member_set_nat @ A5 @ A2 )
% 5.41/5.76 => ( ~ ( member_set_nat @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_set_nat @ A5 @ F4 ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct
% 5.41/5.76 thf(fact_8160_finite__subset__induct,axiom,
% 5.41/5.76 ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ F3 )
% 5.41/5.76 => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ! [A5: complex,F4: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ F4 )
% 5.41/5.76 => ( ( member_complex @ A5 @ A2 )
% 5.41/5.76 => ( ~ ( member_complex @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_complex @ A5 @ F4 ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct
% 5.41/5.76 thf(fact_8161_finite__subset__induct,axiom,
% 5.41/5.76 ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 5.41/5.76 ( ( finite_finite_nat @ F3 )
% 5.41/5.76 => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [A5: nat,F4: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ F4 )
% 5.41/5.76 => ( ( member_nat @ A5 @ A2 )
% 5.41/5.76 => ( ~ ( member_nat @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_nat @ A5 @ F4 ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct
% 5.41/5.76 thf(fact_8162_finite__subset__induct,axiom,
% 5.41/5.76 ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 5.41/5.76 ( ( finite_finite_real @ F3 )
% 5.41/5.76 => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [A5: real,F4: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ F4 )
% 5.41/5.76 => ( ( member_real @ A5 @ A2 )
% 5.41/5.76 => ( ~ ( member_real @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_real @ A5 @ F4 ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct
% 5.41/5.76 thf(fact_8163_finite__subset__induct,axiom,
% 5.41/5.76 ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 5.41/5.76 ( ( finite_finite_int @ F3 )
% 5.41/5.76 => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [A5: int,F4: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ F4 )
% 5.41/5.76 => ( ( member_int @ A5 @ A2 )
% 5.41/5.76 => ( ~ ( member_int @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_int @ A5 @ F4 ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct
% 5.41/5.76 thf(fact_8164_finite__subset__induct_H,axiom,
% 5.41/5.76 ! [F3: set_set_nat,A2: set_set_nat,P: set_set_nat > $o] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ F3 )
% 5.41/5.76 => ( ( ord_le6893508408891458716et_nat @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_set_nat )
% 5.41/5.76 => ( ! [A5: set_nat,F4: set_set_nat] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ F4 )
% 5.41/5.76 => ( ( member_set_nat @ A5 @ A2 )
% 5.41/5.76 => ( ( ord_le6893508408891458716et_nat @ F4 @ A2 )
% 5.41/5.76 => ( ~ ( member_set_nat @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_set_nat @ A5 @ F4 ) ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct'
% 5.41/5.76 thf(fact_8165_finite__subset__induct_H,axiom,
% 5.41/5.76 ! [F3: set_complex,A2: set_complex,P: set_complex > $o] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ F3 )
% 5.41/5.76 => ( ( ord_le211207098394363844omplex @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ! [A5: complex,F4: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ F4 )
% 5.41/5.76 => ( ( member_complex @ A5 @ A2 )
% 5.41/5.76 => ( ( ord_le211207098394363844omplex @ F4 @ A2 )
% 5.41/5.76 => ( ~ ( member_complex @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_complex @ A5 @ F4 ) ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct'
% 5.41/5.76 thf(fact_8166_finite__subset__induct_H,axiom,
% 5.41/5.76 ! [F3: set_nat,A2: set_nat,P: set_nat > $o] :
% 5.41/5.76 ( ( finite_finite_nat @ F3 )
% 5.41/5.76 => ( ( ord_less_eq_set_nat @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [A5: nat,F4: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ F4 )
% 5.41/5.76 => ( ( member_nat @ A5 @ A2 )
% 5.41/5.76 => ( ( ord_less_eq_set_nat @ F4 @ A2 )
% 5.41/5.76 => ( ~ ( member_nat @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_nat @ A5 @ F4 ) ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct'
% 5.41/5.76 thf(fact_8167_finite__subset__induct_H,axiom,
% 5.41/5.76 ! [F3: set_real,A2: set_real,P: set_real > $o] :
% 5.41/5.76 ( ( finite_finite_real @ F3 )
% 5.41/5.76 => ( ( ord_less_eq_set_real @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [A5: real,F4: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ F4 )
% 5.41/5.76 => ( ( member_real @ A5 @ A2 )
% 5.41/5.76 => ( ( ord_less_eq_set_real @ F4 @ A2 )
% 5.41/5.76 => ( ~ ( member_real @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_real @ A5 @ F4 ) ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct'
% 5.41/5.76 thf(fact_8168_finite__subset__induct_H,axiom,
% 5.41/5.76 ! [F3: set_int,A2: set_int,P: set_int > $o] :
% 5.41/5.76 ( ( finite_finite_int @ F3 )
% 5.41/5.76 => ( ( ord_less_eq_set_int @ F3 @ A2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [A5: int,F4: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ F4 )
% 5.41/5.76 => ( ( member_int @ A5 @ A2 )
% 5.41/5.76 => ( ( ord_less_eq_set_int @ F4 @ A2 )
% 5.41/5.76 => ( ~ ( member_int @ A5 @ F4 )
% 5.41/5.76 => ( ( P @ F4 )
% 5.41/5.76 => ( P @ ( insert_int @ A5 @ F4 ) ) ) ) ) ) )
% 5.41/5.76 => ( P @ F3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_subset_induct'
% 5.41/5.76 thf(fact_8169_reals__Archimedean3,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ! [Y2: real] :
% 5.41/5.76 ? [N3: nat] : ( ord_less_real @ Y2 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % reals_Archimedean3
% 5.41/5.76 thf(fact_8170_log__ln,axiom,
% 5.41/5.76 ( ln_ln_real
% 5.41/5.76 = ( log @ ( exp_real @ one_one_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_ln
% 5.41/5.76 thf(fact_8171_int__cases4,axiom,
% 5.41/5.76 ! [M: int] :
% 5.41/5.76 ( ! [N3: nat] :
% 5.41/5.76 ( M
% 5.41/5.76 != ( semiri1314217659103216013at_int @ N3 ) )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.41/5.76 => ( M
% 5.41/5.76 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_cases4
% 5.41/5.76 thf(fact_8172_infinite__remove,axiom,
% 5.41/5.76 ! [S2: set_complex,A: complex] :
% 5.41/5.76 ( ~ ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_remove
% 5.41/5.76 thf(fact_8173_infinite__remove,axiom,
% 5.41/5.76 ! [S2: set_int,A: int] :
% 5.41/5.76 ( ~ ( finite_finite_int @ S2 )
% 5.41/5.76 => ~ ( finite_finite_int @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_remove
% 5.41/5.76 thf(fact_8174_infinite__remove,axiom,
% 5.41/5.76 ! [S2: set_real,A: real] :
% 5.41/5.76 ( ~ ( finite_finite_real @ S2 )
% 5.41/5.76 => ~ ( finite_finite_real @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_remove
% 5.41/5.76 thf(fact_8175_infinite__remove,axiom,
% 5.41/5.76 ! [S2: set_nat,A: nat] :
% 5.41/5.76 ( ~ ( finite_finite_nat @ S2 )
% 5.41/5.76 => ~ ( finite_finite_nat @ ( minus_minus_set_nat @ S2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_remove
% 5.41/5.76 thf(fact_8176_infinite__coinduct,axiom,
% 5.41/5.76 ! [X8: set_complex > $o,A2: set_complex] :
% 5.41/5.76 ( ( X8 @ A2 )
% 5.41/5.76 => ( ! [A7: set_complex] :
% 5.41/5.76 ( ( X8 @ A7 )
% 5.41/5.76 => ? [X4: complex] :
% 5.41/5.76 ( ( member_complex @ X4 @ A7 )
% 5.41/5.76 & ( ( X8 @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) )
% 5.41/5.76 | ~ ( finite3207457112153483333omplex @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) ) ) )
% 5.41/5.76 => ~ ( finite3207457112153483333omplex @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_coinduct
% 5.41/5.76 thf(fact_8177_infinite__coinduct,axiom,
% 5.41/5.76 ! [X8: set_int > $o,A2: set_int] :
% 5.41/5.76 ( ( X8 @ A2 )
% 5.41/5.76 => ( ! [A7: set_int] :
% 5.41/5.76 ( ( X8 @ A7 )
% 5.41/5.76 => ? [X4: int] :
% 5.41/5.76 ( ( member_int @ X4 @ A7 )
% 5.41/5.76 & ( ( X8 @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) )
% 5.41/5.76 | ~ ( finite_finite_int @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) ) ) )
% 5.41/5.76 => ~ ( finite_finite_int @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_coinduct
% 5.41/5.76 thf(fact_8178_infinite__coinduct,axiom,
% 5.41/5.76 ! [X8: set_real > $o,A2: set_real] :
% 5.41/5.76 ( ( X8 @ A2 )
% 5.41/5.76 => ( ! [A7: set_real] :
% 5.41/5.76 ( ( X8 @ A7 )
% 5.41/5.76 => ? [X4: real] :
% 5.41/5.76 ( ( member_real @ X4 @ A7 )
% 5.41/5.76 & ( ( X8 @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) )
% 5.41/5.76 | ~ ( finite_finite_real @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) ) ) )
% 5.41/5.76 => ~ ( finite_finite_real @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_coinduct
% 5.41/5.76 thf(fact_8179_infinite__coinduct,axiom,
% 5.41/5.76 ! [X8: set_nat > $o,A2: set_nat] :
% 5.41/5.76 ( ( X8 @ A2 )
% 5.41/5.76 => ( ! [A7: set_nat] :
% 5.41/5.76 ( ( X8 @ A7 )
% 5.41/5.76 => ? [X4: nat] :
% 5.41/5.76 ( ( member_nat @ X4 @ A7 )
% 5.41/5.76 & ( ( X8 @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) )
% 5.41/5.76 | ~ ( finite_finite_nat @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) ) ) )
% 5.41/5.76 => ~ ( finite_finite_nat @ A2 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_coinduct
% 5.41/5.76 thf(fact_8180_finite__empty__induct,axiom,
% 5.41/5.76 ! [A2: set_set_nat,P: set_set_nat > $o] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ A2 )
% 5.41/5.76 => ( ( P @ A2 )
% 5.41/5.76 => ( ! [A5: set_nat,A7: set_set_nat] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ A7 )
% 5.41/5.76 => ( ( member_set_nat @ A5 @ A7 )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ A5 @ bot_bot_set_set_nat ) ) ) ) ) )
% 5.41/5.76 => ( P @ bot_bot_set_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_empty_induct
% 5.41/5.76 thf(fact_8181_finite__empty__induct,axiom,
% 5.41/5.76 ! [A2: set_complex,P: set_complex > $o] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( P @ A2 )
% 5.41/5.76 => ( ! [A5: complex,A7: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A7 )
% 5.41/5.76 => ( ( member_complex @ A5 @ A7 )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ A5 @ bot_bot_set_complex ) ) ) ) ) )
% 5.41/5.76 => ( P @ bot_bot_set_complex ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_empty_induct
% 5.41/5.76 thf(fact_8182_finite__empty__induct,axiom,
% 5.41/5.76 ! [A2: set_int,P: set_int > $o] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( P @ A2 )
% 5.41/5.76 => ( ! [A5: int,A7: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ A7 )
% 5.41/5.76 => ( ( member_int @ A5 @ A7 )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ A5 @ bot_bot_set_int ) ) ) ) ) )
% 5.41/5.76 => ( P @ bot_bot_set_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_empty_induct
% 5.41/5.76 thf(fact_8183_finite__empty__induct,axiom,
% 5.41/5.76 ! [A2: set_real,P: set_real > $o] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( P @ A2 )
% 5.41/5.76 => ( ! [A5: real,A7: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ A7 )
% 5.41/5.76 => ( ( member_real @ A5 @ A7 )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ A5 @ bot_bot_set_real ) ) ) ) ) )
% 5.41/5.76 => ( P @ bot_bot_set_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_empty_induct
% 5.41/5.76 thf(fact_8184_finite__empty__induct,axiom,
% 5.41/5.76 ! [A2: set_nat,P: set_nat > $o] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ( P @ A2 )
% 5.41/5.76 => ( ! [A5: nat,A7: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ A7 )
% 5.41/5.76 => ( ( member_nat @ A5 @ A7 )
% 5.41/5.76 => ( ( P @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ A5 @ bot_bot_set_nat ) ) ) ) ) )
% 5.41/5.76 => ( P @ bot_bot_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_empty_induct
% 5.41/5.76 thf(fact_8185_Diff__single__insert,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,B3: set_real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 )
% 5.41/5.76 => ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_single_insert
% 5.41/5.76 thf(fact_8186_Diff__single__insert,axiom,
% 5.41/5.76 ! [A2: set_nat,X: nat,B3: set_nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 )
% 5.41/5.76 => ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_single_insert
% 5.41/5.76 thf(fact_8187_Diff__single__insert,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,B3: set_int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 )
% 5.41/5.76 => ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Diff_single_insert
% 5.41/5.76 thf(fact_8188_subset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,B3: set_complex] :
% 5.41/5.76 ( ( ord_le211207098394363844omplex @ A2 @ ( insert_complex @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ord_le211207098394363844omplex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert_iff
% 5.41/5.76 thf(fact_8189_subset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_set_nat,X: set_nat,B3: set_set_nat] :
% 5.41/5.76 ( ( ord_le6893508408891458716et_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_set_nat @ X @ A2 )
% 5.41/5.76 => ( ord_le6893508408891458716et_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_set_nat @ X @ A2 )
% 5.41/5.76 => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert_iff
% 5.41/5.76 thf(fact_8190_subset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,B3: set_real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert_iff
% 5.41/5.76 thf(fact_8191_subset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_nat,X: nat,B3: set_nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert_iff
% 5.41/5.76 thf(fact_8192_subset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,B3: set_int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % subset_insert_iff
% 5.41/5.76 thf(fact_8193_real__of__nat__div4,axiom,
% 5.41/5.76 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_div4
% 5.41/5.76 thf(fact_8194_sum__diff1__nat,axiom,
% 5.41/5.76 ! [A: complex,A2: set_complex,F: complex > nat] :
% 5.41/5.76 ( ( ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( minus_minus_nat @ ( groups5693394587270226106ex_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1_nat
% 5.41/5.76 thf(fact_8195_sum__diff1__nat,axiom,
% 5.41/5.76 ! [A: set_nat,A2: set_set_nat,F: set_nat > nat] :
% 5.41/5.76 ( ( ( member_set_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.41/5.76 = ( minus_minus_nat @ ( groups8294997508430121362at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_set_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups8294997508430121362at_nat @ F @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ A @ bot_bot_set_set_nat ) ) )
% 5.41/5.76 = ( groups8294997508430121362at_nat @ F @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1_nat
% 5.41/5.76 thf(fact_8196_sum__diff1__nat,axiom,
% 5.41/5.76 ! [A: int,A2: set_int,F: int > nat] :
% 5.41/5.76 ( ( ( member_int @ A @ A2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_int @ A @ A2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1_nat
% 5.41/5.76 thf(fact_8197_sum__diff1__nat,axiom,
% 5.41/5.76 ! [A: real,A2: set_real,F: real > nat] :
% 5.41/5.76 ( ( ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( minus_minus_nat @ ( groups1935376822645274424al_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1_nat
% 5.41/5.76 thf(fact_8198_sum__diff1__nat,axiom,
% 5.41/5.76 ! [A: nat,A2: set_nat,F: nat > nat] :
% 5.41/5.76 ( ( ( member_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( minus_minus_nat @ ( groups3542108847815614940at_nat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups3542108847815614940at_nat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( groups3542108847815614940at_nat @ F @ A2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1_nat
% 5.41/5.76 thf(fact_8199_int__ops_I4_J,axiom,
% 5.41/5.76 ! [A: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( suc @ A ) )
% 5.41/5.76 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ one_one_int ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_ops(4)
% 5.41/5.76 thf(fact_8200_int__Suc,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( semiri1314217659103216013at_int @ ( suc @ N ) )
% 5.41/5.76 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_Suc
% 5.41/5.76 thf(fact_8201_zless__iff__Suc__zadd,axiom,
% 5.41/5.76 ( ord_less_int
% 5.41/5.76 = ( ^ [W3: int,Z3: int] :
% 5.41/5.76 ? [N2: nat] :
% 5.41/5.76 ( Z3
% 5.41/5.76 = ( plus_plus_int @ W3 @ ( semiri1314217659103216013at_int @ ( suc @ N2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zless_iff_Suc_zadd
% 5.41/5.76 thf(fact_8202_int__zle__neg,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.41/5.76 = ( ( N = zero_zero_nat )
% 5.41/5.76 & ( M = zero_zero_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_zle_neg
% 5.41/5.76 thf(fact_8203_real__of__nat__div,axiom,
% 5.41/5.76 ! [D: nat,N: nat] :
% 5.41/5.76 ( ( dvd_dvd_nat @ D @ N )
% 5.41/5.76 => ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ D ) )
% 5.41/5.76 = ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_div
% 5.41/5.76 thf(fact_8204_negative__zle__0,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_eq_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) @ zero_zero_int ) ).
% 5.41/5.76
% 5.41/5.76 % negative_zle_0
% 5.41/5.76 thf(fact_8205_nonpos__int__cases,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( ord_less_eq_int @ K @ zero_zero_int )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ( K
% 5.41/5.76 != ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nonpos_int_cases
% 5.41/5.76 thf(fact_8206_mult__inc,axiom,
% 5.41/5.76 ! [X: num,Y: num] :
% 5.41/5.76 ( ( times_times_num @ X @ ( inc @ Y ) )
% 5.41/5.76 = ( plus_plus_num @ ( times_times_num @ X @ Y ) @ X ) ) ).
% 5.41/5.76
% 5.41/5.76 % mult_inc
% 5.41/5.76 thf(fact_8207_set__update__subset__insert,axiom,
% 5.41/5.76 ! [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 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_update_subset_insert
% 5.41/5.76 thf(fact_8208_set__update__subset__insert,axiom,
% 5.41/5.76 ! [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 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_update_subset_insert
% 5.41/5.76 thf(fact_8209_set__update__subset__insert,axiom,
% 5.41/5.76 ! [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 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_update_subset_insert
% 5.41/5.76 thf(fact_8210_set__update__subset__insert,axiom,
% 5.41/5.76 ! [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 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_update_subset_insert
% 5.41/5.76 thf(fact_8211_Compl__insert,axiom,
% 5.41/5.76 ! [X: int,A2: set_int] :
% 5.41/5.76 ( ( uminus1532241313380277803et_int @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( minus_minus_set_int @ ( uminus1532241313380277803et_int @ A2 ) @ ( insert_int @ X @ bot_bot_set_int ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Compl_insert
% 5.41/5.76 thf(fact_8212_Compl__insert,axiom,
% 5.41/5.76 ! [X: real,A2: set_real] :
% 5.41/5.76 ( ( uminus612125837232591019t_real @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( minus_minus_set_real @ ( uminus612125837232591019t_real @ A2 ) @ ( insert_real @ X @ bot_bot_set_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Compl_insert
% 5.41/5.76 thf(fact_8213_Compl__insert,axiom,
% 5.41/5.76 ! [X: nat,A2: set_nat] :
% 5.41/5.76 ( ( uminus5710092332889474511et_nat @ ( insert_nat @ X @ A2 ) )
% 5.41/5.76 = ( minus_minus_set_nat @ ( uminus5710092332889474511et_nat @ A2 ) @ ( insert_nat @ X @ bot_bot_set_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Compl_insert
% 5.41/5.76 thf(fact_8214_less__log2__of__power,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.41/5.76 => ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % less_log2_of_power
% 5.41/5.76 thf(fact_8215_le__log2__of__power,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ M )
% 5.41/5.76 => ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % le_log2_of_power
% 5.41/5.76 thf(fact_8216_log2__of__power__less,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.76 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.76 => ( ord_less_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log2_of_power_less
% 5.41/5.76 thf(fact_8217_log__base__change,axiom,
% 5.41/5.76 ! [A: real,B: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.76 => ( ( A != one_one_real )
% 5.41/5.76 => ( ( log @ B @ X )
% 5.41/5.76 = ( divide_divide_real @ ( log @ A @ X ) @ ( log @ A @ B ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_base_change
% 5.41/5.76 thf(fact_8218_numeral__inc,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( numera6690914467698888265omplex @ ( inc @ X ) )
% 5.41/5.76 = ( plus_plus_complex @ ( numera6690914467698888265omplex @ X ) @ one_one_complex ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_inc
% 5.41/5.76 thf(fact_8219_numeral__inc,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( numeral_numeral_real @ ( inc @ X ) )
% 5.41/5.76 = ( plus_plus_real @ ( numeral_numeral_real @ X ) @ one_one_real ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_inc
% 5.41/5.76 thf(fact_8220_numeral__inc,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( numeral_numeral_rat @ ( inc @ X ) )
% 5.41/5.76 = ( plus_plus_rat @ ( numeral_numeral_rat @ X ) @ one_one_rat ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_inc
% 5.41/5.76 thf(fact_8221_numeral__inc,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( numeral_numeral_nat @ ( inc @ X ) )
% 5.41/5.76 = ( plus_plus_nat @ ( numeral_numeral_nat @ X ) @ one_one_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_inc
% 5.41/5.76 thf(fact_8222_numeral__inc,axiom,
% 5.41/5.76 ! [X: num] :
% 5.41/5.76 ( ( numeral_numeral_int @ ( inc @ X ) )
% 5.41/5.76 = ( plus_plus_int @ ( numeral_numeral_int @ X ) @ one_one_int ) ) ).
% 5.41/5.76
% 5.41/5.76 % numeral_inc
% 5.41/5.76 thf(fact_8223_mod__mult2__eq_H,axiom,
% 5.41/5.76 ! [A: code_integer,M: nat,N: nat] :
% 5.41/5.76 ( ( modulo364778990260209775nteger @ A @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( semiri4939895301339042750nteger @ N ) ) )
% 5.41/5.76 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( semiri4939895301339042750nteger @ M ) @ ( modulo364778990260209775nteger @ ( divide6298287555418463151nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) @ ( semiri4939895301339042750nteger @ N ) ) ) @ ( modulo364778990260209775nteger @ A @ ( semiri4939895301339042750nteger @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mod_mult2_eq'
% 5.41/5.76 thf(fact_8224_mod__mult2__eq_H,axiom,
% 5.41/5.76 ! [A: nat,M: nat,N: nat] :
% 5.41/5.76 ( ( modulo_modulo_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( semiri1316708129612266289at_nat @ N ) ) )
% 5.41/5.76 = ( plus_plus_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ M ) @ ( modulo_modulo_nat @ ( divide_divide_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) @ ( semiri1316708129612266289at_nat @ N ) ) ) @ ( modulo_modulo_nat @ A @ ( semiri1316708129612266289at_nat @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mod_mult2_eq'
% 5.41/5.76 thf(fact_8225_mod__mult2__eq_H,axiom,
% 5.41/5.76 ! [A: int,M: nat,N: nat] :
% 5.41/5.76 ( ( modulo_modulo_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.76 = ( plus_plus_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ M ) @ ( modulo_modulo_int @ ( divide_divide_int @ A @ ( semiri1314217659103216013at_int @ M ) ) @ ( semiri1314217659103216013at_int @ N ) ) ) @ ( modulo_modulo_int @ A @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % mod_mult2_eq'
% 5.41/5.76 thf(fact_8226_field__char__0__class_Oof__nat__div,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri8010041392384452111omplex @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.76 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( semiri8010041392384452111omplex @ M ) @ ( semiri8010041392384452111omplex @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri8010041392384452111omplex @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % field_char_0_class.of_nat_div
% 5.41/5.76 thf(fact_8227_field__char__0__class_Oof__nat__div,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri5074537144036343181t_real @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.76 = ( divide_divide_real @ ( minus_minus_real @ ( semiri5074537144036343181t_real @ M ) @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % field_char_0_class.of_nat_div
% 5.41/5.76 thf(fact_8228_field__char__0__class_Oof__nat__div,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( semiri681578069525770553at_rat @ ( divide_divide_nat @ M @ N ) )
% 5.41/5.76 = ( divide_divide_rat @ ( minus_minus_rat @ ( semiri681578069525770553at_rat @ M ) @ ( semiri681578069525770553at_rat @ ( modulo_modulo_nat @ M @ N ) ) ) @ ( semiri681578069525770553at_rat @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % field_char_0_class.of_nat_div
% 5.41/5.76 thf(fact_8229_remove__induct,axiom,
% 5.41/5.76 ! [P: set_set_nat > $o,B3: set_set_nat] :
% 5.41/5.76 ( ( P @ bot_bot_set_set_nat )
% 5.41/5.76 => ( ( ~ ( finite1152437895449049373et_nat @ B3 )
% 5.41/5.76 => ( P @ B3 ) )
% 5.41/5.76 => ( ! [A7: set_set_nat] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_set_nat )
% 5.41/5.76 => ( ( ord_le6893508408891458716et_nat @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: set_nat] :
% 5.41/5.76 ( ( member_set_nat @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % remove_induct
% 5.41/5.76 thf(fact_8230_remove__induct,axiom,
% 5.41/5.76 ! [P: set_complex > $o,B3: set_complex] :
% 5.41/5.76 ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ( ~ ( finite3207457112153483333omplex @ B3 )
% 5.41/5.76 => ( P @ B3 ) )
% 5.41/5.76 => ( ! [A7: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_complex )
% 5.41/5.76 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: complex] :
% 5.41/5.76 ( ( member_complex @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % remove_induct
% 5.41/5.76 thf(fact_8231_remove__induct,axiom,
% 5.41/5.76 ! [P: set_real > $o,B3: set_real] :
% 5.41/5.76 ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ( ~ ( finite_finite_real @ B3 )
% 5.41/5.76 => ( P @ B3 ) )
% 5.41/5.76 => ( ! [A7: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_real )
% 5.41/5.76 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: real] :
% 5.41/5.76 ( ( member_real @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % remove_induct
% 5.41/5.76 thf(fact_8232_remove__induct,axiom,
% 5.41/5.76 ! [P: set_nat > $o,B3: set_nat] :
% 5.41/5.76 ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ( ~ ( finite_finite_nat @ B3 )
% 5.41/5.76 => ( P @ B3 ) )
% 5.41/5.76 => ( ! [A7: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_nat )
% 5.41/5.76 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: nat] :
% 5.41/5.76 ( ( member_nat @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % remove_induct
% 5.41/5.76 thf(fact_8233_remove__induct,axiom,
% 5.41/5.76 ! [P: set_int > $o,B3: set_int] :
% 5.41/5.76 ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ( ~ ( finite_finite_int @ B3 )
% 5.41/5.76 => ( P @ B3 ) )
% 5.41/5.76 => ( ! [A7: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_int )
% 5.41/5.76 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: int] :
% 5.41/5.76 ( ( member_int @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % remove_induct
% 5.41/5.76 thf(fact_8234_finite__remove__induct,axiom,
% 5.41/5.76 ! [B3: set_set_nat,P: set_set_nat > $o] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ B3 )
% 5.41/5.76 => ( ( P @ bot_bot_set_set_nat )
% 5.41/5.76 => ( ! [A7: set_set_nat] :
% 5.41/5.76 ( ( finite1152437895449049373et_nat @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_set_nat )
% 5.41/5.76 => ( ( ord_le6893508408891458716et_nat @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: set_nat] :
% 5.41/5.76 ( ( member_set_nat @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_2163939370556025621et_nat @ A7 @ ( insert_set_nat @ X4 @ bot_bot_set_set_nat ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_remove_induct
% 5.41/5.76 thf(fact_8235_finite__remove__induct,axiom,
% 5.41/5.76 ! [B3: set_complex,P: set_complex > $o] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ B3 )
% 5.41/5.76 => ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ! [A7: set_complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_complex )
% 5.41/5.76 => ( ( ord_le211207098394363844omplex @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: complex] :
% 5.41/5.76 ( ( member_complex @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_811609699411566653omplex @ A7 @ ( insert_complex @ X4 @ bot_bot_set_complex ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_remove_induct
% 5.41/5.76 thf(fact_8236_finite__remove__induct,axiom,
% 5.41/5.76 ! [B3: set_real,P: set_real > $o] :
% 5.41/5.76 ( ( finite_finite_real @ B3 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [A7: set_real] :
% 5.41/5.76 ( ( finite_finite_real @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_real )
% 5.41/5.76 => ( ( ord_less_eq_set_real @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: real] :
% 5.41/5.76 ( ( member_real @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_real @ A7 @ ( insert_real @ X4 @ bot_bot_set_real ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_remove_induct
% 5.41/5.76 thf(fact_8237_finite__remove__induct,axiom,
% 5.41/5.76 ! [B3: set_nat,P: set_nat > $o] :
% 5.41/5.76 ( ( finite_finite_nat @ B3 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [A7: set_nat] :
% 5.41/5.76 ( ( finite_finite_nat @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_nat )
% 5.41/5.76 => ( ( ord_less_eq_set_nat @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: nat] :
% 5.41/5.76 ( ( member_nat @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_nat @ A7 @ ( insert_nat @ X4 @ bot_bot_set_nat ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_remove_induct
% 5.41/5.76 thf(fact_8238_finite__remove__induct,axiom,
% 5.41/5.76 ! [B3: set_int,P: set_int > $o] :
% 5.41/5.76 ( ( finite_finite_int @ B3 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [A7: set_int] :
% 5.41/5.76 ( ( finite_finite_int @ A7 )
% 5.41/5.76 => ( ( A7 != bot_bot_set_int )
% 5.41/5.76 => ( ( ord_less_eq_set_int @ A7 @ B3 )
% 5.41/5.76 => ( ! [X4: int] :
% 5.41/5.76 ( ( member_int @ X4 @ A7 )
% 5.41/5.76 => ( P @ ( minus_minus_set_int @ A7 @ ( insert_int @ X4 @ bot_bot_set_int ) ) ) )
% 5.41/5.76 => ( P @ A7 ) ) ) ) )
% 5.41/5.76 => ( P @ B3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_remove_induct
% 5.41/5.76 thf(fact_8239_zero__less__imp__eq__int,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.76 => ? [N3: nat] :
% 5.41/5.76 ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.41/5.76 & ( K
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zero_less_imp_eq_int
% 5.41/5.76 thf(fact_8240_pos__int__cases,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( ord_less_int @ zero_zero_int @ K )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ( ( K
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.41/5.76 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % pos_int_cases
% 5.41/5.76 thf(fact_8241_int__cases3,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( K != zero_zero_int )
% 5.41/5.76 => ( ! [N3: nat] :
% 5.41/5.76 ( ( K
% 5.41/5.76 = ( semiri1314217659103216013at_int @ N3 ) )
% 5.41/5.76 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ( ( K
% 5.41/5.76 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.41/5.76 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_cases3
% 5.41/5.76 thf(fact_8242_nat__less__real__le,axiom,
% 5.41/5.76 ( ord_less_nat
% 5.41/5.76 = ( ^ [N2: nat,M3: nat] : ( ord_less_eq_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ M3 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_less_real_le
% 5.41/5.76 thf(fact_8243_nat__le__real__less,axiom,
% 5.41/5.76 ( ord_less_eq_nat
% 5.41/5.76 = ( ^ [N2: nat,M3: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ M3 ) @ one_one_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_le_real_less
% 5.41/5.76 thf(fact_8244_zmult__zless__mono2__lemma,axiom,
% 5.41/5.76 ! [I: int,J: int,K: nat] :
% 5.41/5.76 ( ( ord_less_int @ I @ J )
% 5.41/5.76 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.76 => ( ord_less_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ I ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ K ) @ J ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zmult_zless_mono2_lemma
% 5.41/5.76 thf(fact_8245_not__zle__0__negative,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ~ ( ord_less_eq_int @ zero_zero_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % not_zle_0_negative
% 5.41/5.76 thf(fact_8246_negative__zless__0,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_int @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N ) ) ) @ zero_zero_int ) ).
% 5.41/5.76
% 5.41/5.76 % negative_zless_0
% 5.41/5.76 thf(fact_8247_negD,axiom,
% 5.41/5.76 ! [X: int] :
% 5.41/5.76 ( ( ord_less_int @ X @ zero_zero_int )
% 5.41/5.76 => ? [N3: nat] :
% 5.41/5.76 ( X
% 5.41/5.76 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ ( suc @ N3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % negD
% 5.41/5.76 thf(fact_8248_finite__induct__select,axiom,
% 5.41/5.76 ! [S2: set_complex,P: set_complex > $o] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_complex )
% 5.41/5.76 => ( ! [T5: set_complex] :
% 5.41/5.76 ( ( ord_less_set_complex @ T5 @ S2 )
% 5.41/5.76 => ( ( P @ T5 )
% 5.41/5.76 => ? [X4: complex] :
% 5.41/5.76 ( ( member_complex @ X4 @ ( minus_811609699411566653omplex @ S2 @ T5 ) )
% 5.41/5.76 & ( P @ ( insert_complex @ X4 @ T5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_induct_select
% 5.41/5.76 thf(fact_8249_finite__induct__select,axiom,
% 5.41/5.76 ! [S2: set_int,P: set_int > $o] :
% 5.41/5.76 ( ( finite_finite_int @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_int )
% 5.41/5.76 => ( ! [T5: set_int] :
% 5.41/5.76 ( ( ord_less_set_int @ T5 @ S2 )
% 5.41/5.76 => ( ( P @ T5 )
% 5.41/5.76 => ? [X4: int] :
% 5.41/5.76 ( ( member_int @ X4 @ ( minus_minus_set_int @ S2 @ T5 ) )
% 5.41/5.76 & ( P @ ( insert_int @ X4 @ T5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_induct_select
% 5.41/5.76 thf(fact_8250_finite__induct__select,axiom,
% 5.41/5.76 ! [S2: set_real,P: set_real > $o] :
% 5.41/5.76 ( ( finite_finite_real @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_real )
% 5.41/5.76 => ( ! [T5: set_real] :
% 5.41/5.76 ( ( ord_less_set_real @ T5 @ S2 )
% 5.41/5.76 => ( ( P @ T5 )
% 5.41/5.76 => ? [X4: real] :
% 5.41/5.76 ( ( member_real @ X4 @ ( minus_minus_set_real @ S2 @ T5 ) )
% 5.41/5.76 & ( P @ ( insert_real @ X4 @ T5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_induct_select
% 5.41/5.76 thf(fact_8251_finite__induct__select,axiom,
% 5.41/5.76 ! [S2: set_nat,P: set_nat > $o] :
% 5.41/5.76 ( ( finite_finite_nat @ S2 )
% 5.41/5.76 => ( ( P @ bot_bot_set_nat )
% 5.41/5.76 => ( ! [T5: set_nat] :
% 5.41/5.76 ( ( ord_less_set_nat @ T5 @ S2 )
% 5.41/5.76 => ( ( P @ T5 )
% 5.41/5.76 => ? [X4: nat] :
% 5.41/5.76 ( ( member_nat @ X4 @ ( minus_minus_set_nat @ S2 @ T5 ) )
% 5.41/5.76 & ( P @ ( insert_nat @ X4 @ T5 ) ) ) ) )
% 5.41/5.76 => ( P @ S2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_induct_select
% 5.41/5.76 thf(fact_8252_psubset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,B3: set_complex] :
% 5.41/5.76 ( ( ord_less_set_complex @ A2 @ ( insert_complex @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_complex @ X @ B3 )
% 5.41/5.76 => ( ord_less_set_complex @ A2 @ B3 ) )
% 5.41/5.76 & ( ~ ( member_complex @ X @ B3 )
% 5.41/5.76 => ( ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ord_less_set_complex @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ord_le211207098394363844omplex @ A2 @ B3 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % psubset_insert_iff
% 5.41/5.76 thf(fact_8253_psubset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_set_nat,X: set_nat,B3: set_set_nat] :
% 5.41/5.76 ( ( ord_less_set_set_nat @ A2 @ ( insert_set_nat @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_set_nat @ X @ B3 )
% 5.41/5.76 => ( ord_less_set_set_nat @ A2 @ B3 ) )
% 5.41/5.76 & ( ~ ( member_set_nat @ X @ B3 )
% 5.41/5.76 => ( ( ( member_set_nat @ X @ A2 )
% 5.41/5.76 => ( ord_less_set_set_nat @ ( minus_2163939370556025621et_nat @ A2 @ ( insert_set_nat @ X @ bot_bot_set_set_nat ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_set_nat @ X @ A2 )
% 5.41/5.76 => ( ord_le6893508408891458716et_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % psubset_insert_iff
% 5.41/5.76 thf(fact_8254_psubset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,B3: set_real] :
% 5.41/5.76 ( ( ord_less_set_real @ A2 @ ( insert_real @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_real @ X @ B3 )
% 5.41/5.76 => ( ord_less_set_real @ A2 @ B3 ) )
% 5.41/5.76 & ( ~ ( member_real @ X @ B3 )
% 5.41/5.76 => ( ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ord_less_set_real @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_real @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_real @ A2 @ B3 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % psubset_insert_iff
% 5.41/5.76 thf(fact_8255_psubset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_nat,X: nat,B3: set_nat] :
% 5.41/5.76 ( ( ord_less_set_nat @ A2 @ ( insert_nat @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_nat @ X @ B3 )
% 5.41/5.76 => ( ord_less_set_nat @ A2 @ B3 ) )
% 5.41/5.76 & ( ~ ( member_nat @ X @ B3 )
% 5.41/5.76 => ( ( ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ord_less_set_nat @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ X @ bot_bot_set_nat ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_nat @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_nat @ A2 @ B3 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % psubset_insert_iff
% 5.41/5.76 thf(fact_8256_psubset__insert__iff,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,B3: set_int] :
% 5.41/5.76 ( ( ord_less_set_int @ A2 @ ( insert_int @ X @ B3 ) )
% 5.41/5.76 = ( ( ( member_int @ X @ B3 )
% 5.41/5.76 => ( ord_less_set_int @ A2 @ B3 ) )
% 5.41/5.76 & ( ~ ( member_int @ X @ B3 )
% 5.41/5.76 => ( ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ord_less_set_int @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) @ B3 ) )
% 5.41/5.76 & ( ~ ( member_int @ X @ A2 )
% 5.41/5.76 => ( ord_less_eq_set_int @ A2 @ B3 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % psubset_insert_iff
% 5.41/5.76 thf(fact_8257_set__replicate__Suc,axiom,
% 5.41/5.76 ! [N: nat,X: vEBT_VEBT] :
% 5.41/5.76 ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ ( suc @ N ) @ X ) )
% 5.41/5.76 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_Suc
% 5.41/5.76 thf(fact_8258_set__replicate__Suc,axiom,
% 5.41/5.76 ! [N: nat,X: nat] :
% 5.41/5.76 ( ( set_nat2 @ ( replicate_nat @ ( suc @ N ) @ X ) )
% 5.41/5.76 = ( insert_nat @ X @ bot_bot_set_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_Suc
% 5.41/5.76 thf(fact_8259_set__replicate__Suc,axiom,
% 5.41/5.76 ! [N: nat,X: int] :
% 5.41/5.76 ( ( set_int2 @ ( replicate_int @ ( suc @ N ) @ X ) )
% 5.41/5.76 = ( insert_int @ X @ bot_bot_set_int ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_Suc
% 5.41/5.76 thf(fact_8260_set__replicate__Suc,axiom,
% 5.41/5.76 ! [N: nat,X: real] :
% 5.41/5.76 ( ( set_real2 @ ( replicate_real @ ( suc @ N ) @ X ) )
% 5.41/5.76 = ( insert_real @ X @ bot_bot_set_real ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_Suc
% 5.41/5.76 thf(fact_8261_log2__of__power__le,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ M @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.76 => ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.76 => ( ord_less_eq_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log2_of_power_le
% 5.41/5.76 thf(fact_8262_set__replicate__conv__if,axiom,
% 5.41/5.76 ! [N: nat,X: vEBT_VEBT] :
% 5.41/5.76 ( ( ( N = zero_zero_nat )
% 5.41/5.76 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.41/5.76 = bot_bo8194388402131092736T_VEBT ) )
% 5.41/5.76 & ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_VEBT_VEBT2 @ ( replicate_VEBT_VEBT @ N @ X ) )
% 5.41/5.76 = ( insert_VEBT_VEBT @ X @ bot_bo8194388402131092736T_VEBT ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_conv_if
% 5.41/5.76 thf(fact_8263_set__replicate__conv__if,axiom,
% 5.41/5.76 ! [N: nat,X: nat] :
% 5.41/5.76 ( ( ( N = zero_zero_nat )
% 5.41/5.76 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.41/5.76 = bot_bot_set_nat ) )
% 5.41/5.76 & ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_nat2 @ ( replicate_nat @ N @ X ) )
% 5.41/5.76 = ( insert_nat @ X @ bot_bot_set_nat ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_conv_if
% 5.41/5.76 thf(fact_8264_set__replicate__conv__if,axiom,
% 5.41/5.76 ! [N: nat,X: int] :
% 5.41/5.76 ( ( ( N = zero_zero_nat )
% 5.41/5.76 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.41/5.76 = bot_bot_set_int ) )
% 5.41/5.76 & ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_int2 @ ( replicate_int @ N @ X ) )
% 5.41/5.76 = ( insert_int @ X @ bot_bot_set_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_conv_if
% 5.41/5.76 thf(fact_8265_set__replicate__conv__if,axiom,
% 5.41/5.76 ! [N: nat,X: real] :
% 5.41/5.76 ( ( ( N = zero_zero_nat )
% 5.41/5.76 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 5.41/5.76 = bot_bot_set_real ) )
% 5.41/5.76 & ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ( set_real2 @ ( replicate_real @ N @ X ) )
% 5.41/5.76 = ( insert_real @ X @ bot_bot_set_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_replicate_conv_if
% 5.41/5.76 thf(fact_8266_int__ops_I6_J,axiom,
% 5.41/5.76 ! [A: nat,B: nat] :
% 5.41/5.76 ( ( ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.41/5.76 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.41/5.76 = zero_zero_int ) )
% 5.41/5.76 & ( ~ ( ord_less_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) )
% 5.41/5.76 => ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ A @ B ) )
% 5.41/5.76 = ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % int_ops(6)
% 5.41/5.76 thf(fact_8267_real__of__nat__div__aux,axiom,
% 5.41/5.76 ! [X: nat,D: nat] :
% 5.41/5.76 ( ( divide_divide_real @ ( semiri5074537144036343181t_real @ X ) @ ( semiri5074537144036343181t_real @ D ) )
% 5.41/5.76 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ X @ D ) ) @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ ( modulo_modulo_nat @ X @ D ) ) @ ( semiri5074537144036343181t_real @ D ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_div_aux
% 5.41/5.76 thf(fact_8268_atLeastAtMostPlus1__int__conv,axiom,
% 5.41/5.76 ! [M: int,N: int] :
% 5.41/5.76 ( ( ord_less_eq_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.41/5.76 => ( ( set_or1266510415728281911st_int @ M @ ( plus_plus_int @ one_one_int @ N ) )
% 5.41/5.76 = ( insert_int @ ( plus_plus_int @ one_one_int @ N ) @ ( set_or1266510415728281911st_int @ M @ N ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % atLeastAtMostPlus1_int_conv
% 5.41/5.76 thf(fact_8269_simp__from__to,axiom,
% 5.41/5.76 ( set_or1266510415728281911st_int
% 5.41/5.76 = ( ^ [I5: int,J3: int] : ( if_set_int @ ( ord_less_int @ J3 @ I5 ) @ bot_bot_set_int @ ( insert_int @ I5 @ ( set_or1266510415728281911st_int @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % simp_from_to
% 5.41/5.76 thf(fact_8270_nat__approx__posE,axiom,
% 5.41/5.76 ! [E: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ E )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ~ ( ord_less_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_approx_posE
% 5.41/5.76 thf(fact_8271_nat__approx__posE,axiom,
% 5.41/5.76 ! [E: rat] :
% 5.41/5.76 ( ( ord_less_rat @ zero_zero_rat @ E )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ~ ( ord_less_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ ( suc @ N3 ) ) ) @ E ) ) ).
% 5.41/5.76
% 5.41/5.76 % nat_approx_posE
% 5.41/5.76 thf(fact_8272_log__mult,axiom,
% 5.41/5.76 ! [A: real,X: real,Y: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.76 => ( ( A != one_one_real )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.76 => ( ( log @ A @ ( times_times_real @ X @ Y ) )
% 5.41/5.76 = ( plus_plus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_mult
% 5.41/5.76 thf(fact_8273_of__nat__less__two__power,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_two_power
% 5.41/5.76 thf(fact_8274_of__nat__less__two__power,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_two_power
% 5.41/5.76 thf(fact_8275_of__nat__less__two__power,axiom,
% 5.41/5.76 ! [N: nat] : ( ord_less_int @ ( semiri1314217659103216013at_int @ N ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_less_two_power
% 5.41/5.76 thf(fact_8276_log__divide,axiom,
% 5.41/5.76 ! [A: real,X: real,Y: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.76 => ( ( A != one_one_real )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.76 => ( ( log @ A @ ( divide_divide_real @ X @ Y ) )
% 5.41/5.76 = ( minus_minus_real @ ( log @ A @ X ) @ ( log @ A @ Y ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_divide
% 5.41/5.76 thf(fact_8277_inverse__of__nat__le,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.76 => ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ord_less_eq_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ M ) ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % inverse_of_nat_le
% 5.41/5.76 thf(fact_8278_inverse__of__nat__le,axiom,
% 5.41/5.76 ! [N: nat,M: nat] :
% 5.41/5.76 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.76 => ( ( N != zero_zero_nat )
% 5.41/5.76 => ( ord_less_eq_rat @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ M ) ) @ ( divide_divide_rat @ one_one_rat @ ( semiri681578069525770553at_rat @ N ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % inverse_of_nat_le
% 5.41/5.76 thf(fact_8279_exp__divide__power__eq,axiom,
% 5.41/5.76 ! [N: nat,X: complex] :
% 5.41/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.76 => ( ( power_power_complex @ ( exp_complex @ ( divide1717551699836669952omplex @ X @ ( semiri8010041392384452111omplex @ N ) ) ) @ N )
% 5.41/5.76 = ( exp_complex @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_divide_power_eq
% 5.41/5.76 thf(fact_8280_exp__divide__power__eq,axiom,
% 5.41/5.76 ! [N: nat,X: real] :
% 5.41/5.76 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.76 => ( ( power_power_real @ ( exp_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N )
% 5.41/5.76 = ( exp_real @ X ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_divide_power_eq
% 5.41/5.76 thf(fact_8281_real__archimedian__rdiv__eq__0,axiom,
% 5.41/5.76 ! [X: real,C: real] :
% 5.41/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_eq_real @ zero_zero_real @ C )
% 5.41/5.76 => ( ! [M4: nat] :
% 5.41/5.76 ( ( ord_less_nat @ zero_zero_nat @ M4 )
% 5.41/5.76 => ( ord_less_eq_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M4 ) @ X ) @ C ) )
% 5.41/5.76 => ( X = zero_zero_real ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_archimedian_rdiv_eq_0
% 5.41/5.76 thf(fact_8282_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > real] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real @ G @ A2 )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8283_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > rat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat @ G @ A2 )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8284_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > nat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat @ G @ A2 )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8285_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_complex,X: complex,G: complex > int] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( member_complex @ X @ A2 )
% 5.41/5.76 => ( ( groups5690904116761175830ex_int @ G @ A2 )
% 5.41/5.76 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8286_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > real] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real @ G @ A2 )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8287_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > rat] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat @ G @ A2 )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8288_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_int,X: int,G: int > nat] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( member_int @ X @ A2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat @ G @ A2 )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8289_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > real] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real @ G @ A2 )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8290_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > rat] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat @ G @ A2 )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8291_sum_Oremove,axiom,
% 5.41/5.76 ! [A2: set_real,X: real,G: real > nat] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( member_real @ X @ A2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat @ G @ A2 )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.remove
% 5.41/5.76 thf(fact_8292_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_complex,G: complex > real,X: complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups5808333547571424918x_real @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8293_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_complex,G: complex > rat,X: complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups5058264527183730370ex_rat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8294_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_complex,G: complex > nat,X: complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups5693394587270226106ex_nat @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8295_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_complex,G: complex > int,X: complex] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( groups5690904116761175830ex_int @ G @ ( insert_complex @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_int @ ( G @ X ) @ ( groups5690904116761175830ex_int @ G @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ X @ bot_bot_set_complex ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8296_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_int,G: int > real,X: int] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8778361861064173332t_real @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8297_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_int,G: int > rat,X: int] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups3906332499630173760nt_rat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8298_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_int,G: int > nat,X: int] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat @ G @ ( insert_int @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups4541462559716669496nt_nat @ G @ ( minus_minus_set_int @ A2 @ ( insert_int @ X @ bot_bot_set_int ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8299_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_real,G: real > real,X: real] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_real @ ( G @ X ) @ ( groups8097168146408367636l_real @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8300_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_real,G: real > rat,X: real] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_rat @ ( G @ X ) @ ( groups1300246762558778688al_rat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8301_sum_Oinsert__remove,axiom,
% 5.41/5.76 ! [A2: set_real,G: real > nat,X: real] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat @ G @ ( insert_real @ X @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( G @ X ) @ ( groups1935376822645274424al_nat @ G @ ( minus_minus_set_real @ A2 @ ( insert_real @ X @ bot_bot_set_real ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.insert_remove
% 5.41/5.76 thf(fact_8302_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_complex,A: complex,F: complex > real] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( minus_minus_real @ ( groups5808333547571424918x_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8303_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_int,A: int,F: int > real] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( ( member_int @ A @ A2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( minus_minus_real @ ( groups8778361861064173332t_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_int @ A @ A2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8304_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_real,A: real,F: real > real] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( minus_minus_real @ ( groups8097168146408367636l_real @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8305_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_complex,A: complex,F: complex > rat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( minus_minus_rat @ ( groups5058264527183730370ex_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8306_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_int,A: int,F: int > rat] :
% 5.41/5.76 ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ( ( member_int @ A @ A2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( minus_minus_rat @ ( groups3906332499630173760nt_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_int @ A @ A2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat @ F @ ( minus_minus_set_int @ A2 @ ( insert_int @ A @ bot_bot_set_int ) ) )
% 5.41/5.76 = ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8307_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_real,A: real,F: real > rat] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( minus_minus_rat @ ( groups1300246762558778688al_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8308_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_complex,A: complex,F: complex > int] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ( ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( minus_minus_int @ ( groups5690904116761175830ex_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ A2 )
% 5.41/5.76 => ( ( groups5690904116761175830ex_int @ F @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) )
% 5.41/5.76 = ( groups5690904116761175830ex_int @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8309_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_real,A: real,F: real > int] :
% 5.41/5.76 ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ( ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( minus_minus_int @ ( groups1932886352136224148al_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_real @ A @ A2 )
% 5.41/5.76 => ( ( groups1932886352136224148al_int @ F @ ( minus_minus_set_real @ A2 @ ( insert_real @ A @ bot_bot_set_real ) ) )
% 5.41/5.76 = ( groups1932886352136224148al_int @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8310_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_nat,A: nat,F: nat > rat] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ( ( member_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8311_sum__diff1,axiom,
% 5.41/5.76 ! [A2: set_nat,A: nat,F: nat > int] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ( ( member_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ A2 ) @ ( F @ A ) ) ) )
% 5.41/5.76 & ( ~ ( member_nat @ A @ A2 )
% 5.41/5.76 => ( ( groups3539618377306564664at_int @ F @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ A @ bot_bot_set_nat ) ) )
% 5.41/5.76 = ( groups3539618377306564664at_int @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_diff1
% 5.41/5.76 thf(fact_8312_neg__int__cases,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.76 => ~ ! [N3: nat] :
% 5.41/5.76 ( ( K
% 5.41/5.76 = ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N3 ) ) )
% 5.41/5.76 => ~ ( ord_less_nat @ zero_zero_nat @ N3 ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % neg_int_cases
% 5.41/5.76 thf(fact_8313_zdiff__int__split,axiom,
% 5.41/5.76 ! [P: int > $o,X: nat,Y: nat] :
% 5.41/5.76 ( ( P @ ( semiri1314217659103216013at_int @ ( minus_minus_nat @ X @ Y ) ) )
% 5.41/5.76 = ( ( ( ord_less_eq_nat @ Y @ X )
% 5.41/5.76 => ( P @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ X ) @ ( semiri1314217659103216013at_int @ Y ) ) ) )
% 5.41/5.76 & ( ( ord_less_nat @ X @ Y )
% 5.41/5.76 => ( P @ zero_zero_int ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % zdiff_int_split
% 5.41/5.76 thf(fact_8314_real__of__nat__div2,axiom,
% 5.41/5.76 ! [N: nat,X: nat] : ( ord_less_eq_real @ zero_zero_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_div2
% 5.41/5.76 thf(fact_8315_real__of__nat__div3,axiom,
% 5.41/5.76 ! [N: nat,X: nat] : ( ord_less_eq_real @ ( minus_minus_real @ ( divide_divide_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ X ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ X ) ) ) @ one_one_real ) ).
% 5.41/5.76
% 5.41/5.76 % real_of_nat_div3
% 5.41/5.76 thf(fact_8316_ln__realpow,axiom,
% 5.41/5.76 ! [X: real,N: nat] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ln_ln_real @ ( power_power_real @ X @ N ) )
% 5.41/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % ln_realpow
% 5.41/5.76 thf(fact_8317_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_complex,A: complex,B: complex > real,C: complex > real] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real
% 5.41/5.76 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_real @ ( B @ A ) @ ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5808333547571424918x_real
% 5.41/5.76 @ ^ [K2: complex] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups5808333547571424918x_real @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8318_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_complex,A: complex,B: complex > rat,C: complex > rat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat
% 5.41/5.76 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_rat @ ( B @ A ) @ ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5058264527183730370ex_rat
% 5.41/5.76 @ ^ [K2: complex] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups5058264527183730370ex_rat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8319_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_complex,A: complex,B: complex > nat,C: complex > nat] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat
% 5.41/5.76 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_nat @ ( B @ A ) @ ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5693394587270226106ex_nat
% 5.41/5.76 @ ^ [K2: complex] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups5693394587270226106ex_nat @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8320_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_complex,A: complex,B: complex > int,C: complex > int] :
% 5.41/5.76 ( ( finite3207457112153483333omplex @ S2 )
% 5.41/5.76 => ( ( ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5690904116761175830ex_int
% 5.41/5.76 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_int @ ( B @ A ) @ ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_complex @ A @ S2 )
% 5.41/5.76 => ( ( groups5690904116761175830ex_int
% 5.41/5.76 @ ^ [K2: complex] : ( if_int @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups5690904116761175830ex_int @ C @ ( minus_811609699411566653omplex @ S2 @ ( insert_complex @ A @ bot_bot_set_complex ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8321_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_int,A: int,B: int > real,C: int > real] :
% 5.41/5.76 ( ( finite_finite_int @ S2 )
% 5.41/5.76 => ( ( ( member_int @ A @ S2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real
% 5.41/5.76 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_real @ ( B @ A ) @ ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.76 => ( ( groups8778361861064173332t_real
% 5.41/5.76 @ ^ [K2: int] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups8778361861064173332t_real @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8322_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_int,A: int,B: int > rat,C: int > rat] :
% 5.41/5.76 ( ( finite_finite_int @ S2 )
% 5.41/5.76 => ( ( ( member_int @ A @ S2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat
% 5.41/5.76 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_rat @ ( B @ A ) @ ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.76 => ( ( groups3906332499630173760nt_rat
% 5.41/5.76 @ ^ [K2: int] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups3906332499630173760nt_rat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8323_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_int,A: int,B: int > nat,C: int > nat] :
% 5.41/5.76 ( ( finite_finite_int @ S2 )
% 5.41/5.76 => ( ( ( member_int @ A @ S2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat
% 5.41/5.76 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_nat @ ( B @ A ) @ ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_int @ A @ S2 )
% 5.41/5.76 => ( ( groups4541462559716669496nt_nat
% 5.41/5.76 @ ^ [K2: int] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups4541462559716669496nt_nat @ C @ ( minus_minus_set_int @ S2 @ ( insert_int @ A @ bot_bot_set_int ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8324_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_real,A: real,B: real > real,C: real > real] :
% 5.41/5.76 ( ( finite_finite_real @ S2 )
% 5.41/5.76 => ( ( ( member_real @ A @ S2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real
% 5.41/5.76 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_real @ ( B @ A ) @ ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.76 => ( ( groups8097168146408367636l_real
% 5.41/5.76 @ ^ [K2: real] : ( if_real @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups8097168146408367636l_real @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8325_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_real,A: real,B: real > rat,C: real > rat] :
% 5.41/5.76 ( ( finite_finite_real @ S2 )
% 5.41/5.76 => ( ( ( member_real @ A @ S2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat
% 5.41/5.76 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_rat @ ( B @ A ) @ ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.76 => ( ( groups1300246762558778688al_rat
% 5.41/5.76 @ ^ [K2: real] : ( if_rat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups1300246762558778688al_rat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8326_sum_Odelta__remove,axiom,
% 5.41/5.76 ! [S2: set_real,A: real,B: real > nat,C: real > nat] :
% 5.41/5.76 ( ( finite_finite_real @ S2 )
% 5.41/5.76 => ( ( ( member_real @ A @ S2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat
% 5.41/5.76 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( plus_plus_nat @ ( B @ A ) @ ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) )
% 5.41/5.76 & ( ~ ( member_real @ A @ S2 )
% 5.41/5.76 => ( ( groups1935376822645274424al_nat
% 5.41/5.76 @ ^ [K2: real] : ( if_nat @ ( K2 = A ) @ ( B @ K2 ) @ ( C @ K2 ) )
% 5.41/5.76 @ S2 )
% 5.41/5.76 = ( groups1935376822645274424al_nat @ C @ ( minus_minus_set_real @ S2 @ ( insert_real @ A @ bot_bot_set_real ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.delta_remove
% 5.41/5.76 thf(fact_8327_log__eq__div__ln__mult__log,axiom,
% 5.41/5.76 ! [A: real,B: real,X: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.76 => ( ( A != one_one_real )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.76 => ( ( B != one_one_real )
% 5.41/5.76 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( log @ A @ X )
% 5.41/5.76 = ( times_times_real @ ( divide_divide_real @ ( ln_ln_real @ B ) @ ( ln_ln_real @ A ) ) @ ( log @ B @ X ) ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_eq_div_ln_mult_log
% 5.41/5.76 thf(fact_8328_member__le__sum,axiom,
% 5.41/5.76 ! [I: complex,A2: set_complex,F: complex > real] :
% 5.41/5.76 ( ( member_complex @ I @ A2 )
% 5.41/5.76 => ( ! [X6: complex] :
% 5.41/5.76 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.41/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ord_less_eq_real @ ( F @ I ) @ ( groups5808333547571424918x_real @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8329_member__le__sum,axiom,
% 5.41/5.76 ! [I: int,A2: set_int,F: int > real] :
% 5.41/5.76 ( ( member_int @ I @ A2 )
% 5.41/5.76 => ( ! [X6: int] :
% 5.41/5.76 ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.41/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8778361861064173332t_real @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8330_member__le__sum,axiom,
% 5.41/5.76 ! [I: real,A2: set_real,F: real > real] :
% 5.41/5.76 ( ( member_real @ I @ A2 )
% 5.41/5.76 => ( ! [X6: real] :
% 5.41/5.76 ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.41/5.76 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ord_less_eq_real @ ( F @ I ) @ ( groups8097168146408367636l_real @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8331_member__le__sum,axiom,
% 5.41/5.76 ! [I: complex,A2: set_complex,F: complex > rat] :
% 5.41/5.76 ( ( member_complex @ I @ A2 )
% 5.41/5.76 => ( ! [X6: complex] :
% 5.41/5.76 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.41/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups5058264527183730370ex_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8332_member__le__sum,axiom,
% 5.41/5.76 ! [I: int,A2: set_int,F: int > rat] :
% 5.41/5.76 ( ( member_int @ I @ A2 )
% 5.41/5.76 => ( ! [X6: int] :
% 5.41/5.76 ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.41/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups3906332499630173760nt_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8333_member__le__sum,axiom,
% 5.41/5.76 ! [I: real,A2: set_real,F: real > rat] :
% 5.41/5.76 ( ( member_real @ I @ A2 )
% 5.41/5.76 => ( ! [X6: real] :
% 5.41/5.76 ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.41/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups1300246762558778688al_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8334_member__le__sum,axiom,
% 5.41/5.76 ! [I: nat,A2: set_nat,F: nat > rat] :
% 5.41/5.76 ( ( member_nat @ I @ A2 )
% 5.41/5.76 => ( ! [X6: nat] :
% 5.41/5.76 ( ( member_nat @ X6 @ ( minus_minus_set_nat @ A2 @ ( insert_nat @ I @ bot_bot_set_nat ) ) )
% 5.41/5.76 => ( ord_less_eq_rat @ zero_zero_rat @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ord_less_eq_rat @ ( F @ I ) @ ( groups2906978787729119204at_rat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8335_member__le__sum,axiom,
% 5.41/5.76 ! [I: complex,A2: set_complex,F: complex > nat] :
% 5.41/5.76 ( ( member_complex @ I @ A2 )
% 5.41/5.76 => ( ! [X6: complex] :
% 5.41/5.76 ( ( member_complex @ X6 @ ( minus_811609699411566653omplex @ A2 @ ( insert_complex @ I @ bot_bot_set_complex ) ) )
% 5.41/5.76 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite3207457112153483333omplex @ A2 )
% 5.41/5.76 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups5693394587270226106ex_nat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8336_member__le__sum,axiom,
% 5.41/5.76 ! [I: int,A2: set_int,F: int > nat] :
% 5.41/5.76 ( ( member_int @ I @ A2 )
% 5.41/5.76 => ( ! [X6: int] :
% 5.41/5.76 ( ( member_int @ X6 @ ( minus_minus_set_int @ A2 @ ( insert_int @ I @ bot_bot_set_int ) ) )
% 5.41/5.76 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite_finite_int @ A2 )
% 5.41/5.76 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups4541462559716669496nt_nat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8337_member__le__sum,axiom,
% 5.41/5.76 ! [I: real,A2: set_real,F: real > nat] :
% 5.41/5.76 ( ( member_real @ I @ A2 )
% 5.41/5.76 => ( ! [X6: real] :
% 5.41/5.76 ( ( member_real @ X6 @ ( minus_minus_set_real @ A2 @ ( insert_real @ I @ bot_bot_set_real ) ) )
% 5.41/5.76 => ( ord_less_eq_nat @ zero_zero_nat @ ( F @ X6 ) ) )
% 5.41/5.76 => ( ( finite_finite_real @ A2 )
% 5.41/5.76 => ( ord_less_eq_nat @ ( F @ I ) @ ( groups1935376822645274424al_nat @ F @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % member_le_sum
% 5.41/5.76 thf(fact_8338_linear__plus__1__le__power,axiom,
% 5.41/5.76 ! [X: real,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ord_less_eq_real @ ( plus_plus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) @ one_one_real ) @ ( power_power_real @ ( plus_plus_real @ X @ one_one_real ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % linear_plus_1_le_power
% 5.41/5.76 thf(fact_8339_Bernoulli__inequality,axiom,
% 5.41/5.76 ! [X: real,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.76 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Bernoulli_inequality
% 5.41/5.76 thf(fact_8340_and__nat__unfold,axiom,
% 5.41/5.76 ( bit_se727722235901077358nd_nat
% 5.41/5.76 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.76 ( if_nat
% 5.41/5.76 @ ( ( M3 = zero_zero_nat )
% 5.41/5.76 | ( N2 = zero_zero_nat ) )
% 5.41/5.76 @ zero_zero_nat
% 5.41/5.76 @ ( plus_plus_nat @ ( times_times_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % and_nat_unfold
% 5.41/5.76 thf(fact_8341_and__nat__rec,axiom,
% 5.41/5.76 ( bit_se727722235901077358nd_nat
% 5.41/5.76 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.76 ( plus_plus_nat
% 5.41/5.76 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.76 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.41/5.76 & ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.41/5.76 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se727722235901077358nd_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % and_nat_rec
% 5.41/5.76 thf(fact_8342_double__gauss__sum,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum
% 5.41/5.76 thf(fact_8343_double__gauss__sum,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum
% 5.41/5.76 thf(fact_8344_double__gauss__sum,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum
% 5.41/5.76 thf(fact_8345_double__gauss__sum,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum
% 5.41/5.76 thf(fact_8346_double__gauss__sum,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum
% 5.41/5.76 thf(fact_8347_double__arith__series,axiom,
% 5.41/5.76 ! [A: complex,D: complex,N: nat] :
% 5.41/5.76 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) )
% 5.41/5.76 @ ( groups2073611262835488442omplex
% 5.41/5.76 @ ^ [I5: nat] : ( plus_plus_complex @ A @ ( times_times_complex @ ( semiri8010041392384452111omplex @ I5 ) @ D ) )
% 5.41/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_complex @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ A ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ D ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_arith_series
% 5.41/5.76 thf(fact_8348_double__arith__series,axiom,
% 5.41/5.76 ! [A: rat,D: rat,N: nat] :
% 5.41/5.76 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) )
% 5.41/5.76 @ ( groups2906978787729119204at_rat
% 5.41/5.76 @ ^ [I5: nat] : ( plus_plus_rat @ A @ ( times_times_rat @ ( semiri681578069525770553at_rat @ I5 ) @ D ) )
% 5.41/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_rat @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ A ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ D ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_arith_series
% 5.41/5.76 thf(fact_8349_double__arith__series,axiom,
% 5.41/5.76 ! [A: int,D: int,N: nat] :
% 5.41/5.76 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) )
% 5.41/5.76 @ ( groups3539618377306564664at_int
% 5.41/5.76 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.41/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_arith_series
% 5.41/5.76 thf(fact_8350_double__arith__series,axiom,
% 5.41/5.76 ! [A: nat,D: nat,N: nat] :
% 5.41/5.76 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) )
% 5.41/5.76 @ ( groups3542108847815614940at_nat
% 5.41/5.76 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.41/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_arith_series
% 5.41/5.76 thf(fact_8351_double__arith__series,axiom,
% 5.41/5.76 ! [A: real,D: real,N: nat] :
% 5.41/5.76 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.41/5.76 @ ( groups6591440286371151544t_real
% 5.41/5.76 @ ^ [I5: nat] : ( plus_plus_real @ A @ ( times_times_real @ ( semiri5074537144036343181t_real @ I5 ) @ D ) )
% 5.41/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.76 = ( times_times_real @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ A ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ D ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_arith_series
% 5.41/5.76 thf(fact_8352_gauss__sum,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.76 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % gauss_sum
% 5.41/5.76 thf(fact_8353_gauss__sum,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.76 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % gauss_sum
% 5.41/5.76 thf(fact_8354_arith__series,axiom,
% 5.41/5.76 ! [A: int,D: int,N: nat] :
% 5.41/5.76 ( ( groups3539618377306564664at_int
% 5.41/5.76 @ ^ [I5: nat] : ( plus_plus_int @ A @ ( times_times_int @ ( semiri1314217659103216013at_int @ I5 ) @ D ) )
% 5.41/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.76 = ( divide_divide_int @ ( times_times_int @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ A ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ D ) ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % arith_series
% 5.41/5.76 thf(fact_8355_arith__series,axiom,
% 5.41/5.76 ! [A: nat,D: nat,N: nat] :
% 5.41/5.76 ( ( groups3542108847815614940at_nat
% 5.41/5.76 @ ^ [I5: nat] : ( plus_plus_nat @ A @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ I5 ) @ D ) )
% 5.41/5.76 @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) )
% 5.41/5.76 = ( divide_divide_nat @ ( times_times_nat @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ A ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ D ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % arith_series
% 5.41/5.76 thf(fact_8356_double__gauss__sum__from__Suc__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( groups2073611262835488442omplex @ semiri8010041392384452111omplex @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.41/5.76 = ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum_from_Suc_0
% 5.41/5.76 thf(fact_8357_double__gauss__sum__from__Suc__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( groups2906978787729119204at_rat @ semiri681578069525770553at_rat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.41/5.76 = ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum_from_Suc_0
% 5.41/5.76 thf(fact_8358_double__gauss__sum__from__Suc__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.41/5.76 = ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum_from_Suc_0
% 5.41/5.76 thf(fact_8359_double__gauss__sum__from__Suc__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.41/5.76 = ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum_from_Suc_0
% 5.41/5.76 thf(fact_8360_double__gauss__sum__from__Suc__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( groups6591440286371151544t_real @ semiri5074537144036343181t_real @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) ) )
% 5.41/5.76 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % double_gauss_sum_from_Suc_0
% 5.41/5.76 thf(fact_8361_Bernoulli__inequality__even,axiom,
% 5.41/5.76 ! [N: nat,X: real] :
% 5.41/5.76 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.76 => ( ord_less_eq_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ X ) ) @ ( power_power_real @ ( plus_plus_real @ one_one_real @ X ) @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % Bernoulli_inequality_even
% 5.41/5.76 thf(fact_8362_sum__gp__offset,axiom,
% 5.41/5.76 ! [X: complex,M: nat,N: nat] :
% 5.41/5.76 ( ( ( X = one_one_complex )
% 5.41/5.76 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.41/5.76 = ( plus_plus_complex @ ( semiri8010041392384452111omplex @ N ) @ one_one_complex ) ) )
% 5.41/5.76 & ( ( X != one_one_complex )
% 5.41/5.76 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.41/5.76 = ( divide1717551699836669952omplex @ ( times_times_complex @ ( power_power_complex @ X @ M ) @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_gp_offset
% 5.41/5.76 thf(fact_8363_sum__gp__offset,axiom,
% 5.41/5.76 ! [X: rat,M: nat,N: nat] :
% 5.41/5.76 ( ( ( X = one_one_rat )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.41/5.76 = ( plus_plus_rat @ ( semiri681578069525770553at_rat @ N ) @ one_one_rat ) ) )
% 5.41/5.76 & ( ( X != one_one_rat )
% 5.41/5.76 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.41/5.76 = ( divide_divide_rat @ ( times_times_rat @ ( power_power_rat @ X @ M ) @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_gp_offset
% 5.41/5.76 thf(fact_8364_sum__gp__offset,axiom,
% 5.41/5.76 ! [X: real,M: nat,N: nat] :
% 5.41/5.76 ( ( ( X = one_one_real )
% 5.41/5.76 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.41/5.76 = ( plus_plus_real @ ( semiri5074537144036343181t_real @ N ) @ one_one_real ) ) )
% 5.41/5.76 & ( ( X != one_one_real )
% 5.41/5.76 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_or1269000886237332187st_nat @ M @ ( plus_plus_nat @ M @ N ) ) )
% 5.41/5.76 = ( divide_divide_real @ ( times_times_real @ ( power_power_real @ X @ M ) @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( suc @ N ) ) ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum_gp_offset
% 5.41/5.76 thf(fact_8365_exp__ge__one__plus__x__over__n__power__n,axiom,
% 5.41/5.76 ! [N: nat,X: real] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ X )
% 5.41/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.76 => ( ord_less_eq_real @ ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_ge_one_plus_x_over_n_power_n
% 5.41/5.76 thf(fact_8366_exp__ge__one__minus__x__over__n__power__n,axiom,
% 5.41/5.76 ! [X: real,N: nat] :
% 5.41/5.76 ( ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.76 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.76 => ( ord_less_eq_real @ ( power_power_real @ ( minus_minus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N ) ) ) @ N ) @ ( exp_real @ ( uminus_uminus_real @ X ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % exp_ge_one_minus_x_over_n_power_n
% 5.41/5.76 thf(fact_8367_log__base__10__eq2,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.76 = ( times_times_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ ( bit0 @ one ) ) ) ) @ ( exp_real @ one_one_real ) ) @ ( ln_ln_real @ X ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % log_base_10_eq2
% 5.41/5.76 thf(fact_8368_gauss__sum__from__Suc__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( groups3539618377306564664at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.41/5.76 = ( divide_divide_int @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % gauss_sum_from_Suc_0
% 5.41/5.76 thf(fact_8369_gauss__sum__from__Suc__0,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( groups3542108847815614940at_nat @ semiri1316708129612266289at_nat @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.41/5.76 = ( divide_divide_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ ( plus_plus_nat @ ( semiri1316708129612266289at_nat @ N ) @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % gauss_sum_from_Suc_0
% 5.41/5.76 thf(fact_8370_of__nat__code__if,axiom,
% 5.41/5.76 ( semiri8010041392384452111omplex
% 5.41/5.76 = ( ^ [N2: nat] :
% 5.41/5.76 ( if_complex @ ( N2 = zero_zero_nat ) @ zero_zero_complex
% 5.41/5.76 @ ( produc1917071388513777916omplex
% 5.41/5.76 @ ^ [M3: nat,Q5: nat] : ( if_complex @ ( Q5 = zero_zero_nat ) @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ ( plus_plus_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( semiri8010041392384452111omplex @ M3 ) ) @ one_one_complex ) )
% 5.41/5.76 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_code_if
% 5.41/5.76 thf(fact_8371_of__nat__code__if,axiom,
% 5.41/5.76 ( semiri5074537144036343181t_real
% 5.41/5.76 = ( ^ [N2: nat] :
% 5.41/5.76 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.41/5.76 @ ( produc1703576794950452218t_real
% 5.41/5.76 @ ^ [M3: nat,Q5: nat] : ( if_real @ ( Q5 = zero_zero_nat ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ M3 ) ) @ one_one_real ) )
% 5.41/5.76 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_code_if
% 5.41/5.76 thf(fact_8372_of__nat__code__if,axiom,
% 5.41/5.76 ( semiri681578069525770553at_rat
% 5.41/5.76 = ( ^ [N2: nat] :
% 5.41/5.76 ( if_rat @ ( N2 = zero_zero_nat ) @ zero_zero_rat
% 5.41/5.76 @ ( produc6207742614233964070at_rat
% 5.41/5.76 @ ^ [M3: nat,Q5: nat] : ( if_rat @ ( Q5 = zero_zero_nat ) @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ ( plus_plus_rat @ ( times_times_rat @ ( numeral_numeral_rat @ ( bit0 @ one ) ) @ ( semiri681578069525770553at_rat @ M3 ) ) @ one_one_rat ) )
% 5.41/5.76 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_code_if
% 5.41/5.76 thf(fact_8373_of__nat__code__if,axiom,
% 5.41/5.76 ( semiri1316708129612266289at_nat
% 5.41/5.76 = ( ^ [N2: nat] :
% 5.41/5.76 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.41/5.76 @ ( produc6842872674320459806at_nat
% 5.41/5.76 @ ^ [M3: nat,Q5: nat] : ( if_nat @ ( Q5 = zero_zero_nat ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( semiri1316708129612266289at_nat @ M3 ) ) @ one_one_nat ) )
% 5.41/5.76 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_code_if
% 5.41/5.76 thf(fact_8374_of__nat__code__if,axiom,
% 5.41/5.76 ( semiri1314217659103216013at_int
% 5.41/5.76 = ( ^ [N2: nat] :
% 5.41/5.76 ( if_int @ ( N2 = zero_zero_nat ) @ zero_zero_int
% 5.41/5.76 @ ( produc6840382203811409530at_int
% 5.41/5.76 @ ^ [M3: nat,Q5: nat] : ( if_int @ ( Q5 = zero_zero_nat ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( semiri1314217659103216013at_int @ M3 ) ) @ one_one_int ) )
% 5.41/5.76 @ ( divmod_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % of_nat_code_if
% 5.41/5.76 thf(fact_8375_monoseq__arctan__series,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.76 => ( topolo6980174941875973593q_real
% 5.41/5.76 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % monoseq_arctan_series
% 5.41/5.76 thf(fact_8376_lemma__termdiff3,axiom,
% 5.41/5.76 ! [H2: real,Z: real,K5: real,N: nat] :
% 5.41/5.76 ( ( H2 != zero_zero_real )
% 5.41/5.76 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ K5 )
% 5.41/5.76 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ Z @ H2 ) ) @ K5 )
% 5.41/5.76 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V7735802525324610683m_real @ H2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lemma_termdiff3
% 5.41/5.76 thf(fact_8377_lemma__termdiff3,axiom,
% 5.41/5.76 ! [H2: complex,Z: complex,K5: real,N: nat] :
% 5.41/5.76 ( ( H2 != zero_zero_complex )
% 5.41/5.76 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ K5 )
% 5.41/5.76 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ Z @ H2 ) ) @ K5 )
% 5.41/5.76 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) @ ( times_times_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( semiri5074537144036343181t_real @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) @ ( power_power_real @ K5 @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( real_V1022390504157884413omplex @ H2 ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lemma_termdiff3
% 5.41/5.76 thf(fact_8378_ln__series,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.76 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.76 => ( ( ln_ln_real @ X )
% 5.41/5.76 = ( suminf_real
% 5.41/5.76 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ N2 @ one_one_nat ) ) ) ) @ ( power_power_real @ ( minus_minus_real @ X @ one_one_real ) @ ( suc @ N2 ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % ln_series
% 5.41/5.76 thf(fact_8379_lemma__termdiff2,axiom,
% 5.41/5.76 ! [H2: complex,Z: complex,N: nat] :
% 5.41/5.76 ( ( H2 != zero_zero_complex )
% 5.41/5.76 => ( ( minus_minus_complex @ ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ N ) @ ( power_power_complex @ Z @ N ) ) @ H2 ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.41/5.76 = ( times_times_complex @ H2
% 5.41/5.76 @ ( groups2073611262835488442omplex
% 5.41/5.76 @ ^ [P2: nat] :
% 5.41/5.76 ( groups2073611262835488442omplex
% 5.41/5.76 @ ^ [Q5: nat] : ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ Q5 ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.41/5.76 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 5.41/5.76 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lemma_termdiff2
% 5.41/5.76 thf(fact_8380_lemma__termdiff2,axiom,
% 5.41/5.76 ! [H2: rat,Z: rat,N: nat] :
% 5.41/5.76 ( ( H2 != zero_zero_rat )
% 5.41/5.76 => ( ( minus_minus_rat @ ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ N ) @ ( power_power_rat @ Z @ N ) ) @ H2 ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.41/5.76 = ( times_times_rat @ H2
% 5.41/5.76 @ ( groups2906978787729119204at_rat
% 5.41/5.76 @ ^ [P2: nat] :
% 5.41/5.76 ( groups2906978787729119204at_rat
% 5.41/5.76 @ ^ [Q5: nat] : ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ Q5 ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.41/5.76 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 5.41/5.76 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lemma_termdiff2
% 5.41/5.76 thf(fact_8381_lemma__termdiff2,axiom,
% 5.41/5.76 ! [H2: real,Z: real,N: nat] :
% 5.41/5.76 ( ( H2 != zero_zero_real )
% 5.41/5.76 => ( ( minus_minus_real @ ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ N ) @ ( power_power_real @ Z @ N ) ) @ H2 ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ Z @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) )
% 5.41/5.76 = ( times_times_real @ H2
% 5.41/5.76 @ ( groups6591440286371151544t_real
% 5.41/5.76 @ ^ [P2: nat] :
% 5.41/5.76 ( groups6591440286371151544t_real
% 5.41/5.76 @ ^ [Q5: nat] : ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ Q5 ) @ ( power_power_real @ Z @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Q5 ) ) )
% 5.41/5.76 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) @ P2 ) ) )
% 5.41/5.76 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lemma_termdiff2
% 5.41/5.76 thf(fact_8382_lessThan__eq__iff,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( ( set_ord_lessThan_nat @ X )
% 5.41/5.76 = ( set_ord_lessThan_nat @ Y ) )
% 5.41/5.76 = ( X = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_eq_iff
% 5.41/5.76 thf(fact_8383_lessThan__eq__iff,axiom,
% 5.41/5.76 ! [X: int,Y: int] :
% 5.41/5.76 ( ( ( set_ord_lessThan_int @ X )
% 5.41/5.76 = ( set_ord_lessThan_int @ Y ) )
% 5.41/5.76 = ( X = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_eq_iff
% 5.41/5.76 thf(fact_8384_lessThan__eq__iff,axiom,
% 5.41/5.76 ! [X: real,Y: real] :
% 5.41/5.76 ( ( ( set_or5984915006950818249n_real @ X )
% 5.41/5.76 = ( set_or5984915006950818249n_real @ Y ) )
% 5.41/5.76 = ( X = Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_eq_iff
% 5.41/5.76 thf(fact_8385_lessThan__iff,axiom,
% 5.41/5.76 ! [I: set_nat,K: set_nat] :
% 5.41/5.76 ( ( member_set_nat @ I @ ( set_or890127255671739683et_nat @ K ) )
% 5.41/5.76 = ( ord_less_set_nat @ I @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_iff
% 5.41/5.76 thf(fact_8386_lessThan__iff,axiom,
% 5.41/5.76 ! [I: rat,K: rat] :
% 5.41/5.76 ( ( member_rat @ I @ ( set_ord_lessThan_rat @ K ) )
% 5.41/5.76 = ( ord_less_rat @ I @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_iff
% 5.41/5.76 thf(fact_8387_lessThan__iff,axiom,
% 5.41/5.76 ! [I: num,K: num] :
% 5.41/5.76 ( ( member_num @ I @ ( set_ord_lessThan_num @ K ) )
% 5.41/5.76 = ( ord_less_num @ I @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_iff
% 5.41/5.76 thf(fact_8388_lessThan__iff,axiom,
% 5.41/5.76 ! [I: nat,K: nat] :
% 5.41/5.76 ( ( member_nat @ I @ ( set_ord_lessThan_nat @ K ) )
% 5.41/5.76 = ( ord_less_nat @ I @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_iff
% 5.41/5.76 thf(fact_8389_lessThan__iff,axiom,
% 5.41/5.76 ! [I: int,K: int] :
% 5.41/5.76 ( ( member_int @ I @ ( set_ord_lessThan_int @ K ) )
% 5.41/5.76 = ( ord_less_int @ I @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_iff
% 5.41/5.76 thf(fact_8390_lessThan__iff,axiom,
% 5.41/5.76 ! [I: real,K: real] :
% 5.41/5.76 ( ( member_real @ I @ ( set_or5984915006950818249n_real @ K ) )
% 5.41/5.76 = ( ord_less_real @ I @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_iff
% 5.41/5.76 thf(fact_8391_finite__lessThan,axiom,
% 5.41/5.76 ! [K: nat] : ( finite_finite_nat @ ( set_ord_lessThan_nat @ K ) ) ).
% 5.41/5.76
% 5.41/5.76 % finite_lessThan
% 5.41/5.76 thf(fact_8392_lessThan__subset__iff,axiom,
% 5.41/5.76 ! [X: rat,Y: rat] :
% 5.41/5.76 ( ( ord_less_eq_set_rat @ ( set_ord_lessThan_rat @ X ) @ ( set_ord_lessThan_rat @ Y ) )
% 5.41/5.76 = ( ord_less_eq_rat @ X @ Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_subset_iff
% 5.41/5.76 thf(fact_8393_lessThan__subset__iff,axiom,
% 5.41/5.76 ! [X: num,Y: num] :
% 5.41/5.76 ( ( ord_less_eq_set_num @ ( set_ord_lessThan_num @ X ) @ ( set_ord_lessThan_num @ Y ) )
% 5.41/5.76 = ( ord_less_eq_num @ X @ Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_subset_iff
% 5.41/5.76 thf(fact_8394_lessThan__subset__iff,axiom,
% 5.41/5.76 ! [X: nat,Y: nat] :
% 5.41/5.76 ( ( ord_less_eq_set_nat @ ( set_ord_lessThan_nat @ X ) @ ( set_ord_lessThan_nat @ Y ) )
% 5.41/5.76 = ( ord_less_eq_nat @ X @ Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_subset_iff
% 5.41/5.76 thf(fact_8395_lessThan__subset__iff,axiom,
% 5.41/5.76 ! [X: int,Y: int] :
% 5.41/5.76 ( ( ord_less_eq_set_int @ ( set_ord_lessThan_int @ X ) @ ( set_ord_lessThan_int @ Y ) )
% 5.41/5.76 = ( ord_less_eq_int @ X @ Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_subset_iff
% 5.41/5.76 thf(fact_8396_lessThan__subset__iff,axiom,
% 5.41/5.76 ! [X: real,Y: real] :
% 5.41/5.76 ( ( ord_less_eq_set_real @ ( set_or5984915006950818249n_real @ X ) @ ( set_or5984915006950818249n_real @ Y ) )
% 5.41/5.76 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_subset_iff
% 5.41/5.76 thf(fact_8397_lessThan__0,axiom,
% 5.41/5.76 ( ( set_ord_lessThan_nat @ zero_zero_nat )
% 5.41/5.76 = bot_bot_set_nat ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_0
% 5.41/5.76 thf(fact_8398_sum_OlessThan__Suc,axiom,
% 5.41/5.76 ! [G: nat > rat,N: nat] :
% 5.41/5.76 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.76 = ( plus_plus_rat @ ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.lessThan_Suc
% 5.41/5.76 thf(fact_8399_sum_OlessThan__Suc,axiom,
% 5.41/5.76 ! [G: nat > int,N: nat] :
% 5.41/5.76 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.76 = ( plus_plus_int @ ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.lessThan_Suc
% 5.41/5.76 thf(fact_8400_sum_OlessThan__Suc,axiom,
% 5.41/5.76 ! [G: nat > nat,N: nat] :
% 5.41/5.76 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.76 = ( plus_plus_nat @ ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.lessThan_Suc
% 5.41/5.76 thf(fact_8401_sum_OlessThan__Suc,axiom,
% 5.41/5.76 ! [G: nat > real,N: nat] :
% 5.41/5.76 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.76 = ( plus_plus_real @ ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) @ ( G @ N ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % sum.lessThan_Suc
% 5.41/5.76 thf(fact_8402_single__Diff__lessThan,axiom,
% 5.41/5.76 ! [K: nat] :
% 5.41/5.76 ( ( minus_minus_set_nat @ ( insert_nat @ K @ bot_bot_set_nat ) @ ( set_ord_lessThan_nat @ K ) )
% 5.41/5.76 = ( insert_nat @ K @ bot_bot_set_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % single_Diff_lessThan
% 5.41/5.76 thf(fact_8403_single__Diff__lessThan,axiom,
% 5.41/5.76 ! [K: int] :
% 5.41/5.76 ( ( minus_minus_set_int @ ( insert_int @ K @ bot_bot_set_int ) @ ( set_ord_lessThan_int @ K ) )
% 5.41/5.76 = ( insert_int @ K @ bot_bot_set_int ) ) ).
% 5.41/5.76
% 5.41/5.76 % single_Diff_lessThan
% 5.41/5.76 thf(fact_8404_single__Diff__lessThan,axiom,
% 5.41/5.76 ! [K: real] :
% 5.41/5.76 ( ( minus_minus_set_real @ ( insert_real @ K @ bot_bot_set_real ) @ ( set_or5984915006950818249n_real @ K ) )
% 5.41/5.76 = ( insert_real @ K @ bot_bot_set_real ) ) ).
% 5.41/5.76
% 5.41/5.76 % single_Diff_lessThan
% 5.41/5.76 thf(fact_8405_powser__zero,axiom,
% 5.41/5.76 ! [F: nat > complex] :
% 5.41/5.76 ( ( suminf_complex
% 5.41/5.76 @ ^ [N2: nat] : ( times_times_complex @ ( F @ N2 ) @ ( power_power_complex @ zero_zero_complex @ N2 ) ) )
% 5.41/5.76 = ( F @ zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % powser_zero
% 5.41/5.76 thf(fact_8406_powser__zero,axiom,
% 5.41/5.76 ! [F: nat > real] :
% 5.41/5.76 ( ( suminf_real
% 5.41/5.76 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ zero_zero_real @ N2 ) ) )
% 5.41/5.76 = ( F @ zero_zero_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % powser_zero
% 5.41/5.76 thf(fact_8407_set__encode__insert,axiom,
% 5.41/5.76 ! [A2: set_nat,N: nat] :
% 5.41/5.76 ( ( finite_finite_nat @ A2 )
% 5.41/5.76 => ( ~ ( member_nat @ N @ A2 )
% 5.41/5.76 => ( ( nat_set_encode @ ( insert_nat @ N @ A2 ) )
% 5.41/5.76 = ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ ( nat_set_encode @ A2 ) ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % set_encode_insert
% 5.41/5.76 thf(fact_8408_lessThan__nat__numeral,axiom,
% 5.41/5.76 ! [K: num] :
% 5.41/5.76 ( ( set_ord_lessThan_nat @ ( numeral_numeral_nat @ K ) )
% 5.41/5.76 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_ord_lessThan_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_nat_numeral
% 5.41/5.76 thf(fact_8409_lessThan__Suc,axiom,
% 5.41/5.76 ! [K: nat] :
% 5.41/5.76 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.41/5.76 = ( insert_nat @ K @ ( set_ord_lessThan_nat @ K ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_Suc
% 5.41/5.76 thf(fact_8410_lessThan__non__empty,axiom,
% 5.41/5.76 ! [X: int] :
% 5.41/5.76 ( ( set_ord_lessThan_int @ X )
% 5.41/5.76 != bot_bot_set_int ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_non_empty
% 5.41/5.76 thf(fact_8411_lessThan__non__empty,axiom,
% 5.41/5.76 ! [X: real] :
% 5.41/5.76 ( ( set_or5984915006950818249n_real @ X )
% 5.41/5.76 != bot_bot_set_real ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_non_empty
% 5.41/5.76 thf(fact_8412_infinite__Iio,axiom,
% 5.41/5.76 ! [A: int] :
% 5.41/5.76 ~ ( finite_finite_int @ ( set_ord_lessThan_int @ A ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_Iio
% 5.41/5.76 thf(fact_8413_infinite__Iio,axiom,
% 5.41/5.76 ! [A: real] :
% 5.41/5.76 ~ ( finite_finite_real @ ( set_or5984915006950818249n_real @ A ) ) ).
% 5.41/5.76
% 5.41/5.76 % infinite_Iio
% 5.41/5.76 thf(fact_8414_lessThan__def,axiom,
% 5.41/5.76 ( set_or890127255671739683et_nat
% 5.41/5.76 = ( ^ [U2: set_nat] :
% 5.41/5.76 ( collect_set_nat
% 5.41/5.76 @ ^ [X3: set_nat] : ( ord_less_set_nat @ X3 @ U2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_def
% 5.41/5.76 thf(fact_8415_lessThan__def,axiom,
% 5.41/5.76 ( set_ord_lessThan_rat
% 5.41/5.76 = ( ^ [U2: rat] :
% 5.41/5.76 ( collect_rat
% 5.41/5.76 @ ^ [X3: rat] : ( ord_less_rat @ X3 @ U2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_def
% 5.41/5.76 thf(fact_8416_lessThan__def,axiom,
% 5.41/5.76 ( set_ord_lessThan_num
% 5.41/5.76 = ( ^ [U2: num] :
% 5.41/5.76 ( collect_num
% 5.41/5.76 @ ^ [X3: num] : ( ord_less_num @ X3 @ U2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_def
% 5.41/5.76 thf(fact_8417_lessThan__def,axiom,
% 5.41/5.76 ( set_ord_lessThan_nat
% 5.41/5.76 = ( ^ [U2: nat] :
% 5.41/5.76 ( collect_nat
% 5.41/5.76 @ ^ [X3: nat] : ( ord_less_nat @ X3 @ U2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_def
% 5.41/5.76 thf(fact_8418_lessThan__def,axiom,
% 5.41/5.76 ( set_ord_lessThan_int
% 5.41/5.76 = ( ^ [U2: int] :
% 5.41/5.76 ( collect_int
% 5.41/5.76 @ ^ [X3: int] : ( ord_less_int @ X3 @ U2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_def
% 5.41/5.76 thf(fact_8419_lessThan__def,axiom,
% 5.41/5.76 ( set_or5984915006950818249n_real
% 5.41/5.76 = ( ^ [U2: real] :
% 5.41/5.76 ( collect_real
% 5.41/5.76 @ ^ [X3: real] : ( ord_less_real @ X3 @ U2 ) ) ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_def
% 5.41/5.76 thf(fact_8420_Iio__eq__empty__iff,axiom,
% 5.41/5.76 ! [N: extended_enat] :
% 5.41/5.76 ( ( ( set_or8419480210114673929d_enat @ N )
% 5.41/5.76 = bot_bo7653980558646680370d_enat )
% 5.41/5.76 = ( N = bot_bo4199563552545308370d_enat ) ) ).
% 5.41/5.76
% 5.41/5.76 % Iio_eq_empty_iff
% 5.41/5.76 thf(fact_8421_Iio__eq__empty__iff,axiom,
% 5.41/5.76 ! [N: nat] :
% 5.41/5.76 ( ( ( set_ord_lessThan_nat @ N )
% 5.41/5.76 = bot_bot_set_nat )
% 5.41/5.76 = ( N = bot_bot_nat ) ) ).
% 5.41/5.76
% 5.41/5.76 % Iio_eq_empty_iff
% 5.41/5.76 thf(fact_8422_lessThan__strict__subset__iff,axiom,
% 5.41/5.76 ! [M: rat,N: rat] :
% 5.41/5.76 ( ( ord_less_set_rat @ ( set_ord_lessThan_rat @ M ) @ ( set_ord_lessThan_rat @ N ) )
% 5.41/5.76 = ( ord_less_rat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_strict_subset_iff
% 5.41/5.76 thf(fact_8423_lessThan__strict__subset__iff,axiom,
% 5.41/5.76 ! [M: num,N: num] :
% 5.41/5.76 ( ( ord_less_set_num @ ( set_ord_lessThan_num @ M ) @ ( set_ord_lessThan_num @ N ) )
% 5.41/5.76 = ( ord_less_num @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_strict_subset_iff
% 5.41/5.76 thf(fact_8424_lessThan__strict__subset__iff,axiom,
% 5.41/5.76 ! [M: nat,N: nat] :
% 5.41/5.76 ( ( ord_less_set_nat @ ( set_ord_lessThan_nat @ M ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.76 = ( ord_less_nat @ M @ N ) ) ).
% 5.41/5.76
% 5.41/5.76 % lessThan_strict_subset_iff
% 5.41/5.77 thf(fact_8425_lessThan__strict__subset__iff,axiom,
% 5.41/5.77 ! [M: int,N: int] :
% 5.41/5.77 ( ( ord_less_set_int @ ( set_ord_lessThan_int @ M ) @ ( set_ord_lessThan_int @ N ) )
% 5.41/5.77 = ( ord_less_int @ M @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % lessThan_strict_subset_iff
% 5.41/5.77 thf(fact_8426_lessThan__strict__subset__iff,axiom,
% 5.41/5.77 ! [M: real,N: real] :
% 5.41/5.77 ( ( ord_less_set_real @ ( set_or5984915006950818249n_real @ M ) @ ( set_or5984915006950818249n_real @ N ) )
% 5.41/5.77 = ( ord_less_real @ M @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % lessThan_strict_subset_iff
% 5.41/5.77 thf(fact_8427_complex__mod__minus__le__complex__mod,axiom,
% 5.41/5.77 ! [X: complex] : ( ord_less_eq_real @ ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_mod_minus_le_complex_mod
% 5.41/5.77 thf(fact_8428_complex__mod__triangle__ineq2,axiom,
% 5.41/5.77 ! [B: complex,A: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ B @ A ) ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ A ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_mod_triangle_ineq2
% 5.41/5.77 thf(fact_8429_lessThan__empty__iff,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( ( set_ord_lessThan_nat @ N )
% 5.41/5.77 = bot_bot_set_nat )
% 5.41/5.77 = ( N = zero_zero_nat ) ) ).
% 5.41/5.77
% 5.41/5.77 % lessThan_empty_iff
% 5.41/5.77 thf(fact_8430_finite__nat__bounded,axiom,
% 5.41/5.77 ! [S2: set_nat] :
% 5.41/5.77 ( ( finite_finite_nat @ S2 )
% 5.41/5.77 => ? [K3: nat] : ( ord_less_eq_set_nat @ S2 @ ( set_ord_lessThan_nat @ K3 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % finite_nat_bounded
% 5.41/5.77 thf(fact_8431_finite__nat__iff__bounded,axiom,
% 5.41/5.77 ( finite_finite_nat
% 5.41/5.77 = ( ^ [S6: set_nat] :
% 5.41/5.77 ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_lessThan_nat @ K2 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % finite_nat_iff_bounded
% 5.41/5.77 thf(fact_8432_atLeast0__atMost__Suc,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.41/5.77 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % atLeast0_atMost_Suc
% 5.41/5.77 thf(fact_8433_Icc__eq__insert__lb__nat,axiom,
% 5.41/5.77 ! [M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.77 => ( ( set_or1269000886237332187st_nat @ M @ N )
% 5.41/5.77 = ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Icc_eq_insert_lb_nat
% 5.41/5.77 thf(fact_8434_atLeastAtMostSuc__conv,axiom,
% 5.41/5.77 ! [M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ M @ ( suc @ N ) )
% 5.41/5.77 => ( ( set_or1269000886237332187st_nat @ M @ ( suc @ N ) )
% 5.41/5.77 = ( insert_nat @ ( suc @ N ) @ ( set_or1269000886237332187st_nat @ M @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % atLeastAtMostSuc_conv
% 5.41/5.77 thf(fact_8435_atLeastAtMost__insertL,axiom,
% 5.41/5.77 ! [M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.77 => ( ( insert_nat @ M @ ( set_or1269000886237332187st_nat @ ( suc @ M ) @ N ) )
% 5.41/5.77 = ( set_or1269000886237332187st_nat @ M @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % atLeastAtMost_insertL
% 5.41/5.77 thf(fact_8436_norm__exp,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ X ) ) @ ( exp_real @ ( real_V7735802525324610683m_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_exp
% 5.41/5.77 thf(fact_8437_norm__exp,axiom,
% 5.41/5.77 ! [X: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ X ) ) @ ( exp_real @ ( real_V1022390504157884413omplex @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_exp
% 5.41/5.77 thf(fact_8438_sum_Onat__diff__reindex,axiom,
% 5.41/5.77 ! [G: nat > nat,N: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.nat_diff_reindex
% 5.41/5.77 thf(fact_8439_sum_Onat__diff__reindex,axiom,
% 5.41/5.77 ! [G: nat > real,N: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( G @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.nat_diff_reindex
% 5.41/5.77 thf(fact_8440_sum__diff__distrib,axiom,
% 5.41/5.77 ! [Q: int > nat,P: int > nat,N: int] :
% 5.41/5.77 ( ! [X6: int] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 5.41/5.77 => ( ( minus_minus_nat @ ( groups4541462559716669496nt_nat @ P @ ( set_ord_lessThan_int @ N ) ) @ ( groups4541462559716669496nt_nat @ Q @ ( set_ord_lessThan_int @ N ) ) )
% 5.41/5.77 = ( groups4541462559716669496nt_nat
% 5.41/5.77 @ ^ [X3: int] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_int @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_diff_distrib
% 5.41/5.77 thf(fact_8441_sum__diff__distrib,axiom,
% 5.41/5.77 ! [Q: real > nat,P: real > nat,N: real] :
% 5.41/5.77 ( ! [X6: real] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 5.41/5.77 => ( ( minus_minus_nat @ ( groups1935376822645274424al_nat @ P @ ( set_or5984915006950818249n_real @ N ) ) @ ( groups1935376822645274424al_nat @ Q @ ( set_or5984915006950818249n_real @ N ) ) )
% 5.41/5.77 = ( groups1935376822645274424al_nat
% 5.41/5.77 @ ^ [X3: real] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 5.41/5.77 @ ( set_or5984915006950818249n_real @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_diff_distrib
% 5.41/5.77 thf(fact_8442_sum__diff__distrib,axiom,
% 5.41/5.77 ! [Q: nat > nat,P: nat > nat,N: nat] :
% 5.41/5.77 ( ! [X6: nat] : ( ord_less_eq_nat @ ( Q @ X6 ) @ ( P @ X6 ) )
% 5.41/5.77 => ( ( minus_minus_nat @ ( groups3542108847815614940at_nat @ P @ ( set_ord_lessThan_nat @ N ) ) @ ( groups3542108847815614940at_nat @ Q @ ( set_ord_lessThan_nat @ N ) ) )
% 5.41/5.77 = ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [X3: nat] : ( minus_minus_nat @ ( P @ X3 ) @ ( Q @ X3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_diff_distrib
% 5.41/5.77 thf(fact_8443_sum_OlessThan__Suc__shift,axiom,
% 5.41/5.77 ! [G: nat > rat,N: nat] :
% 5.41/5.77 ( ( groups2906978787729119204at_rat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.77 = ( plus_plus_rat @ ( G @ zero_zero_nat )
% 5.41/5.77 @ ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.lessThan_Suc_shift
% 5.41/5.77 thf(fact_8444_sum_OlessThan__Suc__shift,axiom,
% 5.41/5.77 ! [G: nat > int,N: nat] :
% 5.41/5.77 ( ( groups3539618377306564664at_int @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.77 = ( plus_plus_int @ ( G @ zero_zero_nat )
% 5.41/5.77 @ ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.lessThan_Suc_shift
% 5.41/5.77 thf(fact_8445_sum_OlessThan__Suc__shift,axiom,
% 5.41/5.77 ! [G: nat > nat,N: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.77 = ( plus_plus_nat @ ( G @ zero_zero_nat )
% 5.41/5.77 @ ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.lessThan_Suc_shift
% 5.41/5.77 thf(fact_8446_sum_OlessThan__Suc__shift,axiom,
% 5.41/5.77 ! [G: nat > real,N: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real @ G @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.77 = ( plus_plus_real @ ( G @ zero_zero_nat )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( G @ ( suc @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.lessThan_Suc_shift
% 5.41/5.77 thf(fact_8447_sum__lessThan__telescope,axiom,
% 5.41/5.77 ! [F: nat > rat,M: nat] :
% 5.41/5.77 ( ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( minus_minus_rat @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_lessThan_telescope
% 5.41/5.77 thf(fact_8448_sum__lessThan__telescope,axiom,
% 5.41/5.77 ! [F: nat > int,M: nat] :
% 5.41/5.77 ( ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( minus_minus_int @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_lessThan_telescope
% 5.41/5.77 thf(fact_8449_sum__lessThan__telescope,axiom,
% 5.41/5.77 ! [F: nat > real,M: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ ( suc @ N2 ) ) @ ( F @ N2 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( minus_minus_real @ ( F @ M ) @ ( F @ zero_zero_nat ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_lessThan_telescope
% 5.41/5.77 thf(fact_8450_sum__lessThan__telescope_H,axiom,
% 5.41/5.77 ! [F: nat > rat,M: nat] :
% 5.41/5.77 ( ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [N2: nat] : ( minus_minus_rat @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( minus_minus_rat @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_lessThan_telescope'
% 5.41/5.77 thf(fact_8451_sum__lessThan__telescope_H,axiom,
% 5.41/5.77 ! [F: nat > int,M: nat] :
% 5.41/5.77 ( ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [N2: nat] : ( minus_minus_int @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( minus_minus_int @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_lessThan_telescope'
% 5.41/5.77 thf(fact_8452_sum__lessThan__telescope_H,axiom,
% 5.41/5.77 ! [F: nat > real,M: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( F @ ( suc @ N2 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( minus_minus_real @ ( F @ zero_zero_nat ) @ ( F @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_lessThan_telescope'
% 5.41/5.77 thf(fact_8453_sumr__diff__mult__const2,axiom,
% 5.41/5.77 ! [F: nat > complex,N: nat,R: complex] :
% 5.41/5.77 ( ( minus_minus_complex @ ( groups2073611262835488442omplex @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_complex @ ( semiri8010041392384452111omplex @ N ) @ R ) )
% 5.41/5.77 = ( groups2073611262835488442omplex
% 5.41/5.77 @ ^ [I5: nat] : ( minus_minus_complex @ ( F @ I5 ) @ R )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sumr_diff_mult_const2
% 5.41/5.77 thf(fact_8454_sumr__diff__mult__const2,axiom,
% 5.41/5.77 ! [F: nat > rat,N: nat,R: rat] :
% 5.41/5.77 ( ( minus_minus_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ R ) )
% 5.41/5.77 = ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [I5: nat] : ( minus_minus_rat @ ( F @ I5 ) @ R )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sumr_diff_mult_const2
% 5.41/5.77 thf(fact_8455_sumr__diff__mult__const2,axiom,
% 5.41/5.77 ! [F: nat > int,N: nat,R: int] :
% 5.41/5.77 ( ( minus_minus_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ R ) )
% 5.41/5.77 = ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [I5: nat] : ( minus_minus_int @ ( F @ I5 ) @ R )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sumr_diff_mult_const2
% 5.41/5.77 thf(fact_8456_sumr__diff__mult__const2,axiom,
% 5.41/5.77 ! [F: nat > real,N: nat,R: real] :
% 5.41/5.77 ( ( minus_minus_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ N ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ R ) )
% 5.41/5.77 = ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( minus_minus_real @ ( F @ I5 ) @ R )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sumr_diff_mult_const2
% 5.41/5.77 thf(fact_8457_sum_OatLeast1__atMost__eq,axiom,
% 5.41/5.77 ! [G: nat > nat,N: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.41/5.77 = ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.atLeast1_atMost_eq
% 5.41/5.77 thf(fact_8458_sum_OatLeast1__atMost__eq,axiom,
% 5.41/5.77 ! [G: nat > real,N: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real @ G @ ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.41/5.77 = ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [K2: nat] : ( G @ ( suc @ K2 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum.atLeast1_atMost_eq
% 5.41/5.77 thf(fact_8459_power__diff__1__eq,axiom,
% 5.41/5.77 ! [X: complex,N: nat] :
% 5.41/5.77 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex )
% 5.41/5.77 = ( times_times_complex @ ( minus_minus_complex @ X @ one_one_complex ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_1_eq
% 5.41/5.77 thf(fact_8460_power__diff__1__eq,axiom,
% 5.41/5.77 ! [X: rat,N: nat] :
% 5.41/5.77 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat )
% 5.41/5.77 = ( times_times_rat @ ( minus_minus_rat @ X @ one_one_rat ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_1_eq
% 5.41/5.77 thf(fact_8461_power__diff__1__eq,axiom,
% 5.41/5.77 ! [X: int,N: nat] :
% 5.41/5.77 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ one_one_int )
% 5.41/5.77 = ( times_times_int @ ( minus_minus_int @ X @ one_one_int ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_1_eq
% 5.41/5.77 thf(fact_8462_power__diff__1__eq,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real )
% 5.41/5.77 = ( times_times_real @ ( minus_minus_real @ X @ one_one_real ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_1_eq
% 5.41/5.77 thf(fact_8463_one__diff__power__eq,axiom,
% 5.41/5.77 ! [X: complex,N: nat] :
% 5.41/5.77 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.41/5.77 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X ) @ ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq
% 5.41/5.77 thf(fact_8464_one__diff__power__eq,axiom,
% 5.41/5.77 ! [X: rat,N: nat] :
% 5.41/5.77 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.41/5.77 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X ) @ ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq
% 5.41/5.77 thf(fact_8465_one__diff__power__eq,axiom,
% 5.41/5.77 ! [X: int,N: nat] :
% 5.41/5.77 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.41/5.77 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X ) @ ( groups3539618377306564664at_int @ ( power_power_int @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq
% 5.41/5.77 thf(fact_8466_one__diff__power__eq,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.41/5.77 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X ) @ ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq
% 5.41/5.77 thf(fact_8467_geometric__sum,axiom,
% 5.41/5.77 ! [X: complex,N: nat] :
% 5.41/5.77 ( ( X != one_one_complex )
% 5.41/5.77 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ one_one_complex ) @ ( minus_minus_complex @ X @ one_one_complex ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % geometric_sum
% 5.41/5.77 thf(fact_8468_geometric__sum,axiom,
% 5.41/5.77 ! [X: rat,N: nat] :
% 5.41/5.77 ( ( X != one_one_rat )
% 5.41/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( divide_divide_rat @ ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ one_one_rat ) @ ( minus_minus_rat @ X @ one_one_rat ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % geometric_sum
% 5.41/5.77 thf(fact_8469_geometric__sum,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( X != one_one_real )
% 5.41/5.77 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( divide_divide_real @ ( minus_minus_real @ ( power_power_real @ X @ N ) @ one_one_real ) @ ( minus_minus_real @ X @ one_one_real ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % geometric_sum
% 5.41/5.77 thf(fact_8470_monoseq__realpow,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( topolo6980174941875973593q_real @ ( power_power_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % monoseq_realpow
% 5.41/5.77 thf(fact_8471_sum__gp__strict,axiom,
% 5.41/5.77 ! [X: complex,N: nat] :
% 5.41/5.77 ( ( ( X = one_one_complex )
% 5.41/5.77 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( semiri8010041392384452111omplex @ N ) ) )
% 5.41/5.77 & ( ( X != one_one_complex )
% 5.41/5.77 => ( ( groups2073611262835488442omplex @ ( power_power_complex @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( divide1717551699836669952omplex @ ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) ) @ ( minus_minus_complex @ one_one_complex @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_gp_strict
% 5.41/5.77 thf(fact_8472_sum__gp__strict,axiom,
% 5.41/5.77 ! [X: rat,N: nat] :
% 5.41/5.77 ( ( ( X = one_one_rat )
% 5.41/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( semiri681578069525770553at_rat @ N ) ) )
% 5.41/5.77 & ( ( X != one_one_rat )
% 5.41/5.77 => ( ( groups2906978787729119204at_rat @ ( power_power_rat @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( divide_divide_rat @ ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) ) @ ( minus_minus_rat @ one_one_rat @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_gp_strict
% 5.41/5.77 thf(fact_8473_sum__gp__strict,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( ( X = one_one_real )
% 5.41/5.77 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( semiri5074537144036343181t_real @ N ) ) )
% 5.41/5.77 & ( ( X != one_one_real )
% 5.41/5.77 => ( ( groups6591440286371151544t_real @ ( power_power_real @ X ) @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 = ( divide_divide_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) ) @ ( minus_minus_real @ one_one_real @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_gp_strict
% 5.41/5.77 thf(fact_8474_lemma__termdiff1,axiom,
% 5.41/5.77 ! [Z: complex,H2: complex,M: nat] :
% 5.41/5.77 ( ( groups2073611262835488442omplex
% 5.41/5.77 @ ^ [P2: nat] : ( minus_minus_complex @ ( times_times_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_complex @ Z @ P2 ) ) @ ( power_power_complex @ Z @ M ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( groups2073611262835488442omplex
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_complex @ ( power_power_complex @ Z @ P2 ) @ ( minus_minus_complex @ ( power_power_complex @ ( plus_plus_complex @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_complex @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % lemma_termdiff1
% 5.41/5.77 thf(fact_8475_lemma__termdiff1,axiom,
% 5.41/5.77 ! [Z: rat,H2: rat,M: nat] :
% 5.41/5.77 ( ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [P2: nat] : ( minus_minus_rat @ ( times_times_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_rat @ Z @ P2 ) ) @ ( power_power_rat @ Z @ M ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_rat @ ( power_power_rat @ Z @ P2 ) @ ( minus_minus_rat @ ( power_power_rat @ ( plus_plus_rat @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_rat @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % lemma_termdiff1
% 5.41/5.77 thf(fact_8476_lemma__termdiff1,axiom,
% 5.41/5.77 ! [Z: int,H2: int,M: nat] :
% 5.41/5.77 ( ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [P2: nat] : ( minus_minus_int @ ( times_times_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_int @ Z @ P2 ) ) @ ( power_power_int @ Z @ M ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_int @ ( power_power_int @ Z @ P2 ) @ ( minus_minus_int @ ( power_power_int @ ( plus_plus_int @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_int @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % lemma_termdiff1
% 5.41/5.77 thf(fact_8477_lemma__termdiff1,axiom,
% 5.41/5.77 ! [Z: real,H2: real,M: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [P2: nat] : ( minus_minus_real @ ( times_times_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_real @ Z @ P2 ) ) @ ( power_power_real @ Z @ M ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) )
% 5.41/5.77 = ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_real @ ( power_power_real @ Z @ P2 ) @ ( minus_minus_real @ ( power_power_real @ ( plus_plus_real @ Z @ H2 ) @ ( minus_minus_nat @ M @ P2 ) ) @ ( power_power_real @ Z @ ( minus_minus_nat @ M @ P2 ) ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % lemma_termdiff1
% 5.41/5.77 thf(fact_8478_power__diff__sumr2,axiom,
% 5.41/5.77 ! [X: complex,N: nat,Y: complex] :
% 5.41/5.77 ( ( minus_minus_complex @ ( power_power_complex @ X @ N ) @ ( power_power_complex @ Y @ N ) )
% 5.41/5.77 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.41/5.77 @ ( groups2073611262835488442omplex
% 5.41/5.77 @ ^ [I5: nat] : ( times_times_complex @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_complex @ X @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_sumr2
% 5.41/5.77 thf(fact_8479_power__diff__sumr2,axiom,
% 5.41/5.77 ! [X: rat,N: nat,Y: rat] :
% 5.41/5.77 ( ( minus_minus_rat @ ( power_power_rat @ X @ N ) @ ( power_power_rat @ Y @ N ) )
% 5.41/5.77 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.41/5.77 @ ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [I5: nat] : ( times_times_rat @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_rat @ X @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_sumr2
% 5.41/5.77 thf(fact_8480_power__diff__sumr2,axiom,
% 5.41/5.77 ! [X: int,N: nat,Y: int] :
% 5.41/5.77 ( ( minus_minus_int @ ( power_power_int @ X @ N ) @ ( power_power_int @ Y @ N ) )
% 5.41/5.77 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.41/5.77 @ ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [I5: nat] : ( times_times_int @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_int @ X @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_sumr2
% 5.41/5.77 thf(fact_8481_power__diff__sumr2,axiom,
% 5.41/5.77 ! [X: real,N: nat,Y: real] :
% 5.41/5.77 ( ( minus_minus_real @ ( power_power_real @ X @ N ) @ ( power_power_real @ Y @ N ) )
% 5.41/5.77 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) ) @ ( power_power_real @ X @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_diff_sumr2
% 5.41/5.77 thf(fact_8482_diff__power__eq__sum,axiom,
% 5.41/5.77 ! [X: complex,N: nat,Y: complex] :
% 5.41/5.77 ( ( minus_minus_complex @ ( power_power_complex @ X @ ( suc @ N ) ) @ ( power_power_complex @ Y @ ( suc @ N ) ) )
% 5.41/5.77 = ( times_times_complex @ ( minus_minus_complex @ X @ Y )
% 5.41/5.77 @ ( groups2073611262835488442omplex
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_complex @ ( power_power_complex @ X @ P2 ) @ ( power_power_complex @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % diff_power_eq_sum
% 5.41/5.77 thf(fact_8483_diff__power__eq__sum,axiom,
% 5.41/5.77 ! [X: rat,N: nat,Y: rat] :
% 5.41/5.77 ( ( minus_minus_rat @ ( power_power_rat @ X @ ( suc @ N ) ) @ ( power_power_rat @ Y @ ( suc @ N ) ) )
% 5.41/5.77 = ( times_times_rat @ ( minus_minus_rat @ X @ Y )
% 5.41/5.77 @ ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_rat @ ( power_power_rat @ X @ P2 ) @ ( power_power_rat @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % diff_power_eq_sum
% 5.41/5.77 thf(fact_8484_diff__power__eq__sum,axiom,
% 5.41/5.77 ! [X: int,N: nat,Y: int] :
% 5.41/5.77 ( ( minus_minus_int @ ( power_power_int @ X @ ( suc @ N ) ) @ ( power_power_int @ Y @ ( suc @ N ) ) )
% 5.41/5.77 = ( times_times_int @ ( minus_minus_int @ X @ Y )
% 5.41/5.77 @ ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_int @ ( power_power_int @ X @ P2 ) @ ( power_power_int @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % diff_power_eq_sum
% 5.41/5.77 thf(fact_8485_diff__power__eq__sum,axiom,
% 5.41/5.77 ! [X: real,N: nat,Y: real] :
% 5.41/5.77 ( ( minus_minus_real @ ( power_power_real @ X @ ( suc @ N ) ) @ ( power_power_real @ Y @ ( suc @ N ) ) )
% 5.41/5.77 = ( times_times_real @ ( minus_minus_real @ X @ Y )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [P2: nat] : ( times_times_real @ ( power_power_real @ X @ P2 ) @ ( power_power_real @ Y @ ( minus_minus_nat @ N @ P2 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % diff_power_eq_sum
% 5.41/5.77 thf(fact_8486_set__decode__plus__power__2,axiom,
% 5.41/5.77 ! [N: nat,Z: nat] :
% 5.41/5.77 ( ~ ( member_nat @ N @ ( nat_set_decode @ Z ) )
% 5.41/5.77 => ( ( nat_set_decode @ ( plus_plus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ Z ) )
% 5.41/5.77 = ( insert_nat @ N @ ( nat_set_decode @ Z ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % set_decode_plus_power_2
% 5.41/5.77 thf(fact_8487_real__sum__nat__ivl__bounded2,axiom,
% 5.41/5.77 ! [N: nat,F: nat > rat,K5: rat,K: nat] :
% 5.41/5.77 ( ! [P7: nat] :
% 5.41/5.77 ( ( ord_less_nat @ P7 @ N )
% 5.41/5.77 => ( ord_less_eq_rat @ ( F @ P7 ) @ K5 ) )
% 5.41/5.77 => ( ( ord_less_eq_rat @ zero_zero_rat @ K5 )
% 5.41/5.77 => ( ord_less_eq_rat @ ( groups2906978787729119204at_rat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_rat @ ( semiri681578069525770553at_rat @ N ) @ K5 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sum_nat_ivl_bounded2
% 5.41/5.77 thf(fact_8488_real__sum__nat__ivl__bounded2,axiom,
% 5.41/5.77 ! [N: nat,F: nat > int,K5: int,K: nat] :
% 5.41/5.77 ( ! [P7: nat] :
% 5.41/5.77 ( ( ord_less_nat @ P7 @ N )
% 5.41/5.77 => ( ord_less_eq_int @ ( F @ P7 ) @ K5 ) )
% 5.41/5.77 => ( ( ord_less_eq_int @ zero_zero_int @ K5 )
% 5.41/5.77 => ( ord_less_eq_int @ ( groups3539618377306564664at_int @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_int @ ( semiri1314217659103216013at_int @ N ) @ K5 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sum_nat_ivl_bounded2
% 5.41/5.77 thf(fact_8489_real__sum__nat__ivl__bounded2,axiom,
% 5.41/5.77 ! [N: nat,F: nat > nat,K5: nat,K: nat] :
% 5.41/5.77 ( ! [P7: nat] :
% 5.41/5.77 ( ( ord_less_nat @ P7 @ N )
% 5.41/5.77 => ( ord_less_eq_nat @ ( F @ P7 ) @ K5 ) )
% 5.41/5.77 => ( ( ord_less_eq_nat @ zero_zero_nat @ K5 )
% 5.41/5.77 => ( ord_less_eq_nat @ ( groups3542108847815614940at_nat @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ N ) @ K5 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sum_nat_ivl_bounded2
% 5.41/5.77 thf(fact_8490_real__sum__nat__ivl__bounded2,axiom,
% 5.41/5.77 ! [N: nat,F: nat > real,K5: real,K: nat] :
% 5.41/5.77 ( ! [P7: nat] :
% 5.41/5.77 ( ( ord_less_nat @ P7 @ N )
% 5.41/5.77 => ( ord_less_eq_real @ ( F @ P7 ) @ K5 ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ K5 )
% 5.41/5.77 => ( ord_less_eq_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ K5 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sum_nat_ivl_bounded2
% 5.41/5.77 thf(fact_8491_exp__bound__half,axiom,
% 5.41/5.77 ! [Z: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % exp_bound_half
% 5.41/5.77 thf(fact_8492_exp__bound__half,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % exp_bound_half
% 5.41/5.77 thf(fact_8493_one__diff__power__eq_H,axiom,
% 5.41/5.77 ! [X: complex,N: nat] :
% 5.41/5.77 ( ( minus_minus_complex @ one_one_complex @ ( power_power_complex @ X @ N ) )
% 5.41/5.77 = ( times_times_complex @ ( minus_minus_complex @ one_one_complex @ X )
% 5.41/5.77 @ ( groups2073611262835488442omplex
% 5.41/5.77 @ ^ [I5: nat] : ( power_power_complex @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq'
% 5.41/5.77 thf(fact_8494_one__diff__power__eq_H,axiom,
% 5.41/5.77 ! [X: rat,N: nat] :
% 5.41/5.77 ( ( minus_minus_rat @ one_one_rat @ ( power_power_rat @ X @ N ) )
% 5.41/5.77 = ( times_times_rat @ ( minus_minus_rat @ one_one_rat @ X )
% 5.41/5.77 @ ( groups2906978787729119204at_rat
% 5.41/5.77 @ ^ [I5: nat] : ( power_power_rat @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq'
% 5.41/5.77 thf(fact_8495_one__diff__power__eq_H,axiom,
% 5.41/5.77 ! [X: int,N: nat] :
% 5.41/5.77 ( ( minus_minus_int @ one_one_int @ ( power_power_int @ X @ N ) )
% 5.41/5.77 = ( times_times_int @ ( minus_minus_int @ one_one_int @ X )
% 5.41/5.77 @ ( groups3539618377306564664at_int
% 5.41/5.77 @ ^ [I5: nat] : ( power_power_int @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq'
% 5.41/5.77 thf(fact_8496_one__diff__power__eq_H,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ N ) )
% 5.41/5.77 = ( times_times_real @ ( minus_minus_real @ one_one_real @ X )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ I5 ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_diff_power_eq'
% 5.41/5.77 thf(fact_8497_sum__split__even__odd,axiom,
% 5.41/5.77 ! [F: nat > real,G: nat > real,N: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ ( F @ I5 ) @ ( G @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( F @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( G @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ I5 ) @ one_one_nat ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_split_even_odd
% 5.41/5.77 thf(fact_8498_exp__bound__lemma,axiom,
% 5.41/5.77 ! [Z: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( exp_real @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V7735802525324610683m_real @ Z ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % exp_bound_lemma
% 5.41/5.77 thf(fact_8499_exp__bound__lemma,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( exp_complex @ Z ) ) @ ( plus_plus_real @ one_one_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % exp_bound_lemma
% 5.41/5.77 thf(fact_8500_arctan__series,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( ( arctan @ X )
% 5.41/5.77 = ( suminf_real
% 5.41/5.77 @ ^ [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 ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_series
% 5.41/5.77 thf(fact_8501_norm__divide__numeral,axiom,
% 5.41/5.77 ! [A: real,W: num] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.77 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_divide_numeral
% 5.41/5.77 thf(fact_8502_norm__divide__numeral,axiom,
% 5.41/5.77 ! [A: complex,W: num] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.77 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_divide_numeral
% 5.41/5.77 thf(fact_8503_norm__mult__numeral2,axiom,
% 5.41/5.77 ! [A: real,W: num] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( times_times_real @ A @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.77 = ( times_times_real @ ( real_V7735802525324610683m_real @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_numeral2
% 5.41/5.77 thf(fact_8504_norm__mult__numeral2,axiom,
% 5.41/5.77 ! [A: complex,W: num] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ A @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.77 = ( times_times_real @ ( real_V1022390504157884413omplex @ A ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_numeral2
% 5.41/5.77 thf(fact_8505_norm__mult__numeral1,axiom,
% 5.41/5.77 ! [W: num,A: real] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( times_times_real @ ( numeral_numeral_real @ W ) @ A ) )
% 5.41/5.77 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V7735802525324610683m_real @ A ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_numeral1
% 5.41/5.77 thf(fact_8506_norm__mult__numeral1,axiom,
% 5.41/5.77 ! [W: num,A: complex] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( numera6690914467698888265omplex @ W ) @ A ) )
% 5.41/5.77 = ( times_times_real @ ( numeral_numeral_real @ W ) @ ( real_V1022390504157884413omplex @ A ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_numeral1
% 5.41/5.77 thf(fact_8507_norm__neg__numeral,axiom,
% 5.41/5.77 ! [W: num] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.77 = ( numeral_numeral_real @ W ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_neg_numeral
% 5.41/5.77 thf(fact_8508_norm__neg__numeral,axiom,
% 5.41/5.77 ! [W: num] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.77 = ( numeral_numeral_real @ W ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_neg_numeral
% 5.41/5.77 thf(fact_8509_norm__le__zero__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_le_zero_iff
% 5.41/5.77 thf(fact_8510_norm__le__zero__iff,axiom,
% 5.41/5.77 ! [X: complex] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_le_zero_iff
% 5.41/5.77 thf(fact_8511_norm__zero,axiom,
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ zero_zero_real )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_zero
% 5.41/5.77 thf(fact_8512_norm__zero,axiom,
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ zero_zero_complex )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_zero
% 5.41/5.77 thf(fact_8513_norm__eq__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( real_V7735802525324610683m_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_eq_zero
% 5.41/5.77 thf(fact_8514_norm__eq__zero,axiom,
% 5.41/5.77 ! [X: complex] :
% 5.41/5.77 ( ( ( real_V1022390504157884413omplex @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_eq_zero
% 5.41/5.77 thf(fact_8515_norm__one,axiom,
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ one_one_real )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_one
% 5.41/5.77 thf(fact_8516_norm__one,axiom,
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ one_one_complex )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_one
% 5.41/5.77 thf(fact_8517_norm__numeral,axiom,
% 5.41/5.77 ! [W: num] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( numeral_numeral_real @ W ) )
% 5.41/5.77 = ( numeral_numeral_real @ W ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_numeral
% 5.41/5.77 thf(fact_8518_norm__numeral,axiom,
% 5.41/5.77 ! [W: num] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.77 = ( numeral_numeral_real @ W ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_numeral
% 5.41/5.77 thf(fact_8519_zero__less__norm__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ ( real_V7735802525324610683m_real @ X ) )
% 5.41/5.77 = ( X != zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % zero_less_norm_iff
% 5.41/5.77 thf(fact_8520_zero__less__norm__iff,axiom,
% 5.41/5.77 ! [X: complex] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) )
% 5.41/5.77 = ( X != zero_zero_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % zero_less_norm_iff
% 5.41/5.77 thf(fact_8521_norm__minus__commute,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) )
% 5.41/5.77 = ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ A ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_minus_commute
% 5.41/5.77 thf(fact_8522_norm__minus__commute,axiom,
% 5.41/5.77 ! [A: complex,B: complex] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) )
% 5.41/5.77 = ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ A ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_minus_commute
% 5.41/5.77 thf(fact_8523_norm__not__less__zero,axiom,
% 5.41/5.77 ! [X: complex] :
% 5.41/5.77 ~ ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_not_less_zero
% 5.41/5.77 thf(fact_8524_norm__ge__zero,axiom,
% 5.41/5.77 ! [X: complex] : ( ord_less_eq_real @ zero_zero_real @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_ge_zero
% 5.41/5.77 thf(fact_8525_norm__mult,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) )
% 5.41/5.77 = ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult
% 5.41/5.77 thf(fact_8526_norm__mult,axiom,
% 5.41/5.77 ! [X: complex,Y: complex] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) )
% 5.41/5.77 = ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult
% 5.41/5.77 thf(fact_8527_norm__divide,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.77 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_divide
% 5.41/5.77 thf(fact_8528_norm__divide,axiom,
% 5.41/5.77 ! [A: complex,B: complex] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.77 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_divide
% 5.41/5.77 thf(fact_8529_sum__norm__le,axiom,
% 5.41/5.77 ! [S2: set_real,F: real > complex,G: real > real] :
% 5.41/5.77 ( ! [X6: real] :
% 5.41/5.77 ( ( member_real @ X6 @ S2 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups5754745047067104278omplex @ F @ S2 ) ) @ ( groups8097168146408367636l_real @ G @ S2 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_norm_le
% 5.41/5.77 thf(fact_8530_sum__norm__le,axiom,
% 5.41/5.77 ! [S2: set_set_nat,F: set_nat > complex,G: set_nat > real] :
% 5.41/5.77 ( ! [X6: set_nat] :
% 5.41/5.77 ( ( member_set_nat @ X6 @ S2 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups8255218700646806128omplex @ F @ S2 ) ) @ ( groups5107569545109728110t_real @ G @ S2 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_norm_le
% 5.41/5.77 thf(fact_8531_sum__norm__le,axiom,
% 5.41/5.77 ! [S2: set_int,F: int > complex,G: int > real] :
% 5.41/5.77 ( ! [X6: int] :
% 5.41/5.77 ( ( member_int @ X6 @ S2 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups3049146728041665814omplex @ F @ S2 ) ) @ ( groups8778361861064173332t_real @ G @ S2 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_norm_le
% 5.41/5.77 thf(fact_8532_sum__norm__le,axiom,
% 5.41/5.77 ! [S2: set_nat,F: nat > complex,G: nat > real] :
% 5.41/5.77 ( ! [X6: nat] :
% 5.41/5.77 ( ( member_nat @ X6 @ S2 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_norm_le
% 5.41/5.77 thf(fact_8533_sum__norm__le,axiom,
% 5.41/5.77 ! [S2: set_complex,F: complex > complex,G: complex > real] :
% 5.41/5.77 ( ! [X6: complex] :
% 5.41/5.77 ( ( member_complex @ X6 @ S2 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ S2 ) ) @ ( groups5808333547571424918x_real @ G @ S2 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_norm_le
% 5.41/5.77 thf(fact_8534_sum__norm__le,axiom,
% 5.41/5.77 ! [S2: set_nat,F: nat > real,G: nat > real] :
% 5.41/5.77 ( ! [X6: nat] :
% 5.41/5.77 ( ( member_nat @ X6 @ S2 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( F @ X6 ) ) @ ( G @ X6 ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ S2 ) ) @ ( groups6591440286371151544t_real @ G @ S2 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_norm_le
% 5.41/5.77 thf(fact_8535_norm__power,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) )
% 5.41/5.77 = ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_power
% 5.41/5.77 thf(fact_8536_norm__power,axiom,
% 5.41/5.77 ! [X: complex,N: nat] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) )
% 5.41/5.77 = ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_power
% 5.41/5.77 thf(fact_8537_norm__sum,axiom,
% 5.41/5.77 ! [F: nat > complex,A2: set_nat] :
% 5.41/5.77 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups2073611262835488442omplex @ F @ A2 ) )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 5.41/5.77 @ A2 ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_sum
% 5.41/5.77 thf(fact_8538_norm__sum,axiom,
% 5.41/5.77 ! [F: complex > complex,A2: set_complex] :
% 5.41/5.77 ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( groups7754918857620584856omplex @ F @ A2 ) )
% 5.41/5.77 @ ( groups5808333547571424918x_real
% 5.41/5.77 @ ^ [I5: complex] : ( real_V1022390504157884413omplex @ ( F @ I5 ) )
% 5.41/5.77 @ A2 ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_sum
% 5.41/5.77 thf(fact_8539_norm__sum,axiom,
% 5.41/5.77 ! [F: nat > real,A2: set_nat] :
% 5.41/5.77 ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( groups6591440286371151544t_real @ F @ A2 ) )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [I5: nat] : ( real_V7735802525324610683m_real @ ( F @ I5 ) )
% 5.41/5.77 @ A2 ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_sum
% 5.41/5.77 thf(fact_8540_norm__uminus__minus,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( uminus_uminus_real @ X ) @ Y ) )
% 5.41/5.77 = ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_uminus_minus
% 5.41/5.77 thf(fact_8541_norm__uminus__minus,axiom,
% 5.41/5.77 ! [X: complex,Y: complex] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( uminus1482373934393186551omplex @ X ) @ Y ) )
% 5.41/5.77 = ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_uminus_minus
% 5.41/5.77 thf(fact_8542_nonzero__norm__divide,axiom,
% 5.41/5.77 ! [B: real,A: real] :
% 5.41/5.77 ( ( B != zero_zero_real )
% 5.41/5.77 => ( ( real_V7735802525324610683m_real @ ( divide_divide_real @ A @ B ) )
% 5.41/5.77 = ( divide_divide_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % nonzero_norm_divide
% 5.41/5.77 thf(fact_8543_nonzero__norm__divide,axiom,
% 5.41/5.77 ! [B: complex,A: complex] :
% 5.41/5.77 ( ( B != zero_zero_complex )
% 5.41/5.77 => ( ( real_V1022390504157884413omplex @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.77 = ( divide_divide_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % nonzero_norm_divide
% 5.41/5.77 thf(fact_8544_power__eq__imp__eq__norm,axiom,
% 5.41/5.77 ! [W: real,N: nat,Z: real] :
% 5.41/5.77 ( ( ( power_power_real @ W @ N )
% 5.41/5.77 = ( power_power_real @ Z @ N ) )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( real_V7735802525324610683m_real @ W )
% 5.41/5.77 = ( real_V7735802525324610683m_real @ Z ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_eq_imp_eq_norm
% 5.41/5.77 thf(fact_8545_power__eq__imp__eq__norm,axiom,
% 5.41/5.77 ! [W: complex,N: nat,Z: complex] :
% 5.41/5.77 ( ( ( power_power_complex @ W @ N )
% 5.41/5.77 = ( power_power_complex @ Z @ N ) )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( real_V1022390504157884413omplex @ W )
% 5.41/5.77 = ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_eq_imp_eq_norm
% 5.41/5.77 thf(fact_8546_norm__mult__less,axiom,
% 5.41/5.77 ! [X: real,R: real,Y: real,S: real] :
% 5.41/5.77 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 5.41/5.77 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.41/5.77 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_less
% 5.41/5.77 thf(fact_8547_norm__mult__less,axiom,
% 5.41/5.77 ! [X: complex,R: real,Y: complex,S: real] :
% 5.41/5.77 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 5.41/5.77 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.41/5.77 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ R @ S ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_less
% 5.41/5.77 thf(fact_8548_norm__mult__ineq,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( times_times_real @ X @ Y ) ) @ ( times_times_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_ineq
% 5.41/5.77 thf(fact_8549_norm__mult__ineq,axiom,
% 5.41/5.77 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( times_times_complex @ X @ Y ) ) @ ( times_times_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_mult_ineq
% 5.41/5.77 thf(fact_8550_norm__triangle__lt,axiom,
% 5.41/5.77 ! [X: real,Y: real,E: real] :
% 5.41/5.77 ( ( ord_less_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.41/5.77 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_lt
% 5.41/5.77 thf(fact_8551_norm__triangle__lt,axiom,
% 5.41/5.77 ! [X: complex,Y: complex,E: real] :
% 5.41/5.77 ( ( ord_less_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.41/5.77 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_lt
% 5.41/5.77 thf(fact_8552_norm__add__less,axiom,
% 5.41/5.77 ! [X: real,R: real,Y: real,S: real] :
% 5.41/5.77 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ X ) @ R )
% 5.41/5.77 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ Y ) @ S )
% 5.41/5.77 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_add_less
% 5.41/5.77 thf(fact_8553_norm__add__less,axiom,
% 5.41/5.77 ! [X: complex,R: real,Y: complex,S: real] :
% 5.41/5.77 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ X ) @ R )
% 5.41/5.77 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ Y ) @ S )
% 5.41/5.77 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_add_less
% 5.41/5.77 thf(fact_8554_norm__power__ineq,axiom,
% 5.41/5.77 ! [X: real,N: nat] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( power_power_real @ X @ N ) ) @ ( power_power_real @ ( real_V7735802525324610683m_real @ X ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_power_ineq
% 5.41/5.77 thf(fact_8555_norm__power__ineq,axiom,
% 5.41/5.77 ! [X: complex,N: nat] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( power_power_complex @ X @ N ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ X ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_power_ineq
% 5.41/5.77 thf(fact_8556_norm__triangle__mono,axiom,
% 5.41/5.77 ! [A: real,R: real,B: real,S: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ A ) @ R )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ S )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_mono
% 5.41/5.77 thf(fact_8557_norm__triangle__mono,axiom,
% 5.41/5.77 ! [A: complex,R: real,B: complex,S: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ A ) @ R )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ S )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ ( plus_plus_real @ R @ S ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_mono
% 5.41/5.77 thf(fact_8558_norm__triangle__ineq,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq
% 5.41/5.77 thf(fact_8559_norm__triangle__ineq,axiom,
% 5.41/5.77 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq
% 5.41/5.77 thf(fact_8560_norm__triangle__le,axiom,
% 5.41/5.77 ! [X: real,Y: real,E: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ X @ Y ) ) @ E ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_le
% 5.41/5.77 thf(fact_8561_norm__triangle__le,axiom,
% 5.41/5.77 ! [X: complex,Y: complex,E: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ X @ Y ) ) @ E ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_le
% 5.41/5.77 thf(fact_8562_norm__add__leD,axiom,
% 5.41/5.77 ! [A: real,B: real,C: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) @ C )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ B ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ C ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_add_leD
% 5.41/5.77 thf(fact_8563_norm__add__leD,axiom,
% 5.41/5.77 ! [A: complex,B: complex,C: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) @ C )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ B ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ C ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_add_leD
% 5.41/5.77 thf(fact_8564_norm__diff__triangle__less,axiom,
% 5.41/5.77 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.41/5.77 ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.41/5.77 => ( ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.41/5.77 => ( ord_less_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_triangle_less
% 5.41/5.77 thf(fact_8565_norm__diff__triangle__less,axiom,
% 5.41/5.77 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.41/5.77 ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.41/5.77 => ( ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.41/5.77 => ( ord_less_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_triangle_less
% 5.41/5.77 thf(fact_8566_norm__triangle__le__diff,axiom,
% 5.41/5.77 ! [X: real,Y: real,E: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ X ) @ ( real_V7735802525324610683m_real @ Y ) ) @ E )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_le_diff
% 5.41/5.77 thf(fact_8567_norm__triangle__le__diff,axiom,
% 5.41/5.77 ! [X: complex,Y: complex,E: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) ) @ E )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_le_diff
% 5.41/5.77 thf(fact_8568_norm__diff__triangle__le,axiom,
% 5.41/5.77 ! [X: real,Y: real,E1: real,Z: real,E22: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) @ E1 )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ Y @ Z ) ) @ E22 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_triangle_le
% 5.41/5.77 thf(fact_8569_norm__diff__triangle__le,axiom,
% 5.41/5.77 ! [X: complex,Y: complex,E1: real,Z: complex,E22: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) @ E1 )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Y @ Z ) ) @ E22 )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Z ) ) @ ( plus_plus_real @ E1 @ E22 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_triangle_le
% 5.41/5.77 thf(fact_8570_norm__triangle__ineq4,axiom,
% 5.41/5.77 ! [A: real,B: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq4
% 5.41/5.77 thf(fact_8571_norm__triangle__ineq4,axiom,
% 5.41/5.77 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq4
% 5.41/5.77 thf(fact_8572_norm__triangle__sub,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ X ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ Y ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_sub
% 5.41/5.77 thf(fact_8573_norm__triangle__sub,axiom,
% 5.41/5.77 ! [X: complex,Y: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Y ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_sub
% 5.41/5.77 thf(fact_8574_norm__diff__ineq,axiom,
% 5.41/5.77 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_ineq
% 5.41/5.77 thf(fact_8575_norm__diff__ineq,axiom,
% 5.41/5.77 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( plus_plus_complex @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_ineq
% 5.41/5.77 thf(fact_8576_norm__triangle__ineq2,axiom,
% 5.41/5.77 ! [A: real,B: real] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq2
% 5.41/5.77 thf(fact_8577_norm__triangle__ineq2,axiom,
% 5.41/5.77 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq2
% 5.41/5.77 thf(fact_8578_power__eq__1__iff,axiom,
% 5.41/5.77 ! [W: real,N: nat] :
% 5.41/5.77 ( ( ( power_power_real @ W @ N )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 => ( ( ( real_V7735802525324610683m_real @ W )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_eq_1_iff
% 5.41/5.77 thf(fact_8579_power__eq__1__iff,axiom,
% 5.41/5.77 ! [W: complex,N: nat] :
% 5.41/5.77 ( ( ( power_power_complex @ W @ N )
% 5.41/5.77 = one_one_complex )
% 5.41/5.77 => ( ( ( real_V1022390504157884413omplex @ W )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 | ( N = zero_zero_nat ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % power_eq_1_iff
% 5.41/5.77 thf(fact_8580_norm__diff__triangle__ineq,axiom,
% 5.41/5.77 ! [A: real,B: real,C: real,D: real] : ( ord_less_eq_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ ( plus_plus_real @ A @ B ) @ ( plus_plus_real @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ C ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ B @ D ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_triangle_ineq
% 5.41/5.77 thf(fact_8581_norm__diff__triangle__ineq,axiom,
% 5.41/5.77 ! [A: complex,B: complex,C: complex,D: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( plus_plus_complex @ A @ B ) @ ( plus_plus_complex @ C @ D ) ) ) @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ C ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ B @ D ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_diff_triangle_ineq
% 5.41/5.77 thf(fact_8582_norm__triangle__ineq3,axiom,
% 5.41/5.77 ! [A: real,B: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V7735802525324610683m_real @ A ) @ ( real_V7735802525324610683m_real @ B ) ) ) @ ( real_V7735802525324610683m_real @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq3
% 5.41/5.77 thf(fact_8583_norm__triangle__ineq3,axiom,
% 5.41/5.77 ! [A: complex,B: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ A ) @ ( real_V1022390504157884413omplex @ B ) ) ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_triangle_ineq3
% 5.41/5.77 thf(fact_8584_square__norm__one,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 => ( ( real_V7735802525324610683m_real @ X )
% 5.41/5.77 = one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % square_norm_one
% 5.41/5.77 thf(fact_8585_square__norm__one,axiom,
% 5.41/5.77 ! [X: complex] :
% 5.41/5.77 ( ( ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = one_one_complex )
% 5.41/5.77 => ( ( real_V1022390504157884413omplex @ X )
% 5.41/5.77 = one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % square_norm_one
% 5.41/5.77 thf(fact_8586_norm__power__diff,axiom,
% 5.41/5.77 ! [Z: complex,W: complex,M: nat] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ W ) @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ ( power_power_complex @ Z @ M ) @ ( power_power_complex @ W @ M ) ) ) @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ ( real_V1022390504157884413omplex @ ( minus_minus_complex @ Z @ W ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % norm_power_diff
% 5.41/5.77 thf(fact_8587_sumr__cos__zero__one,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ zero_zero_real @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ ( suc @ N ) ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % sumr_cos_zero_one
% 5.41/5.77 thf(fact_8588_cos__coeff__0,axiom,
% 5.41/5.77 ( ( cos_coeff @ zero_zero_nat )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_coeff_0
% 5.41/5.77 thf(fact_8589_pi__series,axiom,
% 5.41/5.77 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( suminf_real
% 5.41/5.77 @ ^ [K2: nat] : ( divide_divide_real @ ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ one_one_real ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % pi_series
% 5.41/5.77 thf(fact_8590_ceiling__log__nat__eq__powr__iff,axiom,
% 5.41/5.77 ! [B: nat,K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.77 => ( ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.41/5.77 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) )
% 5.41/5.77 = ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.41/5.77 & ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ceiling_log_nat_eq_powr_iff
% 5.41/5.77 thf(fact_8591_summable__arctan__series,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( summable_real
% 5.41/5.77 @ ^ [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 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % summable_arctan_series
% 5.41/5.77 thf(fact_8592_ceiling__log__nat__eq__if,axiom,
% 5.41/5.77 ! [B: nat,N: nat,K: nat] :
% 5.41/5.77 ( ( ord_less_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.41/5.77 => ( ( ord_less_eq_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.41/5.77 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.41/5.77 => ( ( archim7802044766580827645g_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.41/5.77 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ N ) @ one_one_int ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ceiling_log_nat_eq_if
% 5.41/5.77 thf(fact_8593_ceiling__divide__eq__div__numeral,axiom,
% 5.41/5.77 ! [A: num,B: num] :
% 5.41/5.77 ( ( archim7802044766580827645g_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.41/5.77 = ( uminus_uminus_int @ ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ceiling_divide_eq_div_numeral
% 5.41/5.77 thf(fact_8594_ceiling__minus__divide__eq__div__numeral,axiom,
% 5.41/5.77 ! [A: num,B: num] :
% 5.41/5.77 ( ( archim7802044766580827645g_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.41/5.77 = ( uminus_uminus_int @ ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ceiling_minus_divide_eq_div_numeral
% 5.41/5.77 thf(fact_8595_pi__neq__zero,axiom,
% 5.41/5.77 pi != zero_zero_real ).
% 5.41/5.77
% 5.41/5.77 % pi_neq_zero
% 5.41/5.77 thf(fact_8596_pi__gt__zero,axiom,
% 5.41/5.77 ord_less_real @ zero_zero_real @ pi ).
% 5.41/5.77
% 5.41/5.77 % pi_gt_zero
% 5.41/5.77 thf(fact_8597_pi__not__less__zero,axiom,
% 5.41/5.77 ~ ( ord_less_real @ pi @ zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % pi_not_less_zero
% 5.41/5.77 thf(fact_8598_pi__ge__zero,axiom,
% 5.41/5.77 ord_less_eq_real @ zero_zero_real @ pi ).
% 5.41/5.77
% 5.41/5.77 % pi_ge_zero
% 5.41/5.77 thf(fact_8599_summable__rabs__comparison__test,axiom,
% 5.41/5.77 ! [F: nat > real,G: nat > real] :
% 5.41/5.77 ( ? [N8: nat] :
% 5.41/5.77 ! [N3: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.41/5.77 => ( ord_less_eq_real @ ( abs_abs_real @ ( F @ N3 ) ) @ ( G @ N3 ) ) )
% 5.41/5.77 => ( ( summable_real @ G )
% 5.41/5.77 => ( summable_real
% 5.41/5.77 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % summable_rabs_comparison_test
% 5.41/5.77 thf(fact_8600_summable__rabs,axiom,
% 5.41/5.77 ! [F: nat > real] :
% 5.41/5.77 ( ( summable_real
% 5.41/5.77 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( abs_abs_real @ ( suminf_real @ F ) )
% 5.41/5.77 @ ( suminf_real
% 5.41/5.77 @ ^ [N2: nat] : ( abs_abs_real @ ( F @ N2 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % summable_rabs
% 5.41/5.77 thf(fact_8601_pi__less__4,axiom,
% 5.41/5.77 ord_less_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % pi_less_4
% 5.41/5.77 thf(fact_8602_pi__ge__two,axiom,
% 5.41/5.77 ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ).
% 5.41/5.77
% 5.41/5.77 % pi_ge_two
% 5.41/5.77 thf(fact_8603_pi__half__neq__two,axiom,
% 5.41/5.77 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.77 != ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % pi_half_neq_two
% 5.41/5.77 thf(fact_8604_pi__half__neq__zero,axiom,
% 5.41/5.77 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.77 != zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % pi_half_neq_zero
% 5.41/5.77 thf(fact_8605_pi__half__less__two,axiom,
% 5.41/5.77 ord_less_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.41/5.77
% 5.41/5.77 % pi_half_less_two
% 5.41/5.77 thf(fact_8606_pi__half__le__two,axiom,
% 5.41/5.77 ord_less_eq_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.41/5.77
% 5.41/5.77 % pi_half_le_two
% 5.41/5.77 thf(fact_8607_summable__power__series,axiom,
% 5.41/5.77 ! [F: nat > real,Z: real] :
% 5.41/5.77 ( ! [I4: nat] : ( ord_less_eq_real @ ( F @ I4 ) @ one_one_real )
% 5.41/5.77 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( F @ I4 ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Z )
% 5.41/5.77 => ( ( ord_less_real @ Z @ one_one_real )
% 5.41/5.77 => ( summable_real
% 5.41/5.77 @ ^ [I5: nat] : ( times_times_real @ ( F @ I5 ) @ ( power_power_real @ Z @ I5 ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % summable_power_series
% 5.41/5.77 thf(fact_8608_pi__half__gt__zero,axiom,
% 5.41/5.77 ord_less_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % pi_half_gt_zero
% 5.41/5.77 thf(fact_8609_pi__half__ge__zero,axiom,
% 5.41/5.77 ord_less_eq_real @ zero_zero_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % pi_half_ge_zero
% 5.41/5.77 thf(fact_8610_m2pi__less__pi,axiom,
% 5.41/5.77 ord_less_real @ ( uminus_uminus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) @ pi ).
% 5.41/5.77
% 5.41/5.77 % m2pi_less_pi
% 5.41/5.77 thf(fact_8611_arctan__ubound,axiom,
% 5.41/5.77 ! [Y: real] : ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_ubound
% 5.41/5.77 thf(fact_8612_arctan__one,axiom,
% 5.41/5.77 ( ( arctan @ one_one_real )
% 5.41/5.77 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_one
% 5.41/5.77 thf(fact_8613_minus__pi__half__less__zero,axiom,
% 5.41/5.77 ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ zero_zero_real ).
% 5.41/5.77
% 5.41/5.77 % minus_pi_half_less_zero
% 5.41/5.77 thf(fact_8614_arctan__lbound,axiom,
% 5.41/5.77 ! [Y: real] : ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_lbound
% 5.41/5.77 thf(fact_8615_arctan__bounded,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.41/5.77 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_bounded
% 5.41/5.77 thf(fact_8616_machin__Euler,axiom,
% 5.41/5.77 ( ( plus_plus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % machin_Euler
% 5.41/5.77 thf(fact_8617_machin,axiom,
% 5.41/5.77 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit0 @ one ) ) ) ) ) ) @ ( arctan @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit1 @ ( bit0 @ ( bit1 @ ( bit1 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % machin
% 5.41/5.77 thf(fact_8618_sum__pos__lt__pair,axiom,
% 5.41/5.77 ! [F: nat > real,K: nat] :
% 5.41/5.77 ( ( summable_real @ F )
% 5.41/5.77 => ( ! [D3: nat] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( F @ ( plus_plus_nat @ K @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) ) ) @ ( F @ ( plus_plus_nat @ K @ ( plus_plus_nat @ ( times_times_nat @ ( suc @ ( suc @ zero_zero_nat ) ) @ D3 ) @ one_one_nat ) ) ) ) )
% 5.41/5.77 => ( ord_less_real @ ( groups6591440286371151544t_real @ F @ ( set_ord_lessThan_nat @ K ) ) @ ( suminf_real @ F ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_pos_lt_pair
% 5.41/5.77 thf(fact_8619_ceiling__log2__div2,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.41/5.77 = ( plus_plus_int @ ( archim7802044766580827645g_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( divide_divide_nat @ ( minus_minus_nat @ N @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) @ one_one_int ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ceiling_log2_div2
% 5.41/5.77 thf(fact_8620_sin__cos__npi,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( sin_real @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_cos_npi
% 5.41/5.77 thf(fact_8621_cos__pi__eq__zero,axiom,
% 5.41/5.77 ! [M: nat] :
% 5.41/5.77 ( ( cos_real @ ( divide_divide_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ ( suc @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_pi_eq_zero
% 5.41/5.77 thf(fact_8622_and__int_Opsimps,axiom,
% 5.41/5.77 ! [K: int,L2: int] :
% 5.41/5.77 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K @ L2 ) )
% 5.41/5.77 => ( ( ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.77 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.77 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.41/5.77 = ( uminus_uminus_int
% 5.41/5.77 @ ( zero_n2684676970156552555ol_int
% 5.41/5.77 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.41/5.77 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) ) ) ) )
% 5.41/5.77 & ( ~ ( ( member_int @ K @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.77 & ( member_int @ L2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.77 => ( ( bit_se725231765392027082nd_int @ K @ L2 )
% 5.41/5.77 = ( plus_plus_int
% 5.41/5.77 @ ( zero_n2684676970156552555ol_int
% 5.41/5.77 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K )
% 5.41/5.77 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L2 ) ) )
% 5.41/5.77 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % and_int.psimps
% 5.41/5.77 thf(fact_8623_and__int_Opelims,axiom,
% 5.41/5.77 ! [X: int,Xa2: int,Y: int] :
% 5.41/5.77 ( ( ( bit_se725231765392027082nd_int @ X @ Xa2 )
% 5.41/5.77 = Y )
% 5.41/5.77 => ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.41/5.77 => ~ ( ( ( ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.77 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.77 => ( Y
% 5.41/5.77 = ( uminus_uminus_int
% 5.41/5.77 @ ( zero_n2684676970156552555ol_int
% 5.41/5.77 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.41/5.77 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) ) ) ) )
% 5.41/5.77 & ( ~ ( ( member_int @ X @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.77 & ( member_int @ Xa2 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.77 => ( Y
% 5.41/5.77 = ( plus_plus_int
% 5.41/5.77 @ ( zero_n2684676970156552555ol_int
% 5.41/5.77 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ X )
% 5.41/5.77 & ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Xa2 ) ) )
% 5.41/5.77 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( divide_divide_int @ X @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ Xa2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) )
% 5.41/5.77 => ~ ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % and_int.pelims
% 5.41/5.77 thf(fact_8624_Maclaurin__exp__lt,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( X != zero_zero_real )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 5.41/5.77 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.77 & ( ( exp_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_exp_lt
% 5.41/5.77 thf(fact_8625_sin__pi,axiom,
% 5.41/5.77 ( ( sin_real @ pi )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_pi
% 5.41/5.77 thf(fact_8626_sin__pi__minus,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sin_real @ ( minus_minus_real @ pi @ X ) )
% 5.41/5.77 = ( sin_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_pi_minus
% 5.41/5.77 thf(fact_8627_cos__pi,axiom,
% 5.41/5.77 ( ( cos_real @ pi )
% 5.41/5.77 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_pi
% 5.41/5.77 thf(fact_8628_cos__periodic__pi2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( plus_plus_real @ pi @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_periodic_pi2
% 5.41/5.77 thf(fact_8629_cos__periodic__pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( plus_plus_real @ X @ pi ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_periodic_pi
% 5.41/5.77 thf(fact_8630_sin__periodic__pi2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sin_real @ ( plus_plus_real @ pi @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_periodic_pi2
% 5.41/5.77 thf(fact_8631_sin__periodic__pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sin_real @ ( plus_plus_real @ X @ pi ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_periodic_pi
% 5.41/5.77 thf(fact_8632_cos__minus__pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( minus_minus_real @ X @ pi ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_minus_pi
% 5.41/5.77 thf(fact_8633_cos__pi__minus,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( minus_minus_real @ pi @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( cos_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_pi_minus
% 5.41/5.77 thf(fact_8634_sin__minus__pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sin_real @ ( minus_minus_real @ X @ pi ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_minus_pi
% 5.41/5.77 thf(fact_8635_sin__npi2,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( sin_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_npi2
% 5.41/5.77 thf(fact_8636_sin__npi,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_npi
% 5.41/5.77 thf(fact_8637_sin__npi__int,axiom,
% 5.41/5.77 ! [N: int] :
% 5.41/5.77 ( ( sin_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_npi_int
% 5.41/5.77 thf(fact_8638_cos__pi__half,axiom,
% 5.41/5.77 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_pi_half
% 5.41/5.77 thf(fact_8639_sin__two__pi,axiom,
% 5.41/5.77 ( ( sin_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_two_pi
% 5.41/5.77 thf(fact_8640_sin__pi__half,axiom,
% 5.41/5.77 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_pi_half
% 5.41/5.77 thf(fact_8641_cos__two__pi,axiom,
% 5.41/5.77 ( ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_two_pi
% 5.41/5.77 thf(fact_8642_cos__periodic,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.41/5.77 = ( cos_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_periodic
% 5.41/5.77 thf(fact_8643_sin__periodic,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sin_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.41/5.77 = ( sin_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_periodic
% 5.41/5.77 thf(fact_8644_cos__2pi__minus,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.41/5.77 = ( cos_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_2pi_minus
% 5.41/5.77 thf(fact_8645_cos__npi,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.41/5.77 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_npi
% 5.41/5.77 thf(fact_8646_cos__npi2,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( cos_real @ ( times_times_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.41/5.77 = ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_npi2
% 5.41/5.77 thf(fact_8647_sin__2npi,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_2npi
% 5.41/5.77 thf(fact_8648_cos__2npi,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) @ pi ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_2npi
% 5.41/5.77 thf(fact_8649_sin__2pi__minus,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sin_real @ ( minus_minus_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( sin_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_2pi_minus
% 5.41/5.77 thf(fact_8650_sin__int__2pin,axiom,
% 5.41/5.77 ! [N: int] :
% 5.41/5.77 ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_int_2pin
% 5.41/5.77 thf(fact_8651_cos__int__2pin,axiom,
% 5.41/5.77 ! [N: int] :
% 5.41/5.77 ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( ring_1_of_int_real @ N ) ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_int_2pin
% 5.41/5.77 thf(fact_8652_cos__3over2__pi,axiom,
% 5.41/5.77 ( ( cos_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_3over2_pi
% 5.41/5.77 thf(fact_8653_sin__3over2__pi,axiom,
% 5.41/5.77 ( ( sin_real @ ( times_times_real @ ( divide_divide_real @ ( numeral_numeral_real @ ( bit1 @ one ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.41/5.77 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_3over2_pi
% 5.41/5.77 thf(fact_8654_cos__npi__int,axiom,
% 5.41/5.77 ! [N: int] :
% 5.41/5.77 ( ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.41/5.77 = one_one_real ) )
% 5.41/5.77 & ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ( cos_real @ ( times_times_real @ pi @ ( ring_1_of_int_real @ N ) ) )
% 5.41/5.77 = ( uminus_uminus_real @ one_one_real ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_npi_int
% 5.41/5.77 thf(fact_8655_polar__Ex,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ? [R2: real,A5: real] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( times_times_real @ R2 @ ( cos_real @ A5 ) ) )
% 5.41/5.77 & ( Y
% 5.41/5.77 = ( times_times_real @ R2 @ ( sin_real @ A5 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % polar_Ex
% 5.41/5.77 thf(fact_8656_sin__zero__abs__cos__one,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( sin_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 => ( ( abs_abs_real @ ( cos_real @ X ) )
% 5.41/5.77 = one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_zero_abs_cos_one
% 5.41/5.77 thf(fact_8657_sincos__principal__value,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ? [Y5: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ Y5 )
% 5.41/5.77 & ( ord_less_eq_real @ Y5 @ pi )
% 5.41/5.77 & ( ( sin_real @ Y5 )
% 5.41/5.77 = ( sin_real @ X ) )
% 5.41/5.77 & ( ( cos_real @ Y5 )
% 5.41/5.77 = ( cos_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sincos_principal_value
% 5.41/5.77 thf(fact_8658_sin__x__le__x,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ ( sin_real @ X ) @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_x_le_x
% 5.41/5.77 thf(fact_8659_sin__le__one,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( sin_real @ X ) @ one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_le_one
% 5.41/5.77 thf(fact_8660_cos__le__one,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( cos_real @ X ) @ one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_le_one
% 5.41/5.77 thf(fact_8661_abs__sin__x__le__abs__x,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ ( abs_abs_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % abs_sin_x_le_abs_x
% 5.41/5.77 thf(fact_8662_cos__arctan__not__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( arctan @ X ) )
% 5.41/5.77 != zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_arctan_not_zero
% 5.41/5.77 thf(fact_8663_sin__cos__le1,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( plus_plus_real @ ( times_times_real @ ( sin_real @ X ) @ ( sin_real @ Y ) ) @ ( times_times_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) @ one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_cos_le1
% 5.41/5.77 thf(fact_8664_sin__gt__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ pi )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_gt_zero
% 5.41/5.77 thf(fact_8665_sin__x__ge__neg__x,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ ( uminus_uminus_real @ X ) @ ( sin_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_x_ge_neg_x
% 5.41/5.77 thf(fact_8666_sin__ge__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_ge_zero
% 5.41/5.77 thf(fact_8667_sin__ge__minus__one,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( sin_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_ge_minus_one
% 5.41/5.77 thf(fact_8668_cos__inj__pi,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ pi )
% 5.41/5.77 => ( ( ( cos_real @ X )
% 5.41/5.77 = ( cos_real @ Y ) )
% 5.41/5.77 => ( X = Y ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_inj_pi
% 5.41/5.77 thf(fact_8669_cos__mono__le__eq,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ pi )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ Y @ X ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_mono_le_eq
% 5.41/5.77 thf(fact_8670_cos__monotone__0__pi__le,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.77 => ( ord_less_eq_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_monotone_0_pi_le
% 5.41/5.77 thf(fact_8671_cos__ge__minus__one,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ ( cos_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_ge_minus_one
% 5.41/5.77 thf(fact_8672_abs__sin__le__one,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( sin_real @ X ) ) @ one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % abs_sin_le_one
% 5.41/5.77 thf(fact_8673_abs__cos__le__one,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( cos_real @ X ) ) @ one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % abs_cos_le_one
% 5.41/5.77 thf(fact_8674_cos__two__neq__zero,axiom,
% 5.41/5.77 ( ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.77 != zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_two_neq_zero
% 5.41/5.77 thf(fact_8675_cos__mono__less__eq,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ pi )
% 5.41/5.77 => ( ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) )
% 5.41/5.77 = ( ord_less_real @ Y @ X ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_mono_less_eq
% 5.41/5.77 thf(fact_8676_cos__monotone__0__pi,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.77 => ( ord_less_real @ ( cos_real @ X ) @ ( cos_real @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_monotone_0_pi
% 5.41/5.77 thf(fact_8677_sin__eq__0__pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ pi )
% 5.41/5.77 => ( ( ( sin_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 => ( X = zero_zero_real ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_eq_0_pi
% 5.41/5.77 thf(fact_8678_sin__zero__pi__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ pi )
% 5.41/5.77 => ( ( ( sin_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_zero_pi_iff
% 5.41/5.77 thf(fact_8679_cos__monotone__minus__pi__0_H,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_monotone_minus_pi_0'
% 5.41/5.77 thf(fact_8680_sin__zero__iff__int2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( sin_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( ? [I5: int] :
% 5.41/5.77 ( X
% 5.41/5.77 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ pi ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_zero_iff_int2
% 5.41/5.77 thf(fact_8681_sincos__total__pi,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.77 & ( ord_less_eq_real @ T6 @ pi )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( cos_real @ T6 ) )
% 5.41/5.77 & ( Y
% 5.41/5.77 = ( sin_real @ T6 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sincos_total_pi
% 5.41/5.77 thf(fact_8682_sin__expansion__lemma,axiom,
% 5.41/5.77 ! [X: real,M: nat] :
% 5.41/5.77 ( ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_expansion_lemma
% 5.41/5.77 thf(fact_8683_cos__expansion__lemma,axiom,
% 5.41/5.77 ! [X: real,M: nat] :
% 5.41/5.77 ( ( cos_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ ( suc @ M ) ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( sin_real @ ( plus_plus_real @ X @ ( divide_divide_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ M ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_expansion_lemma
% 5.41/5.77 thf(fact_8684_sin__gt__zero__02,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_gt_zero_02
% 5.41/5.77 thf(fact_8685_cos__two__less__zero,axiom,
% 5.41/5.77 ord_less_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.41/5.77
% 5.41/5.77 % cos_two_less_zero
% 5.41/5.77 thf(fact_8686_cos__is__zero,axiom,
% 5.41/5.77 ? [X6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 5.41/5.77 & ( ord_less_eq_real @ X6 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.77 & ( ( cos_real @ X6 )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 & ! [Y2: real] :
% 5.41/5.77 ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.41/5.77 & ( ord_less_eq_real @ Y2 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.77 & ( ( cos_real @ Y2 )
% 5.41/5.77 = zero_zero_real ) )
% 5.41/5.77 => ( Y2 = X6 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_is_zero
% 5.41/5.77 thf(fact_8687_cos__two__le__zero,axiom,
% 5.41/5.77 ord_less_eq_real @ ( cos_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ zero_zero_real ).
% 5.41/5.77
% 5.41/5.77 % cos_two_le_zero
% 5.41/5.77 thf(fact_8688_cos__monotone__minus__pi__0,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ord_less_real @ ( cos_real @ Y ) @ ( cos_real @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_monotone_minus_pi_0
% 5.41/5.77 thf(fact_8689_cos__total,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ? [X6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 5.41/5.77 & ( ord_less_eq_real @ X6 @ pi )
% 5.41/5.77 & ( ( cos_real @ X6 )
% 5.41/5.77 = Y )
% 5.41/5.77 & ! [Y2: real] :
% 5.41/5.77 ( ( ( ord_less_eq_real @ zero_zero_real @ Y2 )
% 5.41/5.77 & ( ord_less_eq_real @ Y2 @ pi )
% 5.41/5.77 & ( ( cos_real @ Y2 )
% 5.41/5.77 = Y ) )
% 5.41/5.77 => ( Y2 = X6 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_total
% 5.41/5.77 thf(fact_8690_sincos__total__pi__half,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.77 & ( ord_less_eq_real @ T6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( cos_real @ T6 ) )
% 5.41/5.77 & ( Y
% 5.41/5.77 = ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sincos_total_pi_half
% 5.41/5.77 thf(fact_8691_sincos__total__2pi__le,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.77 & ( ord_less_eq_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( cos_real @ T6 ) )
% 5.41/5.77 & ( Y
% 5.41/5.77 = ( sin_real @ T6 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sincos_total_2pi_le
% 5.41/5.77 thf(fact_8692_square__fact__le__2__fact,axiom,
% 5.41/5.77 ! [N: nat] : ( ord_less_eq_real @ ( times_times_real @ ( semiri2265585572941072030t_real @ N ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % square_fact_le_2_fact
% 5.41/5.77 thf(fact_8693_sincos__total__2pi,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 => ~ ! [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.77 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 => ( ( X
% 5.41/5.77 = ( cos_real @ T6 ) )
% 5.41/5.77 => ( Y
% 5.41/5.77 != ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sincos_total_2pi
% 5.41/5.77 thf(fact_8694_sin__pi__divide__n__ge__0,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( N != zero_zero_nat )
% 5.41/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_pi_divide_n_ge_0
% 5.41/5.77 thf(fact_8695_sin__gt__zero2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( sin_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_gt_zero2
% 5.41/5.77 thf(fact_8696_sin__lt__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ pi @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_lt_zero
% 5.41/5.77 thf(fact_8697_cos__double__less__one,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.77 => ( ord_less_real @ ( cos_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ X ) ) @ one_one_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_double_less_one
% 5.41/5.77 thf(fact_8698_sin__30,axiom,
% 5.41/5.77 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_30
% 5.41/5.77 thf(fact_8699_cos__gt__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_gt_zero
% 5.41/5.77 thf(fact_8700_sin__monotone__2pi__le,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_monotone_2pi_le
% 5.41/5.77 thf(fact_8701_sin__mono__le__eq,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_mono_le_eq
% 5.41/5.77 thf(fact_8702_sin__inj__pi,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ( sin_real @ X )
% 5.41/5.77 = ( sin_real @ Y ) )
% 5.41/5.77 => ( X = Y ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_inj_pi
% 5.41/5.77 thf(fact_8703_cos__60,axiom,
% 5.41/5.77 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_60
% 5.41/5.77 thf(fact_8704_cos__one__2pi__int,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( cos_real @ X )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 = ( ? [X3: int] :
% 5.41/5.77 ( X
% 5.41/5.77 = ( times_times_real @ ( times_times_real @ ( ring_1_of_int_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_one_2pi_int
% 5.41/5.77 thf(fact_8705_Maclaurin__cos__expansion,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ? [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.77 & ( ( cos_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( 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 @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_cos_expansion
% 5.41/5.77 thf(fact_8706_sin__le__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ pi @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_le_zero
% 5.41/5.77 thf(fact_8707_sin__less__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ord_less_real @ ( sin_real @ X ) @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_less_zero
% 5.41/5.77 thf(fact_8708_sin__monotone__2pi,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_real @ ( sin_real @ Y ) @ ( sin_real @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_monotone_2pi
% 5.41/5.77 thf(fact_8709_sin__mono__less__eq,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ ( sin_real @ X ) @ ( sin_real @ Y ) )
% 5.41/5.77 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_mono_less_eq
% 5.41/5.77 thf(fact_8710_sin__total,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ? [X6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 5.41/5.77 & ( ord_less_eq_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( sin_real @ X6 )
% 5.41/5.77 = Y )
% 5.41/5.77 & ! [Y2: real] :
% 5.41/5.77 ( ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.41/5.77 & ( ord_less_eq_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( sin_real @ Y2 )
% 5.41/5.77 = Y ) )
% 5.41/5.77 => ( Y2 = X6 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_total
% 5.41/5.77 thf(fact_8711_cos__gt__zero__pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_gt_zero_pi
% 5.41/5.77 thf(fact_8712_cos__ge__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( cos_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_ge_zero
% 5.41/5.77 thf(fact_8713_cos__one__2pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( cos_real @ X )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 = ( ? [X3: nat] :
% 5.41/5.77 ( X
% 5.41/5.77 = ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) )
% 5.41/5.77 | ? [X3: nat] :
% 5.41/5.77 ( X
% 5.41/5.77 = ( uminus_uminus_real @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ X3 ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ pi ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_one_2pi
% 5.41/5.77 thf(fact_8714_and__int_Opinduct,axiom,
% 5.41/5.77 ! [A0: int,A12: int,P: int > int > $o] :
% 5.41/5.77 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.41/5.77 => ( ! [K3: int,L4: int] :
% 5.41/5.77 ( ( accp_P1096762738010456898nt_int @ bit_and_int_rel @ ( product_Pair_int_int @ K3 @ L4 ) )
% 5.41/5.77 => ( ( ~ ( ( member_int @ K3 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) )
% 5.41/5.77 & ( member_int @ L4 @ ( insert_int @ zero_zero_int @ ( insert_int @ ( uminus_uminus_int @ one_one_int ) @ bot_bot_set_int ) ) ) )
% 5.41/5.77 => ( P @ ( divide_divide_int @ K3 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L4 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 => ( P @ K3 @ L4 ) ) )
% 5.41/5.77 => ( P @ A0 @ A12 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % and_int.pinduct
% 5.41/5.77 thf(fact_8715_Maclaurin__lemma,axiom,
% 5.41/5.77 ! [H2: real,F: real > real,J: nat > real,N: nat] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.41/5.77 => ? [B8: real] :
% 5.41/5.77 ( ( F @ H2 )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( J @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( times_times_real @ B8 @ ( divide_divide_real @ ( power_power_real @ H2 @ N ) @ ( semiri2265585572941072030t_real @ N ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_lemma
% 5.41/5.77 thf(fact_8716_Maclaurin__minus__cos__expansion,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_real @ X @ T6 )
% 5.41/5.77 & ( ord_less_real @ T6 @ zero_zero_real )
% 5.41/5.77 & ( ( cos_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( 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 @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_minus_cos_expansion
% 5.41/5.77 thf(fact_8717_Maclaurin__cos__expansion2,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.41/5.77 & ( ord_less_real @ T6 @ X )
% 5.41/5.77 & ( ( cos_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( cos_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( 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 @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_cos_expansion2
% 5.41/5.77 thf(fact_8718_sin__pi__divide__n__gt__0,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( sin_real @ ( divide_divide_real @ pi @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_pi_divide_n_gt_0
% 5.41/5.77 thf(fact_8719_Maclaurin__exp__le,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ? [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.77 & ( ( exp_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( divide_divide_real @ ( power_power_real @ X @ M3 ) @ ( semiri2265585572941072030t_real @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( times_times_real @ ( divide_divide_real @ ( exp_real @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_exp_le
% 5.41/5.77 thf(fact_8720_sin__zero__iff__int,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( sin_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( ? [I5: int] :
% 5.41/5.77 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_zero_iff_int
% 5.41/5.77 thf(fact_8721_cos__zero__iff__int,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( cos_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( ? [I5: int] :
% 5.41/5.77 ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ I5 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( times_times_real @ ( ring_1_of_int_real @ I5 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_zero_iff_int
% 5.41/5.77 thf(fact_8722_sin__zero__lemma,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ( sin_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 => ? [N3: nat] :
% 5.41/5.77 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_zero_lemma
% 5.41/5.77 thf(fact_8723_sin__zero__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( sin_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( ? [N2: nat] :
% 5.41/5.77 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.77 | ? [N2: nat] :
% 5.41/5.77 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_zero_iff
% 5.41/5.77 thf(fact_8724_cos__coeff__def,axiom,
% 5.41/5.77 ( cos_coeff
% 5.41/5.77 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_coeff_def
% 5.41/5.77 thf(fact_8725_cos__zero__lemma,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ( cos_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 => ? [N3: nat] :
% 5.41/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N3 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( times_times_real @ ( semiri5074537144036343181t_real @ N3 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_zero_lemma
% 5.41/5.77 thf(fact_8726_cos__zero__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( cos_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( ? [N2: nat] :
% 5.41/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.77 | ? [N2: nat] :
% 5.41/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 )
% 5.41/5.77 & ( X
% 5.41/5.77 = ( uminus_uminus_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N2 ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_zero_iff
% 5.41/5.77 thf(fact_8727_Maclaurin__sin__expansion3,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.41/5.77 & ( ord_less_real @ T6 @ X )
% 5.41/5.77 & ( ( sin_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( 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 @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_sin_expansion3
% 5.41/5.77 thf(fact_8728_Maclaurin__sin__expansion4,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ? [T6: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.41/5.77 & ( ord_less_eq_real @ T6 @ X )
% 5.41/5.77 & ( ( sin_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( 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 @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_sin_expansion4
% 5.41/5.77 thf(fact_8729_Maclaurin__sin__expansion2,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ? [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.77 & ( ( sin_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( 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 @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_sin_expansion2
% 5.41/5.77 thf(fact_8730_Maclaurin__sin__expansion,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ? [T6: real] :
% 5.41/5.77 ( ( sin_real @ X )
% 5.41/5.77 = ( plus_plus_real
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.77 @ ( 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 @ N ) ) @ pi ) ) ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_sin_expansion
% 5.41/5.77 thf(fact_8731_sin__coeff__def,axiom,
% 5.41/5.77 ( sin_coeff
% 5.41/5.77 = ( ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( semiri2265585572941072030t_real @ N2 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_coeff_def
% 5.41/5.77 thf(fact_8732_sin__coeff__0,axiom,
% 5.41/5.77 ( ( sin_coeff @ zero_zero_nat )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % sin_coeff_0
% 5.41/5.77 thf(fact_8733_fact__ge__self,axiom,
% 5.41/5.77 ! [N: nat] : ( ord_less_eq_nat @ N @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_ge_self
% 5.41/5.77 thf(fact_8734_fact__mono__nat,axiom,
% 5.41/5.77 ! [M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.77 => ( ord_less_eq_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_mono_nat
% 5.41/5.77 thf(fact_8735_fact__less__mono__nat,axiom,
% 5.41/5.77 ! [M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.77 => ( ( ord_less_nat @ M @ N )
% 5.41/5.77 => ( ord_less_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_less_mono_nat
% 5.41/5.77 thf(fact_8736_fact__ge__Suc__0__nat,axiom,
% 5.41/5.77 ! [N: nat] : ( ord_less_eq_nat @ ( suc @ zero_zero_nat ) @ ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_ge_Suc_0_nat
% 5.41/5.77 thf(fact_8737_dvd__fact,axiom,
% 5.41/5.77 ! [M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ one_one_nat @ M )
% 5.41/5.77 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.77 => ( dvd_dvd_nat @ M @ ( semiri1408675320244567234ct_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % dvd_fact
% 5.41/5.77 thf(fact_8738_fact__diff__Suc,axiom,
% 5.41/5.77 ! [N: nat,M: nat] :
% 5.41/5.77 ( ( ord_less_nat @ N @ ( suc @ M ) )
% 5.41/5.77 => ( ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) )
% 5.41/5.77 = ( times_times_nat @ ( minus_minus_nat @ ( suc @ M ) @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ M @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_diff_Suc
% 5.41/5.77 thf(fact_8739_fact__div__fact__le__pow,axiom,
% 5.41/5.77 ! [R: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ R @ N )
% 5.41/5.77 => ( ord_less_eq_nat @ ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ R ) ) ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_div_fact_le_pow
% 5.41/5.77 thf(fact_8740_upto_Opinduct,axiom,
% 5.41/5.77 ! [A0: int,A12: int,P: int > int > $o] :
% 5.41/5.77 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ A0 @ A12 ) )
% 5.41/5.77 => ( ! [I4: int,J2: int] :
% 5.41/5.77 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I4 @ J2 ) )
% 5.41/5.77 => ( ( ( ord_less_eq_int @ I4 @ J2 )
% 5.41/5.77 => ( P @ ( plus_plus_int @ I4 @ one_one_int ) @ J2 ) )
% 5.41/5.77 => ( P @ I4 @ J2 ) ) )
% 5.41/5.77 => ( P @ A0 @ A12 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % upto.pinduct
% 5.41/5.77 thf(fact_8741_complex__unimodular__polar,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ( ( ( real_V1022390504157884413omplex @ Z )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 => ~ ! [T6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.77 => ( ( ord_less_real @ T6 @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 => ( Z
% 5.41/5.77 != ( complex2 @ ( cos_real @ T6 ) @ ( sin_real @ T6 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_unimodular_polar
% 5.41/5.77 thf(fact_8742_sin__paired,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( sums_real
% 5.41/5.77 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.41/5.77 @ ( sin_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_paired
% 5.41/5.77 thf(fact_8743_tan__pi,axiom,
% 5.41/5.77 ( ( tan_real @ pi )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % tan_pi
% 5.41/5.77 thf(fact_8744_tan__periodic__pi,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( tan_real @ ( plus_plus_real @ X @ pi ) )
% 5.41/5.77 = ( tan_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_periodic_pi
% 5.41/5.77 thf(fact_8745_tan__npi,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( tan_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % tan_npi
% 5.41/5.77 thf(fact_8746_tan__periodic__n,axiom,
% 5.41/5.77 ! [X: real,N: num] :
% 5.41/5.77 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ N ) @ pi ) ) )
% 5.41/5.77 = ( tan_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_periodic_n
% 5.41/5.77 thf(fact_8747_tan__periodic__nat,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) ) )
% 5.41/5.77 = ( tan_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_periodic_nat
% 5.41/5.77 thf(fact_8748_tan__periodic__int,axiom,
% 5.41/5.77 ! [X: real,I: int] :
% 5.41/5.77 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( ring_1_of_int_real @ I ) @ pi ) ) )
% 5.41/5.77 = ( tan_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_periodic_int
% 5.41/5.77 thf(fact_8749_norm__cos__sin,axiom,
% 5.41/5.77 ! [T: real] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( complex2 @ ( cos_real @ T ) @ ( sin_real @ T ) ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_cos_sin
% 5.41/5.77 thf(fact_8750_tan__periodic,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( tan_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.41/5.77 = ( tan_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_periodic
% 5.41/5.77 thf(fact_8751_complex__diff,axiom,
% 5.41/5.77 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.77 ( ( minus_minus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.41/5.77 = ( complex2 @ ( minus_minus_real @ A @ C ) @ ( minus_minus_real @ B @ D ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_diff
% 5.41/5.77 thf(fact_8752_Complex__eq__numeral,axiom,
% 5.41/5.77 ! [A: real,B: real,W: num] :
% 5.41/5.77 ( ( ( complex2 @ A @ B )
% 5.41/5.77 = ( numera6690914467698888265omplex @ W ) )
% 5.41/5.77 = ( ( A
% 5.41/5.77 = ( numeral_numeral_real @ W ) )
% 5.41/5.77 & ( B = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_eq_numeral
% 5.41/5.77 thf(fact_8753_Complex__eq__0,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( ( complex2 @ A @ B )
% 5.41/5.77 = zero_zero_complex )
% 5.41/5.77 = ( ( A = zero_zero_real )
% 5.41/5.77 & ( B = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_eq_0
% 5.41/5.77 thf(fact_8754_zero__complex_Ocode,axiom,
% 5.41/5.77 ( zero_zero_complex
% 5.41/5.77 = ( complex2 @ zero_zero_real @ zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % zero_complex.code
% 5.41/5.77 thf(fact_8755_complex__add,axiom,
% 5.41/5.77 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.77 ( ( plus_plus_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.41/5.77 = ( complex2 @ ( plus_plus_real @ A @ C ) @ ( plus_plus_real @ B @ D ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_add
% 5.41/5.77 thf(fact_8756_Complex__eq__neg__numeral,axiom,
% 5.41/5.77 ! [A: real,B: real,W: num] :
% 5.41/5.77 ( ( ( complex2 @ A @ B )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.77 = ( ( A
% 5.41/5.77 = ( uminus_uminus_real @ ( numeral_numeral_real @ W ) ) )
% 5.41/5.77 & ( B = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_eq_neg_numeral
% 5.41/5.77 thf(fact_8757_complex__mult,axiom,
% 5.41/5.77 ! [A: real,B: real,C: real,D: real] :
% 5.41/5.77 ( ( times_times_complex @ ( complex2 @ A @ B ) @ ( complex2 @ C @ D ) )
% 5.41/5.77 = ( complex2 @ ( minus_minus_real @ ( times_times_real @ A @ C ) @ ( times_times_real @ B @ D ) ) @ ( plus_plus_real @ ( times_times_real @ A @ D ) @ ( times_times_real @ B @ C ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_mult
% 5.41/5.77 thf(fact_8758_Complex__eq__1,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( ( complex2 @ A @ B )
% 5.41/5.77 = one_one_complex )
% 5.41/5.77 = ( ( A = one_one_real )
% 5.41/5.77 & ( B = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_eq_1
% 5.41/5.77 thf(fact_8759_one__complex_Ocode,axiom,
% 5.41/5.77 ( one_one_complex
% 5.41/5.77 = ( complex2 @ one_one_real @ zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % one_complex.code
% 5.41/5.77 thf(fact_8760_Complex__eq__neg__1,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( ( complex2 @ A @ B )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ one_one_complex ) )
% 5.41/5.77 = ( ( A
% 5.41/5.77 = ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.77 & ( B = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_eq_neg_1
% 5.41/5.77 thf(fact_8761_tan__45,axiom,
% 5.41/5.77 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % tan_45
% 5.41/5.77 thf(fact_8762_power__half__series,axiom,
% 5.41/5.77 ( sums_real
% 5.41/5.77 @ ^ [N2: nat] : ( power_power_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( suc @ N2 ) )
% 5.41/5.77 @ one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % power_half_series
% 5.41/5.77 thf(fact_8763_lemma__tan__total,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.77 => ? [X6: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X6 )
% 5.41/5.77 & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ord_less_real @ Y @ ( tan_real @ X6 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % lemma_tan_total
% 5.41/5.77 thf(fact_8764_tan__gt__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_gt_zero
% 5.41/5.77 thf(fact_8765_lemma__tan__total1,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ? [X6: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 5.41/5.77 & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( tan_real @ X6 )
% 5.41/5.77 = Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % lemma_tan_total1
% 5.41/5.77 thf(fact_8766_tan__mono__lt__eq,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.41/5.77 = ( ord_less_real @ X @ Y ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_mono_lt_eq
% 5.41/5.77 thf(fact_8767_tan__monotone_H,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ Y @ X )
% 5.41/5.77 = ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_monotone'
% 5.41/5.77 thf(fact_8768_tan__monotone,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_real @ ( tan_real @ Y ) @ ( tan_real @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_monotone
% 5.41/5.77 thf(fact_8769_tan__total,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ? [X6: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X6 )
% 5.41/5.77 & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( tan_real @ X6 )
% 5.41/5.77 = Y )
% 5.41/5.77 & ! [Y2: real] :
% 5.41/5.77 ( ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y2 )
% 5.41/5.77 & ( ord_less_real @ Y2 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( tan_real @ Y2 )
% 5.41/5.77 = Y ) )
% 5.41/5.77 => ( Y2 = X6 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_total
% 5.41/5.77 thf(fact_8770_tan__minus__45,axiom,
% 5.41/5.77 ( ( tan_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.77 = ( uminus_uminus_real @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_minus_45
% 5.41/5.77 thf(fact_8771_tan__inverse,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( divide_divide_real @ one_one_real @ ( tan_real @ Y ) )
% 5.41/5.77 = ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_inverse
% 5.41/5.77 thf(fact_8772_sums__if_H,axiom,
% 5.41/5.77 ! [G: nat > real,X: real] :
% 5.41/5.77 ( ( sums_real @ G @ X )
% 5.41/5.77 => ( sums_real
% 5.41/5.77 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ zero_zero_real @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sums_if'
% 5.41/5.77 thf(fact_8773_sums__if,axiom,
% 5.41/5.77 ! [G: nat > real,X: real,F: nat > real,Y: real] :
% 5.41/5.77 ( ( sums_real @ G @ X )
% 5.41/5.77 => ( ( sums_real @ F @ Y )
% 5.41/5.77 => ( sums_real
% 5.41/5.77 @ ^ [N2: nat] : ( if_real @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ ( F @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( G @ ( divide_divide_nat @ ( minus_minus_nat @ N2 @ one_one_nat ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sums_if
% 5.41/5.77 thf(fact_8774_tan__pos__pi2__le,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( tan_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_pos_pi2_le
% 5.41/5.77 thf(fact_8775_tan__total__pos,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ? [X6: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X6 )
% 5.41/5.77 & ( ord_less_real @ X6 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( tan_real @ X6 )
% 5.41/5.77 = Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_total_pos
% 5.41/5.77 thf(fact_8776_tan__less__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ord_less_real @ ( tan_real @ X ) @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_less_zero
% 5.41/5.77 thf(fact_8777_tan__mono__le__eq,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ X @ Y ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_mono_le_eq
% 5.41/5.77 thf(fact_8778_tan__mono__le,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( tan_real @ X ) @ ( tan_real @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_mono_le
% 5.41/5.77 thf(fact_8779_tan__bound__pi2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 => ( ord_less_real @ ( abs_abs_real @ ( tan_real @ X ) ) @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_bound_pi2
% 5.41/5.77 thf(fact_8780_arctan__unique,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ( tan_real @ X )
% 5.41/5.77 = Y )
% 5.41/5.77 => ( ( arctan @ Y )
% 5.41/5.77 = X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_unique
% 5.41/5.77 thf(fact_8781_arctan__tan,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( arctan @ ( tan_real @ X ) )
% 5.41/5.77 = X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_tan
% 5.41/5.77 thf(fact_8782_arctan,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arctan @ Y ) )
% 5.41/5.77 & ( ord_less_real @ ( arctan @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( tan_real @ ( arctan @ Y ) )
% 5.41/5.77 = Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan
% 5.41/5.77 thf(fact_8783_tan__total__pi4,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ? [Z5: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) ) @ Z5 )
% 5.41/5.77 & ( ord_less_real @ Z5 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 & ( ( tan_real @ Z5 )
% 5.41/5.77 = X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_total_pi4
% 5.41/5.77 thf(fact_8784_cos__paired,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( sums_real
% 5.41/5.77 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( semiri2265585572941072030t_real @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) @ ( power_power_real @ X @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.41/5.77 @ ( cos_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_paired
% 5.41/5.77 thf(fact_8785_ceiling__log__eq__powr__iff,axiom,
% 5.41/5.77 ! [X: real,B: real,K: nat] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ( archim7802044766580827645g_real @ ( log @ B @ X ) )
% 5.41/5.77 = ( plus_plus_int @ ( semiri1314217659103216013at_int @ K ) @ one_one_int ) )
% 5.41/5.77 = ( ( ord_less_real @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ K ) ) @ X )
% 5.41/5.77 & ( ord_less_eq_real @ X @ ( powr_real @ B @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ K @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ceiling_log_eq_powr_iff
% 5.41/5.77 thf(fact_8786_sin__tan,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( sin_real @ X )
% 5.41/5.77 = ( divide_divide_real @ ( tan_real @ X ) @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_tan
% 5.41/5.77 thf(fact_8787_real__sqrt__eq__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ( sqrt @ X )
% 5.41/5.77 = ( sqrt @ Y ) )
% 5.41/5.77 = ( X = Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_eq_iff
% 5.41/5.77 thf(fact_8788_real__sqrt__eq__zero__cancel__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( sqrt @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_eq_zero_cancel_iff
% 5.41/5.77 thf(fact_8789_real__sqrt__zero,axiom,
% 5.41/5.77 ( ( sqrt @ zero_zero_real )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_zero
% 5.41/5.77 thf(fact_8790_real__sqrt__less__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.41/5.77 = ( ord_less_real @ X @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_less_iff
% 5.41/5.77 thf(fact_8791_real__sqrt__le__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_le_iff
% 5.41/5.77 thf(fact_8792_real__sqrt__eq__1__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( sqrt @ X )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 = ( X = one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_eq_1_iff
% 5.41/5.77 thf(fact_8793_real__sqrt__one,axiom,
% 5.41/5.77 ( ( sqrt @ one_one_real )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_one
% 5.41/5.77 thf(fact_8794_real__sqrt__lt__0__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.41/5.77 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_lt_0_iff
% 5.41/5.77 thf(fact_8795_real__sqrt__gt__0__iff,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.41/5.77 = ( ord_less_real @ zero_zero_real @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_gt_0_iff
% 5.41/5.77 thf(fact_8796_real__sqrt__le__0__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( sqrt @ X ) @ zero_zero_real )
% 5.41/5.77 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_le_0_iff
% 5.41/5.77 thf(fact_8797_real__sqrt__ge__0__iff,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_ge_0_iff
% 5.41/5.77 thf(fact_8798_powr__gt__zero,axiom,
% 5.41/5.77 ! [X: real,A: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ ( powr_real @ X @ A ) )
% 5.41/5.77 = ( X != zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_gt_zero
% 5.41/5.77 thf(fact_8799_powr__nonneg__iff,axiom,
% 5.41/5.77 ! [A: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( powr_real @ A @ X ) @ zero_zero_real )
% 5.41/5.77 = ( A = zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_nonneg_iff
% 5.41/5.77 thf(fact_8800_real__sqrt__gt__1__iff,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ ( sqrt @ Y ) )
% 5.41/5.77 = ( ord_less_real @ one_one_real @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_gt_1_iff
% 5.41/5.77 thf(fact_8801_real__sqrt__lt__1__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( sqrt @ X ) @ one_one_real )
% 5.41/5.77 = ( ord_less_real @ X @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_lt_1_iff
% 5.41/5.77 thf(fact_8802_real__sqrt__le__1__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( sqrt @ X ) @ one_one_real )
% 5.41/5.77 = ( ord_less_eq_real @ X @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_le_1_iff
% 5.41/5.77 thf(fact_8803_real__sqrt__ge__1__iff,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ one_one_real @ ( sqrt @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ one_one_real @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_ge_1_iff
% 5.41/5.77 thf(fact_8804_powr__less__cancel__iff,axiom,
% 5.41/5.77 ! [X: real,A: real,B: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.41/5.77 = ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_less_cancel_iff
% 5.41/5.77 thf(fact_8805_real__sqrt__mult__self,axiom,
% 5.41/5.77 ! [A: real] :
% 5.41/5.77 ( ( times_times_real @ ( sqrt @ A ) @ ( sqrt @ A ) )
% 5.41/5.77 = ( abs_abs_real @ A ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_mult_self
% 5.41/5.77 thf(fact_8806_real__sqrt__abs2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sqrt @ ( times_times_real @ X @ X ) )
% 5.41/5.77 = ( abs_abs_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_abs2
% 5.41/5.77 thf(fact_8807_real__sqrt__four,axiom,
% 5.41/5.77 ( ( sqrt @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( numeral_numeral_real @ ( bit0 @ one ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_four
% 5.41/5.77 thf(fact_8808_powr__eq__one__iff,axiom,
% 5.41/5.77 ! [A: real,X: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ A )
% 5.41/5.77 => ( ( ( powr_real @ A @ X )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 = ( X = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_eq_one_iff
% 5.41/5.77 thf(fact_8809_powr__one__gt__zero__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( powr_real @ X @ one_one_real )
% 5.41/5.77 = X )
% 5.41/5.77 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_one_gt_zero_iff
% 5.41/5.77 thf(fact_8810_powr__one,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( powr_real @ X @ one_one_real )
% 5.41/5.77 = X ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_one
% 5.41/5.77 thf(fact_8811_powr__le__cancel__iff,axiom,
% 5.41/5.77 ! [X: real,A: real,B: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.41/5.77 = ( ord_less_eq_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_le_cancel_iff
% 5.41/5.77 thf(fact_8812_numeral__powr__numeral__real,axiom,
% 5.41/5.77 ! [M: num,N: num] :
% 5.41/5.77 ( ( powr_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_real @ N ) )
% 5.41/5.77 = ( power_power_real @ ( numeral_numeral_real @ M ) @ ( numeral_numeral_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % numeral_powr_numeral_real
% 5.41/5.77 thf(fact_8813_powr__log__cancel,axiom,
% 5.41/5.77 ! [A: real,X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( A != one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( powr_real @ A @ ( log @ A @ X ) )
% 5.41/5.77 = X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_log_cancel
% 5.41/5.77 thf(fact_8814_log__powr__cancel,axiom,
% 5.41/5.77 ! [A: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( A != one_one_real )
% 5.41/5.77 => ( ( log @ A @ ( powr_real @ A @ Y ) )
% 5.41/5.77 = Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_powr_cancel
% 5.41/5.77 thf(fact_8815_real__sqrt__abs,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sqrt @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( abs_abs_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_abs
% 5.41/5.77 thf(fact_8816_powr__numeral,axiom,
% 5.41/5.77 ! [X: real,N: num] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( powr_real @ X @ ( numeral_numeral_real @ N ) )
% 5.41/5.77 = ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_numeral
% 5.41/5.77 thf(fact_8817_real__sqrt__pow2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = X ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_pow2
% 5.41/5.77 thf(fact_8818_real__sqrt__pow2__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( power_power_real @ ( sqrt @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = X )
% 5.41/5.77 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_pow2_iff
% 5.41/5.77 thf(fact_8819_real__sqrt__sum__squares__mult__squared__eq,axiom,
% 5.41/5.77 ! [X: real,Y: real,Xa2: real,Ya: real] :
% 5.41/5.77 ( ( power_power_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_mult_squared_eq
% 5.41/5.77 thf(fact_8820_square__powr__half,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( powr_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( abs_abs_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % square_powr_half
% 5.41/5.77 thf(fact_8821_real__sqrt__minus,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sqrt @ ( uminus_uminus_real @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( sqrt @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_minus
% 5.41/5.77 thf(fact_8822_real__sqrt__le__mono,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_le_mono
% 5.41/5.77 thf(fact_8823_real__sqrt__power,axiom,
% 5.41/5.77 ! [X: real,K: nat] :
% 5.41/5.77 ( ( sqrt @ ( power_power_real @ X @ K ) )
% 5.41/5.77 = ( power_power_real @ ( sqrt @ X ) @ K ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_power
% 5.41/5.77 thf(fact_8824_real__sqrt__mult,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( sqrt @ ( times_times_real @ X @ Y ) )
% 5.41/5.77 = ( times_times_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_mult
% 5.41/5.77 thf(fact_8825_real__sqrt__divide,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( sqrt @ ( divide_divide_real @ X @ Y ) )
% 5.41/5.77 = ( divide_divide_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_divide
% 5.41/5.77 thf(fact_8826_powr__powr,axiom,
% 5.41/5.77 ! [X: real,A: real,B: real] :
% 5.41/5.77 ( ( powr_real @ ( powr_real @ X @ A ) @ B )
% 5.41/5.77 = ( powr_real @ X @ ( times_times_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_powr
% 5.41/5.77 thf(fact_8827_real__sqrt__less__mono,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ X @ Y )
% 5.41/5.77 => ( ord_less_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_less_mono
% 5.41/5.77 thf(fact_8828_powr__non__neg,axiom,
% 5.41/5.77 ! [A: real,X: real] :
% 5.41/5.77 ~ ( ord_less_real @ ( powr_real @ A @ X ) @ zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % powr_non_neg
% 5.41/5.77 thf(fact_8829_powr__less__mono2__neg,axiom,
% 5.41/5.77 ! [A: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ A @ zero_zero_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ Y )
% 5.41/5.77 => ( ord_less_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_less_mono2_neg
% 5.41/5.77 thf(fact_8830_powr__ge__pzero,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ zero_zero_real @ ( powr_real @ X @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_ge_pzero
% 5.41/5.77 thf(fact_8831_powr__mono2,axiom,
% 5.41/5.77 ! [A: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_mono2
% 5.41/5.77 thf(fact_8832_real__sqrt__gt__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ord_less_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_gt_zero
% 5.41/5.77 thf(fact_8833_real__sqrt__eq__zero__cancel,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ( sqrt @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 => ( X = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_eq_zero_cancel
% 5.41/5.77 thf(fact_8834_real__sqrt__ge__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_ge_zero
% 5.41/5.77 thf(fact_8835_powr__less__mono,axiom,
% 5.41/5.77 ! [A: real,B: real,X: real] :
% 5.41/5.77 ( ( ord_less_real @ A @ B )
% 5.41/5.77 => ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.77 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_less_mono
% 5.41/5.77 thf(fact_8836_powr__less__cancel,axiom,
% 5.41/5.77 ! [X: real,A: real,B: real] :
% 5.41/5.77 ( ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) )
% 5.41/5.77 => ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.77 => ( ord_less_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_less_cancel
% 5.41/5.77 thf(fact_8837_powr__mono,axiom,
% 5.41/5.77 ! [A: real,B: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.77 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ X @ B ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_mono
% 5.41/5.77 thf(fact_8838_real__sqrt__ge__one,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ one_one_real @ ( sqrt @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_ge_one
% 5.41/5.77 thf(fact_8839_powr__mono2_H,axiom,
% 5.41/5.77 ! [A: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ A @ zero_zero_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ ( powr_real @ Y @ A ) @ ( powr_real @ X @ A ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_mono2'
% 5.41/5.77 thf(fact_8840_powr__less__mono2,axiom,
% 5.41/5.77 ! [A: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ Y )
% 5.41/5.77 => ( ord_less_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_less_mono2
% 5.41/5.77 thf(fact_8841_powr__inj,axiom,
% 5.41/5.77 ! [A: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( A != one_one_real )
% 5.41/5.77 => ( ( ( powr_real @ A @ X )
% 5.41/5.77 = ( powr_real @ A @ Y ) )
% 5.41/5.77 = ( X = Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_inj
% 5.41/5.77 thf(fact_8842_gr__one__powr,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ord_less_real @ one_one_real @ ( powr_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % gr_one_powr
% 5.41/5.77 thf(fact_8843_ge__one__powr__ge__zero,axiom,
% 5.41/5.77 ! [X: real,A: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ord_less_eq_real @ one_one_real @ ( powr_real @ X @ A ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ge_one_powr_ge_zero
% 5.41/5.77 thf(fact_8844_powr__mono__both,axiom,
% 5.41/5.77 ! [A: real,B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( ord_less_eq_real @ A @ B )
% 5.41/5.77 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ B ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_mono_both
% 5.41/5.77 thf(fact_8845_powr__le1,axiom,
% 5.41/5.77 ! [A: real,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( powr_real @ X @ A ) @ one_one_real ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_le1
% 5.41/5.77 thf(fact_8846_powr__divide,axiom,
% 5.41/5.77 ! [X: real,Y: real,A: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( powr_real @ ( divide_divide_real @ X @ Y ) @ A )
% 5.41/5.77 = ( divide_divide_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_divide
% 5.41/5.77 thf(fact_8847_powr__mult,axiom,
% 5.41/5.77 ! [X: real,Y: real,A: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( powr_real @ ( times_times_real @ X @ Y ) @ A )
% 5.41/5.77 = ( times_times_real @ ( powr_real @ X @ A ) @ ( powr_real @ Y @ A ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_mult
% 5.41/5.77 thf(fact_8848_real__div__sqrt,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( divide_divide_real @ X @ ( sqrt @ X ) )
% 5.41/5.77 = ( sqrt @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_div_sqrt
% 5.41/5.77 thf(fact_8849_sqrt__add__le__add__sqrt,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ X @ Y ) ) @ ( plus_plus_real @ ( sqrt @ X ) @ ( sqrt @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_add_le_add_sqrt
% 5.41/5.77 thf(fact_8850_le__real__sqrt__sumsq,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( times_times_real @ X @ X ) @ ( times_times_real @ Y @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % le_real_sqrt_sumsq
% 5.41/5.77 thf(fact_8851_divide__powr__uminus,axiom,
% 5.41/5.77 ! [A: real,B: real,C: real] :
% 5.41/5.77 ( ( divide_divide_real @ A @ ( powr_real @ B @ C ) )
% 5.41/5.77 = ( times_times_real @ A @ ( powr_real @ B @ ( uminus_uminus_real @ C ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % divide_powr_uminus
% 5.41/5.77 thf(fact_8852_log__base__powr,axiom,
% 5.41/5.77 ! [A: real,B: real,X: real] :
% 5.41/5.77 ( ( A != zero_zero_real )
% 5.41/5.77 => ( ( log @ ( powr_real @ A @ B ) @ X )
% 5.41/5.77 = ( divide_divide_real @ ( log @ A @ X ) @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_base_powr
% 5.41/5.77 thf(fact_8853_ln__powr,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( X != zero_zero_real )
% 5.41/5.77 => ( ( ln_ln_real @ ( powr_real @ X @ Y ) )
% 5.41/5.77 = ( times_times_real @ Y @ ( ln_ln_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ln_powr
% 5.41/5.77 thf(fact_8854_log__powr,axiom,
% 5.41/5.77 ! [X: real,B: real,Y: real] :
% 5.41/5.77 ( ( X != zero_zero_real )
% 5.41/5.77 => ( ( log @ B @ ( powr_real @ X @ Y ) )
% 5.41/5.77 = ( times_times_real @ Y @ ( log @ B @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_powr
% 5.41/5.77 thf(fact_8855_powr__half__sqrt,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( sqrt @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_half_sqrt
% 5.41/5.77 thf(fact_8856_sqrt2__less__2,axiom,
% 5.41/5.77 ord_less_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt2_less_2
% 5.41/5.77 thf(fact_8857_powr__realpow,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( powr_real @ X @ ( semiri5074537144036343181t_real @ N ) )
% 5.41/5.77 = ( power_power_real @ X @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_realpow
% 5.41/5.77 thf(fact_8858_powr__less__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ ( powr_real @ B @ Y ) @ X )
% 5.41/5.77 = ( ord_less_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_less_iff
% 5.41/5.77 thf(fact_8859_less__powr__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( powr_real @ B @ Y ) )
% 5.41/5.77 = ( ord_less_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % less_powr_iff
% 5.41/5.77 thf(fact_8860_log__less__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ ( log @ B @ X ) @ Y )
% 5.41/5.77 = ( ord_less_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_less_iff
% 5.41/5.77 thf(fact_8861_less__log__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ Y @ ( log @ B @ X ) )
% 5.41/5.77 = ( ord_less_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % less_log_iff
% 5.41/5.77 thf(fact_8862_real__less__rsqrt,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.41/5.77 => ( ord_less_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_less_rsqrt
% 5.41/5.77 thf(fact_8863_sqrt__le__D,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( sqrt @ X ) @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_le_D
% 5.41/5.77 thf(fact_8864_real__le__rsqrt,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ X @ ( sqrt @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_le_rsqrt
% 5.41/5.77 thf(fact_8865_powr__neg__one,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( powr_real @ X @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.77 = ( divide_divide_real @ one_one_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_neg_one
% 5.41/5.77 thf(fact_8866_powr__mult__base,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( times_times_real @ X @ ( powr_real @ X @ Y ) )
% 5.41/5.77 = ( powr_real @ X @ ( plus_plus_real @ one_one_real @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_mult_base
% 5.41/5.77 thf(fact_8867_tan__60,axiom,
% 5.41/5.77 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.41/5.77 = ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_60
% 5.41/5.77 thf(fact_8868_le__log__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ ( log @ B @ X ) )
% 5.41/5.77 = ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % le_log_iff
% 5.41/5.77 thf(fact_8869_log__le__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( log @ B @ X ) @ Y )
% 5.41/5.77 = ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_le_iff
% 5.41/5.77 thf(fact_8870_le__powr__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( powr_real @ B @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ ( log @ B @ X ) @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % le_powr_iff
% 5.41/5.77 thf(fact_8871_powr__le__iff,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( powr_real @ B @ Y ) @ X )
% 5.41/5.77 = ( ord_less_eq_real @ Y @ ( log @ B @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_le_iff
% 5.41/5.77 thf(fact_8872_real__le__lsqrt,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_le_lsqrt
% 5.41/5.77 thf(fact_8873_real__sqrt__unique,axiom,
% 5.41/5.77 ! [Y: real,X: real] :
% 5.41/5.77 ( ( ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( sqrt @ X )
% 5.41/5.77 = Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_unique
% 5.41/5.77 thf(fact_8874_lemma__real__divide__sqrt__less,axiom,
% 5.41/5.77 ! [U: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ U )
% 5.41/5.77 => ( ord_less_real @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ U ) ) ).
% 5.41/5.77
% 5.41/5.77 % lemma_real_divide_sqrt_less
% 5.41/5.77 thf(fact_8875_real__sqrt__sum__squares__eq__cancel,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = X )
% 5.41/5.77 => ( Y = zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_eq_cancel
% 5.41/5.77 thf(fact_8876_real__sqrt__sum__squares__eq__cancel2,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = Y )
% 5.41/5.77 => ( X = zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_eq_cancel2
% 5.41/5.77 thf(fact_8877_real__sqrt__sum__squares__ge1,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_ge1
% 5.41/5.77 thf(fact_8878_real__sqrt__sum__squares__ge2,axiom,
% 5.41/5.77 ! [Y: real,X: real] : ( ord_less_eq_real @ Y @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_ge2
% 5.41/5.77 thf(fact_8879_real__sqrt__sum__squares__triangle__ineq,axiom,
% 5.41/5.77 ! [A: real,C: real,B: real,D: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( plus_plus_real @ A @ C ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( plus_plus_real @ B @ D ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ C @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ D @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_triangle_ineq
% 5.41/5.77 thf(fact_8880_sqrt__ge__absD,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ Y ) )
% 5.41/5.77 => ( ord_less_eq_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_ge_absD
% 5.41/5.77 thf(fact_8881_ln__powr__bound,axiom,
% 5.41/5.77 ! [X: real,A: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ord_less_eq_real @ ( ln_ln_real @ X ) @ ( divide_divide_real @ ( powr_real @ X @ A ) @ A ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ln_powr_bound
% 5.41/5.77 thf(fact_8882_ln__powr__bound2,axiom,
% 5.41/5.77 ! [X: real,A: real] :
% 5.41/5.77 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ord_less_eq_real @ ( powr_real @ ( ln_ln_real @ X ) @ A ) @ ( times_times_real @ ( powr_real @ A @ A ) @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ln_powr_bound2
% 5.41/5.77 thf(fact_8883_cos__45,axiom,
% 5.41/5.77 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_45
% 5.41/5.77 thf(fact_8884_sin__45,axiom,
% 5.41/5.77 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_45
% 5.41/5.77 thf(fact_8885_add__log__eq__powr,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.77 => ( ( B != one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( plus_plus_real @ Y @ ( log @ B @ X ) )
% 5.41/5.77 = ( log @ B @ ( times_times_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % add_log_eq_powr
% 5.41/5.77 thf(fact_8886_log__add__eq__powr,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.77 => ( ( B != one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( plus_plus_real @ ( log @ B @ X ) @ Y )
% 5.41/5.77 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ Y ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_add_eq_powr
% 5.41/5.77 thf(fact_8887_minus__log__eq__powr,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.77 => ( ( B != one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( minus_minus_real @ Y @ ( log @ B @ X ) )
% 5.41/5.77 = ( log @ B @ ( divide_divide_real @ ( powr_real @ B @ Y ) @ X ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % minus_log_eq_powr
% 5.41/5.77 thf(fact_8888_real__less__lsqrt,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_real @ ( sqrt @ X ) @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_less_lsqrt
% 5.41/5.77 thf(fact_8889_sqrt__sum__squares__le__sum,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_sum_squares_le_sum
% 5.41/5.77 thf(fact_8890_sqrt__even__pow2,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ( sqrt @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.77 = ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_even_pow2
% 5.41/5.77 thf(fact_8891_tan__30,axiom,
% 5.41/5.77 ( ( tan_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_30
% 5.41/5.77 thf(fact_8892_real__sqrt__ge__abs1,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_ge_abs1
% 5.41/5.77 thf(fact_8893_real__sqrt__ge__abs2,axiom,
% 5.41/5.77 ! [Y: real,X: real] : ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_ge_abs2
% 5.41/5.77 thf(fact_8894_sqrt__sum__squares__le__sum__abs,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( plus_plus_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_sum_squares_le_sum_abs
% 5.41/5.77 thf(fact_8895_ln__sqrt,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ln_ln_real @ ( sqrt @ X ) )
% 5.41/5.77 = ( divide_divide_real @ ( ln_ln_real @ X ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ln_sqrt
% 5.41/5.77 thf(fact_8896_arsinh__real__def,axiom,
% 5.41/5.77 ( arsinh_real
% 5.41/5.77 = ( ^ [X3: real] : ( ln_ln_real @ ( plus_plus_real @ X3 @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arsinh_real_def
% 5.41/5.77 thf(fact_8897_cos__30,axiom,
% 5.41/5.77 ( ( cos_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ ( bit1 @ one ) ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_30
% 5.41/5.77 thf(fact_8898_sin__60,axiom,
% 5.41/5.77 ( ( sin_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) )
% 5.41/5.77 = ( divide_divide_real @ ( sqrt @ ( numeral_numeral_real @ ( bit1 @ one ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_60
% 5.41/5.77 thf(fact_8899_log__minus__eq__powr,axiom,
% 5.41/5.77 ! [B: real,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.77 => ( ( B != one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( minus_minus_real @ ( log @ B @ X ) @ Y )
% 5.41/5.77 = ( log @ B @ ( times_times_real @ X @ ( powr_real @ B @ ( uminus_uminus_real @ Y ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_minus_eq_powr
% 5.41/5.77 thf(fact_8900_complex__norm,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( complex2 @ X @ Y ) )
% 5.41/5.77 = ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_norm
% 5.41/5.77 thf(fact_8901_arsinh__real__aux,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arsinh_real_aux
% 5.41/5.77 thf(fact_8902_real__sqrt__power__even,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( power_power_real @ ( sqrt @ X ) @ N )
% 5.41/5.77 = ( power_power_real @ X @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_power_even
% 5.41/5.77 thf(fact_8903_real__sqrt__sum__squares__mult__ge__zero,axiom,
% 5.41/5.77 ! [X: real,Y: real,Xa2: real,Ya: real] : ( ord_less_eq_real @ zero_zero_real @ ( sqrt @ ( times_times_real @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( plus_plus_real @ ( power_power_real @ Xa2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Ya @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_mult_ge_zero
% 5.41/5.77 thf(fact_8904_arith__geo__mean__sqrt,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ord_less_eq_real @ ( sqrt @ ( times_times_real @ X @ Y ) ) @ ( divide_divide_real @ ( plus_plus_real @ X @ Y ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arith_geo_mean_sqrt
% 5.41/5.77 thf(fact_8905_powr__neg__numeral,axiom,
% 5.41/5.77 ! [X: real,N: num] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( powr_real @ X @ ( uminus_uminus_real @ ( numeral_numeral_real @ N ) ) )
% 5.41/5.77 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % powr_neg_numeral
% 5.41/5.77 thf(fact_8906_cos__x__y__le__one,axiom,
% 5.41/5.77 ! [X: real,Y: real] : ( ord_less_eq_real @ ( abs_abs_real @ ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % cos_x_y_le_one
% 5.41/5.77 thf(fact_8907_real__sqrt__sum__squares__less,axiom,
% 5.41/5.77 ! [X: real,U: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ ( abs_abs_real @ Y ) @ ( divide_divide_real @ U @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_sum_squares_less
% 5.41/5.77 thf(fact_8908_arcosh__real__def,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.77 => ( ( arcosh_real @ X )
% 5.41/5.77 = ( ln_ln_real @ ( plus_plus_real @ X @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcosh_real_def
% 5.41/5.77 thf(fact_8909_cos__arctan,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cos_real @ ( arctan @ X ) )
% 5.41/5.77 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_arctan
% 5.41/5.77 thf(fact_8910_sin__arctan,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sin_real @ ( arctan @ X ) )
% 5.41/5.77 = ( divide_divide_real @ X @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_arctan
% 5.41/5.77 thf(fact_8911_sqrt__sum__squares__half__less,axiom,
% 5.41/5.77 ! [X: real,U: real,Y: real] :
% 5.41/5.77 ( ( ord_less_real @ X @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ Y @ ( divide_divide_real @ U @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ord_less_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ U ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_sum_squares_half_less
% 5.41/5.77 thf(fact_8912_sin__cos__sqrt,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ ( sin_real @ X ) )
% 5.41/5.77 => ( ( sin_real @ X )
% 5.41/5.77 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ ( cos_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_cos_sqrt
% 5.41/5.77 thf(fact_8913_arctan__half,axiom,
% 5.41/5.77 ( arctan
% 5.41/5.77 = ( ^ [X3: real] : ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( arctan @ ( divide_divide_real @ X3 @ ( plus_plus_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arctan_half
% 5.41/5.77 thf(fact_8914_cos__tan,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( abs_abs_real @ X ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( cos_real @ X )
% 5.41/5.77 = ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ one_one_real @ ( power_power_real @ ( tan_real @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_tan
% 5.41/5.77 thf(fact_8915_vebt__mint_Opelims,axiom,
% 5.41/5.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.41/5.77 ( ( ( vEBT_vebt_mint @ X )
% 5.41/5.77 = Y )
% 5.41/5.77 => ( ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ X )
% 5.41/5.77 => ( ! [A5: $o,B5: $o] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.77 => ( ( ( A5
% 5.41/5.77 => ( Y
% 5.41/5.77 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.77 & ( ~ A5
% 5.41/5.77 => ( ( B5
% 5.41/5.77 => ( Y
% 5.41/5.77 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.77 & ( ~ B5
% 5.41/5.77 => ( Y = none_nat ) ) ) ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.41/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.77 => ( ( Y = none_nat )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.41/5.77 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.41/5.77 => ( ( Y
% 5.41/5.77 = ( some_nat @ Mi2 ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_mint_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % vebt_mint.pelims
% 5.41/5.77 thf(fact_8916_vebt__maxt_Opelims,axiom,
% 5.41/5.77 ! [X: vEBT_VEBT,Y: option_nat] :
% 5.41/5.77 ( ( ( vEBT_vebt_maxt @ X )
% 5.41/5.77 = Y )
% 5.41/5.77 => ( ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ X )
% 5.41/5.77 => ( ! [A5: $o,B5: $o] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ A5 @ B5 ) )
% 5.41/5.77 => ( ( ( B5
% 5.41/5.77 => ( Y
% 5.41/5.77 = ( some_nat @ one_one_nat ) ) )
% 5.41/5.77 & ( ~ B5
% 5.41/5.77 => ( ( A5
% 5.41/5.77 => ( Y
% 5.41/5.77 = ( some_nat @ zero_zero_nat ) ) )
% 5.41/5.77 & ( ~ A5
% 5.41/5.77 => ( Y = none_nat ) ) ) ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Leaf @ A5 @ B5 ) ) ) )
% 5.41/5.77 => ( ! [Uu2: nat,Uv2: list_VEBT_VEBT,Uw2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) )
% 5.41/5.77 => ( ( Y = none_nat )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uu2 @ Uv2 @ Uw2 ) ) ) )
% 5.41/5.77 => ~ ! [Mi2: nat,Ma2: nat,Ux2: nat,Uy2: list_VEBT_VEBT,Uz2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) )
% 5.41/5.77 => ( ( Y
% 5.41/5.77 = ( some_nat @ Ma2 ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_vebt_maxt_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ ( product_Pair_nat_nat @ Mi2 @ Ma2 ) ) @ Ux2 @ Uy2 @ Uz2 ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % vebt_maxt.pelims
% 5.41/5.77 thf(fact_8917_complex__exp__exists,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ? [A5: complex,R2: real] :
% 5.41/5.77 ( Z
% 5.41/5.77 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( exp_complex @ A5 ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_exp_exists
% 5.41/5.77 thf(fact_8918_complex__of__real__def,axiom,
% 5.41/5.77 ( real_V4546457046886955230omplex
% 5.41/5.77 = ( ^ [R5: real] : ( complex2 @ R5 @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_of_real_def
% 5.41/5.77 thf(fact_8919_complex__of__real__code,axiom,
% 5.41/5.77 ( real_V4546457046886955230omplex
% 5.41/5.77 = ( ^ [X3: real] : ( complex2 @ X3 @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_of_real_code
% 5.41/5.77 thf(fact_8920_complex__eq__cancel__iff2,axiom,
% 5.41/5.77 ! [X: real,Y: real,Xa2: real] :
% 5.41/5.77 ( ( ( complex2 @ X @ Y )
% 5.41/5.77 = ( real_V4546457046886955230omplex @ Xa2 ) )
% 5.41/5.77 = ( ( X = Xa2 )
% 5.41/5.77 & ( Y = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_eq_cancel_iff2
% 5.41/5.77 thf(fact_8921_complex__of__real__mult__Complex,axiom,
% 5.41/5.77 ! [R: real,X: real,Y: real] :
% 5.41/5.77 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 5.41/5.77 = ( complex2 @ ( times_times_real @ R @ X ) @ ( times_times_real @ R @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_of_real_mult_Complex
% 5.41/5.77 thf(fact_8922_Complex__mult__complex__of__real,axiom,
% 5.41/5.77 ! [X: real,Y: real,R: real] :
% 5.41/5.77 ( ( times_times_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.41/5.77 = ( complex2 @ ( times_times_real @ X @ R ) @ ( times_times_real @ Y @ R ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_mult_complex_of_real
% 5.41/5.77 thf(fact_8923_complex__of__real__add__Complex,axiom,
% 5.41/5.77 ! [R: real,X: real,Y: real] :
% 5.41/5.77 ( ( plus_plus_complex @ ( real_V4546457046886955230omplex @ R ) @ ( complex2 @ X @ Y ) )
% 5.41/5.77 = ( complex2 @ ( plus_plus_real @ R @ X ) @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_of_real_add_Complex
% 5.41/5.77 thf(fact_8924_Complex__add__complex__of__real,axiom,
% 5.41/5.77 ! [X: real,Y: real,R: real] :
% 5.41/5.77 ( ( plus_plus_complex @ ( complex2 @ X @ Y ) @ ( real_V4546457046886955230omplex @ R ) )
% 5.41/5.77 = ( complex2 @ ( plus_plus_real @ X @ R ) @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_add_complex_of_real
% 5.41/5.77 thf(fact_8925_cos__arcsin,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( ( cos_real @ ( arcsin @ X ) )
% 5.41/5.77 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_arcsin
% 5.41/5.77 thf(fact_8926_sin__arccos__abs,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.77 => ( ( sin_real @ ( arccos @ Y ) )
% 5.41/5.77 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ Y @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_arccos_abs
% 5.41/5.77 thf(fact_8927_sin__arccos,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( ( sin_real @ ( arccos @ X ) )
% 5.41/5.77 = ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_arccos
% 5.41/5.77 thf(fact_8928_arcsin__0,axiom,
% 5.41/5.77 ( ( arcsin @ zero_zero_real )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_0
% 5.41/5.77 thf(fact_8929_arccos__1,axiom,
% 5.41/5.77 ( ( arccos @ one_one_real )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_1
% 5.41/5.77 thf(fact_8930_arccos__minus__1,axiom,
% 5.41/5.77 ( ( arccos @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.77 = pi ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_minus_1
% 5.41/5.77 thf(fact_8931_cos__arccos,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( cos_real @ ( arccos @ Y ) )
% 5.41/5.77 = Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_arccos
% 5.41/5.77 thf(fact_8932_sin__arcsin,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( sin_real @ ( arcsin @ Y ) )
% 5.41/5.77 = Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_arcsin
% 5.41/5.77 thf(fact_8933_arccos__0,axiom,
% 5.41/5.77 ( ( arccos @ zero_zero_real )
% 5.41/5.77 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_0
% 5.41/5.77 thf(fact_8934_arcsin__1,axiom,
% 5.41/5.77 ( ( arcsin @ one_one_real )
% 5.41/5.77 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_1
% 5.41/5.77 thf(fact_8935_arcsin__minus__1,axiom,
% 5.41/5.77 ( ( arcsin @ ( uminus_uminus_real @ one_one_real ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_minus_1
% 5.41/5.77 thf(fact_8936_arccos__le__arccos,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_le_arccos
% 5.41/5.77 thf(fact_8937_arccos__eq__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 & ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real ) )
% 5.41/5.77 => ( ( ( arccos @ X )
% 5.41/5.77 = ( arccos @ Y ) )
% 5.41/5.77 = ( X = Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_eq_iff
% 5.41/5.77 thf(fact_8938_arccos__le__mono,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_le_mono
% 5.41/5.77 thf(fact_8939_arcsin__le__arcsin,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_le_arcsin
% 5.41/5.77 thf(fact_8940_arcsin__minus,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( ( arcsin @ ( uminus_uminus_real @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( arcsin @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_minus
% 5.41/5.77 thf(fact_8941_arcsin__eq__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.77 => ( ( ( arcsin @ X )
% 5.41/5.77 = ( arcsin @ Y ) )
% 5.41/5.77 = ( X = Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_eq_iff
% 5.41/5.77 thf(fact_8942_arcsin__le__mono,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_le_mono
% 5.41/5.77 thf(fact_8943_arccos__lbound,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_lbound
% 5.41/5.77 thf(fact_8944_arccos__less__arccos,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_real @ ( arccos @ Y ) @ ( arccos @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_less_arccos
% 5.41/5.77 thf(fact_8945_arccos__less__mono,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ ( arccos @ X ) @ ( arccos @ Y ) )
% 5.41/5.77 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_less_mono
% 5.41/5.77 thf(fact_8946_arccos__ubound,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_ubound
% 5.41/5.77 thf(fact_8947_arccos__cos,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.77 => ( ( arccos @ ( cos_real @ X ) )
% 5.41/5.77 = X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_cos
% 5.41/5.77 thf(fact_8948_arcsin__less__arcsin,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_less_arcsin
% 5.41/5.77 thf(fact_8949_arcsin__less__mono,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ ( arcsin @ X ) @ ( arcsin @ Y ) )
% 5.41/5.77 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_less_mono
% 5.41/5.77 thf(fact_8950_cos__arccos__abs,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ Y ) @ one_one_real )
% 5.41/5.77 => ( ( cos_real @ ( arccos @ Y ) )
% 5.41/5.77 = Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_arccos_abs
% 5.41/5.77 thf(fact_8951_arccos__cos__eq__abs,axiom,
% 5.41/5.77 ! [Theta: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ Theta ) @ pi )
% 5.41/5.77 => ( ( arccos @ ( cos_real @ Theta ) )
% 5.41/5.77 = ( abs_abs_real @ Theta ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_cos_eq_abs
% 5.41/5.77 thf(fact_8952_arccos__lt__bounded,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.41/5.77 & ( ord_less_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_lt_bounded
% 5.41/5.77 thf(fact_8953_arccos__bounded,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.41/5.77 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_bounded
% 5.41/5.77 thf(fact_8954_sin__arccos__nonzero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.77 => ( ( sin_real @ ( arccos @ X ) )
% 5.41/5.77 != zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sin_arccos_nonzero
% 5.41/5.77 thf(fact_8955_arccos__cos2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.41/5.77 => ( ( arccos @ ( cos_real @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_cos2
% 5.41/5.77 thf(fact_8956_arccos__minus,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.41/5.77 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_minus
% 5.41/5.77 thf(fact_8957_cos__arcsin__nonzero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.77 => ( ( cos_real @ ( arcsin @ X ) )
% 5.41/5.77 != zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cos_arcsin_nonzero
% 5.41/5.77 thf(fact_8958_arccos,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ ( arccos @ Y ) )
% 5.41/5.77 & ( ord_less_eq_real @ ( arccos @ Y ) @ pi )
% 5.41/5.77 & ( ( cos_real @ ( arccos @ Y ) )
% 5.41/5.77 = Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos
% 5.41/5.77 thf(fact_8959_arccos__minus__abs,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.77 => ( ( arccos @ ( uminus_uminus_real @ X ) )
% 5.41/5.77 = ( minus_minus_real @ pi @ ( arccos @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_minus_abs
% 5.41/5.77 thf(fact_8960_arccos__le__pi2,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( arccos @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_le_pi2
% 5.41/5.77 thf(fact_8961_arcsin__lt__bounded,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.41/5.77 & ( ord_less_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_lt_bounded
% 5.41/5.77 thf(fact_8962_arcsin__bounded,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.41/5.77 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_bounded
% 5.41/5.77 thf(fact_8963_arcsin__ubound,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_ubound
% 5.41/5.77 thf(fact_8964_arcsin__lbound,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_lbound
% 5.41/5.77 thf(fact_8965_arcsin__sin,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( arcsin @ ( sin_real @ X ) )
% 5.41/5.77 = X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_sin
% 5.41/5.77 thf(fact_8966_le__arcsin__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ ( arcsin @ X ) )
% 5.41/5.77 = ( ord_less_eq_real @ ( sin_real @ Y ) @ X ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % le_arcsin_iff
% 5.41/5.77 thf(fact_8967_arcsin__le__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( arcsin @ X ) @ Y )
% 5.41/5.77 = ( ord_less_eq_real @ X @ ( sin_real @ Y ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_le_iff
% 5.41/5.77 thf(fact_8968_arcsin__pi,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.41/5.77 & ( ord_less_eq_real @ ( arcsin @ Y ) @ pi )
% 5.41/5.77 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.41/5.77 = Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin_pi
% 5.41/5.77 thf(fact_8969_arcsin,axiom,
% 5.41/5.77 ! [Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( uminus_uminus_real @ one_one_real ) @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ one_one_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( arcsin @ Y ) )
% 5.41/5.77 & ( ord_less_eq_real @ ( arcsin @ Y ) @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 & ( ( sin_real @ ( arcsin @ Y ) )
% 5.41/5.77 = Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcsin
% 5.41/5.77 thf(fact_8970_arccos__cos__eq__abs__2pi,axiom,
% 5.41/5.77 ! [Theta: real] :
% 5.41/5.77 ~ ! [K3: int] :
% 5.41/5.77 ( ( arccos @ ( cos_real @ Theta ) )
% 5.41/5.77 != ( abs_abs_real @ ( minus_minus_real @ Theta @ ( times_times_real @ ( ring_1_of_int_real @ K3 ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % arccos_cos_eq_abs_2pi
% 5.41/5.77 thf(fact_8971_exp__two__pi__i_H,axiom,
% 5.41/5.77 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = one_one_complex ) ).
% 5.41/5.77
% 5.41/5.77 % exp_two_pi_i'
% 5.41/5.77 thf(fact_8972_exp__two__pi__i,axiom,
% 5.41/5.77 ( ( exp_complex @ ( times_times_complex @ ( times_times_complex @ ( numera6690914467698888265omplex @ ( bit0 @ one ) ) @ ( real_V4546457046886955230omplex @ pi ) ) @ imaginary_unit ) )
% 5.41/5.77 = one_one_complex ) ).
% 5.41/5.77
% 5.41/5.77 % exp_two_pi_i
% 5.41/5.77 thf(fact_8973_binomial__code,axiom,
% 5.41/5.77 ( binomial
% 5.41/5.77 = ( ^ [N2: nat,K2: nat] : ( if_nat @ ( ord_less_nat @ N2 @ K2 ) @ zero_zero_nat @ ( if_nat @ ( ord_less_nat @ N2 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K2 ) ) @ ( binomial @ N2 @ ( minus_minus_nat @ N2 @ K2 ) ) @ ( divide_divide_nat @ ( set_fo2584398358068434914at_nat @ times_times_nat @ ( plus_plus_nat @ ( minus_minus_nat @ N2 @ K2 ) @ one_one_nat ) @ N2 @ one_one_nat ) @ ( semiri1408675320244567234ct_nat @ K2 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_code
% 5.41/5.77 thf(fact_8974_binomial__n__n,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( binomial @ N @ N )
% 5.41/5.77 = one_one_nat ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_n_n
% 5.41/5.77 thf(fact_8975_binomial__1,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( binomial @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.77 = N ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_1
% 5.41/5.77 thf(fact_8976_binomial__0__Suc,axiom,
% 5.41/5.77 ! [K: nat] :
% 5.41/5.77 ( ( binomial @ zero_zero_nat @ ( suc @ K ) )
% 5.41/5.77 = zero_zero_nat ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_0_Suc
% 5.41/5.77 thf(fact_8977_binomial__eq__0__iff,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( ( binomial @ N @ K )
% 5.41/5.77 = zero_zero_nat )
% 5.41/5.77 = ( ord_less_nat @ N @ K ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_eq_0_iff
% 5.41/5.77 thf(fact_8978_binomial__Suc__Suc,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.41/5.77 = ( plus_plus_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_Suc_Suc
% 5.41/5.77 thf(fact_8979_binomial__n__0,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( binomial @ N @ zero_zero_nat )
% 5.41/5.77 = one_one_nat ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_n_0
% 5.41/5.77 thf(fact_8980_norm__ii,axiom,
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ imaginary_unit )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_ii
% 5.41/5.77 thf(fact_8981_complex__i__mult__minus,axiom,
% 5.41/5.77 ! [X: complex] :
% 5.41/5.77 ( ( times_times_complex @ imaginary_unit @ ( times_times_complex @ imaginary_unit @ X ) )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_i_mult_minus
% 5.41/5.77 thf(fact_8982_divide__i,axiom,
% 5.41/5.77 ! [X: complex] :
% 5.41/5.77 ( ( divide1717551699836669952omplex @ X @ imaginary_unit )
% 5.41/5.77 = ( times_times_complex @ ( uminus1482373934393186551omplex @ imaginary_unit ) @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % divide_i
% 5.41/5.77 thf(fact_8983_zero__less__binomial__iff,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) )
% 5.41/5.77 = ( ord_less_eq_nat @ K @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % zero_less_binomial_iff
% 5.41/5.77 thf(fact_8984_i__squared,axiom,
% 5.41/5.77 ( ( times_times_complex @ imaginary_unit @ imaginary_unit )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % i_squared
% 5.41/5.77 thf(fact_8985_divide__numeral__i,axiom,
% 5.41/5.77 ! [Z: complex,N: num] :
% 5.41/5.77 ( ( divide1717551699836669952omplex @ Z @ ( times_times_complex @ ( numera6690914467698888265omplex @ N ) @ imaginary_unit ) )
% 5.41/5.77 = ( divide1717551699836669952omplex @ ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) @ ( numera6690914467698888265omplex @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % divide_numeral_i
% 5.41/5.77 thf(fact_8986_power2__i,axiom,
% 5.41/5.77 ( ( power_power_complex @ imaginary_unit @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % power2_i
% 5.41/5.77 thf(fact_8987_exp__pi__i,axiom,
% 5.41/5.77 ( ( exp_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ pi ) @ imaginary_unit ) )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % exp_pi_i
% 5.41/5.77 thf(fact_8988_exp__pi__i_H,axiom,
% 5.41/5.77 ( ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ pi ) ) )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % exp_pi_i'
% 5.41/5.77 thf(fact_8989_i__even__power,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( power_power_complex @ imaginary_unit @ ( times_times_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = ( power_power_complex @ ( uminus1482373934393186551omplex @ one_one_complex ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % i_even_power
% 5.41/5.77 thf(fact_8990_choose__one,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( binomial @ N @ one_one_nat )
% 5.41/5.77 = N ) ).
% 5.41/5.77
% 5.41/5.77 % choose_one
% 5.41/5.77 thf(fact_8991_complex__i__not__zero,axiom,
% 5.41/5.77 imaginary_unit != zero_zero_complex ).
% 5.41/5.77
% 5.41/5.77 % complex_i_not_zero
% 5.41/5.77 thf(fact_8992_complex__i__not__one,axiom,
% 5.41/5.77 imaginary_unit != one_one_complex ).
% 5.41/5.77
% 5.41/5.77 % complex_i_not_one
% 5.41/5.77 thf(fact_8993_complex__i__not__numeral,axiom,
% 5.41/5.77 ! [W: num] :
% 5.41/5.77 ( imaginary_unit
% 5.41/5.77 != ( numera6690914467698888265omplex @ W ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_i_not_numeral
% 5.41/5.77 thf(fact_8994_binomial__eq__0,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( ord_less_nat @ N @ K )
% 5.41/5.77 => ( ( binomial @ N @ K )
% 5.41/5.77 = zero_zero_nat ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_eq_0
% 5.41/5.77 thf(fact_8995_Suc__times__binomial,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) )
% 5.41/5.77 = ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Suc_times_binomial
% 5.41/5.77 thf(fact_8996_Suc__times__binomial__eq,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) )
% 5.41/5.77 = ( times_times_nat @ ( binomial @ ( suc @ N ) @ ( suc @ K ) ) @ ( suc @ K ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Suc_times_binomial_eq
% 5.41/5.77 thf(fact_8997_binomial__symmetric,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.77 => ( ( binomial @ N @ K )
% 5.41/5.77 = ( binomial @ N @ ( minus_minus_nat @ N @ K ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_symmetric
% 5.41/5.77 thf(fact_8998_choose__mult__lemma,axiom,
% 5.41/5.77 ! [M: nat,R: nat,K: nat] :
% 5.41/5.77 ( ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ ( plus_plus_nat @ M @ K ) ) @ ( binomial @ ( plus_plus_nat @ M @ K ) @ K ) )
% 5.41/5.77 = ( times_times_nat @ ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ M @ R ) @ K ) @ K ) @ ( binomial @ ( plus_plus_nat @ M @ R ) @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_mult_lemma
% 5.41/5.77 thf(fact_8999_binomial__le__pow,axiom,
% 5.41/5.77 ! [R: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ R @ N )
% 5.41/5.77 => ( ord_less_eq_nat @ ( binomial @ N @ R ) @ ( power_power_nat @ N @ R ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_le_pow
% 5.41/5.77 thf(fact_9000_i__times__eq__iff,axiom,
% 5.41/5.77 ! [W: complex,Z: complex] :
% 5.41/5.77 ( ( ( times_times_complex @ imaginary_unit @ W )
% 5.41/5.77 = Z )
% 5.41/5.77 = ( W
% 5.41/5.77 = ( uminus1482373934393186551omplex @ ( times_times_complex @ imaginary_unit @ Z ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % i_times_eq_iff
% 5.41/5.77 thf(fact_9001_zero__less__binomial,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.77 => ( ord_less_nat @ zero_zero_nat @ ( binomial @ N @ K ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % zero_less_binomial
% 5.41/5.77 thf(fact_9002_Suc__times__binomial__add,axiom,
% 5.41/5.77 ! [A: nat,B: nat] :
% 5.41/5.77 ( ( times_times_nat @ ( suc @ A ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ ( suc @ A ) ) )
% 5.41/5.77 = ( times_times_nat @ ( suc @ B ) @ ( binomial @ ( suc @ ( plus_plus_nat @ A @ B ) ) @ A ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Suc_times_binomial_add
% 5.41/5.77 thf(fact_9003_binomial__Suc__Suc__eq__times,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( binomial @ ( suc @ N ) @ ( suc @ K ) )
% 5.41/5.77 = ( divide_divide_nat @ ( times_times_nat @ ( suc @ N ) @ ( binomial @ N @ K ) ) @ ( suc @ K ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_Suc_Suc_eq_times
% 5.41/5.77 thf(fact_9004_choose__mult,axiom,
% 5.41/5.77 ! [K: nat,M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ K @ M )
% 5.41/5.77 => ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.77 => ( ( times_times_nat @ ( binomial @ N @ M ) @ ( binomial @ M @ K ) )
% 5.41/5.77 = ( times_times_nat @ ( binomial @ N @ K ) @ ( binomial @ ( minus_minus_nat @ N @ K ) @ ( minus_minus_nat @ M @ K ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_mult
% 5.41/5.77 thf(fact_9005_binomial__absorb__comp,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( times_times_nat @ ( minus_minus_nat @ N @ K ) @ ( binomial @ N @ K ) )
% 5.41/5.77 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_absorb_comp
% 5.41/5.77 thf(fact_9006_complex__i__not__neg__numeral,axiom,
% 5.41/5.77 ! [W: num] :
% 5.41/5.77 ( imaginary_unit
% 5.41/5.77 != ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_i_not_neg_numeral
% 5.41/5.77 thf(fact_9007_imaginary__unit_Ocode,axiom,
% 5.41/5.77 ( imaginary_unit
% 5.41/5.77 = ( complex2 @ zero_zero_real @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % imaginary_unit.code
% 5.41/5.77 thf(fact_9008_Complex__eq__i,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ( complex2 @ X @ Y )
% 5.41/5.77 = imaginary_unit )
% 5.41/5.77 = ( ( X = zero_zero_real )
% 5.41/5.77 & ( Y = one_one_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_eq_i
% 5.41/5.77 thf(fact_9009_binomial__absorption,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( times_times_nat @ ( suc @ K ) @ ( binomial @ N @ ( suc @ K ) ) )
% 5.41/5.77 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_absorption
% 5.41/5.77 thf(fact_9010_i__mult__Complex,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( times_times_complex @ imaginary_unit @ ( complex2 @ A @ B ) )
% 5.41/5.77 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.41/5.77
% 5.41/5.77 % i_mult_Complex
% 5.41/5.77 thf(fact_9011_Complex__mult__i,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( times_times_complex @ ( complex2 @ A @ B ) @ imaginary_unit )
% 5.41/5.77 = ( complex2 @ ( uminus_uminus_real @ B ) @ A ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_mult_i
% 5.41/5.77 thf(fact_9012_binomial__fact__lemma,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.77 => ( ( times_times_nat @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) @ ( binomial @ N @ K ) )
% 5.41/5.77 = ( semiri1408675320244567234ct_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_fact_lemma
% 5.41/5.77 thf(fact_9013_binomial__mono,axiom,
% 5.41/5.77 ! [K: nat,K6: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ K @ K6 )
% 5.41/5.77 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.41/5.77 => ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_mono
% 5.41/5.77 thf(fact_9014_binomial__maximum_H,axiom,
% 5.41/5.77 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ K ) @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_maximum'
% 5.41/5.77 thf(fact_9015_binomial__maximum,axiom,
% 5.41/5.77 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_maximum
% 5.41/5.77 thf(fact_9016_binomial__antimono,axiom,
% 5.41/5.77 ! [K: nat,K6: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ K @ K6 )
% 5.41/5.77 => ( ( ord_less_eq_nat @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ K )
% 5.41/5.77 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.41/5.77 => ( ord_less_eq_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_antimono
% 5.41/5.77 thf(fact_9017_binomial__le__pow2,axiom,
% 5.41/5.77 ! [N: nat,K: nat] : ( ord_less_eq_nat @ ( binomial @ N @ K ) @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_le_pow2
% 5.41/5.77 thf(fact_9018_choose__reduce__nat,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.77 => ( ( binomial @ N @ K )
% 5.41/5.77 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_reduce_nat
% 5.41/5.77 thf(fact_9019_times__binomial__minus1__eq,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.77 => ( ( times_times_nat @ K @ ( binomial @ N @ K ) )
% 5.41/5.77 = ( times_times_nat @ N @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( minus_minus_nat @ K @ one_one_nat ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % times_binomial_minus1_eq
% 5.41/5.77 thf(fact_9020_binomial__altdef__nat,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ K @ N )
% 5.41/5.77 => ( ( binomial @ N @ K )
% 5.41/5.77 = ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ N ) @ ( times_times_nat @ ( semiri1408675320244567234ct_nat @ K ) @ ( semiri1408675320244567234ct_nat @ ( minus_minus_nat @ N @ K ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_altdef_nat
% 5.41/5.77 thf(fact_9021_i__complex__of__real,axiom,
% 5.41/5.77 ! [R: real] :
% 5.41/5.77 ( ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ R ) )
% 5.41/5.77 = ( complex2 @ zero_zero_real @ R ) ) ).
% 5.41/5.77
% 5.41/5.77 % i_complex_of_real
% 5.41/5.77 thf(fact_9022_complex__of__real__i,axiom,
% 5.41/5.77 ! [R: real] :
% 5.41/5.77 ( ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ imaginary_unit )
% 5.41/5.77 = ( complex2 @ zero_zero_real @ R ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_of_real_i
% 5.41/5.77 thf(fact_9023_Complex__eq,axiom,
% 5.41/5.77 ( complex2
% 5.41/5.77 = ( ^ [A3: real,B2: real] : ( plus_plus_complex @ ( real_V4546457046886955230omplex @ A3 ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Complex_eq
% 5.41/5.77 thf(fact_9024_binomial__less__binomial__Suc,axiom,
% 5.41/5.77 ! [K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ K @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.77 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ ( suc @ K ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_less_binomial_Suc
% 5.41/5.77 thf(fact_9025_binomial__strict__mono,axiom,
% 5.41/5.77 ! [K: nat,K6: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ K @ K6 )
% 5.41/5.77 => ( ( ord_less_eq_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K6 ) @ N )
% 5.41/5.77 => ( ord_less_nat @ ( binomial @ N @ K ) @ ( binomial @ N @ K6 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_strict_mono
% 5.41/5.77 thf(fact_9026_binomial__strict__antimono,axiom,
% 5.41/5.77 ! [K: nat,K6: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ K @ K6 )
% 5.41/5.77 => ( ( ord_less_eq_nat @ N @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) )
% 5.41/5.77 => ( ( ord_less_eq_nat @ K6 @ N )
% 5.41/5.77 => ( ord_less_nat @ ( binomial @ N @ K6 ) @ ( binomial @ N @ K ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_strict_antimono
% 5.41/5.77 thf(fact_9027_central__binomial__odd,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ( binomial @ N @ ( suc @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = ( binomial @ N @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % central_binomial_odd
% 5.41/5.77 thf(fact_9028_binomial__addition__formula,axiom,
% 5.41/5.77 ! [N: nat,K: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( binomial @ N @ ( suc @ K ) )
% 5.41/5.77 = ( plus_plus_nat @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ ( suc @ K ) ) @ ( binomial @ ( minus_minus_nat @ N @ one_one_nat ) @ K ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_addition_formula
% 5.41/5.77 thf(fact_9029_choose__two,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( binomial @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = ( divide_divide_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_two
% 5.41/5.77 thf(fact_9030_complex__split__polar,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ? [R2: real,A5: real] :
% 5.41/5.77 ( Z
% 5.41/5.77 = ( times_times_complex @ ( real_V4546457046886955230omplex @ R2 ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A5 ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A5 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_split_polar
% 5.41/5.77 thf(fact_9031_cmod__unit__one,axiom,
% 5.41/5.77 ! [A: real] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % cmod_unit_one
% 5.41/5.77 thf(fact_9032_cmod__complex__polar,axiom,
% 5.41/5.77 ! [R: real,A: real] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ R ) @ ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( cos_real @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sin_real @ A ) ) ) ) ) )
% 5.41/5.77 = ( abs_abs_real @ R ) ) ).
% 5.41/5.77
% 5.41/5.77 % cmod_complex_polar
% 5.41/5.77 thf(fact_9033_central__binomial__lower__bound,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ord_less_eq_real @ ( divide_divide_real @ ( power_power_real @ ( numeral_numeral_real @ ( bit0 @ ( bit0 @ one ) ) ) @ N ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) ) @ ( semiri5074537144036343181t_real @ ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % central_binomial_lower_bound
% 5.41/5.77 thf(fact_9034_Arg__minus__ii,axiom,
% 5.41/5.77 ( ( arg @ ( uminus1482373934393186551omplex @ imaginary_unit ) )
% 5.41/5.77 = ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Arg_minus_ii
% 5.41/5.77 thf(fact_9035_csqrt__ii,axiom,
% 5.41/5.77 ( ( csqrt @ imaginary_unit )
% 5.41/5.77 = ( divide1717551699836669952omplex @ ( plus_plus_complex @ one_one_complex @ imaginary_unit ) @ ( real_V4546457046886955230omplex @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % csqrt_ii
% 5.41/5.77 thf(fact_9036_Arg__ii,axiom,
% 5.41/5.77 ( ( arg @ imaginary_unit )
% 5.41/5.77 = ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Arg_ii
% 5.41/5.77 thf(fact_9037_finite__atMost,axiom,
% 5.41/5.77 ! [K: nat] : ( finite_finite_nat @ ( set_ord_atMost_nat @ K ) ) ).
% 5.41/5.77
% 5.41/5.77 % finite_atMost
% 5.41/5.77 thf(fact_9038_csqrt__0,axiom,
% 5.41/5.77 ( ( csqrt @ zero_zero_complex )
% 5.41/5.77 = zero_zero_complex ) ).
% 5.41/5.77
% 5.41/5.77 % csqrt_0
% 5.41/5.77 thf(fact_9039_csqrt__eq__0,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ( ( ( csqrt @ Z )
% 5.41/5.77 = zero_zero_complex )
% 5.41/5.77 = ( Z = zero_zero_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % csqrt_eq_0
% 5.41/5.77 thf(fact_9040_csqrt__eq__1,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ( ( ( csqrt @ Z )
% 5.41/5.77 = one_one_complex )
% 5.41/5.77 = ( Z = one_one_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % csqrt_eq_1
% 5.41/5.77 thf(fact_9041_csqrt__1,axiom,
% 5.41/5.77 ( ( csqrt @ one_one_complex )
% 5.41/5.77 = one_one_complex ) ).
% 5.41/5.77
% 5.41/5.77 % csqrt_1
% 5.41/5.77 thf(fact_9042_atMost__0,axiom,
% 5.41/5.77 ( ( set_ord_atMost_nat @ zero_zero_nat )
% 5.41/5.77 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ).
% 5.41/5.77
% 5.41/5.77 % atMost_0
% 5.41/5.77 thf(fact_9043_power2__csqrt,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ( ( power_power_complex @ ( csqrt @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = Z ) ).
% 5.41/5.77
% 5.41/5.77 % power2_csqrt
% 5.41/5.77 thf(fact_9044_atMost__atLeast0,axiom,
% 5.41/5.77 ( set_ord_atMost_nat
% 5.41/5.77 = ( set_or1269000886237332187st_nat @ zero_zero_nat ) ) ).
% 5.41/5.77
% 5.41/5.77 % atMost_atLeast0
% 5.41/5.77 thf(fact_9045_lessThan__Suc__atMost,axiom,
% 5.41/5.77 ! [K: nat] :
% 5.41/5.77 ( ( set_ord_lessThan_nat @ ( suc @ K ) )
% 5.41/5.77 = ( set_ord_atMost_nat @ K ) ) ).
% 5.41/5.77
% 5.41/5.77 % lessThan_Suc_atMost
% 5.41/5.77 thf(fact_9046_atMost__Suc,axiom,
% 5.41/5.77 ! [K: nat] :
% 5.41/5.77 ( ( set_ord_atMost_nat @ ( suc @ K ) )
% 5.41/5.77 = ( insert_nat @ ( suc @ K ) @ ( set_ord_atMost_nat @ K ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % atMost_Suc
% 5.41/5.77 thf(fact_9047_finite__nat__iff__bounded__le,axiom,
% 5.41/5.77 ( finite_finite_nat
% 5.41/5.77 = ( ^ [S6: set_nat] :
% 5.41/5.77 ? [K2: nat] : ( ord_less_eq_set_nat @ S6 @ ( set_ord_atMost_nat @ K2 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % finite_nat_iff_bounded_le
% 5.41/5.77 thf(fact_9048_atMost__nat__numeral,axiom,
% 5.41/5.77 ! [K: num] :
% 5.41/5.77 ( ( set_ord_atMost_nat @ ( numeral_numeral_nat @ K ) )
% 5.41/5.77 = ( insert_nat @ ( numeral_numeral_nat @ K ) @ ( set_ord_atMost_nat @ ( pred_numeral @ K ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % atMost_nat_numeral
% 5.41/5.77 thf(fact_9049_Arg__zero,axiom,
% 5.41/5.77 ( ( arg @ zero_zero_complex )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % Arg_zero
% 5.41/5.77 thf(fact_9050_sum__choose__lower,axiom,
% 5.41/5.77 ! [R: nat,N: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [K2: nat] : ( binomial @ ( plus_plus_nat @ R @ K2 ) @ K2 )
% 5.41/5.77 @ ( set_ord_atMost_nat @ N ) )
% 5.41/5.77 = ( binomial @ ( suc @ ( plus_plus_nat @ R @ N ) ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_choose_lower
% 5.41/5.77 thf(fact_9051_choose__rising__sum_I2_J,axiom,
% 5.41/5.77 ! [N: nat,M: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.41/5.77 @ ( set_ord_atMost_nat @ M ) )
% 5.41/5.77 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ M ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_rising_sum(2)
% 5.41/5.77 thf(fact_9052_choose__rising__sum_I1_J,axiom,
% 5.41/5.77 ! [N: nat,M: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [J3: nat] : ( binomial @ ( plus_plus_nat @ N @ J3 ) @ N )
% 5.41/5.77 @ ( set_ord_atMost_nat @ M ) )
% 5.41/5.77 = ( binomial @ ( plus_plus_nat @ ( plus_plus_nat @ N @ M ) @ one_one_nat ) @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_rising_sum(1)
% 5.41/5.77 thf(fact_9053_atLeast1__atMost__eq__remove0,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( set_or1269000886237332187st_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.77 = ( minus_minus_set_nat @ ( set_ord_atMost_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % atLeast1_atMost_eq_remove0
% 5.41/5.77 thf(fact_9054_sum__choose__diagonal,axiom,
% 5.41/5.77 ! [M: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.77 => ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [K2: nat] : ( binomial @ ( minus_minus_nat @ N @ K2 ) @ ( minus_minus_nat @ M @ K2 ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ M ) )
% 5.41/5.77 = ( binomial @ ( suc @ N ) @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sum_choose_diagonal
% 5.41/5.77 thf(fact_9055_vandermonde,axiom,
% 5.41/5.77 ! [M: nat,N: nat,R: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [K2: nat] : ( times_times_nat @ ( binomial @ M @ K2 ) @ ( binomial @ N @ ( minus_minus_nat @ R @ K2 ) ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ R ) )
% 5.41/5.77 = ( binomial @ ( plus_plus_nat @ M @ N ) @ R ) ) ).
% 5.41/5.77
% 5.41/5.77 % vandermonde
% 5.41/5.77 thf(fact_9056_of__real__sqrt,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( real_V4546457046886955230omplex @ ( sqrt @ X ) )
% 5.41/5.77 = ( csqrt @ ( real_V4546457046886955230omplex @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % of_real_sqrt
% 5.41/5.77 thf(fact_9057_choose__row__sum,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat @ ( binomial @ N ) @ ( set_ord_atMost_nat @ N ) )
% 5.41/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_row_sum
% 5.41/5.77 thf(fact_9058_Arg__bounded,axiom,
% 5.41/5.77 ! [Z: complex] :
% 5.41/5.77 ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.41/5.77 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ).
% 5.41/5.77
% 5.41/5.77 % Arg_bounded
% 5.41/5.77 thf(fact_9059_binomial,axiom,
% 5.41/5.77 ! [A: nat,B: nat,N: nat] :
% 5.41/5.77 ( ( power_power_nat @ ( plus_plus_nat @ A @ B ) @ N )
% 5.41/5.77 = ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [K2: nat] : ( times_times_nat @ ( times_times_nat @ ( semiri1316708129612266289at_nat @ ( binomial @ N @ K2 ) ) @ ( power_power_nat @ A @ K2 ) ) @ ( power_power_nat @ B @ ( minus_minus_nat @ N @ K2 ) ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial
% 5.41/5.77 thf(fact_9060_polynomial__product__nat,axiom,
% 5.41/5.77 ! [M: nat,A: nat > nat,N: nat,B: nat > nat,X: nat] :
% 5.41/5.77 ( ! [I4: nat] :
% 5.41/5.77 ( ( ord_less_nat @ M @ I4 )
% 5.41/5.77 => ( ( A @ I4 )
% 5.41/5.77 = zero_zero_nat ) )
% 5.41/5.77 => ( ! [J2: nat] :
% 5.41/5.77 ( ( ord_less_nat @ N @ J2 )
% 5.41/5.77 => ( ( B @ J2 )
% 5.41/5.77 = zero_zero_nat ) )
% 5.41/5.77 => ( ( times_times_nat
% 5.41/5.77 @ ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( power_power_nat @ X @ I5 ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ M ) )
% 5.41/5.77 @ ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [J3: nat] : ( times_times_nat @ ( B @ J3 ) @ ( power_power_nat @ X @ J3 ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ N ) ) )
% 5.41/5.77 = ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [R5: nat] :
% 5.41/5.77 ( times_times_nat
% 5.41/5.77 @ ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [K2: nat] : ( times_times_nat @ ( A @ K2 ) @ ( B @ ( minus_minus_nat @ R5 @ K2 ) ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ R5 ) )
% 5.41/5.77 @ ( power_power_nat @ X @ R5 ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ ( plus_plus_nat @ M @ N ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % polynomial_product_nat
% 5.41/5.77 thf(fact_9061_choose__square__sum,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [K2: nat] : ( power_power_nat @ ( binomial @ N @ K2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ N ) )
% 5.41/5.77 = ( binomial @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ N ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_square_sum
% 5.41/5.77 thf(fact_9062_binomial__r__part__sum,axiom,
% 5.41/5.77 ! [M: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat @ ( binomial @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) @ one_one_nat ) ) @ ( set_ord_atMost_nat @ M ) )
% 5.41/5.77 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % binomial_r_part_sum
% 5.41/5.77 thf(fact_9063_choose__linear__sum,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( groups3542108847815614940at_nat
% 5.41/5.77 @ ^ [I5: nat] : ( times_times_nat @ I5 @ ( binomial @ N @ I5 ) )
% 5.41/5.77 @ ( set_ord_atMost_nat @ N ) )
% 5.41/5.77 = ( times_times_nat @ N @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % choose_linear_sum
% 5.41/5.77 thf(fact_9064_of__nat__id,axiom,
% 5.41/5.77 ( semiri1316708129612266289at_nat
% 5.41/5.77 = ( ^ [N2: nat] : N2 ) ) ).
% 5.41/5.77
% 5.41/5.77 % of_nat_id
% 5.41/5.77 thf(fact_9065_real__scaleR__def,axiom,
% 5.41/5.77 real_V1485227260804924795R_real = times_times_real ).
% 5.41/5.77
% 5.41/5.77 % real_scaleR_def
% 5.41/5.77 thf(fact_9066_complex__scaleR,axiom,
% 5.41/5.77 ! [R: real,A: real,B: real] :
% 5.41/5.77 ( ( real_V2046097035970521341omplex @ R @ ( complex2 @ A @ B ) )
% 5.41/5.77 = ( complex2 @ ( times_times_real @ R @ A ) @ ( times_times_real @ R @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_scaleR
% 5.41/5.77 thf(fact_9067_cis__minus__pi__half,axiom,
% 5.41/5.77 ( ( cis @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ imaginary_unit ) ) ).
% 5.41/5.77
% 5.41/5.77 % cis_minus_pi_half
% 5.41/5.77 thf(fact_9068_floor__log__nat__eq__powr__iff,axiom,
% 5.41/5.77 ! [B: nat,K: nat,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ K )
% 5.41/5.77 => ( ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.41/5.77 = ( semiri1314217659103216013at_int @ N ) )
% 5.41/5.77 = ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.41/5.77 & ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_log_nat_eq_powr_iff
% 5.41/5.77 thf(fact_9069_norm__cis,axiom,
% 5.41/5.77 ! [A: real] :
% 5.41/5.77 ( ( real_V1022390504157884413omplex @ ( cis @ A ) )
% 5.41/5.77 = one_one_real ) ).
% 5.41/5.77
% 5.41/5.77 % norm_cis
% 5.41/5.77 thf(fact_9070_cis__zero,axiom,
% 5.41/5.77 ( ( cis @ zero_zero_real )
% 5.41/5.77 = one_one_complex ) ).
% 5.41/5.77
% 5.41/5.77 % cis_zero
% 5.41/5.77 thf(fact_9071_cis__pi,axiom,
% 5.41/5.77 ( ( cis @ pi )
% 5.41/5.77 = ( uminus1482373934393186551omplex @ one_one_complex ) ) ).
% 5.41/5.77
% 5.41/5.77 % cis_pi
% 5.41/5.77 thf(fact_9072_floor__divide__eq__div__numeral,axiom,
% 5.41/5.77 ! [A: num,B: num] :
% 5.41/5.77 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) )
% 5.41/5.77 = ( divide_divide_int @ ( numeral_numeral_int @ A ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_divide_eq_div_numeral
% 5.41/5.77 thf(fact_9073_cis__pi__half,axiom,
% 5.41/5.77 ( ( cis @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.77 = imaginary_unit ) ).
% 5.41/5.77
% 5.41/5.77 % cis_pi_half
% 5.41/5.77 thf(fact_9074_floor__one__divide__eq__div__numeral,axiom,
% 5.41/5.77 ! [B: num] :
% 5.41/5.77 ( ( archim6058952711729229775r_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) )
% 5.41/5.77 = ( divide_divide_int @ one_one_int @ ( numeral_numeral_int @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_one_divide_eq_div_numeral
% 5.41/5.77 thf(fact_9075_cis__2pi,axiom,
% 5.41/5.77 ( ( cis @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) )
% 5.41/5.77 = one_one_complex ) ).
% 5.41/5.77
% 5.41/5.77 % cis_2pi
% 5.41/5.77 thf(fact_9076_floor__minus__divide__eq__div__numeral,axiom,
% 5.41/5.77 ! [A: num,B: num] :
% 5.41/5.77 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ ( numeral_numeral_real @ A ) @ ( numeral_numeral_real @ B ) ) ) )
% 5.41/5.77 = ( divide_divide_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ A ) ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_minus_divide_eq_div_numeral
% 5.41/5.77 thf(fact_9077_floor__minus__one__divide__eq__div__numeral,axiom,
% 5.41/5.77 ! [B: num] :
% 5.41/5.77 ( ( archim6058952711729229775r_real @ ( uminus_uminus_real @ ( divide_divide_real @ one_one_real @ ( numeral_numeral_real @ B ) ) ) )
% 5.41/5.77 = ( divide_divide_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_minus_one_divide_eq_div_numeral
% 5.41/5.77 thf(fact_9078_real__sqrt__inverse,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( sqrt @ ( inverse_inverse_real @ X ) )
% 5.41/5.77 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_sqrt_inverse
% 5.41/5.77 thf(fact_9079_cis__neq__zero,axiom,
% 5.41/5.77 ! [A: real] :
% 5.41/5.77 ( ( cis @ A )
% 5.41/5.77 != zero_zero_complex ) ).
% 5.41/5.77
% 5.41/5.77 % cis_neq_zero
% 5.41/5.77 thf(fact_9080_divide__real__def,axiom,
% 5.41/5.77 ( divide_divide_real
% 5.41/5.77 = ( ^ [X3: real,Y3: real] : ( times_times_real @ X3 @ ( inverse_inverse_real @ Y3 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % divide_real_def
% 5.41/5.77 thf(fact_9081_cis__mult,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( times_times_complex @ ( cis @ A ) @ ( cis @ B ) )
% 5.41/5.77 = ( cis @ ( plus_plus_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cis_mult
% 5.41/5.77 thf(fact_9082_cis__divide,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( divide1717551699836669952omplex @ ( cis @ A ) @ ( cis @ B ) )
% 5.41/5.77 = ( cis @ ( minus_minus_real @ A @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cis_divide
% 5.41/5.77 thf(fact_9083_inverse__powr,axiom,
% 5.41/5.77 ! [Y: real,A: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( powr_real @ ( inverse_inverse_real @ Y ) @ A )
% 5.41/5.77 = ( inverse_inverse_real @ ( powr_real @ Y @ A ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % inverse_powr
% 5.41/5.77 thf(fact_9084_real__of__int__floor__add__one__gt,axiom,
% 5.41/5.77 ! [R: real] : ( ord_less_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_of_int_floor_add_one_gt
% 5.41/5.77 thf(fact_9085_floor__eq,axiom,
% 5.41/5.77 ! [N: int,X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.41/5.77 => ( ( archim6058952711729229775r_real @ X )
% 5.41/5.77 = N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_eq
% 5.41/5.77 thf(fact_9086_real__of__int__floor__add__one__ge,axiom,
% 5.41/5.77 ! [R: real] : ( ord_less_eq_real @ R @ ( plus_plus_real @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) @ one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_of_int_floor_add_one_ge
% 5.41/5.77 thf(fact_9087_real__of__int__floor__gt__diff__one,axiom,
% 5.41/5.77 ! [R: real] : ( ord_less_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_of_int_floor_gt_diff_one
% 5.41/5.77 thf(fact_9088_real__of__int__floor__ge__diff__one,axiom,
% 5.41/5.77 ! [R: real] : ( ord_less_eq_real @ ( minus_minus_real @ R @ one_one_real ) @ ( ring_1_of_int_real @ ( archim6058952711729229775r_real @ R ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_of_int_floor_ge_diff_one
% 5.41/5.77 thf(fact_9089_forall__pos__mono__1,axiom,
% 5.41/5.77 ! [P: real > $o,E: real] :
% 5.41/5.77 ( ! [D3: real,E2: real] :
% 5.41/5.77 ( ( ord_less_real @ D3 @ E2 )
% 5.41/5.77 => ( ( P @ D3 )
% 5.41/5.77 => ( P @ E2 ) ) )
% 5.41/5.77 => ( ! [N3: nat] : ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N3 ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.41/5.77 => ( P @ E ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % forall_pos_mono_1
% 5.41/5.77 thf(fact_9090_DeMoivre,axiom,
% 5.41/5.77 ! [A: real,N: nat] :
% 5.41/5.77 ( ( power_power_complex @ ( cis @ A ) @ N )
% 5.41/5.77 = ( cis @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % DeMoivre
% 5.41/5.77 thf(fact_9091_forall__pos__mono,axiom,
% 5.41/5.77 ! [P: real > $o,E: real] :
% 5.41/5.77 ( ! [D3: real,E2: real] :
% 5.41/5.77 ( ( ord_less_real @ D3 @ E2 )
% 5.41/5.77 => ( ( P @ D3 )
% 5.41/5.77 => ( P @ E2 ) ) )
% 5.41/5.77 => ( ! [N3: nat] :
% 5.41/5.77 ( ( N3 != zero_zero_nat )
% 5.41/5.77 => ( P @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N3 ) ) ) )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ E )
% 5.41/5.77 => ( P @ E ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % forall_pos_mono
% 5.41/5.77 thf(fact_9092_real__arch__inverse,axiom,
% 5.41/5.77 ! [E: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ E )
% 5.41/5.77 = ( ? [N2: nat] :
% 5.41/5.77 ( ( N2 != zero_zero_nat )
% 5.41/5.77 & ( ord_less_real @ zero_zero_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) )
% 5.41/5.77 & ( ord_less_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ N2 ) ) @ E ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_arch_inverse
% 5.41/5.77 thf(fact_9093_sqrt__divide__self__eq,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( divide_divide_real @ ( sqrt @ X ) @ X )
% 5.41/5.77 = ( inverse_inverse_real @ ( sqrt @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sqrt_divide_self_eq
% 5.41/5.77 thf(fact_9094_ln__inverse,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ln_ln_real @ ( inverse_inverse_real @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( ln_ln_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % ln_inverse
% 5.41/5.77 thf(fact_9095_floor__eq2,axiom,
% 5.41/5.77 ! [N: int,X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ N ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ ( plus_plus_real @ ( ring_1_of_int_real @ N ) @ one_one_real ) )
% 5.41/5.77 => ( ( archim6058952711729229775r_real @ X )
% 5.41/5.77 = N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_eq2
% 5.41/5.77 thf(fact_9096_floor__divide__real__eq__div,axiom,
% 5.41/5.77 ! [B: int,A: real] :
% 5.41/5.77 ( ( ord_less_eq_int @ zero_zero_int @ B )
% 5.41/5.77 => ( ( archim6058952711729229775r_real @ ( divide_divide_real @ A @ ( ring_1_of_int_real @ B ) ) )
% 5.41/5.77 = ( divide_divide_int @ ( archim6058952711729229775r_real @ A ) @ B ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_divide_real_eq_div
% 5.41/5.77 thf(fact_9097_log__inverse,axiom,
% 5.41/5.77 ! [A: real,X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.77 => ( ( A != one_one_real )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( log @ A @ ( inverse_inverse_real @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( log @ A @ X ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % log_inverse
% 5.41/5.77 thf(fact_9098_cis__conv__exp,axiom,
% 5.41/5.77 ( cis
% 5.41/5.77 = ( ^ [B2: real] : ( exp_complex @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ B2 ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cis_conv_exp
% 5.41/5.77 thf(fact_9099_exp__plus__inverse__exp,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % exp_plus_inverse_exp
% 5.41/5.77 thf(fact_9100_plus__inverse__ge__2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % plus_inverse_ge_2
% 5.41/5.77 thf(fact_9101_real__inv__sqrt__pow2,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( power_power_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.77 = ( inverse_inverse_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_inv_sqrt_pow2
% 5.41/5.77 thf(fact_9102_tan__cot,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.41/5.77 = ( inverse_inverse_real @ ( tan_real @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % tan_cot
% 5.41/5.77 thf(fact_9103_real__le__x__sinh,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ X @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_le_x_sinh
% 5.41/5.77 thf(fact_9104_real__le__abs__sinh,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( abs_abs_real @ X ) @ ( abs_abs_real @ ( divide_divide_real @ ( minus_minus_real @ ( exp_real @ X ) @ ( inverse_inverse_real @ ( exp_real @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_le_abs_sinh
% 5.41/5.77 thf(fact_9105_floor__log__eq__powr__iff,axiom,
% 5.41/5.77 ! [X: real,B: real,K: int] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ one_one_real @ B )
% 5.41/5.77 => ( ( ( archim6058952711729229775r_real @ ( log @ B @ X ) )
% 5.41/5.77 = K )
% 5.41/5.77 = ( ( ord_less_eq_real @ ( powr_real @ B @ ( ring_1_of_int_real @ K ) ) @ X )
% 5.41/5.77 & ( ord_less_real @ X @ ( powr_real @ B @ ( ring_1_of_int_real @ ( plus_plus_int @ K @ one_one_int ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_log_eq_powr_iff
% 5.41/5.77 thf(fact_9106_floor__log2__div2,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.77 => ( ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.41/5.77 = ( plus_plus_int @ ( archim6058952711729229775r_real @ ( log @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( semiri5074537144036343181t_real @ ( divide_divide_nat @ N @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ one_one_int ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_log2_div2
% 5.41/5.77 thf(fact_9107_floor__log__nat__eq__if,axiom,
% 5.41/5.77 ! [B: nat,N: nat,K: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ ( power_power_nat @ B @ N ) @ K )
% 5.41/5.77 => ( ( ord_less_nat @ K @ ( power_power_nat @ B @ ( plus_plus_nat @ N @ one_one_nat ) ) )
% 5.41/5.77 => ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ B )
% 5.41/5.77 => ( ( archim6058952711729229775r_real @ ( log @ ( semiri5074537144036343181t_real @ B ) @ ( semiri5074537144036343181t_real @ K ) ) )
% 5.41/5.77 = ( semiri1314217659103216013at_int @ N ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % floor_log_nat_eq_if
% 5.41/5.77 thf(fact_9108_Maclaurin__sin__bound,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ord_less_eq_real
% 5.41/5.77 @ ( abs_abs_real
% 5.41/5.77 @ ( minus_minus_real @ ( sin_real @ X )
% 5.41/5.77 @ ( groups6591440286371151544t_real
% 5.41/5.77 @ ^ [M3: nat] : ( times_times_real @ ( sin_coeff @ M3 ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N ) ) ) )
% 5.41/5.77 @ ( times_times_real @ ( inverse_inverse_real @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( abs_abs_real @ X ) @ N ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % Maclaurin_sin_bound
% 5.41/5.77 thf(fact_9109_bij__betw__roots__unity,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( bij_betw_nat_complex
% 5.41/5.77 @ ^ [K2: nat] : ( cis @ ( divide_divide_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ ( semiri5074537144036343181t_real @ K2 ) ) @ ( semiri5074537144036343181t_real @ N ) ) )
% 5.41/5.77 @ ( set_ord_lessThan_nat @ N )
% 5.41/5.77 @ ( collect_complex
% 5.41/5.77 @ ^ [Z3: complex] :
% 5.41/5.77 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.77 = one_one_complex ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % bij_betw_roots_unity
% 5.41/5.77 thf(fact_9110_sinh__real__zero__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ( sinh_real @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_real_zero_iff
% 5.41/5.77 thf(fact_9111_sinh__real__le__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ ( sinh_real @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ X @ Y ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_real_le_iff
% 5.41/5.77 thf(fact_9112_sinh__real__neg__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.41/5.77 = ( ord_less_real @ X @ zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_real_neg_iff
% 5.41/5.77 thf(fact_9113_sinh__real__pos__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.41/5.77 = ( ord_less_real @ zero_zero_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_real_pos_iff
% 5.41/5.77 thf(fact_9114_sinh__real__nonpos__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ ( sinh_real @ X ) @ zero_zero_real )
% 5.41/5.77 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_real_nonpos_iff
% 5.41/5.77 thf(fact_9115_sinh__real__nonneg__iff,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ ( sinh_real @ X ) )
% 5.41/5.77 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_real_nonneg_iff
% 5.41/5.77 thf(fact_9116_divide__complex__def,axiom,
% 5.41/5.77 ( divide1717551699836669952omplex
% 5.41/5.77 = ( ^ [X3: complex,Y3: complex] : ( times_times_complex @ X3 @ ( invers8013647133539491842omplex @ Y3 ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % divide_complex_def
% 5.41/5.77 thf(fact_9117_fact__eq__fact__times,axiom,
% 5.41/5.77 ! [N: nat,M: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.77 => ( ( semiri1408675320244567234ct_nat @ M )
% 5.41/5.77 = ( times_times_nat @ ( semiri1408675320244567234ct_nat @ N )
% 5.41/5.77 @ ( groups708209901874060359at_nat
% 5.41/5.77 @ ^ [X3: nat] : X3
% 5.41/5.77 @ ( set_or1269000886237332187st_nat @ ( suc @ N ) @ M ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_eq_fact_times
% 5.41/5.77 thf(fact_9118_fact__div__fact,axiom,
% 5.41/5.77 ! [N: nat,M: nat] :
% 5.41/5.77 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.77 => ( ( divide_divide_nat @ ( semiri1408675320244567234ct_nat @ M ) @ ( semiri1408675320244567234ct_nat @ N ) )
% 5.41/5.77 = ( groups708209901874060359at_nat
% 5.41/5.77 @ ^ [X3: nat] : X3
% 5.41/5.77 @ ( set_or1269000886237332187st_nat @ ( plus_plus_nat @ N @ one_one_nat ) @ M ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % fact_div_fact
% 5.41/5.77 thf(fact_9119_complex__inverse,axiom,
% 5.41/5.77 ! [A: real,B: real] :
% 5.41/5.77 ( ( invers8013647133539491842omplex @ ( complex2 @ A @ B ) )
% 5.41/5.77 = ( complex2 @ ( divide_divide_real @ A @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ B ) @ ( plus_plus_real @ ( power_power_real @ A @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % complex_inverse
% 5.41/5.77 thf(fact_9120_sinh__ln__real,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( sinh_real @ ( ln_ln_real @ X ) )
% 5.41/5.77 = ( divide_divide_real @ ( minus_minus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_ln_real
% 5.41/5.77 thf(fact_9121_VEBT__internal_OminNull_Opelims_I1_J,axiom,
% 5.41/5.77 ! [X: vEBT_VEBT,Y: $o] :
% 5.41/5.77 ( ( ( vEBT_VEBT_minNull @ X )
% 5.41/5.77 = Y )
% 5.41/5.77 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.41/5.77 => ( ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 5.41/5.77 => ( Y
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) ) )
% 5.41/5.77 => ( ! [Uv2: $o] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.41/5.77 => ( ~ Y
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) ) )
% 5.41/5.77 => ( ! [Uu2: $o] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.41/5.77 => ( ~ Y
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) ) )
% 5.41/5.77 => ( ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.41/5.77 => ( Y
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) )
% 5.41/5.77 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.41/5.77 => ( ~ Y
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % VEBT_internal.minNull.pelims(1)
% 5.41/5.77 thf(fact_9122_sinh__le__cosh__real,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ ( sinh_real @ X ) @ ( cosh_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % sinh_le_cosh_real
% 5.41/5.77 thf(fact_9123_cosh__real__nonzero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cosh_real @ X )
% 5.41/5.77 != zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_nonzero
% 5.41/5.77 thf(fact_9124_cosh__real__pos,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_pos
% 5.41/5.77 thf(fact_9125_cosh__real__nonneg,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ zero_zero_real @ ( cosh_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_nonneg
% 5.41/5.77 thf(fact_9126_cosh__real__nonneg__le__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_nonneg_le_iff
% 5.41/5.77 thf(fact_9127_cosh__real__nonpos__le__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ Y @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_nonpos_le_iff
% 5.41/5.77 thf(fact_9128_cosh__real__ge__1,axiom,
% 5.41/5.77 ! [X: real] : ( ord_less_eq_real @ one_one_real @ ( cosh_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_ge_1
% 5.41/5.77 thf(fact_9129_cosh__real__nonpos__less__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ( ord_less_eq_real @ Y @ zero_zero_real )
% 5.41/5.77 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.41/5.77 = ( ord_less_real @ Y @ X ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_nonpos_less_iff
% 5.41/5.77 thf(fact_9130_cosh__real__nonneg__less__iff,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.77 => ( ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) )
% 5.41/5.77 = ( ord_less_real @ X @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_nonneg_less_iff
% 5.41/5.77 thf(fact_9131_cosh__real__strict__mono,axiom,
% 5.41/5.77 ! [X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ Y )
% 5.41/5.77 => ( ord_less_real @ ( cosh_real @ X ) @ ( cosh_real @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_real_strict_mono
% 5.41/5.77 thf(fact_9132_prod__int__eq,axiom,
% 5.41/5.77 ! [I: nat,J: nat] :
% 5.41/5.77 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.41/5.77 = ( groups1705073143266064639nt_int
% 5.41/5.77 @ ^ [X3: int] : X3
% 5.41/5.77 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ J ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % prod_int_eq
% 5.41/5.77 thf(fact_9133_arcosh__cosh__real,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( arcosh_real @ ( cosh_real @ X ) )
% 5.41/5.77 = X ) ) ).
% 5.41/5.77
% 5.41/5.77 % arcosh_cosh_real
% 5.41/5.77 thf(fact_9134_prod__int__plus__eq,axiom,
% 5.41/5.77 ! [I: nat,J: nat] :
% 5.41/5.77 ( ( groups705719431365010083at_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ I @ ( plus_plus_nat @ I @ J ) ) )
% 5.41/5.77 = ( groups1705073143266064639nt_int
% 5.41/5.77 @ ^ [X3: int] : X3
% 5.41/5.77 @ ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ I ) @ ( semiri1314217659103216013at_int @ ( plus_plus_nat @ I @ J ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % prod_int_plus_eq
% 5.41/5.77 thf(fact_9135_cosh__ln__real,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( cosh_real @ ( ln_ln_real @ X ) )
% 5.41/5.77 = ( divide_divide_real @ ( plus_plus_real @ X @ ( inverse_inverse_real @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cosh_ln_real
% 5.41/5.77 thf(fact_9136_VEBT__internal_OminNull_Opelims_I3_J,axiom,
% 5.41/5.77 ! [X: vEBT_VEBT] :
% 5.41/5.77 ( ~ ( vEBT_VEBT_minNull @ X )
% 5.41/5.77 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.41/5.77 => ( ! [Uv2: $o] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ $true @ Uv2 ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $true @ Uv2 ) ) )
% 5.41/5.77 => ( ! [Uu2: $o] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ Uu2 @ $true ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ Uu2 @ $true ) ) )
% 5.41/5.77 => ~ ! [Uz2: product_prod_nat_nat,Va3: nat,Vb2: list_VEBT_VEBT,Vc2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ ( some_P7363390416028606310at_nat @ Uz2 ) @ Va3 @ Vb2 @ Vc2 ) ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % VEBT_internal.minNull.pelims(3)
% 5.41/5.77 thf(fact_9137_VEBT__internal_OminNull_Opelims_I2_J,axiom,
% 5.41/5.77 ! [X: vEBT_VEBT] :
% 5.41/5.77 ( ( vEBT_VEBT_minNull @ X )
% 5.41/5.77 => ( ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ X )
% 5.41/5.77 => ( ( ( X
% 5.41/5.77 = ( vEBT_Leaf @ $false @ $false ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Leaf @ $false @ $false ) ) )
% 5.41/5.77 => ~ ! [Uw2: nat,Ux2: list_VEBT_VEBT,Uy2: vEBT_VEBT] :
% 5.41/5.77 ( ( X
% 5.41/5.77 = ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) )
% 5.41/5.77 => ~ ( accp_VEBT_VEBT @ vEBT_V6963167321098673237ll_rel @ ( vEBT_Node @ none_P5556105721700978146at_nat @ Uw2 @ Ux2 @ Uy2 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % VEBT_internal.minNull.pelims(2)
% 5.41/5.77 thf(fact_9138_bij__betw__nth__root__unity,axiom,
% 5.41/5.77 ! [C: complex,N: nat] :
% 5.41/5.77 ( ( C != zero_zero_complex )
% 5.41/5.77 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( bij_be1856998921033663316omplex @ ( times_times_complex @ ( times_times_complex @ ( real_V4546457046886955230omplex @ ( root @ N @ ( real_V1022390504157884413omplex @ C ) ) ) @ ( cis @ ( divide_divide_real @ ( arg @ C ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) )
% 5.41/5.77 @ ( collect_complex
% 5.41/5.77 @ ^ [Z3: complex] :
% 5.41/5.77 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.77 = one_one_complex ) )
% 5.41/5.77 @ ( collect_complex
% 5.41/5.77 @ ^ [Z3: complex] :
% 5.41/5.77 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.77 = C ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % bij_betw_nth_root_unity
% 5.41/5.77 thf(fact_9139_cot__less__zero,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( ord_less_real @ ( divide_divide_real @ ( uminus_uminus_real @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X )
% 5.41/5.77 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.77 => ( ord_less_real @ ( cot_real @ X ) @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % cot_less_zero
% 5.41/5.77 thf(fact_9140_int__ge__less__than__def,axiom,
% 5.41/5.77 ( int_ge_less_than
% 5.41/5.77 = ( ^ [D2: int] :
% 5.41/5.77 ( collec213857154873943460nt_int
% 5.41/5.77 @ ( produc4947309494688390418_int_o
% 5.41/5.77 @ ^ [Z6: int,Z3: int] :
% 5.41/5.77 ( ( ord_less_eq_int @ D2 @ Z6 )
% 5.41/5.77 & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % int_ge_less_than_def
% 5.41/5.77 thf(fact_9141_int__ge__less__than2__def,axiom,
% 5.41/5.77 ( int_ge_less_than2
% 5.41/5.77 = ( ^ [D2: int] :
% 5.41/5.77 ( collec213857154873943460nt_int
% 5.41/5.77 @ ( produc4947309494688390418_int_o
% 5.41/5.77 @ ^ [Z6: int,Z3: int] :
% 5.41/5.77 ( ( ord_less_eq_int @ D2 @ Z3 )
% 5.41/5.77 & ( ord_less_int @ Z6 @ Z3 ) ) ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % int_ge_less_than2_def
% 5.41/5.77 thf(fact_9142_real__root__zero,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( root @ N @ zero_zero_real )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_zero
% 5.41/5.77 thf(fact_9143_real__root__Suc__0,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( root @ ( suc @ zero_zero_nat ) @ X )
% 5.41/5.77 = X ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_Suc_0
% 5.41/5.77 thf(fact_9144_real__root__eq__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ( root @ N @ X )
% 5.41/5.77 = ( root @ N @ Y ) )
% 5.41/5.77 = ( X = Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_eq_iff
% 5.41/5.77 thf(fact_9145_root__0,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( root @ zero_zero_nat @ X )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % root_0
% 5.41/5.77 thf(fact_9146_cot__pi,axiom,
% 5.41/5.77 ( ( cot_real @ pi )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cot_pi
% 5.41/5.77 thf(fact_9147_real__root__eq__0__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ( root @ N @ X )
% 5.41/5.77 = zero_zero_real )
% 5.41/5.77 = ( X = zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_eq_0_iff
% 5.41/5.77 thf(fact_9148_real__root__less__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 5.41/5.77 = ( ord_less_real @ X @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_less_iff
% 5.41/5.77 thf(fact_9149_real__root__le__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ X @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_le_iff
% 5.41/5.77 thf(fact_9150_real__root__eq__1__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ( root @ N @ X )
% 5.41/5.77 = one_one_real )
% 5.41/5.77 = ( X = one_one_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_eq_1_iff
% 5.41/5.77 thf(fact_9151_real__root__one,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( root @ N @ one_one_real )
% 5.41/5.77 = one_one_real ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_one
% 5.41/5.77 thf(fact_9152_real__root__gt__0__iff,axiom,
% 5.41/5.77 ! [N: nat,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.41/5.77 = ( ord_less_real @ zero_zero_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_gt_0_iff
% 5.41/5.77 thf(fact_9153_real__root__lt__0__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.41/5.77 = ( ord_less_real @ X @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_lt_0_iff
% 5.41/5.77 thf(fact_9154_real__root__ge__0__iff,axiom,
% 5.41/5.77 ! [N: nat,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ zero_zero_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_ge_0_iff
% 5.41/5.77 thf(fact_9155_real__root__le__0__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ zero_zero_real )
% 5.41/5.77 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_le_0_iff
% 5.41/5.77 thf(fact_9156_real__root__lt__1__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ ( root @ N @ X ) @ one_one_real )
% 5.41/5.77 = ( ord_less_real @ X @ one_one_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_lt_1_iff
% 5.41/5.77 thf(fact_9157_real__root__gt__1__iff,axiom,
% 5.41/5.77 ! [N: nat,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ one_one_real @ ( root @ N @ Y ) )
% 5.41/5.77 = ( ord_less_real @ one_one_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_gt_1_iff
% 5.41/5.77 thf(fact_9158_real__root__le__1__iff,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_eq_real @ ( root @ N @ X ) @ one_one_real )
% 5.41/5.77 = ( ord_less_eq_real @ X @ one_one_real ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_le_1_iff
% 5.41/5.77 thf(fact_9159_real__root__ge__1__iff,axiom,
% 5.41/5.77 ! [N: nat,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_eq_real @ one_one_real @ ( root @ N @ Y ) )
% 5.41/5.77 = ( ord_less_eq_real @ one_one_real @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_ge_1_iff
% 5.41/5.77 thf(fact_9160_cot__npi,axiom,
% 5.41/5.77 ! [N: nat] :
% 5.41/5.77 ( ( cot_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ pi ) )
% 5.41/5.77 = zero_zero_real ) ).
% 5.41/5.77
% 5.41/5.77 % cot_npi
% 5.41/5.77 thf(fact_9161_real__root__pow__pos2,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.41/5.77 = X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_pow_pos2
% 5.41/5.77 thf(fact_9162_cot__periodic,axiom,
% 5.41/5.77 ! [X: real] :
% 5.41/5.77 ( ( cot_real @ ( plus_plus_real @ X @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.41/5.77 = ( cot_real @ X ) ) ).
% 5.41/5.77
% 5.41/5.77 % cot_periodic
% 5.41/5.77 thf(fact_9163_real__root__inverse,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( root @ N @ ( inverse_inverse_real @ X ) )
% 5.41/5.77 = ( inverse_inverse_real @ ( root @ N @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_inverse
% 5.41/5.77 thf(fact_9164_real__root__divide,axiom,
% 5.41/5.77 ! [N: nat,X: real,Y: real] :
% 5.41/5.77 ( ( root @ N @ ( divide_divide_real @ X @ Y ) )
% 5.41/5.77 = ( divide_divide_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_divide
% 5.41/5.77 thf(fact_9165_real__root__commute,axiom,
% 5.41/5.77 ! [M: nat,N: nat,X: real] :
% 5.41/5.77 ( ( root @ M @ ( root @ N @ X ) )
% 5.41/5.77 = ( root @ N @ ( root @ M @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_commute
% 5.41/5.77 thf(fact_9166_real__root__mult__exp,axiom,
% 5.41/5.77 ! [M: nat,N: nat,X: real] :
% 5.41/5.77 ( ( root @ ( times_times_nat @ M @ N ) @ X )
% 5.41/5.77 = ( root @ M @ ( root @ N @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_mult_exp
% 5.41/5.77 thf(fact_9167_real__root__mult,axiom,
% 5.41/5.77 ! [N: nat,X: real,Y: real] :
% 5.41/5.77 ( ( root @ N @ ( times_times_real @ X @ Y ) )
% 5.41/5.77 = ( times_times_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_mult
% 5.41/5.77 thf(fact_9168_real__root__minus,axiom,
% 5.41/5.77 ! [N: nat,X: real] :
% 5.41/5.77 ( ( root @ N @ ( uminus_uminus_real @ X ) )
% 5.41/5.77 = ( uminus_uminus_real @ ( root @ N @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_minus
% 5.41/5.77 thf(fact_9169_real__root__pos__pos__le,axiom,
% 5.41/5.77 ! [X: real,N: nat] :
% 5.41/5.77 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.77 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_pos_pos_le
% 5.41/5.77 thf(fact_9170_real__root__less__mono,axiom,
% 5.41/5.77 ! [N: nat,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.77 => ( ( ord_less_real @ X @ Y )
% 5.41/5.77 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 5.41/5.77
% 5.41/5.77 % real_root_less_mono
% 5.41/5.77 thf(fact_9171_real__root__le__mono,axiom,
% 5.41/5.77 ! [N: nat,X: real,Y: real] :
% 5.41/5.77 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_eq_real @ X @ Y )
% 5.41/5.78 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_le_mono
% 5.41/5.78 thf(fact_9172_real__root__power,axiom,
% 5.41/5.78 ! [N: nat,X: real,K: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( root @ N @ ( power_power_real @ X @ K ) )
% 5.41/5.78 = ( power_power_real @ ( root @ N @ X ) @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_power
% 5.41/5.78 thf(fact_9173_real__root__abs,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( root @ N @ ( abs_abs_real @ X ) )
% 5.41/5.78 = ( abs_abs_real @ ( root @ N @ X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_abs
% 5.41/5.78 thf(fact_9174_real__root__gt__zero,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ord_less_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_gt_zero
% 5.41/5.78 thf(fact_9175_real__root__strict__decreasing,axiom,
% 5.41/5.78 ! [N: nat,N4: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_nat @ N @ N4 )
% 5.41/5.78 => ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.78 => ( ord_less_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_strict_decreasing
% 5.41/5.78 thf(fact_9176_sqrt__def,axiom,
% 5.41/5.78 ( sqrt
% 5.41/5.78 = ( root @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sqrt_def
% 5.41/5.78 thf(fact_9177_root__abs__power,axiom,
% 5.41/5.78 ! [N: nat,Y: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( abs_abs_real @ ( root @ N @ ( power_power_real @ Y @ N ) ) )
% 5.41/5.78 = ( abs_abs_real @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % root_abs_power
% 5.41/5.78 thf(fact_9178_real__root__pos__pos,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ord_less_eq_real @ zero_zero_real @ ( root @ N @ X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_pos_pos
% 5.41/5.78 thf(fact_9179_real__root__strict__increasing,axiom,
% 5.41/5.78 ! [N: nat,N4: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_nat @ N @ N4 )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.78 => ( ord_less_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_strict_increasing
% 5.41/5.78 thf(fact_9180_real__root__decreasing,axiom,
% 5.41/5.78 ! [N: nat,N4: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.78 => ( ( ord_less_eq_real @ one_one_real @ X )
% 5.41/5.78 => ( ord_less_eq_real @ ( root @ N4 @ X ) @ ( root @ N @ X ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_decreasing
% 5.41/5.78 thf(fact_9181_real__root__pow__pos,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.41/5.78 = X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_pow_pos
% 5.41/5.78 thf(fact_9182_real__root__pos__unique,axiom,
% 5.41/5.78 ! [N: nat,Y: real,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_eq_real @ zero_zero_real @ Y )
% 5.41/5.78 => ( ( ( power_power_real @ Y @ N )
% 5.41/5.78 = X )
% 5.41/5.78 => ( ( root @ N @ X )
% 5.41/5.78 = Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_pos_unique
% 5.41/5.78 thf(fact_9183_real__root__power__cancel,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.41/5.78 = X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_power_cancel
% 5.41/5.78 thf(fact_9184_odd__real__root__pow,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.78 => ( ( power_power_real @ ( root @ N @ X ) @ N )
% 5.41/5.78 = X ) ) ).
% 5.41/5.78
% 5.41/5.78 % odd_real_root_pow
% 5.41/5.78 thf(fact_9185_odd__real__root__unique,axiom,
% 5.41/5.78 ! [N: nat,Y: real,X: real] :
% 5.41/5.78 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.78 => ( ( ( power_power_real @ Y @ N )
% 5.41/5.78 = X )
% 5.41/5.78 => ( ( root @ N @ X )
% 5.41/5.78 = Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % odd_real_root_unique
% 5.41/5.78 thf(fact_9186_odd__real__root__power__cancel,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.78 => ( ( root @ N @ ( power_power_real @ X @ N ) )
% 5.41/5.78 = X ) ) ).
% 5.41/5.78
% 5.41/5.78 % odd_real_root_power_cancel
% 5.41/5.78 thf(fact_9187_real__root__increasing,axiom,
% 5.41/5.78 ! [N: nat,N4: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_eq_nat @ N @ N4 )
% 5.41/5.78 => ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.78 => ( ord_less_eq_real @ ( root @ N @ X ) @ ( root @ N4 @ X ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_root_increasing
% 5.41/5.78 thf(fact_9188_ln__root,axiom,
% 5.41/5.78 ! [N: nat,B: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.78 => ( ( ln_ln_real @ ( root @ N @ B ) )
% 5.41/5.78 = ( divide_divide_real @ ( ln_ln_real @ B ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % ln_root
% 5.41/5.78 thf(fact_9189_log__root,axiom,
% 5.41/5.78 ! [N: nat,A: real,B: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ A )
% 5.41/5.78 => ( ( log @ B @ ( root @ N @ A ) )
% 5.41/5.78 = ( divide_divide_real @ ( log @ B @ A ) @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % log_root
% 5.41/5.78 thf(fact_9190_log__base__root,axiom,
% 5.41/5.78 ! [N: nat,B: real,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ B )
% 5.41/5.78 => ( ( log @ ( root @ N @ B ) @ X )
% 5.41/5.78 = ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( log @ B @ X ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % log_base_root
% 5.41/5.78 thf(fact_9191_root__powr__inverse,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( root @ N @ X )
% 5.41/5.78 = ( powr_real @ X @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % root_powr_inverse
% 5.41/5.78 thf(fact_9192_cot__gt__zero,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( ord_less_real @ X @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.78 => ( ord_less_real @ zero_zero_real @ ( cot_real @ X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cot_gt_zero
% 5.41/5.78 thf(fact_9193_tan__cot_H,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( tan_real @ ( minus_minus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ X ) )
% 5.41/5.78 = ( cot_real @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % tan_cot'
% 5.41/5.78 thf(fact_9194_arctan__def,axiom,
% 5.41/5.78 ( arctan
% 5.41/5.78 = ( ^ [Y3: real] :
% 5.41/5.78 ( the_real
% 5.41/5.78 @ ^ [X3: real] :
% 5.41/5.78 ( ( ord_less_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.41/5.78 & ( ord_less_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.78 & ( ( tan_real @ X3 )
% 5.41/5.78 = Y3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % arctan_def
% 5.41/5.78 thf(fact_9195_arcsin__def,axiom,
% 5.41/5.78 ( arcsin
% 5.41/5.78 = ( ^ [Y3: real] :
% 5.41/5.78 ( the_real
% 5.41/5.78 @ ^ [X3: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ X3 )
% 5.41/5.78 & ( ord_less_eq_real @ X3 @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.78 & ( ( sin_real @ X3 )
% 5.41/5.78 = Y3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % arcsin_def
% 5.41/5.78 thf(fact_9196_signed__take__bit__eq__take__bit__minus,axiom,
% 5.41/5.78 ( bit_ri631733984087533419it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ ( bit_se2923211474154528505it_int @ ( suc @ N2 ) @ K2 ) @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( suc @ N2 ) ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % signed_take_bit_eq_take_bit_minus
% 5.41/5.78 thf(fact_9197_modulo__int__unfold,axiom,
% 5.41/5.78 ! [L2: int,K: int,N: nat,M: nat] :
% 5.41/5.78 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( ( sgn_sgn_int @ K )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( N = zero_zero_nat ) )
% 5.41/5.78 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.78 = ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) ) )
% 5.41/5.78 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( ( sgn_sgn_int @ K )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( N = zero_zero_nat ) )
% 5.41/5.78 => ( ( ( ( sgn_sgn_int @ K )
% 5.41/5.78 = ( sgn_sgn_int @ L2 ) )
% 5.41/5.78 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.78 = ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) )
% 5.41/5.78 & ( ( ( sgn_sgn_int @ K )
% 5.41/5.78 != ( sgn_sgn_int @ L2 ) )
% 5.41/5.78 => ( ( modulo_modulo_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.78 = ( times_times_int @ ( sgn_sgn_int @ L2 )
% 5.41/5.78 @ ( minus_minus_int
% 5.41/5.78 @ ( semiri1314217659103216013at_int
% 5.41/5.78 @ ( times_times_nat @ N
% 5.41/5.78 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.78 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) )
% 5.41/5.78 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ M @ N ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % modulo_int_unfold
% 5.41/5.78 thf(fact_9198_dvd__mult__sgn__iff,axiom,
% 5.41/5.78 ! [L2: int,K: int,R: int] :
% 5.41/5.78 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ K @ ( sgn_sgn_int @ R ) ) )
% 5.41/5.78 = ( ( dvd_dvd_int @ L2 @ K )
% 5.41/5.78 | ( R = zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % dvd_mult_sgn_iff
% 5.41/5.78 thf(fact_9199_dvd__sgn__mult__iff,axiom,
% 5.41/5.78 ! [L2: int,R: int,K: int] :
% 5.41/5.78 ( ( dvd_dvd_int @ L2 @ ( times_times_int @ ( sgn_sgn_int @ R ) @ K ) )
% 5.41/5.78 = ( ( dvd_dvd_int @ L2 @ K )
% 5.41/5.78 | ( R = zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % dvd_sgn_mult_iff
% 5.41/5.78 thf(fact_9200_mult__sgn__dvd__iff,axiom,
% 5.41/5.78 ! [L2: int,R: int,K: int] :
% 5.41/5.78 ( ( dvd_dvd_int @ ( times_times_int @ L2 @ ( sgn_sgn_int @ R ) ) @ K )
% 5.41/5.78 = ( ( dvd_dvd_int @ L2 @ K )
% 5.41/5.78 & ( ( R = zero_zero_int )
% 5.41/5.78 => ( K = zero_zero_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % mult_sgn_dvd_iff
% 5.41/5.78 thf(fact_9201_sgn__mult__dvd__iff,axiom,
% 5.41/5.78 ! [R: int,L2: int,K: int] :
% 5.41/5.78 ( ( dvd_dvd_int @ ( times_times_int @ ( sgn_sgn_int @ R ) @ L2 ) @ K )
% 5.41/5.78 = ( ( dvd_dvd_int @ L2 @ K )
% 5.41/5.78 & ( ( R = zero_zero_int )
% 5.41/5.78 => ( K = zero_zero_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_mult_dvd_iff
% 5.41/5.78 thf(fact_9202_signed__take__bit__nonnegative__iff,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri631733984087533419it_int @ N @ K ) )
% 5.41/5.78 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % signed_take_bit_nonnegative_iff
% 5.41/5.78 thf(fact_9203_signed__take__bit__negative__iff,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( ord_less_int @ ( bit_ri631733984087533419it_int @ N @ K ) @ zero_zero_int )
% 5.41/5.78 = ( bit_se1146084159140164899it_int @ K @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % signed_take_bit_negative_iff
% 5.41/5.78 thf(fact_9204_bit__minus__numeral__Bit0__Suc__iff,axiom,
% 5.41/5.78 ! [W: num,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( suc @ N ) )
% 5.41/5.78 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_minus_numeral_Bit0_Suc_iff
% 5.41/5.78 thf(fact_9205_bit__minus__numeral__Bit1__Suc__iff,axiom,
% 5.41/5.78 ! [W: num,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( suc @ N ) )
% 5.41/5.78 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_minus_numeral_Bit1_Suc_iff
% 5.41/5.78 thf(fact_9206_bit__minus__numeral__int_I1_J,axiom,
% 5.41/5.78 ! [W: num,N: num] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.78 = ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ ( pred_numeral @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_minus_numeral_int(1)
% 5.41/5.78 thf(fact_9207_bit__minus__numeral__int_I2_J,axiom,
% 5.41/5.78 ! [W: num,N: num] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ W ) ) ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.78 = ( ~ ( bit_se1146084159140164899it_int @ ( numeral_numeral_int @ W ) @ ( pred_numeral @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_minus_numeral_int(2)
% 5.41/5.78 thf(fact_9208_bit__and__int__iff,axiom,
% 5.41/5.78 ! [K: int,L2: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( bit_se725231765392027082nd_int @ K @ L2 ) @ N )
% 5.41/5.78 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.41/5.78 & ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_and_int_iff
% 5.41/5.78 thf(fact_9209_int__sgnE,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ~ ! [N3: nat,L4: int] :
% 5.41/5.78 ( K
% 5.41/5.78 != ( times_times_int @ ( sgn_sgn_int @ L4 ) @ ( semiri1314217659103216013at_int @ N3 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_sgnE
% 5.41/5.78 thf(fact_9210_div__eq__sgn__abs,axiom,
% 5.41/5.78 ! [K: int,L2: int] :
% 5.41/5.78 ( ( ( sgn_sgn_int @ K )
% 5.41/5.78 = ( sgn_sgn_int @ L2 ) )
% 5.41/5.78 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.78 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % div_eq_sgn_abs
% 5.41/5.78 thf(fact_9211_bit__not__int__iff_H,axiom,
% 5.41/5.78 ! [K: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( minus_minus_int @ ( uminus_uminus_int @ K ) @ one_one_int ) @ N )
% 5.41/5.78 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_not_int_iff'
% 5.41/5.78 thf(fact_9212_sgn__mod,axiom,
% 5.41/5.78 ! [L2: int,K: int] :
% 5.41/5.78 ( ( L2 != zero_zero_int )
% 5.41/5.78 => ( ~ ( dvd_dvd_int @ L2 @ K )
% 5.41/5.78 => ( ( sgn_sgn_int @ ( modulo_modulo_int @ K @ L2 ) )
% 5.41/5.78 = ( sgn_sgn_int @ L2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_mod
% 5.41/5.78 thf(fact_9213_ln__neg__is__const,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.78 => ( ( ln_ln_real @ X )
% 5.41/5.78 = ( the_real
% 5.41/5.78 @ ^ [X3: real] : $false ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % ln_neg_is_const
% 5.41/5.78 thf(fact_9214_zsgn__def,axiom,
% 5.41/5.78 ( sgn_sgn_int
% 5.41/5.78 = ( ^ [I5: int] : ( if_int @ ( I5 = zero_zero_int ) @ zero_zero_int @ ( if_int @ ( ord_less_int @ zero_zero_int @ I5 ) @ one_one_int @ ( uminus_uminus_int @ one_one_int ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % zsgn_def
% 5.41/5.78 thf(fact_9215_div__sgn__abs__cancel,axiom,
% 5.41/5.78 ! [V: int,K: int,L2: int] :
% 5.41/5.78 ( ( V != zero_zero_int )
% 5.41/5.78 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ K ) ) @ ( times_times_int @ ( sgn_sgn_int @ V ) @ ( abs_abs_int @ L2 ) ) )
% 5.41/5.78 = ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % div_sgn_abs_cancel
% 5.41/5.78 thf(fact_9216_bit__imp__take__bit__positive,axiom,
% 5.41/5.78 ! [N: nat,M: nat,K: int] :
% 5.41/5.78 ( ( ord_less_nat @ N @ M )
% 5.41/5.78 => ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.41/5.78 => ( ord_less_int @ zero_zero_int @ ( bit_se2923211474154528505it_int @ M @ K ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_imp_take_bit_positive
% 5.41/5.78 thf(fact_9217_div__dvd__sgn__abs,axiom,
% 5.41/5.78 ! [L2: int,K: int] :
% 5.41/5.78 ( ( dvd_dvd_int @ L2 @ K )
% 5.41/5.78 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.78 = ( times_times_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( sgn_sgn_int @ L2 ) ) @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % div_dvd_sgn_abs
% 5.41/5.78 thf(fact_9218_bit__concat__bit__iff,axiom,
% 5.41/5.78 ! [M: nat,K: int,L2: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( bit_concat_bit @ M @ K @ L2 ) @ N )
% 5.41/5.78 = ( ( ( ord_less_nat @ N @ M )
% 5.41/5.78 & ( bit_se1146084159140164899it_int @ K @ N ) )
% 5.41/5.78 | ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.78 & ( bit_se1146084159140164899it_int @ L2 @ ( minus_minus_nat @ N @ M ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_concat_bit_iff
% 5.41/5.78 thf(fact_9219_signed__take__bit__eq__concat__bit,axiom,
% 5.41/5.78 ( bit_ri631733984087533419it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( bit_concat_bit @ N2 @ K2 @ ( uminus_uminus_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % signed_take_bit_eq_concat_bit
% 5.41/5.78 thf(fact_9220_int__bit__bound,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ~ ! [N3: nat] :
% 5.41/5.78 ( ! [M2: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ N3 @ M2 )
% 5.41/5.78 => ( ( bit_se1146084159140164899it_int @ K @ M2 )
% 5.41/5.78 = ( bit_se1146084159140164899it_int @ K @ N3 ) ) )
% 5.41/5.78 => ~ ( ( ord_less_nat @ zero_zero_nat @ N3 )
% 5.41/5.78 => ( ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N3 @ one_one_nat ) )
% 5.41/5.78 = ( ~ ( bit_se1146084159140164899it_int @ K @ N3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_bit_bound
% 5.41/5.78 thf(fact_9221_bit__int__def,axiom,
% 5.41/5.78 ( bit_se1146084159140164899it_int
% 5.41/5.78 = ( ^ [K2: int,N2: nat] :
% 5.41/5.78 ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_int_def
% 5.41/5.78 thf(fact_9222_arccos__def,axiom,
% 5.41/5.78 ( arccos
% 5.41/5.78 = ( ^ [Y3: real] :
% 5.41/5.78 ( the_real
% 5.41/5.78 @ ^ [X3: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.41/5.78 & ( ord_less_eq_real @ X3 @ pi )
% 5.41/5.78 & ( ( cos_real @ X3 )
% 5.41/5.78 = Y3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % arccos_def
% 5.41/5.78 thf(fact_9223_eucl__rel__int__remainderI,axiom,
% 5.41/5.78 ! [R: int,L2: int,K: int,Q2: int] :
% 5.41/5.78 ( ( ( sgn_sgn_int @ R )
% 5.41/5.78 = ( sgn_sgn_int @ L2 ) )
% 5.41/5.78 => ( ( ord_less_int @ ( abs_abs_int @ R ) @ ( abs_abs_int @ L2 ) )
% 5.41/5.78 => ( ( K
% 5.41/5.78 = ( plus_plus_int @ ( times_times_int @ Q2 @ L2 ) @ R ) )
% 5.41/5.78 => ( eucl_rel_int @ K @ L2 @ ( product_Pair_int_int @ Q2 @ R ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % eucl_rel_int_remainderI
% 5.41/5.78 thf(fact_9224_eucl__rel__int_Ocases,axiom,
% 5.41/5.78 ! [A12: int,A23: int,A32: product_prod_int_int] :
% 5.41/5.78 ( ( eucl_rel_int @ A12 @ A23 @ A32 )
% 5.41/5.78 => ( ( ( A23 = zero_zero_int )
% 5.41/5.78 => ( A32
% 5.41/5.78 != ( product_Pair_int_int @ zero_zero_int @ A12 ) ) )
% 5.41/5.78 => ( ! [Q3: int] :
% 5.41/5.78 ( ( A32
% 5.41/5.78 = ( product_Pair_int_int @ Q3 @ zero_zero_int ) )
% 5.41/5.78 => ( ( A23 != zero_zero_int )
% 5.41/5.78 => ( A12
% 5.41/5.78 != ( times_times_int @ Q3 @ A23 ) ) ) )
% 5.41/5.78 => ~ ! [R2: int,Q3: int] :
% 5.41/5.78 ( ( A32
% 5.41/5.78 = ( product_Pair_int_int @ Q3 @ R2 ) )
% 5.41/5.78 => ( ( ( sgn_sgn_int @ R2 )
% 5.41/5.78 = ( sgn_sgn_int @ A23 ) )
% 5.41/5.78 => ( ( ord_less_int @ ( abs_abs_int @ R2 ) @ ( abs_abs_int @ A23 ) )
% 5.41/5.78 => ( A12
% 5.41/5.78 != ( plus_plus_int @ ( times_times_int @ Q3 @ A23 ) @ R2 ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % eucl_rel_int.cases
% 5.41/5.78 thf(fact_9225_eucl__rel__int_Osimps,axiom,
% 5.41/5.78 ( eucl_rel_int
% 5.41/5.78 = ( ^ [A1: int,A22: int,A33: product_prod_int_int] :
% 5.41/5.78 ( ? [K2: int] :
% 5.41/5.78 ( ( A1 = K2 )
% 5.41/5.78 & ( A22 = zero_zero_int )
% 5.41/5.78 & ( A33
% 5.41/5.78 = ( product_Pair_int_int @ zero_zero_int @ K2 ) ) )
% 5.41/5.78 | ? [L: int,K2: int,Q5: int] :
% 5.41/5.78 ( ( A1 = K2 )
% 5.41/5.78 & ( A22 = L )
% 5.41/5.78 & ( A33
% 5.41/5.78 = ( product_Pair_int_int @ Q5 @ zero_zero_int ) )
% 5.41/5.78 & ( L != zero_zero_int )
% 5.41/5.78 & ( K2
% 5.41/5.78 = ( times_times_int @ Q5 @ L ) ) )
% 5.41/5.78 | ? [R5: int,L: int,K2: int,Q5: int] :
% 5.41/5.78 ( ( A1 = K2 )
% 5.41/5.78 & ( A22 = L )
% 5.41/5.78 & ( A33
% 5.41/5.78 = ( product_Pair_int_int @ Q5 @ R5 ) )
% 5.41/5.78 & ( ( sgn_sgn_int @ R5 )
% 5.41/5.78 = ( sgn_sgn_int @ L ) )
% 5.41/5.78 & ( ord_less_int @ ( abs_abs_int @ R5 ) @ ( abs_abs_int @ L ) )
% 5.41/5.78 & ( K2
% 5.41/5.78 = ( plus_plus_int @ ( times_times_int @ Q5 @ L ) @ R5 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % eucl_rel_int.simps
% 5.41/5.78 thf(fact_9226_div__noneq__sgn__abs,axiom,
% 5.41/5.78 ! [L2: int,K: int] :
% 5.41/5.78 ( ( L2 != zero_zero_int )
% 5.41/5.78 => ( ( ( sgn_sgn_int @ K )
% 5.41/5.78 != ( sgn_sgn_int @ L2 ) )
% 5.41/5.78 => ( ( divide_divide_int @ K @ L2 )
% 5.41/5.78 = ( minus_minus_int @ ( uminus_uminus_int @ ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) ) )
% 5.41/5.78 @ ( zero_n2684676970156552555ol_int
% 5.41/5.78 @ ~ ( dvd_dvd_int @ L2 @ K ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % div_noneq_sgn_abs
% 5.41/5.78 thf(fact_9227_set__bit__eq,axiom,
% 5.41/5.78 ( bit_se7879613467334960850it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] :
% 5.41/5.78 ( plus_plus_int @ K2
% 5.41/5.78 @ ( times_times_int
% 5.41/5.78 @ ( zero_n2684676970156552555ol_int
% 5.41/5.78 @ ~ ( bit_se1146084159140164899it_int @ K2 @ N2 ) )
% 5.41/5.78 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % set_bit_eq
% 5.41/5.78 thf(fact_9228_unset__bit__eq,axiom,
% 5.41/5.78 ( bit_se4203085406695923979it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( minus_minus_int @ K2 @ ( times_times_int @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K2 @ N2 ) ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % unset_bit_eq
% 5.41/5.78 thf(fact_9229_pi__half,axiom,
% 5.41/5.78 ( ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.78 = ( the_real
% 5.41/5.78 @ ^ [X3: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.41/5.78 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.78 & ( ( cos_real @ X3 )
% 5.41/5.78 = zero_zero_real ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % pi_half
% 5.41/5.78 thf(fact_9230_pi__def,axiom,
% 5.41/5.78 ( pi
% 5.41/5.78 = ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) )
% 5.41/5.78 @ ( the_real
% 5.41/5.78 @ ^ [X3: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ zero_zero_real @ X3 )
% 5.41/5.78 & ( ord_less_eq_real @ X3 @ ( numeral_numeral_real @ ( bit0 @ one ) ) )
% 5.41/5.78 & ( ( cos_real @ X3 )
% 5.41/5.78 = zero_zero_real ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % pi_def
% 5.41/5.78 thf(fact_9231_take__bit__Suc__from__most,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( bit_se2923211474154528505it_int @ ( suc @ N ) @ K )
% 5.41/5.78 = ( plus_plus_int @ ( times_times_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) @ ( zero_n2684676970156552555ol_int @ ( bit_se1146084159140164899it_int @ K @ N ) ) ) @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % take_bit_Suc_from_most
% 5.41/5.78 thf(fact_9232_divide__int__unfold,axiom,
% 5.41/5.78 ! [L2: int,K: int,N: nat,M: nat] :
% 5.41/5.78 ( ( ( ( ( sgn_sgn_int @ L2 )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( ( sgn_sgn_int @ K )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( N = zero_zero_nat ) )
% 5.41/5.78 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.78 = zero_zero_int ) )
% 5.41/5.78 & ( ~ ( ( ( sgn_sgn_int @ L2 )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( ( sgn_sgn_int @ K )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 | ( N = zero_zero_nat ) )
% 5.41/5.78 => ( ( ( ( sgn_sgn_int @ K )
% 5.41/5.78 = ( sgn_sgn_int @ L2 ) )
% 5.41/5.78 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.78 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ M @ N ) ) ) )
% 5.41/5.78 & ( ( ( sgn_sgn_int @ K )
% 5.41/5.78 != ( sgn_sgn_int @ L2 ) )
% 5.41/5.78 => ( ( divide_divide_int @ ( times_times_int @ ( sgn_sgn_int @ K ) @ ( semiri1314217659103216013at_int @ M ) ) @ ( times_times_int @ ( sgn_sgn_int @ L2 ) @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.78 = ( uminus_uminus_int
% 5.41/5.78 @ ( semiri1314217659103216013at_int
% 5.41/5.78 @ ( plus_plus_nat @ ( divide_divide_nat @ M @ N )
% 5.41/5.78 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.78 @ ~ ( dvd_dvd_nat @ N @ M ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divide_int_unfold
% 5.41/5.78 thf(fact_9233_modulo__int__def,axiom,
% 5.41/5.78 ( modulo_modulo_int
% 5.41/5.78 = ( ^ [K2: int,L: int] :
% 5.41/5.78 ( if_int @ ( L = zero_zero_int ) @ K2
% 5.41/5.78 @ ( if_int
% 5.41/5.78 @ ( ( sgn_sgn_int @ K2 )
% 5.41/5.78 = ( sgn_sgn_int @ L ) )
% 5.41/5.78 @ ( times_times_int @ ( sgn_sgn_int @ L ) @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) )
% 5.41/5.78 @ ( times_times_int @ ( sgn_sgn_int @ L )
% 5.41/5.78 @ ( minus_minus_int
% 5.41/5.78 @ ( times_times_int @ ( abs_abs_int @ L )
% 5.41/5.78 @ ( zero_n2684676970156552555ol_int
% 5.41/5.78 @ ~ ( dvd_dvd_int @ L @ K2 ) ) )
% 5.41/5.78 @ ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % modulo_int_def
% 5.41/5.78 thf(fact_9234_divide__int__def,axiom,
% 5.41/5.78 ( divide_divide_int
% 5.41/5.78 = ( ^ [K2: int,L: int] :
% 5.41/5.78 ( if_int @ ( L = zero_zero_int ) @ zero_zero_int
% 5.41/5.78 @ ( if_int
% 5.41/5.78 @ ( ( sgn_sgn_int @ K2 )
% 5.41/5.78 = ( sgn_sgn_int @ L ) )
% 5.41/5.78 @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) ) )
% 5.41/5.78 @ ( uminus_uminus_int
% 5.41/5.78 @ ( semiri1314217659103216013at_int
% 5.41/5.78 @ ( plus_plus_nat @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K2 ) ) @ ( nat2 @ ( abs_abs_int @ L ) ) )
% 5.41/5.78 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.78 @ ~ ( dvd_dvd_int @ L @ K2 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divide_int_def
% 5.41/5.78 thf(fact_9235_powr__int,axiom,
% 5.41/5.78 ! [X: real,I: int] :
% 5.41/5.78 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( ( ord_less_eq_int @ zero_zero_int @ I )
% 5.41/5.78 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.41/5.78 = ( power_power_real @ X @ ( nat2 @ I ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_int @ zero_zero_int @ I )
% 5.41/5.78 => ( ( powr_real @ X @ ( ring_1_of_int_real @ I ) )
% 5.41/5.78 = ( divide_divide_real @ one_one_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ I ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % powr_int
% 5.41/5.78 thf(fact_9236_zero__le__sgn__iff,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ zero_zero_real @ ( sgn_sgn_real @ X ) )
% 5.41/5.78 = ( ord_less_eq_real @ zero_zero_real @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % zero_le_sgn_iff
% 5.41/5.78 thf(fact_9237_sgn__le__0__iff,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( sgn_sgn_real @ X ) @ zero_zero_real )
% 5.41/5.78 = ( ord_less_eq_real @ X @ zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_le_0_iff
% 5.41/5.78 thf(fact_9238_nat__numeral,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( nat2 @ ( numeral_numeral_int @ K ) )
% 5.41/5.78 = ( numeral_numeral_nat @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_numeral
% 5.41/5.78 thf(fact_9239_nat__1,axiom,
% 5.41/5.78 ( ( nat2 @ one_one_int )
% 5.41/5.78 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_1
% 5.41/5.78 thf(fact_9240_nat__le__0,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.41/5.78 => ( ( nat2 @ Z )
% 5.41/5.78 = zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_le_0
% 5.41/5.78 thf(fact_9241_nat__0__iff,axiom,
% 5.41/5.78 ! [I: int] :
% 5.41/5.78 ( ( ( nat2 @ I )
% 5.41/5.78 = zero_zero_nat )
% 5.41/5.78 = ( ord_less_eq_int @ I @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_0_iff
% 5.41/5.78 thf(fact_9242_zless__nat__conj,axiom,
% 5.41/5.78 ! [W: int,Z: int] :
% 5.41/5.78 ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.41/5.78 = ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.78 & ( ord_less_int @ W @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % zless_nat_conj
% 5.41/5.78 thf(fact_9243_nat__neg__numeral,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( nat2 @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % nat_neg_numeral
% 5.41/5.78 thf(fact_9244_nat__zminus__int,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( nat2 @ ( uminus_uminus_int @ ( semiri1314217659103216013at_int @ N ) ) )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % nat_zminus_int
% 5.41/5.78 thf(fact_9245_int__nat__eq,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.41/5.78 = Z ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.41/5.78 = zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_nat_eq
% 5.41/5.78 thf(fact_9246_zero__less__nat__eq,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ ( nat2 @ Z ) )
% 5.41/5.78 = ( ord_less_int @ zero_zero_int @ Z ) ) ).
% 5.41/5.78
% 5.41/5.78 % zero_less_nat_eq
% 5.41/5.78 thf(fact_9247_diff__nat__numeral,axiom,
% 5.41/5.78 ! [V: num,V3: num] :
% 5.41/5.78 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ ( numeral_numeral_nat @ V3 ) )
% 5.41/5.78 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ ( numeral_numeral_int @ V3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % diff_nat_numeral
% 5.41/5.78 thf(fact_9248_nat__eq__numeral__power__cancel__iff,axiom,
% 5.41/5.78 ! [Y: int,X: num,N: nat] :
% 5.41/5.78 ( ( ( nat2 @ Y )
% 5.41/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.41/5.78 = ( Y
% 5.41/5.78 = ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_eq_numeral_power_cancel_iff
% 5.41/5.78 thf(fact_9249_numeral__power__eq__nat__cancel__iff,axiom,
% 5.41/5.78 ! [X: num,N: nat,Y: int] :
% 5.41/5.78 ( ( ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N )
% 5.41/5.78 = ( nat2 @ Y ) )
% 5.41/5.78 = ( ( power_power_int @ ( numeral_numeral_int @ X ) @ N )
% 5.41/5.78 = Y ) ) ).
% 5.41/5.78
% 5.41/5.78 % numeral_power_eq_nat_cancel_iff
% 5.41/5.78 thf(fact_9250_nat__ceiling__le__eq,axiom,
% 5.41/5.78 ! [X: real,A: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) @ A )
% 5.41/5.78 = ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ A ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_ceiling_le_eq
% 5.41/5.78 thf(fact_9251_one__less__nat__eq,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ( ( ord_less_nat @ ( suc @ zero_zero_nat ) @ ( nat2 @ Z ) )
% 5.41/5.78 = ( ord_less_int @ one_one_int @ Z ) ) ).
% 5.41/5.78
% 5.41/5.78 % one_less_nat_eq
% 5.41/5.78 thf(fact_9252_nat__numeral__diff__1,axiom,
% 5.41/5.78 ! [V: num] :
% 5.41/5.78 ( ( minus_minus_nat @ ( numeral_numeral_nat @ V ) @ one_one_nat )
% 5.41/5.78 = ( nat2 @ ( minus_minus_int @ ( numeral_numeral_int @ V ) @ one_one_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_numeral_diff_1
% 5.41/5.78 thf(fact_9253_nat__less__numeral__power__cancel__iff,axiom,
% 5.41/5.78 ! [A: int,X: num,N: nat] :
% 5.41/5.78 ( ( ord_less_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.41/5.78 = ( ord_less_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_less_numeral_power_cancel_iff
% 5.41/5.78 thf(fact_9254_numeral__power__less__nat__cancel__iff,axiom,
% 5.41/5.78 ! [X: num,N: nat,A: int] :
% 5.41/5.78 ( ( ord_less_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.41/5.78 = ( ord_less_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.78
% 5.41/5.78 % numeral_power_less_nat_cancel_iff
% 5.41/5.78 thf(fact_9255_numeral__power__le__nat__cancel__iff,axiom,
% 5.41/5.78 ! [X: num,N: nat,A: int] :
% 5.41/5.78 ( ( ord_less_eq_nat @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) @ ( nat2 @ A ) )
% 5.41/5.78 = ( ord_less_eq_int @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) @ A ) ) ).
% 5.41/5.78
% 5.41/5.78 % numeral_power_le_nat_cancel_iff
% 5.41/5.78 thf(fact_9256_nat__le__numeral__power__cancel__iff,axiom,
% 5.41/5.78 ! [A: int,X: num,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ ( nat2 @ A ) @ ( power_power_nat @ ( numeral_numeral_nat @ X ) @ N ) )
% 5.41/5.78 = ( ord_less_eq_int @ A @ ( power_power_int @ ( numeral_numeral_int @ X ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_le_numeral_power_cancel_iff
% 5.41/5.78 thf(fact_9257_bit__nat__iff,axiom,
% 5.41/5.78 ! [K: int,N: nat] :
% 5.41/5.78 ( ( bit_se1148574629649215175it_nat @ ( nat2 @ K ) @ N )
% 5.41/5.78 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.78 & ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_nat_iff
% 5.41/5.78 thf(fact_9258_not__bit__Suc__0__Suc,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( suc @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % not_bit_Suc_0_Suc
% 5.41/5.78 thf(fact_9259_bit__Suc__0__iff,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.78 = ( N = zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_Suc_0_iff
% 5.41/5.78 thf(fact_9260_nat__zero__as__int,axiom,
% 5.41/5.78 ( zero_zero_nat
% 5.41/5.78 = ( nat2 @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_zero_as_int
% 5.41/5.78 thf(fact_9261_nat__numeral__as__int,axiom,
% 5.41/5.78 ( numeral_numeral_nat
% 5.41/5.78 = ( ^ [I5: num] : ( nat2 @ ( numeral_numeral_int @ I5 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_numeral_as_int
% 5.41/5.78 thf(fact_9262_nat__mono,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ X @ Y )
% 5.41/5.78 => ( ord_less_eq_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_mono
% 5.41/5.78 thf(fact_9263_ex__nat,axiom,
% 5.41/5.78 ( ( ^ [P3: nat > $o] :
% 5.41/5.78 ? [X7: nat] : ( P3 @ X7 ) )
% 5.41/5.78 = ( ^ [P4: nat > $o] :
% 5.41/5.78 ? [X3: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.41/5.78 & ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % ex_nat
% 5.41/5.78 thf(fact_9264_all__nat,axiom,
% 5.41/5.78 ( ( ^ [P3: nat > $o] :
% 5.41/5.78 ! [X7: nat] : ( P3 @ X7 ) )
% 5.41/5.78 = ( ^ [P4: nat > $o] :
% 5.41/5.78 ! [X3: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X3 )
% 5.41/5.78 => ( P4 @ ( nat2 @ X3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % all_nat
% 5.41/5.78 thf(fact_9265_eq__nat__nat__iff,axiom,
% 5.41/5.78 ! [Z: int,Z7: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.41/5.78 => ( ( ( nat2 @ Z )
% 5.41/5.78 = ( nat2 @ Z7 ) )
% 5.41/5.78 = ( Z = Z7 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % eq_nat_nat_iff
% 5.41/5.78 thf(fact_9266_nat__one__as__int,axiom,
% 5.41/5.78 ( one_one_nat
% 5.41/5.78 = ( nat2 @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_one_as_int
% 5.41/5.78 thf(fact_9267_unset__bit__nat__def,axiom,
% 5.41/5.78 ( bit_se4205575877204974255it_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se4203085406695923979it_int @ M3 @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % unset_bit_nat_def
% 5.41/5.78 thf(fact_9268_nat__mask__eq,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( nat2 @ ( bit_se2000444600071755411sk_int @ N ) )
% 5.41/5.78 = ( bit_se2002935070580805687sk_nat @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_mask_eq
% 5.41/5.78 thf(fact_9269_not__bit__Suc__0__numeral,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ~ ( bit_se1148574629649215175it_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % not_bit_Suc_0_numeral
% 5.41/5.78 thf(fact_9270_sgn__root,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( sgn_sgn_real @ ( root @ N @ X ) )
% 5.41/5.78 = ( sgn_sgn_real @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_root
% 5.41/5.78 thf(fact_9271_nat__mono__iff,axiom,
% 5.41/5.78 ! [Z: int,W: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.41/5.78 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_mono_iff
% 5.41/5.78 thf(fact_9272_zless__nat__eq__int__zless,axiom,
% 5.41/5.78 ! [M: nat,Z: int] :
% 5.41/5.78 ( ( ord_less_nat @ M @ ( nat2 @ Z ) )
% 5.41/5.78 = ( ord_less_int @ ( semiri1314217659103216013at_int @ M ) @ Z ) ) ).
% 5.41/5.78
% 5.41/5.78 % zless_nat_eq_int_zless
% 5.41/5.78 thf(fact_9273_nat__le__iff,axiom,
% 5.41/5.78 ! [X: int,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ ( nat2 @ X ) @ N )
% 5.41/5.78 = ( ord_less_eq_int @ X @ ( semiri1314217659103216013at_int @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_le_iff
% 5.41/5.78 thf(fact_9274_int__eq__iff,axiom,
% 5.41/5.78 ! [M: nat,Z: int] :
% 5.41/5.78 ( ( ( semiri1314217659103216013at_int @ M )
% 5.41/5.78 = Z )
% 5.41/5.78 = ( ( M
% 5.41/5.78 = ( nat2 @ Z ) )
% 5.41/5.78 & ( ord_less_eq_int @ zero_zero_int @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_eq_iff
% 5.41/5.78 thf(fact_9275_nat__0__le,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( semiri1314217659103216013at_int @ ( nat2 @ Z ) )
% 5.41/5.78 = Z ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_0_le
% 5.41/5.78 thf(fact_9276_nat__int__add,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) )
% 5.41/5.78 = ( plus_plus_nat @ A @ B ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_int_add
% 5.41/5.78 thf(fact_9277_int__minus,axiom,
% 5.41/5.78 ! [N: nat,M: nat] :
% 5.41/5.78 ( ( semiri1314217659103216013at_int @ ( minus_minus_nat @ N @ M ) )
% 5.41/5.78 = ( semiri1314217659103216013at_int @ ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ N ) @ ( semiri1314217659103216013at_int @ M ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_minus
% 5.41/5.78 thf(fact_9278_nat__abs__mult__distrib,axiom,
% 5.41/5.78 ! [W: int,Z: int] :
% 5.41/5.78 ( ( nat2 @ ( abs_abs_int @ ( times_times_int @ W @ Z ) ) )
% 5.41/5.78 = ( times_times_nat @ ( nat2 @ ( abs_abs_int @ W ) ) @ ( nat2 @ ( abs_abs_int @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_abs_mult_distrib
% 5.41/5.78 thf(fact_9279_and__nat__def,axiom,
% 5.41/5.78 ( bit_se727722235901077358nd_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se725231765392027082nd_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_nat_def
% 5.41/5.78 thf(fact_9280_nat__plus__as__int,axiom,
% 5.41/5.78 ( plus_plus_nat
% 5.41/5.78 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_plus_as_int
% 5.41/5.78 thf(fact_9281_nat__times__as__int,axiom,
% 5.41/5.78 ( times_times_nat
% 5.41/5.78 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( times_times_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_times_as_int
% 5.41/5.78 thf(fact_9282_real__nat__ceiling__ge,axiom,
% 5.41/5.78 ! [X: real] : ( ord_less_eq_real @ X @ ( semiri5074537144036343181t_real @ ( nat2 @ ( archim7802044766580827645g_real @ X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_nat_ceiling_ge
% 5.41/5.78 thf(fact_9283_nat__minus__as__int,axiom,
% 5.41/5.78 ( minus_minus_nat
% 5.41/5.78 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_minus_as_int
% 5.41/5.78 thf(fact_9284_nat__div__as__int,axiom,
% 5.41/5.78 ( divide_divide_nat
% 5.41/5.78 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( divide_divide_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_div_as_int
% 5.41/5.78 thf(fact_9285_nat__mod__as__int,axiom,
% 5.41/5.78 ( modulo_modulo_nat
% 5.41/5.78 = ( ^ [A3: nat,B2: nat] : ( nat2 @ ( modulo_modulo_int @ ( semiri1314217659103216013at_int @ A3 ) @ ( semiri1314217659103216013at_int @ B2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_mod_as_int
% 5.41/5.78 thf(fact_9286_cis__Arg,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( Z != zero_zero_complex )
% 5.41/5.78 => ( ( cis @ ( arg @ Z ) )
% 5.41/5.78 = ( sgn_sgn_complex @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cis_Arg
% 5.41/5.78 thf(fact_9287_sgn__real__def,axiom,
% 5.41/5.78 ( sgn_sgn_real
% 5.41/5.78 = ( ^ [A3: real] : ( if_real @ ( A3 = zero_zero_real ) @ zero_zero_real @ ( if_real @ ( ord_less_real @ zero_zero_real @ A3 ) @ one_one_real @ ( uminus_uminus_real @ one_one_real ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_real_def
% 5.41/5.78 thf(fact_9288_nat__less__eq__zless,axiom,
% 5.41/5.78 ! [W: int,Z: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.41/5.78 => ( ( ord_less_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.41/5.78 = ( ord_less_int @ W @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_less_eq_zless
% 5.41/5.78 thf(fact_9289_nat__le__eq__zle,axiom,
% 5.41/5.78 ! [W: int,Z: int] :
% 5.41/5.78 ( ( ( ord_less_int @ zero_zero_int @ W )
% 5.41/5.78 | ( ord_less_eq_int @ zero_zero_int @ Z ) )
% 5.41/5.78 => ( ( ord_less_eq_nat @ ( nat2 @ W ) @ ( nat2 @ Z ) )
% 5.41/5.78 = ( ord_less_eq_int @ W @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_le_eq_zle
% 5.41/5.78 thf(fact_9290_nat__eq__iff,axiom,
% 5.41/5.78 ! [W: int,M: nat] :
% 5.41/5.78 ( ( ( nat2 @ W )
% 5.41/5.78 = M )
% 5.41/5.78 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.41/5.78 => ( W
% 5.41/5.78 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.41/5.78 => ( M = zero_zero_nat ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_eq_iff
% 5.41/5.78 thf(fact_9291_nat__eq__iff2,axiom,
% 5.41/5.78 ! [M: nat,W: int] :
% 5.41/5.78 ( ( M
% 5.41/5.78 = ( nat2 @ W ) )
% 5.41/5.78 = ( ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.41/5.78 => ( W
% 5.41/5.78 = ( semiri1314217659103216013at_int @ M ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_int @ zero_zero_int @ W )
% 5.41/5.78 => ( M = zero_zero_nat ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_eq_iff2
% 5.41/5.78 thf(fact_9292_split__nat,axiom,
% 5.41/5.78 ! [P: nat > $o,I: int] :
% 5.41/5.78 ( ( P @ ( nat2 @ I ) )
% 5.41/5.78 = ( ! [N2: nat] :
% 5.41/5.78 ( ( I
% 5.41/5.78 = ( semiri1314217659103216013at_int @ N2 ) )
% 5.41/5.78 => ( P @ N2 ) )
% 5.41/5.78 & ( ( ord_less_int @ I @ zero_zero_int )
% 5.41/5.78 => ( P @ zero_zero_nat ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % split_nat
% 5.41/5.78 thf(fact_9293_le__nat__iff,axiom,
% 5.41/5.78 ! [K: int,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.78 => ( ( ord_less_eq_nat @ N @ ( nat2 @ K ) )
% 5.41/5.78 = ( ord_less_eq_int @ ( semiri1314217659103216013at_int @ N ) @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % le_nat_iff
% 5.41/5.78 thf(fact_9294_nat__add__distrib,axiom,
% 5.41/5.78 ! [Z: int,Z7: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.41/5.78 => ( ( nat2 @ ( plus_plus_int @ Z @ Z7 ) )
% 5.41/5.78 = ( plus_plus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_add_distrib
% 5.41/5.78 thf(fact_9295_nat__mult__distrib,axiom,
% 5.41/5.78 ! [Z: int,Z7: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.41/5.78 = ( times_times_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_mult_distrib
% 5.41/5.78 thf(fact_9296_Suc__as__int,axiom,
% 5.41/5.78 ( suc
% 5.41/5.78 = ( ^ [A3: nat] : ( nat2 @ ( plus_plus_int @ ( semiri1314217659103216013at_int @ A3 ) @ one_one_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Suc_as_int
% 5.41/5.78 thf(fact_9297_nat__diff__distrib,axiom,
% 5.41/5.78 ! [Z7: int,Z: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Z7 )
% 5.41/5.78 => ( ( ord_less_eq_int @ Z7 @ Z )
% 5.41/5.78 => ( ( nat2 @ ( minus_minus_int @ Z @ Z7 ) )
% 5.41/5.78 = ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_diff_distrib
% 5.41/5.78 thf(fact_9298_nat__diff__distrib_H,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( ( nat2 @ ( minus_minus_int @ X @ Y ) )
% 5.41/5.78 = ( minus_minus_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_diff_distrib'
% 5.41/5.78 thf(fact_9299_nat__abs__triangle__ineq,axiom,
% 5.41/5.78 ! [K: int,L2: int] : ( ord_less_eq_nat @ ( nat2 @ ( abs_abs_int @ ( plus_plus_int @ K @ L2 ) ) ) @ ( plus_plus_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_abs_triangle_ineq
% 5.41/5.78 thf(fact_9300_nat__div__distrib,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.41/5.78 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_div_distrib
% 5.41/5.78 thf(fact_9301_nat__div__distrib_H,axiom,
% 5.41/5.78 ! [Y: int,X: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( ( nat2 @ ( divide_divide_int @ X @ Y ) )
% 5.41/5.78 = ( divide_divide_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_div_distrib'
% 5.41/5.78 thf(fact_9302_nat__power__eq,axiom,
% 5.41/5.78 ! [Z: int,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( nat2 @ ( power_power_int @ Z @ N ) )
% 5.41/5.78 = ( power_power_nat @ ( nat2 @ Z ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_power_eq
% 5.41/5.78 thf(fact_9303_nat__floor__neg,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ X @ zero_zero_real )
% 5.41/5.78 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.41/5.78 = zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_floor_neg
% 5.41/5.78 thf(fact_9304_nat__mod__distrib,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( ( nat2 @ ( modulo_modulo_int @ X @ Y ) )
% 5.41/5.78 = ( modulo_modulo_nat @ ( nat2 @ X ) @ ( nat2 @ Y ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_mod_distrib
% 5.41/5.78 thf(fact_9305_div__abs__eq__div__nat,axiom,
% 5.41/5.78 ! [K: int,L2: int] :
% 5.41/5.78 ( ( divide_divide_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.41/5.78 = ( semiri1314217659103216013at_int @ ( divide_divide_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % div_abs_eq_div_nat
% 5.41/5.78 thf(fact_9306_floor__eq3,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.41/5.78 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.41/5.78 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.41/5.78 = N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % floor_eq3
% 5.41/5.78 thf(fact_9307_le__nat__floor,axiom,
% 5.41/5.78 ! [X: nat,A: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ X ) @ A )
% 5.41/5.78 => ( ord_less_eq_nat @ X @ ( nat2 @ ( archim6058952711729229775r_real @ A ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % le_nat_floor
% 5.41/5.78 thf(fact_9308_mod__abs__eq__div__nat,axiom,
% 5.41/5.78 ! [K: int,L2: int] :
% 5.41/5.78 ( ( modulo_modulo_int @ ( abs_abs_int @ K ) @ ( abs_abs_int @ L2 ) )
% 5.41/5.78 = ( semiri1314217659103216013at_int @ ( modulo_modulo_nat @ ( nat2 @ ( abs_abs_int @ K ) ) @ ( nat2 @ ( abs_abs_int @ L2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % mod_abs_eq_div_nat
% 5.41/5.78 thf(fact_9309_nat__take__bit__eq,axiom,
% 5.41/5.78 ! [K: int,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.78 => ( ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) )
% 5.41/5.78 = ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_take_bit_eq
% 5.41/5.78 thf(fact_9310_take__bit__nat__eq,axiom,
% 5.41/5.78 ! [K: int,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.78 => ( ( bit_se2925701944663578781it_nat @ N @ ( nat2 @ K ) )
% 5.41/5.78 = ( nat2 @ ( bit_se2923211474154528505it_int @ N @ K ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % take_bit_nat_eq
% 5.41/5.78 thf(fact_9311_nat__2,axiom,
% 5.41/5.78 ( ( nat2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.78 = ( suc @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_2
% 5.41/5.78 thf(fact_9312_sgn__power__injE,axiom,
% 5.41/5.78 ! [A: real,N: nat,X: real,B: real] :
% 5.41/5.78 ( ( ( times_times_real @ ( sgn_sgn_real @ A ) @ ( power_power_real @ ( abs_abs_real @ A ) @ N ) )
% 5.41/5.78 = X )
% 5.41/5.78 => ( ( X
% 5.41/5.78 = ( times_times_real @ ( sgn_sgn_real @ B ) @ ( power_power_real @ ( abs_abs_real @ B ) @ N ) ) )
% 5.41/5.78 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( A = B ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_power_injE
% 5.41/5.78 thf(fact_9313_Suc__nat__eq__nat__zadd1,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( ( suc @ ( nat2 @ Z ) )
% 5.41/5.78 = ( nat2 @ ( plus_plus_int @ one_one_int @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Suc_nat_eq_nat_zadd1
% 5.41/5.78 thf(fact_9314_nat__less__iff,axiom,
% 5.41/5.78 ! [W: int,M: nat] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ W )
% 5.41/5.78 => ( ( ord_less_nat @ ( nat2 @ W ) @ M )
% 5.41/5.78 = ( ord_less_int @ W @ ( semiri1314217659103216013at_int @ M ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_less_iff
% 5.41/5.78 thf(fact_9315_nat__mult__distrib__neg,axiom,
% 5.41/5.78 ! [Z: int,Z7: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ Z @ zero_zero_int )
% 5.41/5.78 => ( ( nat2 @ ( times_times_int @ Z @ Z7 ) )
% 5.41/5.78 = ( times_times_nat @ ( nat2 @ ( uminus_uminus_int @ Z ) ) @ ( nat2 @ ( uminus_uminus_int @ Z7 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_mult_distrib_neg
% 5.41/5.78 thf(fact_9316_nat__abs__int__diff,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( ( ord_less_eq_nat @ A @ B )
% 5.41/5.78 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.41/5.78 = ( minus_minus_nat @ B @ A ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_nat @ A @ B )
% 5.41/5.78 => ( ( nat2 @ ( abs_abs_int @ ( minus_minus_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) )
% 5.41/5.78 = ( minus_minus_nat @ A @ B ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_abs_int_diff
% 5.41/5.78 thf(fact_9317_floor__eq4,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( semiri5074537144036343181t_real @ N ) @ X )
% 5.41/5.78 => ( ( ord_less_real @ X @ ( semiri5074537144036343181t_real @ ( suc @ N ) ) )
% 5.41/5.78 => ( ( nat2 @ ( archim6058952711729229775r_real @ X ) )
% 5.41/5.78 = N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % floor_eq4
% 5.41/5.78 thf(fact_9318_diff__nat__eq__if,axiom,
% 5.41/5.78 ! [Z7: int,Z: int] :
% 5.41/5.78 ( ( ( ord_less_int @ Z7 @ zero_zero_int )
% 5.41/5.78 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.41/5.78 = ( nat2 @ Z ) ) )
% 5.41/5.78 & ( ~ ( ord_less_int @ Z7 @ zero_zero_int )
% 5.41/5.78 => ( ( minus_minus_nat @ ( nat2 @ Z ) @ ( nat2 @ Z7 ) )
% 5.41/5.78 = ( if_nat @ ( ord_less_int @ ( minus_minus_int @ Z @ Z7 ) @ zero_zero_int ) @ zero_zero_nat @ ( nat2 @ ( minus_minus_int @ Z @ Z7 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % diff_nat_eq_if
% 5.41/5.78 thf(fact_9319_bit__nat__def,axiom,
% 5.41/5.78 ( bit_se1148574629649215175it_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.78 ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_nat_def
% 5.41/5.78 thf(fact_9320_root__sgn__power,axiom,
% 5.41/5.78 ! [N: nat,Y: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( root @ N @ ( times_times_real @ ( sgn_sgn_real @ Y ) @ ( power_power_real @ ( abs_abs_real @ Y ) @ N ) ) )
% 5.41/5.78 = Y ) ) ).
% 5.41/5.78
% 5.41/5.78 % root_sgn_power
% 5.41/5.78 thf(fact_9321_sgn__power__root,axiom,
% 5.41/5.78 ! [N: nat,X: real] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( times_times_real @ ( sgn_sgn_real @ ( root @ N @ X ) ) @ ( power_power_real @ ( abs_abs_real @ ( root @ N @ X ) ) @ N ) )
% 5.41/5.78 = X ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_power_root
% 5.41/5.78 thf(fact_9322_nat__dvd__iff,axiom,
% 5.41/5.78 ! [Z: int,M: nat] :
% 5.41/5.78 ( ( dvd_dvd_nat @ ( nat2 @ Z ) @ M )
% 5.41/5.78 = ( ( ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( dvd_dvd_int @ Z @ ( semiri1314217659103216013at_int @ M ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_int @ zero_zero_int @ Z )
% 5.41/5.78 => ( M = zero_zero_nat ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_dvd_iff
% 5.41/5.78 thf(fact_9323_cis__Arg__unique,axiom,
% 5.41/5.78 ! [Z: complex,X: real] :
% 5.41/5.78 ( ( ( sgn_sgn_complex @ Z )
% 5.41/5.78 = ( cis @ X ) )
% 5.41/5.78 => ( ( ord_less_real @ ( uminus_uminus_real @ pi ) @ X )
% 5.41/5.78 => ( ( ord_less_eq_real @ X @ pi )
% 5.41/5.78 => ( ( arg @ Z )
% 5.41/5.78 = X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cis_Arg_unique
% 5.41/5.78 thf(fact_9324_split__root,axiom,
% 5.41/5.78 ! [P: real > $o,N: nat,X: real] :
% 5.41/5.78 ( ( P @ ( root @ N @ X ) )
% 5.41/5.78 = ( ( ( N = zero_zero_nat )
% 5.41/5.78 => ( P @ zero_zero_real ) )
% 5.41/5.78 & ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ! [Y3: real] :
% 5.41/5.78 ( ( ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N ) )
% 5.41/5.78 = X )
% 5.41/5.78 => ( P @ Y3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % split_root
% 5.41/5.78 thf(fact_9325_Arg__correct,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( Z != zero_zero_complex )
% 5.41/5.78 => ( ( ( sgn_sgn_complex @ Z )
% 5.41/5.78 = ( cis @ ( arg @ Z ) ) )
% 5.41/5.78 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ ( arg @ Z ) )
% 5.41/5.78 & ( ord_less_eq_real @ ( arg @ Z ) @ pi ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Arg_correct
% 5.41/5.78 thf(fact_9326_even__nat__iff,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.78 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( nat2 @ K ) )
% 5.41/5.78 = ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % even_nat_iff
% 5.41/5.78 thf(fact_9327_powr__real__of__int,axiom,
% 5.41/5.78 ! [X: real,N: int] :
% 5.41/5.78 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.78 => ( ( ( ord_less_eq_int @ zero_zero_int @ N )
% 5.41/5.78 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.41/5.78 = ( power_power_real @ X @ ( nat2 @ N ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_int @ zero_zero_int @ N )
% 5.41/5.78 => ( ( powr_real @ X @ ( ring_1_of_int_real @ N ) )
% 5.41/5.78 = ( inverse_inverse_real @ ( power_power_real @ X @ ( nat2 @ ( uminus_uminus_int @ N ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % powr_real_of_int
% 5.41/5.78 thf(fact_9328_arctan__inverse,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( X != zero_zero_real )
% 5.41/5.78 => ( ( arctan @ ( divide_divide_real @ one_one_real @ X ) )
% 5.41/5.78 = ( minus_minus_real @ ( divide_divide_real @ ( times_times_real @ ( sgn_sgn_real @ X ) @ pi ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( arctan @ X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % arctan_inverse
% 5.41/5.78 thf(fact_9329_Arg__def,axiom,
% 5.41/5.78 ( arg
% 5.41/5.78 = ( ^ [Z3: complex] :
% 5.41/5.78 ( if_real @ ( Z3 = zero_zero_complex ) @ zero_zero_real
% 5.41/5.78 @ ( fChoice_real
% 5.41/5.78 @ ^ [A3: real] :
% 5.41/5.78 ( ( ( sgn_sgn_complex @ Z3 )
% 5.41/5.78 = ( cis @ A3 ) )
% 5.41/5.78 & ( ord_less_real @ ( uminus_uminus_real @ pi ) @ A3 )
% 5.41/5.78 & ( ord_less_eq_real @ A3 @ pi ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Arg_def
% 5.41/5.78 thf(fact_9330_or__int__unfold,axiom,
% 5.41/5.78 ( bit_se1409905431419307370or_int
% 5.41/5.78 = ( ^ [K2: int,L: int] :
% 5.41/5.78 ( if_int
% 5.41/5.78 @ ( ( K2
% 5.41/5.78 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.78 | ( L
% 5.41/5.78 = ( uminus_uminus_int @ one_one_int ) ) )
% 5.41/5.78 @ ( uminus_uminus_int @ one_one_int )
% 5.41/5.78 @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( ord_max_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_int_unfold
% 5.41/5.78 thf(fact_9331_or__nonnegative__int__iff,axiom,
% 5.41/5.78 ! [K: int,L2: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) )
% 5.41/5.78 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.78 & ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nonnegative_int_iff
% 5.41/5.78 thf(fact_9332_or__negative__int__iff,axiom,
% 5.41/5.78 ! [K: int,L2: int] :
% 5.41/5.78 ( ( ord_less_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ zero_zero_int )
% 5.41/5.78 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.78 | ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_negative_int_iff
% 5.41/5.78 thf(fact_9333_or__minus__numerals_I6_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ one_one_int )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(6)
% 5.41/5.78 thf(fact_9334_or__minus__numerals_I2_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(2)
% 5.41/5.78 thf(fact_9335_bit__or__int__iff,axiom,
% 5.41/5.78 ! [K: int,L2: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( bit_se1409905431419307370or_int @ K @ L2 ) @ N )
% 5.41/5.78 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.41/5.78 | ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_or_int_iff
% 5.41/5.78 thf(fact_9336_or__greater__eq,axiom,
% 5.41/5.78 ! [L2: int,K: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ L2 )
% 5.41/5.78 => ( ord_less_eq_int @ K @ ( bit_se1409905431419307370or_int @ K @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_greater_eq
% 5.41/5.78 thf(fact_9337_OR__lower,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se1409905431419307370or_int @ X @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % OR_lower
% 5.41/5.78 thf(fact_9338_plus__and__or,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ( ( plus_plus_int @ ( bit_se725231765392027082nd_int @ X @ Y ) @ ( bit_se1409905431419307370or_int @ X @ Y ) )
% 5.41/5.78 = ( plus_plus_int @ X @ Y ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_and_or
% 5.41/5.78 thf(fact_9339_OR__upper,axiom,
% 5.41/5.78 ! [X: int,N: nat,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.78 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.78 => ( ord_less_int @ ( bit_se1409905431419307370or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % OR_upper
% 5.41/5.78 thf(fact_9340_or__int__rec,axiom,
% 5.41/5.78 ( bit_se1409905431419307370or_int
% 5.41/5.78 = ( ^ [K2: int,L: int] :
% 5.41/5.78 ( plus_plus_int
% 5.41/5.78 @ ( zero_n2684676970156552555ol_int
% 5.41/5.78 @ ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 )
% 5.41/5.78 | ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) )
% 5.41/5.78 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_int_rec
% 5.41/5.78 thf(fact_9341_or__minus__numerals_I5_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ one_one_int )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(5)
% 5.41/5.78 thf(fact_9342_or__minus__numerals_I1_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ one @ ( bitM @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(1)
% 5.41/5.78 thf(fact_9343_cis__multiple__2pi,axiom,
% 5.41/5.78 ! [N: real] :
% 5.41/5.78 ( ( member_real @ N @ ring_1_Ints_real )
% 5.41/5.78 => ( ( cis @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.41/5.78 = one_one_complex ) ) ).
% 5.41/5.78
% 5.41/5.78 % cis_multiple_2pi
% 5.41/5.78 thf(fact_9344_or__nat__numerals_I2_J,axiom,
% 5.41/5.78 ! [Y: num] :
% 5.41/5.78 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nat_numerals(2)
% 5.41/5.78 thf(fact_9345_or__nat__numerals_I4_J,axiom,
% 5.41/5.78 ! [X: num] :
% 5.41/5.78 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nat_numerals(4)
% 5.41/5.78 thf(fact_9346_or__nat__numerals_I3_J,axiom,
% 5.41/5.78 ! [X: num] :
% 5.41/5.78 ( ( bit_se1412395901928357646or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nat_numerals(3)
% 5.41/5.78 thf(fact_9347_or__nat__numerals_I1_J,axiom,
% 5.41/5.78 ! [Y: num] :
% 5.41/5.78 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nat_numerals(1)
% 5.41/5.78 thf(fact_9348_or__minus__numerals_I8_J,axiom,
% 5.41/5.78 ! [N: num,M: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(8)
% 5.41/5.78 thf(fact_9349_or__minus__numerals_I4_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bit0 @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(4)
% 5.41/5.78 thf(fact_9350_or__minus__numerals_I7_J,axiom,
% 5.41/5.78 ! [N: num,M: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(7)
% 5.41/5.78 thf(fact_9351_or__minus__numerals_I3_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ ( bitM @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_numerals(3)
% 5.41/5.78 thf(fact_9352_or__not__num__neg_Osimps_I1_J,axiom,
% 5.41/5.78 ( ( bit_or_not_num_neg @ one @ one )
% 5.41/5.78 = one ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(1)
% 5.41/5.78 thf(fact_9353_or__not__num__neg_Osimps_I4_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ one )
% 5.41/5.78 = ( bit0 @ one ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(4)
% 5.41/5.78 thf(fact_9354_or__not__num__neg_Osimps_I6_J,axiom,
% 5.41/5.78 ! [N: num,M: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit1 @ M ) )
% 5.41/5.78 = ( bit0 @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(6)
% 5.41/5.78 thf(fact_9355_or__not__num__neg_Osimps_I7_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ one )
% 5.41/5.78 = one ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(7)
% 5.41/5.78 thf(fact_9356_or__not__num__neg_Osimps_I3_J,axiom,
% 5.41/5.78 ! [M: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ one @ ( bit1 @ M ) )
% 5.41/5.78 = ( bit1 @ M ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(3)
% 5.41/5.78 thf(fact_9357_or__not__num__neg_Osimps_I5_J,axiom,
% 5.41/5.78 ! [N: num,M: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ ( bit0 @ N ) @ ( bit0 @ M ) )
% 5.41/5.78 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(5)
% 5.41/5.78 thf(fact_9358_or__not__num__neg_Osimps_I9_J,axiom,
% 5.41/5.78 ! [N: num,M: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit1 @ M ) )
% 5.41/5.78 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(9)
% 5.41/5.78 thf(fact_9359_or__nat__def,axiom,
% 5.41/5.78 ( bit_se1412395901928357646or_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se1409905431419307370or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nat_def
% 5.41/5.78 thf(fact_9360_or__not__num__neg_Osimps_I2_J,axiom,
% 5.41/5.78 ! [M: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ one @ ( bit0 @ M ) )
% 5.41/5.78 = ( bit1 @ M ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(2)
% 5.41/5.78 thf(fact_9361_or__not__num__neg_Osimps_I8_J,axiom,
% 5.41/5.78 ! [N: num,M: num] :
% 5.41/5.78 ( ( bit_or_not_num_neg @ ( bit1 @ N ) @ ( bit0 @ M ) )
% 5.41/5.78 = ( bitM @ ( bit_or_not_num_neg @ N @ M ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.simps(8)
% 5.41/5.78 thf(fact_9362_sin__times__pi__eq__0,axiom,
% 5.41/5.78 ! [X: real] :
% 5.41/5.78 ( ( ( sin_real @ ( times_times_real @ X @ pi ) )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 = ( member_real @ X @ ring_1_Ints_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % sin_times_pi_eq_0
% 5.41/5.78 thf(fact_9363_or__not__num__neg_Oelims,axiom,
% 5.41/5.78 ! [X: num,Xa2: num,Y: num] :
% 5.41/5.78 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( ( X = one )
% 5.41/5.78 => ( ( Xa2 = one )
% 5.41/5.78 => ( Y != one ) ) )
% 5.41/5.78 => ( ( ( X = one )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit0 @ M4 ) )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( bit1 @ M4 ) ) ) )
% 5.41/5.78 => ( ( ( X = one )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( bit1 @ M4 ) ) ) )
% 5.41/5.78 => ( ( ? [N3: num] :
% 5.41/5.78 ( X
% 5.41/5.78 = ( bit0 @ N3 ) )
% 5.41/5.78 => ( ( Xa2 = one )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( bit0 @ one ) ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit0 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit0 @ M4 ) )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit0 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.41/5.78 => ( ( ? [N3: num] :
% 5.41/5.78 ( X
% 5.41/5.78 = ( bit1 @ N3 ) )
% 5.41/5.78 => ( ( Xa2 = one )
% 5.41/5.78 => ( Y != one ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit1 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit0 @ M4 ) )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) )
% 5.41/5.78 => ~ ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit1 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.elims
% 5.41/5.78 thf(fact_9364_sin__integer__2pi,axiom,
% 5.41/5.78 ! [N: real] :
% 5.41/5.78 ( ( member_real @ N @ ring_1_Ints_real )
% 5.41/5.78 => ( ( sin_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.41/5.78 = zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % sin_integer_2pi
% 5.41/5.78 thf(fact_9365_cos__integer__2pi,axiom,
% 5.41/5.78 ! [N: real] :
% 5.41/5.78 ( ( member_real @ N @ ring_1_Ints_real )
% 5.41/5.78 => ( ( cos_real @ ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) @ N ) )
% 5.41/5.78 = one_one_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % cos_integer_2pi
% 5.41/5.78 thf(fact_9366_or__Suc__0__eq,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se1412395901928357646or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_Suc_0_eq
% 5.41/5.78 thf(fact_9367_Suc__0__or__eq,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se1412395901928357646or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.78 = ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Suc_0_or_eq
% 5.41/5.78 thf(fact_9368_or__nat__rec,axiom,
% 5.41/5.78 ( bit_se1412395901928357646or_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.78 ( plus_plus_nat
% 5.41/5.78 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.78 @ ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 )
% 5.41/5.78 | ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.41/5.78 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nat_rec
% 5.41/5.78 thf(fact_9369_or__nat__unfold,axiom,
% 5.41/5.78 ( bit_se1412395901928357646or_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( ord_max_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se1412395901928357646or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_nat_unfold
% 5.41/5.78 thf(fact_9370_or__not__num__neg_Opelims,axiom,
% 5.41/5.78 ! [X: num,Xa2: num,Y: num] :
% 5.41/5.78 ( ( ( bit_or_not_num_neg @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ X @ Xa2 ) )
% 5.41/5.78 => ( ( ( X = one )
% 5.41/5.78 => ( ( Xa2 = one )
% 5.41/5.78 => ( ( Y = one )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ one ) ) ) ) )
% 5.41/5.78 => ( ( ( X = one )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit0 @ M4 ) )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit0 @ M4 ) ) ) ) ) )
% 5.41/5.78 => ( ( ( X = one )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ one @ ( bit1 @ M4 ) ) ) ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit0 @ N3 ) )
% 5.41/5.78 => ( ( Xa2 = one )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( bit0 @ one ) )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ one ) ) ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit0 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit0 @ M4 ) )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit0 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( bit0 @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit0 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit1 @ N3 ) )
% 5.41/5.78 => ( ( Xa2 = one )
% 5.41/5.78 => ( ( Y = one )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ one ) ) ) ) )
% 5.41/5.78 => ( ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit1 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit0 @ M4 ) )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit0 @ M4 ) ) ) ) ) )
% 5.41/5.78 => ~ ! [N3: num] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( bit1 @ N3 ) )
% 5.41/5.78 => ! [M4: num] :
% 5.41/5.78 ( ( Xa2
% 5.41/5.78 = ( bit1 @ M4 ) )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( bitM @ ( bit_or_not_num_neg @ N3 @ M4 ) ) )
% 5.41/5.78 => ~ ( accp_P3113834385874906142um_num @ bit_or3848514188828904588eg_rel @ ( product_Pair_num_num @ ( bit1 @ N3 ) @ ( bit1 @ M4 ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_num_neg.pelims
% 5.41/5.78 thf(fact_9371_xor__Suc__0__eq,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se6528837805403552850or_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.78 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.78 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_Suc_0_eq
% 5.41/5.78 thf(fact_9372_Suc__0__xor__eq,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.78 = ( minus_minus_nat @ ( plus_plus_nat @ N @ ( zero_n2687167440665602831ol_nat @ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.78 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.78 @ ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Suc_0_xor_eq
% 5.41/5.78 thf(fact_9373_xor__nat__numerals_I1_J,axiom,
% 5.41/5.78 ! [Y: num] :
% 5.41/5.78 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit0 @ Y ) ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit1 @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nat_numerals(1)
% 5.41/5.78 thf(fact_9374_xor__nat__numerals_I2_J,axiom,
% 5.41/5.78 ! [Y: num] :
% 5.41/5.78 ( ( bit_se6528837805403552850or_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ ( bit1 @ Y ) ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit0 @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nat_numerals(2)
% 5.41/5.78 thf(fact_9375_xor__nat__numerals_I3_J,axiom,
% 5.41/5.78 ! [X: num] :
% 5.41/5.78 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit0 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit1 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nat_numerals(3)
% 5.41/5.78 thf(fact_9376_xor__nat__numerals_I4_J,axiom,
% 5.41/5.78 ! [X: num] :
% 5.41/5.78 ( ( bit_se6528837805403552850or_nat @ ( numeral_numeral_nat @ ( bit1 @ X ) ) @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit0 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nat_numerals(4)
% 5.41/5.78 thf(fact_9377_xor__nat__unfold,axiom,
% 5.41/5.78 ( bit_se6528837805403552850or_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( if_nat @ ( M3 = zero_zero_nat ) @ N2 @ ( if_nat @ ( N2 = zero_zero_nat ) @ M3 @ ( plus_plus_nat @ ( modulo_modulo_nat @ ( plus_plus_nat @ ( modulo_modulo_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( modulo_modulo_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nat_unfold
% 5.41/5.78 thf(fact_9378_xor__nat__rec,axiom,
% 5.41/5.78 ( bit_se6528837805403552850or_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.78 ( plus_plus_nat
% 5.41/5.78 @ ( zero_n2687167440665602831ol_nat
% 5.41/5.78 @ ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ M3 ) )
% 5.41/5.78 != ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) )
% 5.41/5.78 @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( bit_se6528837805403552850or_nat @ ( divide_divide_nat @ M3 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( divide_divide_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nat_rec
% 5.41/5.78 thf(fact_9379_horner__sum__of__bool__2__less,axiom,
% 5.41/5.78 ! [Bs: list_o] : ( ord_less_int @ ( groups9116527308978886569_o_int @ zero_n2684676970156552555ol_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ Bs ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( size_size_list_o @ Bs ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % horner_sum_of_bool_2_less
% 5.41/5.78 thf(fact_9380_push__bit__nonnegative__int__iff,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.41/5.78 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % push_bit_nonnegative_int_iff
% 5.41/5.78 thf(fact_9381_push__bit__negative__int__iff,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( ord_less_int @ ( bit_se545348938243370406it_int @ N @ K ) @ zero_zero_int )
% 5.41/5.78 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % push_bit_negative_int_iff
% 5.41/5.78 thf(fact_9382_concat__bit__of__zero__1,axiom,
% 5.41/5.78 ! [N: nat,L2: int] :
% 5.41/5.78 ( ( bit_concat_bit @ N @ zero_zero_int @ L2 )
% 5.41/5.78 = ( bit_se545348938243370406it_int @ N @ L2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % concat_bit_of_zero_1
% 5.41/5.78 thf(fact_9383_xor__nonnegative__int__iff,axiom,
% 5.41/5.78 ! [K: int,L2: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) )
% 5.41/5.78 = ( ( ord_less_eq_int @ zero_zero_int @ K )
% 5.41/5.78 = ( ord_less_eq_int @ zero_zero_int @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nonnegative_int_iff
% 5.41/5.78 thf(fact_9384_xor__negative__int__iff,axiom,
% 5.41/5.78 ! [K: int,L2: int] :
% 5.41/5.78 ( ( ord_less_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ zero_zero_int )
% 5.41/5.78 = ( ( ord_less_int @ K @ zero_zero_int )
% 5.41/5.78 != ( ord_less_int @ L2 @ zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_negative_int_iff
% 5.41/5.78 thf(fact_9385_push__bit__of__Suc__0,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se547839408752420682it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % push_bit_of_Suc_0
% 5.41/5.78 thf(fact_9386_bit__xor__int__iff,axiom,
% 5.41/5.78 ! [K: int,L2: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( bit_se6526347334894502574or_int @ K @ L2 ) @ N )
% 5.41/5.78 = ( ( bit_se1146084159140164899it_int @ K @ N )
% 5.41/5.78 != ( bit_se1146084159140164899it_int @ L2 @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_xor_int_iff
% 5.41/5.78 thf(fact_9387_flip__bit__int__def,axiom,
% 5.41/5.78 ( bit_se2159334234014336723it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( bit_se6526347334894502574or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % flip_bit_int_def
% 5.41/5.78 thf(fact_9388_push__bit__nat__eq,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( bit_se547839408752420682it_nat @ N @ ( nat2 @ K ) )
% 5.41/5.78 = ( nat2 @ ( bit_se545348938243370406it_int @ N @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % push_bit_nat_eq
% 5.41/5.78 thf(fact_9389_XOR__lower,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( ord_less_eq_int @ zero_zero_int @ ( bit_se6526347334894502574or_int @ X @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % XOR_lower
% 5.41/5.78 thf(fact_9390_set__bit__nat__def,axiom,
% 5.41/5.78 ( bit_se7882103937844011126it_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( bit_se1412395901928357646or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % set_bit_nat_def
% 5.41/5.78 thf(fact_9391_flip__bit__nat__def,axiom,
% 5.41/5.78 ( bit_se2161824704523386999it_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( bit_se6528837805403552850or_nat @ N2 @ ( bit_se547839408752420682it_nat @ M3 @ one_one_nat ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % flip_bit_nat_def
% 5.41/5.78 thf(fact_9392_bit__push__bit__iff__int,axiom,
% 5.41/5.78 ! [M: nat,K: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( bit_se545348938243370406it_int @ M @ K ) @ N )
% 5.41/5.78 = ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.78 & ( bit_se1146084159140164899it_int @ K @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_push_bit_iff_int
% 5.41/5.78 thf(fact_9393_xor__nat__def,axiom,
% 5.41/5.78 ( bit_se6528837805403552850or_nat
% 5.41/5.78 = ( ^ [M3: nat,N2: nat] : ( nat2 @ ( bit_se6526347334894502574or_int @ ( semiri1314217659103216013at_int @ M3 ) @ ( semiri1314217659103216013at_int @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_nat_def
% 5.41/5.78 thf(fact_9394_bit__push__bit__iff__nat,axiom,
% 5.41/5.78 ! [M: nat,Q2: nat,N: nat] :
% 5.41/5.78 ( ( bit_se1148574629649215175it_nat @ ( bit_se547839408752420682it_nat @ M @ Q2 ) @ N )
% 5.41/5.78 = ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.78 & ( bit_se1148574629649215175it_nat @ Q2 @ ( minus_minus_nat @ N @ M ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_push_bit_iff_nat
% 5.41/5.78 thf(fact_9395_concat__bit__eq,axiom,
% 5.41/5.78 ( bit_concat_bit
% 5.41/5.78 = ( ^ [N2: nat,K2: int,L: int] : ( plus_plus_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % concat_bit_eq
% 5.41/5.78 thf(fact_9396_concat__bit__def,axiom,
% 5.41/5.78 ( bit_concat_bit
% 5.41/5.78 = ( ^ [N2: nat,K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se2923211474154528505it_int @ N2 @ K2 ) @ ( bit_se545348938243370406it_int @ N2 @ L ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % concat_bit_def
% 5.41/5.78 thf(fact_9397_set__bit__int__def,axiom,
% 5.41/5.78 ( bit_se7879613467334960850it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( bit_se1409905431419307370or_int @ K2 @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % set_bit_int_def
% 5.41/5.78 thf(fact_9398_push__bit__nat__def,axiom,
% 5.41/5.78 ( bit_se547839408752420682it_nat
% 5.41/5.78 = ( ^ [N2: nat,M3: nat] : ( times_times_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % push_bit_nat_def
% 5.41/5.78 thf(fact_9399_push__bit__int__def,axiom,
% 5.41/5.78 ( bit_se545348938243370406it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( times_times_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % push_bit_int_def
% 5.41/5.78 thf(fact_9400_push__bit__minus__one,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se545348938243370406it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % push_bit_minus_one
% 5.41/5.78 thf(fact_9401_XOR__upper,axiom,
% 5.41/5.78 ! [X: int,N: nat,Y: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_int @ X @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.78 => ( ( ord_less_int @ Y @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) )
% 5.41/5.78 => ( ord_less_int @ ( bit_se6526347334894502574or_int @ X @ Y ) @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % XOR_upper
% 5.41/5.78 thf(fact_9402_xor__int__rec,axiom,
% 5.41/5.78 ( bit_se6526347334894502574or_int
% 5.41/5.78 = ( ^ [K2: int,L: int] :
% 5.41/5.78 ( plus_plus_int
% 5.41/5.78 @ ( zero_n2684676970156552555ol_int
% 5.41/5.78 @ ( ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) )
% 5.41/5.78 != ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ L ) ) ) )
% 5.41/5.78 @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_int_rec
% 5.41/5.78 thf(fact_9403_xor__int__unfold,axiom,
% 5.41/5.78 ( bit_se6526347334894502574or_int
% 5.41/5.78 = ( ^ [K2: int,L: int] :
% 5.41/5.78 ( if_int
% 5.41/5.78 @ ( K2
% 5.41/5.78 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.78 @ ( bit_ri7919022796975470100ot_int @ L )
% 5.41/5.78 @ ( if_int
% 5.41/5.78 @ ( L
% 5.41/5.78 = ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.78 @ ( bit_ri7919022796975470100ot_int @ K2 )
% 5.41/5.78 @ ( if_int @ ( K2 = zero_zero_int ) @ L @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( plus_plus_int @ ( abs_abs_int @ ( minus_minus_int @ ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( modulo_modulo_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se6526347334894502574or_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) @ ( divide_divide_int @ L @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_int_unfold
% 5.41/5.78 thf(fact_9404_Sum__Ico__nat,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( groups3542108847815614940at_nat
% 5.41/5.78 @ ^ [X3: nat] : X3
% 5.41/5.78 @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.41/5.78 = ( divide_divide_nat @ ( minus_minus_nat @ ( times_times_nat @ N @ ( minus_minus_nat @ N @ one_one_nat ) ) @ ( times_times_nat @ M @ ( minus_minus_nat @ M @ one_one_nat ) ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Sum_Ico_nat
% 5.41/5.78 thf(fact_9405_finite__atLeastLessThan,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_atLeastLessThan
% 5.41/5.78 thf(fact_9406_not__negative__int__iff,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( ord_less_int @ ( bit_ri7919022796975470100ot_int @ K ) @ zero_zero_int )
% 5.41/5.78 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % not_negative_int_iff
% 5.41/5.78 thf(fact_9407_not__nonnegative__int__iff,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.41/5.78 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % not_nonnegative_int_iff
% 5.41/5.78 thf(fact_9408_atLeastLessThan__singleton,axiom,
% 5.41/5.78 ! [M: nat] :
% 5.41/5.78 ( ( set_or4665077453230672383an_nat @ M @ ( suc @ M ) )
% 5.41/5.78 = ( insert_nat @ M @ bot_bot_set_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastLessThan_singleton
% 5.41/5.78 thf(fact_9409_or__minus__minus__numerals,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_minus_minus_numerals
% 5.41/5.78 thf(fact_9410_and__minus__minus__numerals,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ ( bit_se1409905431419307370or_int @ ( minus_minus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( minus_minus_int @ ( numeral_numeral_int @ N ) @ one_one_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_minus_minus_numerals
% 5.41/5.78 thf(fact_9411_bit__not__int__iff,axiom,
% 5.41/5.78 ! [K: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ K ) @ N )
% 5.41/5.78 = ( ~ ( bit_se1146084159140164899it_int @ K @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_not_int_iff
% 5.41/5.78 thf(fact_9412_all__nat__less__eq,axiom,
% 5.41/5.78 ! [N: nat,P: nat > $o] :
% 5.41/5.78 ( ( ! [M3: nat] :
% 5.41/5.78 ( ( ord_less_nat @ M3 @ N )
% 5.41/5.78 => ( P @ M3 ) ) )
% 5.41/5.78 = ( ! [X3: nat] :
% 5.41/5.78 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.41/5.78 => ( P @ X3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % all_nat_less_eq
% 5.41/5.78 thf(fact_9413_ex__nat__less__eq,axiom,
% 5.41/5.78 ! [N: nat,P: nat > $o] :
% 5.41/5.78 ( ( ? [M3: nat] :
% 5.41/5.78 ( ( ord_less_nat @ M3 @ N )
% 5.41/5.78 & ( P @ M3 ) ) )
% 5.41/5.78 = ( ? [X3: nat] :
% 5.41/5.78 ( ( member_nat @ X3 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.41/5.78 & ( P @ X3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % ex_nat_less_eq
% 5.41/5.78 thf(fact_9414_atLeastLessThanSuc__atLeastAtMost,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] :
% 5.41/5.78 ( ( set_or4665077453230672383an_nat @ L2 @ ( suc @ U ) )
% 5.41/5.78 = ( set_or1269000886237332187st_nat @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastLessThanSuc_atLeastAtMost
% 5.41/5.78 thf(fact_9415_lessThan__atLeast0,axiom,
% 5.41/5.78 ( set_ord_lessThan_nat
% 5.41/5.78 = ( set_or4665077453230672383an_nat @ zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % lessThan_atLeast0
% 5.41/5.78 thf(fact_9416_atLeastLessThan0,axiom,
% 5.41/5.78 ! [M: nat] :
% 5.41/5.78 ( ( set_or4665077453230672383an_nat @ M @ zero_zero_nat )
% 5.41/5.78 = bot_bot_set_nat ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastLessThan0
% 5.41/5.78 thf(fact_9417_or__int__def,axiom,
% 5.41/5.78 ( bit_se1409905431419307370or_int
% 5.41/5.78 = ( ^ [K2: int,L: int] : ( bit_ri7919022796975470100ot_int @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ ( bit_ri7919022796975470100ot_int @ L ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_int_def
% 5.41/5.78 thf(fact_9418_not__int__def,axiom,
% 5.41/5.78 ( bit_ri7919022796975470100ot_int
% 5.41/5.78 = ( ^ [K2: int] : ( minus_minus_int @ ( uminus_uminus_int @ K2 ) @ one_one_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % not_int_def
% 5.41/5.78 thf(fact_9419_and__not__numerals_I1_J,axiom,
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.41/5.78 = zero_zero_int ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(1)
% 5.41/5.78 thf(fact_9420_or__not__numerals_I1_J,axiom,
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(1)
% 5.41/5.78 thf(fact_9421_atLeast0__lessThan__Suc,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.41/5.78 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeast0_lessThan_Suc
% 5.41/5.78 thf(fact_9422_unset__bit__int__def,axiom,
% 5.41/5.78 ( bit_se4203085406695923979it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ ( bit_se545348938243370406it_int @ N2 @ one_one_int ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % unset_bit_int_def
% 5.41/5.78 thf(fact_9423_xor__int__def,axiom,
% 5.41/5.78 ( bit_se6526347334894502574or_int
% 5.41/5.78 = ( ^ [K2: int,L: int] : ( bit_se1409905431419307370or_int @ ( bit_se725231765392027082nd_int @ K2 @ ( bit_ri7919022796975470100ot_int @ L ) ) @ ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ K2 ) @ L ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_int_def
% 5.41/5.78 thf(fact_9424_subset__eq__atLeast0__lessThan__finite,axiom,
% 5.41/5.78 ! [N4: set_nat,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.41/5.78 => ( finite_finite_nat @ N4 ) ) ).
% 5.41/5.78
% 5.41/5.78 % subset_eq_atLeast0_lessThan_finite
% 5.41/5.78 thf(fact_9425_not__int__div__2,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( divide_divide_int @ ( bit_ri7919022796975470100ot_int @ K ) @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % not_int_div_2
% 5.41/5.78 thf(fact_9426_even__not__iff__int,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ K ) )
% 5.41/5.78 = ( ~ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % even_not_iff_int
% 5.41/5.78 thf(fact_9427_and__not__numerals_I4_J,axiom,
% 5.41/5.78 ! [M: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.41/5.78 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(4)
% 5.41/5.78 thf(fact_9428_and__not__numerals_I2_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = one_one_int ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(2)
% 5.41/5.78 thf(fact_9429_or__not__numerals_I2_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(2)
% 5.41/5.78 thf(fact_9430_or__not__numerals_I4_J,axiom,
% 5.41/5.78 ! [M: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(4)
% 5.41/5.78 thf(fact_9431_bit__minus__int__iff,axiom,
% 5.41/5.78 ! [K: int,N: nat] :
% 5.41/5.78 ( ( bit_se1146084159140164899it_int @ ( uminus_uminus_int @ K ) @ N )
% 5.41/5.78 = ( bit_se1146084159140164899it_int @ ( bit_ri7919022796975470100ot_int @ ( minus_minus_int @ K @ one_one_int ) ) @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_minus_int_iff
% 5.41/5.78 thf(fact_9432_int__numeral__or__not__num__neg,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_numeral_or_not_num_neg
% 5.41/5.78 thf(fact_9433_int__numeral__not__or__num__neg,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit_or_not_num_neg @ N @ M ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_numeral_not_or_num_neg
% 5.41/5.78 thf(fact_9434_numeral__or__not__num__eq,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( numeral_numeral_int @ ( bit_or_not_num_neg @ M @ N ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % numeral_or_not_num_eq
% 5.41/5.78 thf(fact_9435_atLeastLessThanSuc,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.78 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.41/5.78 = ( insert_nat @ N @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_nat @ M @ N )
% 5.41/5.78 => ( ( set_or4665077453230672383an_nat @ M @ ( suc @ N ) )
% 5.41/5.78 = bot_bot_set_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastLessThanSuc
% 5.41/5.78 thf(fact_9436_prod__Suc__Suc__fact,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N ) )
% 5.41/5.78 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % prod_Suc_Suc_fact
% 5.41/5.78 thf(fact_9437_prod__Suc__fact,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( groups708209901874060359at_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.41/5.78 = ( semiri1408675320244567234ct_nat @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % prod_Suc_fact
% 5.41/5.78 thf(fact_9438_and__not__numerals_I5_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(5)
% 5.41/5.78 thf(fact_9439_and__not__numerals_I7_J,axiom,
% 5.41/5.78 ! [M: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.41/5.78 = ( numeral_numeral_int @ ( bit0 @ M ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(7)
% 5.41/5.78 thf(fact_9440_or__not__numerals_I3_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(3)
% 5.41/5.78 thf(fact_9441_and__not__numerals_I3_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ one_one_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = zero_zero_int ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(3)
% 5.41/5.78 thf(fact_9442_or__not__numerals_I7_J,axiom,
% 5.41/5.78 ! [M: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ one_one_int ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(7)
% 5.41/5.78 thf(fact_9443_atLeastLessThan__nat__numeral,axiom,
% 5.41/5.78 ! [M: nat,K: num] :
% 5.41/5.78 ( ( ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.41/5.78 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.41/5.78 = ( insert_nat @ ( pred_numeral @ K ) @ ( set_or4665077453230672383an_nat @ M @ ( pred_numeral @ K ) ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_nat @ M @ ( pred_numeral @ K ) )
% 5.41/5.78 => ( ( set_or4665077453230672383an_nat @ M @ ( numeral_numeral_nat @ K ) )
% 5.41/5.78 = bot_bot_set_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastLessThan_nat_numeral
% 5.41/5.78 thf(fact_9444_and__not__numerals_I9_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(9)
% 5.41/5.78 thf(fact_9445_and__not__numerals_I6_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(6)
% 5.41/5.78 thf(fact_9446_or__not__numerals_I6_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(6)
% 5.41/5.78 thf(fact_9447_or__not__numerals_I5_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit0 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(5)
% 5.41/5.78 thf(fact_9448_atLeast1__lessThan__eq__remove0,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( set_or4665077453230672383an_nat @ ( suc @ zero_zero_nat ) @ N )
% 5.41/5.78 = ( minus_minus_set_nat @ ( set_ord_lessThan_nat @ N ) @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeast1_lessThan_eq_remove0
% 5.41/5.78 thf(fact_9449_and__not__numerals_I8_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % and_not_numerals(8)
% 5.41/5.78 thf(fact_9450_or__not__numerals_I9_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.78 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(9)
% 5.41/5.78 thf(fact_9451_or__not__numerals_I8_J,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ ( bit1 @ M ) ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.78 = ( plus_plus_int @ one_one_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_se1409905431419307370or_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % or_not_numerals(8)
% 5.41/5.78 thf(fact_9452_not__int__rec,axiom,
% 5.41/5.78 ( bit_ri7919022796975470100ot_int
% 5.41/5.78 = ( ^ [K2: int] : ( plus_plus_int @ ( zero_n2684676970156552555ol_int @ ( dvd_dvd_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ K2 ) ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( bit_ri7919022796975470100ot_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % not_int_rec
% 5.41/5.78 thf(fact_9453_sum__power2,axiom,
% 5.41/5.78 ! [K: nat] :
% 5.41/5.78 ( ( groups3542108847815614940at_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ K ) )
% 5.41/5.78 = ( minus_minus_nat @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K ) @ one_one_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % sum_power2
% 5.41/5.78 thf(fact_9454_Chebyshev__sum__upper__nat,axiom,
% 5.41/5.78 ! [N: nat,A: nat > nat,B: nat > nat] :
% 5.41/5.78 ( ! [I4: nat,J2: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.41/5.78 => ( ( ord_less_nat @ J2 @ N )
% 5.41/5.78 => ( ord_less_eq_nat @ ( A @ I4 ) @ ( A @ J2 ) ) ) )
% 5.41/5.78 => ( ! [I4: nat,J2: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ I4 @ J2 )
% 5.41/5.78 => ( ( ord_less_nat @ J2 @ N )
% 5.41/5.78 => ( ord_less_eq_nat @ ( B @ J2 ) @ ( B @ I4 ) ) ) )
% 5.41/5.78 => ( ord_less_eq_nat
% 5.41/5.78 @ ( times_times_nat @ N
% 5.41/5.78 @ ( groups3542108847815614940at_nat
% 5.41/5.78 @ ^ [I5: nat] : ( times_times_nat @ ( A @ I5 ) @ ( B @ I5 ) )
% 5.41/5.78 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) )
% 5.41/5.78 @ ( times_times_nat @ ( groups3542108847815614940at_nat @ A @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) @ ( groups3542108847815614940at_nat @ B @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Chebyshev_sum_upper_nat
% 5.41/5.78 thf(fact_9455_finite__atLeastLessThan__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_atLeastLessThan_int
% 5.41/5.78 thf(fact_9456_finite__atLeastZeroLessThan__int,axiom,
% 5.41/5.78 ! [U: int] : ( finite_finite_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_atLeastZeroLessThan_int
% 5.41/5.78 thf(fact_9457_atLeastLessThanPlusOne__atLeastAtMost__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( set_or4662586982721622107an_int @ L2 @ ( plus_plus_int @ U @ one_one_int ) )
% 5.41/5.78 = ( set_or1266510415728281911st_int @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastLessThanPlusOne_atLeastAtMost_int
% 5.41/5.78 thf(fact_9458_Cauchy__iff2,axiom,
% 5.41/5.78 ( topolo4055970368930404560y_real
% 5.41/5.78 = ( ^ [X2: nat > real] :
% 5.41/5.78 ! [J3: nat] :
% 5.41/5.78 ? [M8: nat] :
% 5.41/5.78 ! [M3: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ M8 @ M3 )
% 5.41/5.78 => ! [N2: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ M8 @ N2 )
% 5.41/5.78 => ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ ( X2 @ M3 ) @ ( X2 @ N2 ) ) ) @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ J3 ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Cauchy_iff2
% 5.41/5.78 thf(fact_9459_VEBT_Osize_I3_J,axiom,
% 5.41/5.78 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.41/5.78 ( ( size_size_VEBT_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.41/5.78 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ size_size_VEBT_VEBT @ X13 ) @ ( size_size_VEBT_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % VEBT.size(3)
% 5.41/5.78 thf(fact_9460_VEBT_Osize__gen_I1_J,axiom,
% 5.41/5.78 ! [X11: option4927543243414619207at_nat,X12: nat,X13: list_VEBT_VEBT,X14: vEBT_VEBT] :
% 5.41/5.78 ( ( vEBT_size_VEBT @ ( vEBT_Node @ X11 @ X12 @ X13 @ X14 ) )
% 5.41/5.78 = ( plus_plus_nat @ ( plus_plus_nat @ ( size_list_VEBT_VEBT @ vEBT_size_VEBT @ X13 ) @ ( vEBT_size_VEBT @ X14 ) ) @ ( suc @ zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % VEBT.size_gen(1)
% 5.41/5.78 thf(fact_9461_valid__eq,axiom,
% 5.41/5.78 vEBT_VEBT_valid = vEBT_invar_vebt ).
% 5.41/5.78
% 5.41/5.78 % valid_eq
% 5.41/5.78 thf(fact_9462_valid__eq1,axiom,
% 5.41/5.78 ! [T: vEBT_VEBT,D: nat] :
% 5.41/5.78 ( ( vEBT_invar_vebt @ T @ D )
% 5.41/5.78 => ( vEBT_VEBT_valid @ T @ D ) ) ).
% 5.41/5.78
% 5.41/5.78 % valid_eq1
% 5.41/5.78 thf(fact_9463_valid__eq2,axiom,
% 5.41/5.78 ! [T: vEBT_VEBT,D: nat] :
% 5.41/5.78 ( ( vEBT_VEBT_valid @ T @ D )
% 5.41/5.78 => ( vEBT_invar_vebt @ T @ D ) ) ).
% 5.41/5.78
% 5.41/5.78 % valid_eq2
% 5.41/5.78 thf(fact_9464_VEBT__internal_Ovalid_H_Osimps_I1_J,axiom,
% 5.41/5.78 ! [Uu: $o,Uv: $o,D: nat] :
% 5.41/5.78 ( ( vEBT_VEBT_valid @ ( vEBT_Leaf @ Uu @ Uv ) @ D )
% 5.41/5.78 = ( D = one_one_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % VEBT_internal.valid'.simps(1)
% 5.41/5.78 thf(fact_9465_VEBT_Osize__gen_I2_J,axiom,
% 5.41/5.78 ! [X21: $o,X222: $o] :
% 5.41/5.78 ( ( vEBT_size_VEBT @ ( vEBT_Leaf @ X21 @ X222 ) )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % VEBT.size_gen(2)
% 5.41/5.78 thf(fact_9466_Code__Target__Int_Opositive__def,axiom,
% 5.41/5.78 code_Target_positive = numeral_numeral_int ).
% 5.41/5.78
% 5.41/5.78 % Code_Target_Int.positive_def
% 5.41/5.78 thf(fact_9467_csqrt_Osimps_I1_J,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( re @ ( csqrt @ Z ) )
% 5.41/5.78 = ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt.simps(1)
% 5.41/5.78 thf(fact_9468_complex__Re__numeral,axiom,
% 5.41/5.78 ! [V: num] :
% 5.41/5.78 ( ( re @ ( numera6690914467698888265omplex @ V ) )
% 5.41/5.78 = ( numeral_numeral_real @ V ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_Re_numeral
% 5.41/5.78 thf(fact_9469_Re__divide__numeral,axiom,
% 5.41/5.78 ! [Z: complex,W: num] :
% 5.41/5.78 ( ( re @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.78 = ( divide_divide_real @ ( re @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_divide_numeral
% 5.41/5.78 thf(fact_9470_cos__Arg__i__mult__zero,axiom,
% 5.41/5.78 ! [Y: complex] :
% 5.41/5.78 ( ( Y != zero_zero_complex )
% 5.41/5.78 => ( ( ( re @ Y )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 => ( ( cos_real @ ( arg @ Y ) )
% 5.41/5.78 = zero_zero_real ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cos_Arg_i_mult_zero
% 5.41/5.78 thf(fact_9471_imaginary__unit_Osimps_I1_J,axiom,
% 5.41/5.78 ( ( re @ imaginary_unit )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % imaginary_unit.simps(1)
% 5.41/5.78 thf(fact_9472_complex__Re__le__cmod,axiom,
% 5.41/5.78 ! [X: complex] : ( ord_less_eq_real @ ( re @ X ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_Re_le_cmod
% 5.41/5.78 thf(fact_9473_zero__complex_Osimps_I1_J,axiom,
% 5.41/5.78 ( ( re @ zero_zero_complex )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % zero_complex.simps(1)
% 5.41/5.78 thf(fact_9474_one__complex_Osimps_I1_J,axiom,
% 5.41/5.78 ( ( re @ one_one_complex )
% 5.41/5.78 = one_one_real ) ).
% 5.41/5.78
% 5.41/5.78 % one_complex.simps(1)
% 5.41/5.78 thf(fact_9475_plus__complex_Osimps_I1_J,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( re @ ( plus_plus_complex @ X @ Y ) )
% 5.41/5.78 = ( plus_plus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_complex.simps(1)
% 5.41/5.78 thf(fact_9476_scaleR__complex_Osimps_I1_J,axiom,
% 5.41/5.78 ! [R: real,X: complex] :
% 5.41/5.78 ( ( re @ ( real_V2046097035970521341omplex @ R @ X ) )
% 5.41/5.78 = ( times_times_real @ R @ ( re @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % scaleR_complex.simps(1)
% 5.41/5.78 thf(fact_9477_minus__complex_Osimps_I1_J,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( re @ ( minus_minus_complex @ X @ Y ) )
% 5.41/5.78 = ( minus_minus_real @ ( re @ X ) @ ( re @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_complex.simps(1)
% 5.41/5.78 thf(fact_9478_abs__Re__le__cmod,axiom,
% 5.41/5.78 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % abs_Re_le_cmod
% 5.41/5.78 thf(fact_9479_Re__csqrt,axiom,
% 5.41/5.78 ! [Z: complex] : ( ord_less_eq_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_csqrt
% 5.41/5.78 thf(fact_9480_cmod__plus__Re__le__0__iff,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ zero_zero_real )
% 5.41/5.78 = ( ( re @ Z )
% 5.41/5.78 = ( uminus_uminus_real @ ( real_V1022390504157884413omplex @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cmod_plus_Re_le_0_iff
% 5.41/5.78 thf(fact_9481_cos__n__Re__cis__pow__n,axiom,
% 5.41/5.78 ! [N: nat,A: real] :
% 5.41/5.78 ( ( cos_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.41/5.78 = ( re @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cos_n_Re_cis_pow_n
% 5.41/5.78 thf(fact_9482_csqrt_Ocode,axiom,
% 5.41/5.78 ( csqrt
% 5.41/5.78 = ( ^ [Z3: complex] :
% 5.41/5.78 ( complex2 @ ( sqrt @ ( divide_divide_real @ ( plus_plus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.78 @ ( times_times_real
% 5.41/5.78 @ ( if_real
% 5.41/5.78 @ ( ( im @ Z3 )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 @ one_one_real
% 5.41/5.78 @ ( sgn_sgn_real @ ( im @ Z3 ) ) )
% 5.41/5.78 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z3 ) @ ( re @ Z3 ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt.code
% 5.41/5.78 thf(fact_9483_csqrt_Osimps_I2_J,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( im @ ( csqrt @ Z ) )
% 5.41/5.78 = ( times_times_real
% 5.41/5.78 @ ( if_real
% 5.41/5.78 @ ( ( im @ Z )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 @ one_one_real
% 5.41/5.78 @ ( sgn_sgn_real @ ( im @ Z ) ) )
% 5.41/5.78 @ ( sqrt @ ( divide_divide_real @ ( minus_minus_real @ ( real_V1022390504157884413omplex @ Z ) @ ( re @ Z ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt.simps(2)
% 5.41/5.78 thf(fact_9484_csqrt__of__real__nonpos,axiom,
% 5.41/5.78 ! [X: complex] :
% 5.41/5.78 ( ( ( im @ X )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 => ( ( ord_less_eq_real @ ( re @ X ) @ zero_zero_real )
% 5.41/5.78 => ( ( csqrt @ X )
% 5.41/5.78 = ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( sqrt @ ( abs_abs_real @ ( re @ X ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt_of_real_nonpos
% 5.41/5.78 thf(fact_9485_complex__Im__fact,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( im @ ( semiri5044797733671781792omplex @ N ) )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % complex_Im_fact
% 5.41/5.78 thf(fact_9486_complex__Im__of__int,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ( ( im @ ( ring_17405671764205052669omplex @ Z ) )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % complex_Im_of_int
% 5.41/5.78 thf(fact_9487_complex__Im__of__nat,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( im @ ( semiri8010041392384452111omplex @ N ) )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % complex_Im_of_nat
% 5.41/5.78 thf(fact_9488_Im__complex__of__real,axiom,
% 5.41/5.78 ! [Z: real] :
% 5.41/5.78 ( ( im @ ( real_V4546457046886955230omplex @ Z ) )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % Im_complex_of_real
% 5.41/5.78 thf(fact_9489_Im__power__real,axiom,
% 5.41/5.78 ! [X: complex,N: nat] :
% 5.41/5.78 ( ( ( im @ X )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 => ( ( im @ ( power_power_complex @ X @ N ) )
% 5.41/5.78 = zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_power_real
% 5.41/5.78 thf(fact_9490_complex__Im__numeral,axiom,
% 5.41/5.78 ! [V: num] :
% 5.41/5.78 ( ( im @ ( numera6690914467698888265omplex @ V ) )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % complex_Im_numeral
% 5.41/5.78 thf(fact_9491_Im__i__times,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( im @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.41/5.78 = ( re @ Z ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_i_times
% 5.41/5.78 thf(fact_9492_Re__power__real,axiom,
% 5.41/5.78 ! [X: complex,N: nat] :
% 5.41/5.78 ( ( ( im @ X )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 => ( ( re @ ( power_power_complex @ X @ N ) )
% 5.41/5.78 = ( power_power_real @ ( re @ X ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_power_real
% 5.41/5.78 thf(fact_9493_Re__i__times,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( re @ ( times_times_complex @ imaginary_unit @ Z ) )
% 5.41/5.78 = ( uminus_uminus_real @ ( im @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_i_times
% 5.41/5.78 thf(fact_9494_Im__divide__numeral,axiom,
% 5.41/5.78 ! [Z: complex,W: num] :
% 5.41/5.78 ( ( im @ ( divide1717551699836669952omplex @ Z @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.78 = ( divide_divide_real @ ( im @ Z ) @ ( numeral_numeral_real @ W ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_divide_numeral
% 5.41/5.78 thf(fact_9495_csqrt__of__real__nonneg,axiom,
% 5.41/5.78 ! [X: complex] :
% 5.41/5.78 ( ( ( im @ X )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 => ( ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) )
% 5.41/5.78 => ( ( csqrt @ X )
% 5.41/5.78 = ( real_V4546457046886955230omplex @ ( sqrt @ ( re @ X ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt_of_real_nonneg
% 5.41/5.78 thf(fact_9496_csqrt__minus,axiom,
% 5.41/5.78 ! [X: complex] :
% 5.41/5.78 ( ( ( ord_less_real @ ( im @ X ) @ zero_zero_real )
% 5.41/5.78 | ( ( ( im @ X )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( re @ X ) ) ) )
% 5.41/5.78 => ( ( csqrt @ ( uminus1482373934393186551omplex @ X ) )
% 5.41/5.78 = ( times_times_complex @ imaginary_unit @ ( csqrt @ X ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt_minus
% 5.41/5.78 thf(fact_9497_imaginary__unit_Osimps_I2_J,axiom,
% 5.41/5.78 ( ( im @ imaginary_unit )
% 5.41/5.78 = one_one_real ) ).
% 5.41/5.78
% 5.41/5.78 % imaginary_unit.simps(2)
% 5.41/5.78 thf(fact_9498_zero__complex_Osimps_I2_J,axiom,
% 5.41/5.78 ( ( im @ zero_zero_complex )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % zero_complex.simps(2)
% 5.41/5.78 thf(fact_9499_one__complex_Osimps_I2_J,axiom,
% 5.41/5.78 ( ( im @ one_one_complex )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % one_complex.simps(2)
% 5.41/5.78 thf(fact_9500_plus__complex_Osimps_I2_J,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( im @ ( plus_plus_complex @ X @ Y ) )
% 5.41/5.78 = ( plus_plus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_complex.simps(2)
% 5.41/5.78 thf(fact_9501_scaleR__complex_Osimps_I2_J,axiom,
% 5.41/5.78 ! [R: real,X: complex] :
% 5.41/5.78 ( ( im @ ( real_V2046097035970521341omplex @ R @ X ) )
% 5.41/5.78 = ( times_times_real @ R @ ( im @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % scaleR_complex.simps(2)
% 5.41/5.78 thf(fact_9502_minus__complex_Osimps_I2_J,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( im @ ( minus_minus_complex @ X @ Y ) )
% 5.41/5.78 = ( minus_minus_real @ ( im @ X ) @ ( im @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_complex.simps(2)
% 5.41/5.78 thf(fact_9503_complex__is__Int__iff,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( member_complex @ Z @ ring_1_Ints_complex )
% 5.41/5.78 = ( ( ( im @ Z )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 & ? [I5: int] :
% 5.41/5.78 ( ( re @ Z )
% 5.41/5.78 = ( ring_1_of_int_real @ I5 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_is_Int_iff
% 5.41/5.78 thf(fact_9504_abs__Im__le__cmod,axiom,
% 5.41/5.78 ! [X: complex] : ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( real_V1022390504157884413omplex @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % abs_Im_le_cmod
% 5.41/5.78 thf(fact_9505_times__complex_Osimps_I2_J,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( im @ ( times_times_complex @ X @ Y ) )
% 5.41/5.78 = ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % times_complex.simps(2)
% 5.41/5.78 thf(fact_9506_cmod__eq__Re,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( ( im @ Z )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 => ( ( real_V1022390504157884413omplex @ Z )
% 5.41/5.78 = ( abs_abs_real @ ( re @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cmod_eq_Re
% 5.41/5.78 thf(fact_9507_cmod__eq__Im,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( ( re @ Z )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 => ( ( real_V1022390504157884413omplex @ Z )
% 5.41/5.78 = ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cmod_eq_Im
% 5.41/5.78 thf(fact_9508_Im__eq__0,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( ( abs_abs_real @ ( re @ Z ) )
% 5.41/5.78 = ( real_V1022390504157884413omplex @ Z ) )
% 5.41/5.78 => ( ( im @ Z )
% 5.41/5.78 = zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_eq_0
% 5.41/5.78 thf(fact_9509_cmod__Re__le__iff,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( ( im @ X )
% 5.41/5.78 = ( im @ Y ) )
% 5.41/5.78 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.41/5.78 = ( ord_less_eq_real @ ( abs_abs_real @ ( re @ X ) ) @ ( abs_abs_real @ ( re @ Y ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cmod_Re_le_iff
% 5.41/5.78 thf(fact_9510_cmod__Im__le__iff,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( ( re @ X )
% 5.41/5.78 = ( re @ Y ) )
% 5.41/5.78 => ( ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ X ) @ ( real_V1022390504157884413omplex @ Y ) )
% 5.41/5.78 = ( ord_less_eq_real @ ( abs_abs_real @ ( im @ X ) ) @ ( abs_abs_real @ ( im @ Y ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cmod_Im_le_iff
% 5.41/5.78 thf(fact_9511_times__complex_Osimps_I1_J,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( re @ ( times_times_complex @ X @ Y ) )
% 5.41/5.78 = ( minus_minus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % times_complex.simps(1)
% 5.41/5.78 thf(fact_9512_plus__complex_Ocode,axiom,
% 5.41/5.78 ( plus_plus_complex
% 5.41/5.78 = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( plus_plus_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( plus_plus_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_complex.code
% 5.41/5.78 thf(fact_9513_scaleR__complex_Ocode,axiom,
% 5.41/5.78 ( real_V2046097035970521341omplex
% 5.41/5.78 = ( ^ [R5: real,X3: complex] : ( complex2 @ ( times_times_real @ R5 @ ( re @ X3 ) ) @ ( times_times_real @ R5 @ ( im @ X3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % scaleR_complex.code
% 5.41/5.78 thf(fact_9514_minus__complex_Ocode,axiom,
% 5.41/5.78 ( minus_minus_complex
% 5.41/5.78 = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( minus_minus_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( minus_minus_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_complex.code
% 5.41/5.78 thf(fact_9515_csqrt__principal,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( ord_less_real @ zero_zero_real @ ( re @ ( csqrt @ Z ) ) )
% 5.41/5.78 | ( ( ( re @ ( csqrt @ Z ) )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( im @ ( csqrt @ Z ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt_principal
% 5.41/5.78 thf(fact_9516_cmod__le,axiom,
% 5.41/5.78 ! [Z: complex] : ( ord_less_eq_real @ ( real_V1022390504157884413omplex @ Z ) @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cmod_le
% 5.41/5.78 thf(fact_9517_sin__n__Im__cis__pow__n,axiom,
% 5.41/5.78 ! [N: nat,A: real] :
% 5.41/5.78 ( ( sin_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ A ) )
% 5.41/5.78 = ( im @ ( power_power_complex @ ( cis @ A ) @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sin_n_Im_cis_pow_n
% 5.41/5.78 thf(fact_9518_Re__exp,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( re @ ( exp_complex @ Z ) )
% 5.41/5.78 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( cos_real @ ( im @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_exp
% 5.41/5.78 thf(fact_9519_Im__exp,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( im @ ( exp_complex @ Z ) )
% 5.41/5.78 = ( times_times_real @ ( exp_real @ ( re @ Z ) ) @ ( sin_real @ ( im @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_exp
% 5.41/5.78 thf(fact_9520_complex__eq,axiom,
% 5.41/5.78 ! [A: complex] :
% 5.41/5.78 ( A
% 5.41/5.78 = ( plus_plus_complex @ ( real_V4546457046886955230omplex @ ( re @ A ) ) @ ( times_times_complex @ imaginary_unit @ ( real_V4546457046886955230omplex @ ( im @ A ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_eq
% 5.41/5.78 thf(fact_9521_times__complex_Ocode,axiom,
% 5.41/5.78 ( times_times_complex
% 5.41/5.78 = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( minus_minus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y3 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % times_complex.code
% 5.41/5.78 thf(fact_9522_exp__eq__polar,axiom,
% 5.41/5.78 ( exp_complex
% 5.41/5.78 = ( ^ [Z3: complex] : ( times_times_complex @ ( real_V4546457046886955230omplex @ ( exp_real @ ( re @ Z3 ) ) ) @ ( cis @ ( im @ Z3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % exp_eq_polar
% 5.41/5.78 thf(fact_9523_cmod__power2,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.78 = ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cmod_power2
% 5.41/5.78 thf(fact_9524_Im__power2,axiom,
% 5.41/5.78 ! [X: complex] :
% 5.41/5.78 ( ( im @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.78 = ( times_times_real @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ X ) ) @ ( im @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_power2
% 5.41/5.78 thf(fact_9525_Re__power2,axiom,
% 5.41/5.78 ! [X: complex] :
% 5.41/5.78 ( ( re @ ( power_power_complex @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.78 = ( minus_minus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_power2
% 5.41/5.78 thf(fact_9526_complex__eq__0,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( Z = zero_zero_complex )
% 5.41/5.78 = ( ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.78 = zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_eq_0
% 5.41/5.78 thf(fact_9527_norm__complex__def,axiom,
% 5.41/5.78 ( real_V1022390504157884413omplex
% 5.41/5.78 = ( ^ [Z3: complex] : ( sqrt @ ( plus_plus_real @ ( power_power_real @ ( re @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % norm_complex_def
% 5.41/5.78 thf(fact_9528_inverse__complex_Osimps_I1_J,axiom,
% 5.41/5.78 ! [X: complex] :
% 5.41/5.78 ( ( re @ ( invers8013647133539491842omplex @ X ) )
% 5.41/5.78 = ( divide_divide_real @ ( re @ X ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % inverse_complex.simps(1)
% 5.41/5.78 thf(fact_9529_complex__neq__0,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( Z != zero_zero_complex )
% 5.41/5.78 = ( ord_less_real @ zero_zero_real @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_neq_0
% 5.41/5.78 thf(fact_9530_Re__divide,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( re @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.41/5.78 = ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( im @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_divide
% 5.41/5.78 thf(fact_9531_csqrt__unique,axiom,
% 5.41/5.78 ! [W: complex,Z: complex] :
% 5.41/5.78 ( ( ( power_power_complex @ W @ ( numeral_numeral_nat @ ( bit0 @ one ) ) )
% 5.41/5.78 = Z )
% 5.41/5.78 => ( ( ( ord_less_real @ zero_zero_real @ ( re @ W ) )
% 5.41/5.78 | ( ( ( re @ W )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( im @ W ) ) ) )
% 5.41/5.78 => ( ( csqrt @ Z )
% 5.41/5.78 = W ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt_unique
% 5.41/5.78 thf(fact_9532_csqrt__square,axiom,
% 5.41/5.78 ! [B: complex] :
% 5.41/5.78 ( ( ( ord_less_real @ zero_zero_real @ ( re @ B ) )
% 5.41/5.78 | ( ( ( re @ B )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 & ( ord_less_eq_real @ zero_zero_real @ ( im @ B ) ) ) )
% 5.41/5.78 => ( ( csqrt @ ( power_power_complex @ B @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.78 = B ) ) ).
% 5.41/5.78
% 5.41/5.78 % csqrt_square
% 5.41/5.78 thf(fact_9533_inverse__complex_Osimps_I2_J,axiom,
% 5.41/5.78 ! [X: complex] :
% 5.41/5.78 ( ( im @ ( invers8013647133539491842omplex @ X ) )
% 5.41/5.78 = ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % inverse_complex.simps(2)
% 5.41/5.78 thf(fact_9534_Im__divide,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( im @ ( divide1717551699836669952omplex @ X @ Y ) )
% 5.41/5.78 = ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X ) @ ( re @ Y ) ) @ ( times_times_real @ ( re @ X ) @ ( im @ Y ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_divide
% 5.41/5.78 thf(fact_9535_complex__abs__le__norm,axiom,
% 5.41/5.78 ! [Z: complex] : ( ord_less_eq_real @ ( plus_plus_real @ ( abs_abs_real @ ( re @ Z ) ) @ ( abs_abs_real @ ( im @ Z ) ) ) @ ( times_times_real @ ( sqrt @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( real_V1022390504157884413omplex @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_abs_le_norm
% 5.41/5.78 thf(fact_9536_complex__unit__circle,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( Z != zero_zero_complex )
% 5.41/5.78 => ( ( plus_plus_real @ ( power_power_real @ ( divide_divide_real @ ( re @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( divide_divide_real @ ( im @ Z ) @ ( real_V1022390504157884413omplex @ Z ) ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.78 = one_one_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_unit_circle
% 5.41/5.78 thf(fact_9537_inverse__complex_Ocode,axiom,
% 5.41/5.78 ( invers8013647133539491842omplex
% 5.41/5.78 = ( ^ [X3: complex] : ( complex2 @ ( divide_divide_real @ ( re @ X3 ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( uminus_uminus_real @ ( im @ X3 ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ X3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % inverse_complex.code
% 5.41/5.78 thf(fact_9538_Complex__divide,axiom,
% 5.41/5.78 ( divide1717551699836669952omplex
% 5.41/5.78 = ( ^ [X3: complex,Y3: complex] : ( complex2 @ ( divide_divide_real @ ( plus_plus_real @ ( times_times_real @ ( re @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( im @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( divide_divide_real @ ( minus_minus_real @ ( times_times_real @ ( im @ X3 ) @ ( re @ Y3 ) ) @ ( times_times_real @ ( re @ X3 ) @ ( im @ Y3 ) ) ) @ ( plus_plus_real @ ( power_power_real @ ( re @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Y3 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Complex_divide
% 5.41/5.78 thf(fact_9539_Im__Reals__divide,axiom,
% 5.41/5.78 ! [R: complex,Z: complex] :
% 5.41/5.78 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.41/5.78 => ( ( im @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.41/5.78 = ( divide_divide_real @ ( times_times_real @ ( uminus_uminus_real @ ( re @ R ) ) @ ( im @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_Reals_divide
% 5.41/5.78 thf(fact_9540_Re__Reals__divide,axiom,
% 5.41/5.78 ! [R: complex,Z: complex] :
% 5.41/5.78 ( ( member_complex @ R @ real_V2521375963428798218omplex )
% 5.41/5.78 => ( ( re @ ( divide1717551699836669952omplex @ R @ Z ) )
% 5.41/5.78 = ( divide_divide_real @ ( times_times_real @ ( re @ R ) @ ( re @ Z ) ) @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_Reals_divide
% 5.41/5.78 thf(fact_9541_imaginary__eq__real__iff,axiom,
% 5.41/5.78 ! [Y: complex,X: complex] :
% 5.41/5.78 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.41/5.78 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.41/5.78 => ( ( ( times_times_complex @ imaginary_unit @ Y )
% 5.41/5.78 = X )
% 5.41/5.78 = ( ( X = zero_zero_complex )
% 5.41/5.78 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % imaginary_eq_real_iff
% 5.41/5.78 thf(fact_9542_real__eq__imaginary__iff,axiom,
% 5.41/5.78 ! [Y: complex,X: complex] :
% 5.41/5.78 ( ( member_complex @ Y @ real_V2521375963428798218omplex )
% 5.41/5.78 => ( ( member_complex @ X @ real_V2521375963428798218omplex )
% 5.41/5.78 => ( ( X
% 5.41/5.78 = ( times_times_complex @ imaginary_unit @ Y ) )
% 5.41/5.78 = ( ( X = zero_zero_complex )
% 5.41/5.78 & ( Y = zero_zero_complex ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % real_eq_imaginary_iff
% 5.41/5.78 thf(fact_9543_complex__is__Real__iff,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( member_complex @ Z @ real_V2521375963428798218omplex )
% 5.41/5.78 = ( ( im @ Z )
% 5.41/5.78 = zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_is_Real_iff
% 5.41/5.78 thf(fact_9544_Complex__in__Reals,axiom,
% 5.41/5.78 ! [X: real] : ( member_complex @ ( complex2 @ X @ zero_zero_real ) @ real_V2521375963428798218omplex ) ).
% 5.41/5.78
% 5.41/5.78 % Complex_in_Reals
% 5.41/5.78 thf(fact_9545_complex__diff__cnj,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( minus_minus_complex @ Z @ ( cnj @ Z ) )
% 5.41/5.78 = ( times_times_complex @ ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( im @ Z ) ) ) @ imaginary_unit ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_diff_cnj
% 5.41/5.78 thf(fact_9546_complex__mult__cnj,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( times_times_complex @ Z @ ( cnj @ Z ) )
% 5.41/5.78 = ( real_V4546457046886955230omplex @ ( plus_plus_real @ ( power_power_real @ ( re @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ ( power_power_real @ ( im @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_mult_cnj
% 5.41/5.78 thf(fact_9547_complex__cnj__mult,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( cnj @ ( times_times_complex @ X @ Y ) )
% 5.41/5.78 = ( times_times_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_mult
% 5.41/5.78 thf(fact_9548_complex__cnj__zero,axiom,
% 5.41/5.78 ( ( cnj @ zero_zero_complex )
% 5.41/5.78 = zero_zero_complex ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_zero
% 5.41/5.78 thf(fact_9549_complex__cnj__zero__iff,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( ( cnj @ Z )
% 5.41/5.78 = zero_zero_complex )
% 5.41/5.78 = ( Z = zero_zero_complex ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_zero_iff
% 5.41/5.78 thf(fact_9550_complex__cnj__one__iff,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( ( cnj @ Z )
% 5.41/5.78 = one_one_complex )
% 5.41/5.78 = ( Z = one_one_complex ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_one_iff
% 5.41/5.78 thf(fact_9551_complex__cnj__one,axiom,
% 5.41/5.78 ( ( cnj @ one_one_complex )
% 5.41/5.78 = one_one_complex ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_one
% 5.41/5.78 thf(fact_9552_complex__cnj__power,axiom,
% 5.41/5.78 ! [X: complex,N: nat] :
% 5.41/5.78 ( ( cnj @ ( power_power_complex @ X @ N ) )
% 5.41/5.78 = ( power_power_complex @ ( cnj @ X ) @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_power
% 5.41/5.78 thf(fact_9553_complex__cnj__add,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( cnj @ ( plus_plus_complex @ X @ Y ) )
% 5.41/5.78 = ( plus_plus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_add
% 5.41/5.78 thf(fact_9554_complex__cnj__numeral,axiom,
% 5.41/5.78 ! [W: num] :
% 5.41/5.78 ( ( cnj @ ( numera6690914467698888265omplex @ W ) )
% 5.41/5.78 = ( numera6690914467698888265omplex @ W ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_numeral
% 5.41/5.78 thf(fact_9555_complex__cnj__diff,axiom,
% 5.41/5.78 ! [X: complex,Y: complex] :
% 5.41/5.78 ( ( cnj @ ( minus_minus_complex @ X @ Y ) )
% 5.41/5.78 = ( minus_minus_complex @ ( cnj @ X ) @ ( cnj @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_diff
% 5.41/5.78 thf(fact_9556_complex__cnj__neg__numeral,axiom,
% 5.41/5.78 ! [W: num] :
% 5.41/5.78 ( ( cnj @ ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) )
% 5.41/5.78 = ( uminus1482373934393186551omplex @ ( numera6690914467698888265omplex @ W ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_cnj_neg_numeral
% 5.41/5.78 thf(fact_9557_complex__In__mult__cnj__zero,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( im @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.41/5.78 = zero_zero_real ) ).
% 5.41/5.78
% 5.41/5.78 % complex_In_mult_cnj_zero
% 5.41/5.78 thf(fact_9558_Re__complex__div__eq__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ( re @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 = ( ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.41/5.78 = zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_complex_div_eq_0
% 5.41/5.78 thf(fact_9559_Im__complex__div__eq__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ( im @ ( divide1717551699836669952omplex @ A @ B ) )
% 5.41/5.78 = zero_zero_real )
% 5.41/5.78 = ( ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) )
% 5.41/5.78 = zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_complex_div_eq_0
% 5.41/5.78 thf(fact_9560_complex__mod__sqrt__Re__mult__cnj,axiom,
% 5.41/5.78 ( real_V1022390504157884413omplex
% 5.41/5.78 = ( ^ [Z3: complex] : ( sqrt @ ( re @ ( times_times_complex @ Z3 @ ( cnj @ Z3 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_mod_sqrt_Re_mult_cnj
% 5.41/5.78 thf(fact_9561_Re__complex__div__gt__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.41/5.78 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_complex_div_gt_0
% 5.41/5.78 thf(fact_9562_Re__complex__div__lt__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.41/5.78 = ( ord_less_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_complex_div_lt_0
% 5.41/5.78 thf(fact_9563_Re__complex__div__ge__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_eq_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.41/5.78 = ( ord_less_eq_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_complex_div_ge_0
% 5.41/5.78 thf(fact_9564_Re__complex__div__le__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.41/5.78 = ( ord_less_eq_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Re_complex_div_le_0
% 5.41/5.78 thf(fact_9565_Im__complex__div__gt__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.41/5.78 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_complex_div_gt_0
% 5.41/5.78 thf(fact_9566_Im__complex__div__lt__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.41/5.78 = ( ord_less_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_complex_div_lt_0
% 5.41/5.78 thf(fact_9567_Im__complex__div__ge__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_eq_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.41/5.78 = ( ord_less_eq_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_complex_div_ge_0
% 5.41/5.78 thf(fact_9568_Im__complex__div__le__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) @ zero_zero_real )
% 5.41/5.78 = ( ord_less_eq_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) @ zero_zero_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % Im_complex_div_le_0
% 5.41/5.78 thf(fact_9569_complex__mod__mult__cnj,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( real_V1022390504157884413omplex @ ( times_times_complex @ Z @ ( cnj @ Z ) ) )
% 5.41/5.78 = ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_mod_mult_cnj
% 5.41/5.78 thf(fact_9570_complex__div__gt__0,axiom,
% 5.41/5.78 ! [A: complex,B: complex] :
% 5.41/5.78 ( ( ( ord_less_real @ zero_zero_real @ ( re @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.41/5.78 = ( ord_less_real @ zero_zero_real @ ( re @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) )
% 5.41/5.78 & ( ( ord_less_real @ zero_zero_real @ ( im @ ( divide1717551699836669952omplex @ A @ B ) ) )
% 5.41/5.78 = ( ord_less_real @ zero_zero_real @ ( im @ ( times_times_complex @ A @ ( cnj @ B ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_div_gt_0
% 5.41/5.78 thf(fact_9571_complex__norm__square,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ Z ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) )
% 5.41/5.78 = ( times_times_complex @ Z @ ( cnj @ Z ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_norm_square
% 5.41/5.78 thf(fact_9572_complex__add__cnj,axiom,
% 5.41/5.78 ! [Z: complex] :
% 5.41/5.78 ( ( plus_plus_complex @ Z @ ( cnj @ Z ) )
% 5.41/5.78 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ Z ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_add_cnj
% 5.41/5.78 thf(fact_9573_complex__div__cnj,axiom,
% 5.41/5.78 ( divide1717551699836669952omplex
% 5.41/5.78 = ( ^ [A3: complex,B2: complex] : ( divide1717551699836669952omplex @ ( times_times_complex @ A3 @ ( cnj @ B2 ) ) @ ( real_V4546457046886955230omplex @ ( power_power_real @ ( real_V1022390504157884413omplex @ B2 ) @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % complex_div_cnj
% 5.41/5.78 thf(fact_9574_cnj__add__mult__eq__Re,axiom,
% 5.41/5.78 ! [Z: complex,W: complex] :
% 5.41/5.78 ( ( plus_plus_complex @ ( times_times_complex @ Z @ ( cnj @ W ) ) @ ( times_times_complex @ ( cnj @ Z ) @ W ) )
% 5.41/5.78 = ( real_V4546457046886955230omplex @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ ( re @ ( times_times_complex @ Z @ ( cnj @ W ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % cnj_add_mult_eq_Re
% 5.41/5.78 thf(fact_9575_divmod__step__integer__def,axiom,
% 5.41/5.78 ( unique4921790084139445826nteger
% 5.41/5.78 = ( ^ [L: num] :
% 5.41/5.78 ( produc6916734918728496179nteger
% 5.41/5.78 @ ^ [Q5: code_integer,R5: code_integer] : ( if_Pro6119634080678213985nteger @ ( ord_le3102999989581377725nteger @ ( numera6620942414471956472nteger @ L ) @ R5 ) @ ( produc1086072967326762835nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ R5 @ ( numera6620942414471956472nteger @ L ) ) ) @ ( produc1086072967326762835nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ Q5 ) @ R5 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_step_integer_def
% 5.41/5.78 thf(fact_9576_card__lessThan,axiom,
% 5.41/5.78 ! [U: nat] :
% 5.41/5.78 ( ( finite_card_nat @ ( set_ord_lessThan_nat @ U ) )
% 5.41/5.78 = U ) ).
% 5.41/5.78
% 5.41/5.78 % card_lessThan
% 5.41/5.78 thf(fact_9577_card__Collect__less__nat,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( finite_card_nat
% 5.41/5.78 @ ( collect_nat
% 5.41/5.78 @ ^ [I5: nat] : ( ord_less_nat @ I5 @ N ) ) )
% 5.41/5.78 = N ) ).
% 5.41/5.78
% 5.41/5.78 % card_Collect_less_nat
% 5.41/5.78 thf(fact_9578_card__atMost,axiom,
% 5.41/5.78 ! [U: nat] :
% 5.41/5.78 ( ( finite_card_nat @ ( set_ord_atMost_nat @ U ) )
% 5.41/5.78 = ( suc @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_atMost
% 5.41/5.78 thf(fact_9579_card__atLeastLessThan,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] :
% 5.41/5.78 ( ( finite_card_nat @ ( set_or4665077453230672383an_nat @ L2 @ U ) )
% 5.41/5.78 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_atLeastLessThan
% 5.41/5.78 thf(fact_9580_card__Collect__le__nat,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( finite_card_nat
% 5.41/5.78 @ ( collect_nat
% 5.41/5.78 @ ^ [I5: nat] : ( ord_less_eq_nat @ I5 @ N ) ) )
% 5.41/5.78 = ( suc @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_Collect_le_nat
% 5.41/5.78 thf(fact_9581_card__atLeastAtMost,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] :
% 5.41/5.78 ( ( finite_card_nat @ ( set_or1269000886237332187st_nat @ L2 @ U ) )
% 5.41/5.78 = ( minus_minus_nat @ ( suc @ U ) @ L2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_atLeastAtMost
% 5.41/5.78 thf(fact_9582_card__atLeastLessThan__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ L2 @ U ) )
% 5.41/5.78 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_atLeastLessThan_int
% 5.41/5.78 thf(fact_9583_card__atLeastAtMost__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( finite_card_int @ ( set_or1266510415728281911st_int @ L2 @ U ) )
% 5.41/5.78 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ U @ L2 ) @ one_one_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_atLeastAtMost_int
% 5.41/5.78 thf(fact_9584_minus__integer__code_I1_J,axiom,
% 5.41/5.78 ! [K: code_integer] :
% 5.41/5.78 ( ( minus_8373710615458151222nteger @ K @ zero_z3403309356797280102nteger )
% 5.41/5.78 = K ) ).
% 5.41/5.78
% 5.41/5.78 % minus_integer_code(1)
% 5.41/5.78 thf(fact_9585_minus__integer__code_I2_J,axiom,
% 5.41/5.78 ! [L2: code_integer] :
% 5.41/5.78 ( ( minus_8373710615458151222nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.41/5.78 = ( uminus1351360451143612070nteger @ L2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_integer_code(2)
% 5.41/5.78 thf(fact_9586_times__integer__code_I1_J,axiom,
% 5.41/5.78 ! [K: code_integer] :
% 5.41/5.78 ( ( times_3573771949741848930nteger @ K @ zero_z3403309356797280102nteger )
% 5.41/5.78 = zero_z3403309356797280102nteger ) ).
% 5.41/5.78
% 5.41/5.78 % times_integer_code(1)
% 5.41/5.78 thf(fact_9587_times__integer__code_I2_J,axiom,
% 5.41/5.78 ! [L2: code_integer] :
% 5.41/5.78 ( ( times_3573771949741848930nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.41/5.78 = zero_z3403309356797280102nteger ) ).
% 5.41/5.78
% 5.41/5.78 % times_integer_code(2)
% 5.41/5.78 thf(fact_9588_plus__integer__code_I2_J,axiom,
% 5.41/5.78 ! [L2: code_integer] :
% 5.41/5.78 ( ( plus_p5714425477246183910nteger @ zero_z3403309356797280102nteger @ L2 )
% 5.41/5.78 = L2 ) ).
% 5.41/5.78
% 5.41/5.78 % plus_integer_code(2)
% 5.41/5.78 thf(fact_9589_plus__integer__code_I1_J,axiom,
% 5.41/5.78 ! [K: code_integer] :
% 5.41/5.78 ( ( plus_p5714425477246183910nteger @ K @ zero_z3403309356797280102nteger )
% 5.41/5.78 = K ) ).
% 5.41/5.78
% 5.41/5.78 % plus_integer_code(1)
% 5.41/5.78 thf(fact_9590_less__eq__integer__code_I1_J,axiom,
% 5.41/5.78 ord_le3102999989581377725nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ).
% 5.41/5.78
% 5.41/5.78 % less_eq_integer_code(1)
% 5.41/5.78 thf(fact_9591_exhaustive__integer_H_Ocases,axiom,
% 5.41/5.78 ! [X: produc8763457246119570046nteger] :
% 5.41/5.78 ~ ! [F2: code_integer > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 5.41/5.78 ( X
% 5.41/5.78 != ( produc6137756002093451184nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % exhaustive_integer'.cases
% 5.41/5.78 thf(fact_9592_full__exhaustive__integer_H_Ocases,axiom,
% 5.41/5.78 ! [X: produc1908205239877642774nteger] :
% 5.41/5.78 ~ ! [F2: produc6241069584506657477e_term > option6357759511663192854e_term,D3: code_integer,I4: code_integer] :
% 5.41/5.78 ( X
% 5.41/5.78 != ( produc8603105652947943368nteger @ F2 @ ( produc1086072967326762835nteger @ D3 @ I4 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % full_exhaustive_integer'.cases
% 5.41/5.78 thf(fact_9593_divmod__integer_H__def,axiom,
% 5.41/5.78 ( unique3479559517661332726nteger
% 5.41/5.78 = ( ^ [M3: num,N2: num] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) @ ( modulo364778990260209775nteger @ ( numera6620942414471956472nteger @ M3 ) @ ( numera6620942414471956472nteger @ N2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_integer'_def
% 5.41/5.78 thf(fact_9594_sgn__integer__code,axiom,
% 5.41/5.78 ( sgn_sgn_Code_integer
% 5.41/5.78 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( K2 = zero_z3403309356797280102nteger ) @ zero_z3403309356797280102nteger @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ one_one_Code_integer ) @ one_one_Code_integer ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_integer_code
% 5.41/5.78 thf(fact_9595_nat_Odisc__eq__case_I2_J,axiom,
% 5.41/5.78 ! [Nat: nat] :
% 5.41/5.78 ( ( Nat != zero_zero_nat )
% 5.41/5.78 = ( case_nat_o @ $false
% 5.41/5.78 @ ^ [Uu3: nat] : $true
% 5.41/5.78 @ Nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat.disc_eq_case(2)
% 5.41/5.78 thf(fact_9596_nat_Odisc__eq__case_I1_J,axiom,
% 5.41/5.78 ! [Nat: nat] :
% 5.41/5.78 ( ( Nat = zero_zero_nat )
% 5.41/5.78 = ( case_nat_o @ $true
% 5.41/5.78 @ ^ [Uu3: nat] : $false
% 5.41/5.78 @ Nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat.disc_eq_case(1)
% 5.41/5.78 thf(fact_9597_zero__natural_Orsp,axiom,
% 5.41/5.78 zero_zero_nat = zero_zero_nat ).
% 5.41/5.78
% 5.41/5.78 % zero_natural.rsp
% 5.41/5.78 thf(fact_9598_card__less,axiom,
% 5.41/5.78 ! [M5: set_nat,I: nat] :
% 5.41/5.78 ( ( member_nat @ zero_zero_nat @ M5 )
% 5.41/5.78 => ( ( finite_card_nat
% 5.41/5.78 @ ( collect_nat
% 5.41/5.78 @ ^ [K2: nat] :
% 5.41/5.78 ( ( member_nat @ K2 @ M5 )
% 5.41/5.78 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) )
% 5.41/5.78 != zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_less
% 5.41/5.78 thf(fact_9599_card__less__Suc,axiom,
% 5.41/5.78 ! [M5: set_nat,I: nat] :
% 5.41/5.78 ( ( member_nat @ zero_zero_nat @ M5 )
% 5.41/5.78 => ( ( suc
% 5.41/5.78 @ ( finite_card_nat
% 5.41/5.78 @ ( collect_nat
% 5.41/5.78 @ ^ [K2: nat] :
% 5.41/5.78 ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 5.41/5.78 & ( ord_less_nat @ K2 @ I ) ) ) ) )
% 5.41/5.78 = ( finite_card_nat
% 5.41/5.78 @ ( collect_nat
% 5.41/5.78 @ ^ [K2: nat] :
% 5.41/5.78 ( ( member_nat @ K2 @ M5 )
% 5.41/5.78 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_less_Suc
% 5.41/5.78 thf(fact_9600_card__less__Suc2,axiom,
% 5.41/5.78 ! [M5: set_nat,I: nat] :
% 5.41/5.78 ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.41/5.78 => ( ( finite_card_nat
% 5.41/5.78 @ ( collect_nat
% 5.41/5.78 @ ^ [K2: nat] :
% 5.41/5.78 ( ( member_nat @ ( suc @ K2 ) @ M5 )
% 5.41/5.78 & ( ord_less_nat @ K2 @ I ) ) ) )
% 5.41/5.78 = ( finite_card_nat
% 5.41/5.78 @ ( collect_nat
% 5.41/5.78 @ ^ [K2: nat] :
% 5.41/5.78 ( ( member_nat @ K2 @ M5 )
% 5.41/5.78 & ( ord_less_nat @ K2 @ ( suc @ I ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_less_Suc2
% 5.41/5.78 thf(fact_9601_card__atLeastZeroLessThan__int,axiom,
% 5.41/5.78 ! [U: int] :
% 5.41/5.78 ( ( finite_card_int @ ( set_or4662586982721622107an_int @ zero_zero_int @ U ) )
% 5.41/5.78 = ( nat2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_atLeastZeroLessThan_int
% 5.41/5.78 thf(fact_9602_zero__integer_Orsp,axiom,
% 5.41/5.78 zero_zero_int = zero_zero_int ).
% 5.41/5.78
% 5.41/5.78 % zero_integer.rsp
% 5.41/5.78 thf(fact_9603_one__integer_Orsp,axiom,
% 5.41/5.78 one_one_int = one_one_int ).
% 5.41/5.78
% 5.41/5.78 % one_integer.rsp
% 5.41/5.78 thf(fact_9604_subset__card__intvl__is__intvl,axiom,
% 5.41/5.78 ! [A2: set_nat,K: nat] :
% 5.41/5.78 ( ( ord_less_eq_set_nat @ A2 @ ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) )
% 5.41/5.78 => ( A2
% 5.41/5.78 = ( set_or4665077453230672383an_nat @ K @ ( plus_plus_nat @ K @ ( finite_card_nat @ A2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % subset_card_intvl_is_intvl
% 5.41/5.78 thf(fact_9605_one__natural_Orsp,axiom,
% 5.41/5.78 one_one_nat = one_one_nat ).
% 5.41/5.78
% 5.41/5.78 % one_natural.rsp
% 5.41/5.78 thf(fact_9606_less__eq__nat_Osimps_I2_J,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ ( suc @ M ) @ N )
% 5.41/5.78 = ( case_nat_o @ $false @ ( ord_less_eq_nat @ M ) @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_eq_nat.simps(2)
% 5.41/5.78 thf(fact_9607_max__Suc2,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( ord_max_nat @ M @ ( suc @ N ) )
% 5.41/5.78 = ( case_nat_nat @ ( suc @ N )
% 5.41/5.78 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ M6 @ N ) )
% 5.41/5.78 @ M ) ) ).
% 5.41/5.78
% 5.41/5.78 % max_Suc2
% 5.41/5.78 thf(fact_9608_max__Suc1,axiom,
% 5.41/5.78 ! [N: nat,M: nat] :
% 5.41/5.78 ( ( ord_max_nat @ ( suc @ N ) @ M )
% 5.41/5.78 = ( case_nat_nat @ ( suc @ N )
% 5.41/5.78 @ ^ [M6: nat] : ( suc @ ( ord_max_nat @ N @ M6 ) )
% 5.41/5.78 @ M ) ) ).
% 5.41/5.78
% 5.41/5.78 % max_Suc1
% 5.41/5.78 thf(fact_9609_subset__eq__atLeast0__lessThan__card,axiom,
% 5.41/5.78 ! [N4: set_nat,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_set_nat @ N4 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) )
% 5.41/5.78 => ( ord_less_eq_nat @ ( finite_card_nat @ N4 ) @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % subset_eq_atLeast0_lessThan_card
% 5.41/5.78 thf(fact_9610_card__sum__le__nat__sum,axiom,
% 5.41/5.78 ! [S2: set_nat] :
% 5.41/5.78 ( ord_less_eq_nat
% 5.41/5.78 @ ( groups3542108847815614940at_nat
% 5.41/5.78 @ ^ [X3: nat] : X3
% 5.41/5.78 @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( finite_card_nat @ S2 ) ) )
% 5.41/5.78 @ ( groups3542108847815614940at_nat
% 5.41/5.78 @ ^ [X3: nat] : X3
% 5.41/5.78 @ S2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_sum_le_nat_sum
% 5.41/5.78 thf(fact_9611_card__nth__roots,axiom,
% 5.41/5.78 ! [C: complex,N: nat] :
% 5.41/5.78 ( ( C != zero_zero_complex )
% 5.41/5.78 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( finite_card_complex
% 5.41/5.78 @ ( collect_complex
% 5.41/5.78 @ ^ [Z3: complex] :
% 5.41/5.78 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.78 = C ) ) )
% 5.41/5.78 = N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_nth_roots
% 5.41/5.78 thf(fact_9612_card__roots__unity__eq,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( finite_card_complex
% 5.41/5.78 @ ( collect_complex
% 5.41/5.78 @ ^ [Z3: complex] :
% 5.41/5.78 ( ( power_power_complex @ Z3 @ N )
% 5.41/5.78 = one_one_complex ) ) )
% 5.41/5.78 = N ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_roots_unity_eq
% 5.41/5.78 thf(fact_9613_diff__Suc,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( minus_minus_nat @ M @ ( suc @ N ) )
% 5.41/5.78 = ( case_nat_nat @ zero_zero_nat
% 5.41/5.78 @ ^ [K2: nat] : K2
% 5.41/5.78 @ ( minus_minus_nat @ M @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % diff_Suc
% 5.41/5.78 thf(fact_9614_integer__of__int__code,axiom,
% 5.41/5.78 ( code_integer_of_int
% 5.41/5.78 = ( ^ [K2: int] :
% 5.41/5.78 ( if_Code_integer @ ( ord_less_int @ K2 @ zero_zero_int ) @ ( uminus1351360451143612070nteger @ ( code_integer_of_int @ ( uminus_uminus_int @ K2 ) ) )
% 5.41/5.78 @ ( if_Code_integer @ ( K2 = zero_zero_int ) @ zero_z3403309356797280102nteger
% 5.41/5.78 @ ( if_Code_integer
% 5.41/5.78 @ ( ( modulo_modulo_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) )
% 5.41/5.78 @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ ( code_integer_of_int @ ( divide_divide_int @ K2 @ ( numeral_numeral_int @ ( bit0 @ one ) ) ) ) ) @ one_one_Code_integer ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % integer_of_int_code
% 5.41/5.78 thf(fact_9615_abs__integer__code,axiom,
% 5.41/5.78 ( abs_abs_Code_integer
% 5.41/5.78 = ( ^ [K2: code_integer] : ( if_Code_integer @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus1351360451143612070nteger @ K2 ) @ K2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % abs_integer_code
% 5.41/5.78 thf(fact_9616_uminus__integer__code_I1_J,axiom,
% 5.41/5.78 ( ( uminus1351360451143612070nteger @ zero_z3403309356797280102nteger )
% 5.41/5.78 = zero_z3403309356797280102nteger ) ).
% 5.41/5.78
% 5.41/5.78 % uminus_integer_code(1)
% 5.41/5.78 thf(fact_9617_zero__integer__def,axiom,
% 5.41/5.78 ( zero_z3403309356797280102nteger
% 5.41/5.78 = ( code_integer_of_int @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % zero_integer_def
% 5.41/5.78 thf(fact_9618_less__integer__code_I1_J,axiom,
% 5.41/5.78 ~ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ).
% 5.41/5.78
% 5.41/5.78 % less_integer_code(1)
% 5.41/5.78 thf(fact_9619_modulo__integer_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: int,X: int] :
% 5.41/5.78 ( ( modulo364778990260209775nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.41/5.78 = ( code_integer_of_int @ ( modulo_modulo_int @ Xa2 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % modulo_integer.abs_eq
% 5.41/5.78 thf(fact_9620_plus__integer_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: int,X: int] :
% 5.41/5.78 ( ( plus_p5714425477246183910nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.41/5.78 = ( code_integer_of_int @ ( plus_plus_int @ Xa2 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_integer.abs_eq
% 5.41/5.78 thf(fact_9621_times__integer_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: int,X: int] :
% 5.41/5.78 ( ( times_3573771949741848930nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.41/5.78 = ( code_integer_of_int @ ( times_times_int @ Xa2 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % times_integer.abs_eq
% 5.41/5.78 thf(fact_9622_one__integer__def,axiom,
% 5.41/5.78 ( one_one_Code_integer
% 5.41/5.78 = ( code_integer_of_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % one_integer_def
% 5.41/5.78 thf(fact_9623_less__eq__integer_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: int,X: int] :
% 5.41/5.78 ( ( ord_le3102999989581377725nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.41/5.78 = ( ord_less_eq_int @ Xa2 @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_eq_integer.abs_eq
% 5.41/5.78 thf(fact_9624_minus__integer_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: int,X: int] :
% 5.41/5.78 ( ( minus_8373710615458151222nteger @ ( code_integer_of_int @ Xa2 ) @ ( code_integer_of_int @ X ) )
% 5.41/5.78 = ( code_integer_of_int @ ( minus_minus_int @ Xa2 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_integer.abs_eq
% 5.41/5.78 thf(fact_9625_Code__Numeral_Opositive__def,axiom,
% 5.41/5.78 code_positive = numera6620942414471956472nteger ).
% 5.41/5.78
% 5.41/5.78 % Code_Numeral.positive_def
% 5.41/5.78 thf(fact_9626_integer__of__num_I3_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( code_integer_of_num @ ( bit1 @ N ) )
% 5.41/5.78 = ( plus_p5714425477246183910nteger @ ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) @ one_one_Code_integer ) ) ).
% 5.41/5.78
% 5.41/5.78 % integer_of_num(3)
% 5.41/5.78 thf(fact_9627_integer__of__num__def,axiom,
% 5.41/5.78 code_integer_of_num = numera6620942414471956472nteger ).
% 5.41/5.78
% 5.41/5.78 % integer_of_num_def
% 5.41/5.78 thf(fact_9628_integer__of__num__triv_I1_J,axiom,
% 5.41/5.78 ( ( code_integer_of_num @ one )
% 5.41/5.78 = one_one_Code_integer ) ).
% 5.41/5.78
% 5.41/5.78 % integer_of_num_triv(1)
% 5.41/5.78 thf(fact_9629_integer__of__num_I2_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( code_integer_of_num @ ( bit0 @ N ) )
% 5.41/5.78 = ( plus_p5714425477246183910nteger @ ( code_integer_of_num @ N ) @ ( code_integer_of_num @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % integer_of_num(2)
% 5.41/5.78 thf(fact_9630_integer__of__num__triv_I2_J,axiom,
% 5.41/5.78 ( ( code_integer_of_num @ ( bit0 @ one ) )
% 5.41/5.78 = ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % integer_of_num_triv(2)
% 5.41/5.78 thf(fact_9631_int__of__integer__code,axiom,
% 5.41/5.78 ( code_int_of_integer
% 5.41/5.78 = ( ^ [K2: code_integer] :
% 5.41/5.78 ( if_int @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( uminus_uminus_int @ ( code_int_of_integer @ ( uminus1351360451143612070nteger @ K2 ) ) )
% 5.41/5.78 @ ( if_int @ ( K2 = zero_z3403309356797280102nteger ) @ zero_zero_int
% 5.41/5.78 @ ( produc1553301316500091796er_int
% 5.41/5.78 @ ^ [L: code_integer,J3: code_integer] : ( if_int @ ( J3 = zero_z3403309356797280102nteger ) @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ ( plus_plus_int @ ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( code_int_of_integer @ L ) ) @ one_one_int ) )
% 5.41/5.78 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_of_integer_code
% 5.41/5.78 thf(fact_9632_bit__cut__integer__def,axiom,
% 5.41/5.78 ( code_bit_cut_integer
% 5.41/5.78 = ( ^ [K2: code_integer] :
% 5.41/5.78 ( produc6677183202524767010eger_o @ ( divide6298287555418463151nteger @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) )
% 5.41/5.78 @ ~ ( dvd_dvd_Code_integer @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) @ K2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_cut_integer_def
% 5.41/5.78 thf(fact_9633_num__of__integer__code,axiom,
% 5.41/5.78 ( code_num_of_integer
% 5.41/5.78 = ( ^ [K2: code_integer] :
% 5.41/5.78 ( if_num @ ( ord_le3102999989581377725nteger @ K2 @ one_one_Code_integer ) @ one
% 5.41/5.78 @ ( produc7336495610019696514er_num
% 5.41/5.78 @ ^ [L: code_integer,J3: code_integer] : ( if_num @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ ( plus_plus_num @ ( plus_plus_num @ ( code_num_of_integer @ L ) @ ( code_num_of_integer @ L ) ) @ one ) )
% 5.41/5.78 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % num_of_integer_code
% 5.41/5.78 thf(fact_9634_zero__integer_Orep__eq,axiom,
% 5.41/5.78 ( ( code_int_of_integer @ zero_z3403309356797280102nteger )
% 5.41/5.78 = zero_zero_int ) ).
% 5.41/5.78
% 5.41/5.78 % zero_integer.rep_eq
% 5.41/5.78 thf(fact_9635_int__of__integer__numeral,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( code_int_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.41/5.78 = ( numeral_numeral_int @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_of_integer_numeral
% 5.41/5.78 thf(fact_9636_plus__integer_Orep__eq,axiom,
% 5.41/5.78 ! [X: code_integer,Xa2: code_integer] :
% 5.41/5.78 ( ( code_int_of_integer @ ( plus_p5714425477246183910nteger @ X @ Xa2 ) )
% 5.41/5.78 = ( plus_plus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_integer.rep_eq
% 5.41/5.78 thf(fact_9637_times__integer_Orep__eq,axiom,
% 5.41/5.78 ! [X: code_integer,Xa2: code_integer] :
% 5.41/5.78 ( ( code_int_of_integer @ ( times_3573771949741848930nteger @ X @ Xa2 ) )
% 5.41/5.78 = ( times_times_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % times_integer.rep_eq
% 5.41/5.78 thf(fact_9638_one__integer_Orep__eq,axiom,
% 5.41/5.78 ( ( code_int_of_integer @ one_one_Code_integer )
% 5.41/5.78 = one_one_int ) ).
% 5.41/5.78
% 5.41/5.78 % one_integer.rep_eq
% 5.41/5.78 thf(fact_9639_minus__integer_Orep__eq,axiom,
% 5.41/5.78 ! [X: code_integer,Xa2: code_integer] :
% 5.41/5.78 ( ( code_int_of_integer @ ( minus_8373710615458151222nteger @ X @ Xa2 ) )
% 5.41/5.78 = ( minus_minus_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_integer.rep_eq
% 5.41/5.78 thf(fact_9640_modulo__integer_Orep__eq,axiom,
% 5.41/5.78 ! [X: code_integer,Xa2: code_integer] :
% 5.41/5.78 ( ( code_int_of_integer @ ( modulo364778990260209775nteger @ X @ Xa2 ) )
% 5.41/5.78 = ( modulo_modulo_int @ ( code_int_of_integer @ X ) @ ( code_int_of_integer @ Xa2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % modulo_integer.rep_eq
% 5.41/5.78 thf(fact_9641_integer__less__eq__iff,axiom,
% 5.41/5.78 ( ord_le3102999989581377725nteger
% 5.41/5.78 = ( ^ [K2: code_integer,L: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ K2 ) @ ( code_int_of_integer @ L ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % integer_less_eq_iff
% 5.41/5.78 thf(fact_9642_less__eq__integer_Orep__eq,axiom,
% 5.41/5.78 ( ord_le3102999989581377725nteger
% 5.41/5.78 = ( ^ [X3: code_integer,Xa4: code_integer] : ( ord_less_eq_int @ ( code_int_of_integer @ X3 ) @ ( code_int_of_integer @ Xa4 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_eq_integer.rep_eq
% 5.41/5.78 thf(fact_9643_divmod__integer__def,axiom,
% 5.41/5.78 ( code_divmod_integer
% 5.41/5.78 = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ K2 @ L ) @ ( modulo364778990260209775nteger @ K2 @ L ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_integer_def
% 5.41/5.78 thf(fact_9644_bit__cut__integer__code,axiom,
% 5.41/5.78 ( code_bit_cut_integer
% 5.41/5.78 = ( ^ [K2: code_integer] :
% 5.41/5.78 ( if_Pro5737122678794959658eger_o @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc6677183202524767010eger_o @ zero_z3403309356797280102nteger @ $false )
% 5.41/5.78 @ ( produc9125791028180074456eger_o
% 5.41/5.78 @ ^ [R5: code_integer,S7: code_integer] : ( produc6677183202524767010eger_o @ ( if_Code_integer @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ R5 @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ S7 ) ) @ ( S7 = one_one_Code_integer ) )
% 5.41/5.78 @ ( code_divmod_abs @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bit_cut_integer_code
% 5.41/5.78 thf(fact_9645_nat__of__integer__code,axiom,
% 5.41/5.78 ( code_nat_of_integer
% 5.41/5.78 = ( ^ [K2: code_integer] :
% 5.41/5.78 ( if_nat @ ( ord_le3102999989581377725nteger @ K2 @ zero_z3403309356797280102nteger ) @ zero_zero_nat
% 5.41/5.78 @ ( produc1555791787009142072er_nat
% 5.41/5.78 @ ^ [L: code_integer,J3: code_integer] : ( if_nat @ ( J3 = zero_z3403309356797280102nteger ) @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ ( plus_plus_nat @ ( plus_plus_nat @ ( code_nat_of_integer @ L ) @ ( code_nat_of_integer @ L ) ) @ one_one_nat ) )
% 5.41/5.78 @ ( code_divmod_integer @ K2 @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_of_integer_code
% 5.41/5.78 thf(fact_9646_of__nat__of__integer,axiom,
% 5.41/5.78 ! [K: code_integer] :
% 5.41/5.78 ( ( semiri4939895301339042750nteger @ ( code_nat_of_integer @ K ) )
% 5.41/5.78 = ( ord_max_Code_integer @ zero_z3403309356797280102nteger @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % of_nat_of_integer
% 5.41/5.78 thf(fact_9647_nat__of__integer__non__positive,axiom,
% 5.41/5.78 ! [K: code_integer] :
% 5.41/5.78 ( ( ord_le3102999989581377725nteger @ K @ zero_z3403309356797280102nteger )
% 5.41/5.78 => ( ( code_nat_of_integer @ K )
% 5.41/5.78 = zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_of_integer_non_positive
% 5.41/5.78 thf(fact_9648_nat__of__integer__code__post_I1_J,axiom,
% 5.41/5.78 ( ( code_nat_of_integer @ zero_z3403309356797280102nteger )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % nat_of_integer_code_post(1)
% 5.41/5.78 thf(fact_9649_nat__of__integer__code__post_I3_J,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( code_nat_of_integer @ ( numera6620942414471956472nteger @ K ) )
% 5.41/5.78 = ( numeral_numeral_nat @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_of_integer_code_post(3)
% 5.41/5.78 thf(fact_9650_divmod__abs__code_I6_J,axiom,
% 5.41/5.78 ! [J: code_integer] :
% 5.41/5.78 ( ( code_divmod_abs @ zero_z3403309356797280102nteger @ J )
% 5.41/5.78 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_abs_code(6)
% 5.41/5.78 thf(fact_9651_nat__of__integer__code__post_I2_J,axiom,
% 5.41/5.78 ( ( code_nat_of_integer @ one_one_Code_integer )
% 5.41/5.78 = one_one_nat ) ).
% 5.41/5.78
% 5.41/5.78 % nat_of_integer_code_post(2)
% 5.41/5.78 thf(fact_9652_divmod__abs__code_I5_J,axiom,
% 5.41/5.78 ! [J: code_integer] :
% 5.41/5.78 ( ( code_divmod_abs @ J @ zero_z3403309356797280102nteger )
% 5.41/5.78 = ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ ( abs_abs_Code_integer @ J ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_abs_code(5)
% 5.41/5.78 thf(fact_9653_pred__def,axiom,
% 5.41/5.78 ( pred
% 5.41/5.78 = ( case_nat_nat @ zero_zero_nat
% 5.41/5.78 @ ^ [X24: nat] : X24 ) ) ).
% 5.41/5.78
% 5.41/5.78 % pred_def
% 5.41/5.78 thf(fact_9654_divmod__abs__def,axiom,
% 5.41/5.78 ( code_divmod_abs
% 5.41/5.78 = ( ^ [K2: code_integer,L: code_integer] : ( produc1086072967326762835nteger @ ( divide6298287555418463151nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_abs_def
% 5.41/5.78 thf(fact_9655_divmod__integer__code,axiom,
% 5.41/5.78 ( code_divmod_integer
% 5.41/5.78 = ( ^ [K2: code_integer,L: code_integer] :
% 5.41/5.78 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.41/5.78 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ L )
% 5.41/5.78 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ zero_z3403309356797280102nteger @ K2 ) @ ( code_divmod_abs @ K2 @ L )
% 5.41/5.78 @ ( produc6916734918728496179nteger
% 5.41/5.78 @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ L @ S7 ) ) )
% 5.41/5.78 @ ( code_divmod_abs @ K2 @ L ) ) )
% 5.41/5.78 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.41/5.78 @ ( produc6499014454317279255nteger @ uminus1351360451143612070nteger
% 5.41/5.78 @ ( if_Pro6119634080678213985nteger @ ( ord_le6747313008572928689nteger @ K2 @ zero_z3403309356797280102nteger ) @ ( code_divmod_abs @ K2 @ L )
% 5.41/5.78 @ ( produc6916734918728496179nteger
% 5.41/5.78 @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ L ) @ S7 ) ) )
% 5.41/5.78 @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_integer_code
% 5.41/5.78 thf(fact_9656_binomial__def,axiom,
% 5.41/5.78 ( binomial
% 5.41/5.78 = ( ^ [N2: nat,K2: nat] :
% 5.41/5.78 ( finite_card_set_nat
% 5.41/5.78 @ ( collect_set_nat
% 5.41/5.78 @ ^ [K7: set_nat] :
% 5.41/5.78 ( ( member_set_nat @ K7 @ ( pow_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N2 ) ) )
% 5.41/5.78 & ( ( finite_card_nat @ K7 )
% 5.41/5.78 = K2 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % binomial_def
% 5.41/5.78 thf(fact_9657_bezw__0,axiom,
% 5.41/5.78 ! [X: nat] :
% 5.41/5.78 ( ( bezw @ X @ zero_zero_nat )
% 5.41/5.78 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezw_0
% 5.41/5.78 thf(fact_9658_floor__real__def,axiom,
% 5.41/5.78 ( archim6058952711729229775r_real
% 5.41/5.78 = ( ^ [X3: real] :
% 5.41/5.78 ( the_int
% 5.41/5.78 @ ^ [Z3: int] :
% 5.41/5.78 ( ( ord_less_eq_real @ ( ring_1_of_int_real @ Z3 ) @ X3 )
% 5.41/5.78 & ( ord_less_real @ X3 @ ( ring_1_of_int_real @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % floor_real_def
% 5.41/5.78 thf(fact_9659_floor__rat__def,axiom,
% 5.41/5.78 ( archim3151403230148437115or_rat
% 5.41/5.78 = ( ^ [X3: rat] :
% 5.41/5.78 ( the_int
% 5.41/5.78 @ ^ [Z3: int] :
% 5.41/5.78 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ Z3 ) @ X3 )
% 5.41/5.78 & ( ord_less_rat @ X3 @ ( ring_1_of_int_rat @ ( plus_plus_int @ Z3 @ one_one_int ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % floor_rat_def
% 5.41/5.78 thf(fact_9660_drop__bit__numeral__minus__bit1,axiom,
% 5.41/5.78 ! [L2: num,K: num] :
% 5.41/5.78 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.41/5.78 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_numeral_minus_bit1
% 5.41/5.78 thf(fact_9661_Suc__0__mod__numeral,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( modulo_modulo_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.78 = ( product_snd_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Suc_0_mod_numeral
% 5.41/5.78 thf(fact_9662_drop__bit__nonnegative__int__iff,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ ( bit_se8568078237143864401it_int @ N @ K ) )
% 5.41/5.78 = ( ord_less_eq_int @ zero_zero_int @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_nonnegative_int_iff
% 5.41/5.78 thf(fact_9663_drop__bit__negative__int__iff,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( ord_less_int @ ( bit_se8568078237143864401it_int @ N @ K ) @ zero_zero_int )
% 5.41/5.78 = ( ord_less_int @ K @ zero_zero_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_negative_int_iff
% 5.41/5.78 thf(fact_9664_drop__bit__minus__one,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ one_one_int ) )
% 5.41/5.78 = ( uminus_uminus_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_minus_one
% 5.41/5.78 thf(fact_9665_snd__divmod__nat,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( product_snd_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.41/5.78 = ( modulo_modulo_nat @ M @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % snd_divmod_nat
% 5.41/5.78 thf(fact_9666_drop__bit__Suc__minus__bit0,axiom,
% 5.41/5.78 ! [N: nat,K: num] :
% 5.41/5.78 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.41/5.78 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_Suc_minus_bit0
% 5.41/5.78 thf(fact_9667_drop__bit__numeral__minus__bit0,axiom,
% 5.41/5.78 ! [L2: num,K: num] :
% 5.41/5.78 ( ( bit_se8568078237143864401it_int @ ( numeral_numeral_nat @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ K ) ) ) )
% 5.41/5.78 = ( bit_se8568078237143864401it_int @ ( pred_numeral @ L2 ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_numeral_minus_bit0
% 5.41/5.78 thf(fact_9668_drop__bit__Suc__minus__bit1,axiom,
% 5.41/5.78 ! [N: nat,K: num] :
% 5.41/5.78 ( ( bit_se8568078237143864401it_int @ ( suc @ N ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ K ) ) ) )
% 5.41/5.78 = ( bit_se8568078237143864401it_int @ N @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( inc @ K ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_Suc_minus_bit1
% 5.41/5.78 thf(fact_9669_less__eq__rat__def,axiom,
% 5.41/5.78 ( ord_less_eq_rat
% 5.41/5.78 = ( ^ [X3: rat,Y3: rat] :
% 5.41/5.78 ( ( ord_less_rat @ X3 @ Y3 )
% 5.41/5.78 | ( X3 = Y3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_eq_rat_def
% 5.41/5.78 thf(fact_9670_abs__rat__def,axiom,
% 5.41/5.78 ( abs_abs_rat
% 5.41/5.78 = ( ^ [A3: rat] : ( if_rat @ ( ord_less_rat @ A3 @ zero_zero_rat ) @ ( uminus_uminus_rat @ A3 ) @ A3 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % abs_rat_def
% 5.41/5.78 thf(fact_9671_sgn__rat__def,axiom,
% 5.41/5.78 ( sgn_sgn_rat
% 5.41/5.78 = ( ^ [A3: rat] : ( if_rat @ ( A3 = zero_zero_rat ) @ zero_zero_rat @ ( if_rat @ ( ord_less_rat @ zero_zero_rat @ A3 ) @ one_one_rat @ ( uminus_uminus_rat @ one_one_rat ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_rat_def
% 5.41/5.78 thf(fact_9672_obtain__pos__sum,axiom,
% 5.41/5.78 ! [R: rat] :
% 5.41/5.78 ( ( ord_less_rat @ zero_zero_rat @ R )
% 5.41/5.78 => ~ ! [S3: rat] :
% 5.41/5.78 ( ( ord_less_rat @ zero_zero_rat @ S3 )
% 5.41/5.78 => ! [T6: rat] :
% 5.41/5.78 ( ( ord_less_rat @ zero_zero_rat @ T6 )
% 5.41/5.78 => ( R
% 5.41/5.78 != ( plus_plus_rat @ S3 @ T6 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % obtain_pos_sum
% 5.41/5.78 thf(fact_9673_drop__bit__push__bit__int,axiom,
% 5.41/5.78 ! [M: nat,N: nat,K: int] :
% 5.41/5.78 ( ( bit_se8568078237143864401it_int @ M @ ( bit_se545348938243370406it_int @ N @ K ) )
% 5.41/5.78 = ( bit_se8568078237143864401it_int @ ( minus_minus_nat @ M @ N ) @ ( bit_se545348938243370406it_int @ ( minus_minus_nat @ N @ M ) @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_push_bit_int
% 5.41/5.78 thf(fact_9674_drop__bit__int__def,axiom,
% 5.41/5.78 ( bit_se8568078237143864401it_int
% 5.41/5.78 = ( ^ [N2: nat,K2: int] : ( divide_divide_int @ K2 @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_int_def
% 5.41/5.78 thf(fact_9675_rat__inverse__code,axiom,
% 5.41/5.78 ! [P5: rat] :
% 5.41/5.78 ( ( quotient_of @ ( inverse_inverse_rat @ P5 ) )
% 5.41/5.78 = ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [A3: int,B2: int] : ( if_Pro3027730157355071871nt_int @ ( A3 = zero_zero_int ) @ ( product_Pair_int_int @ zero_zero_int @ one_one_int ) @ ( product_Pair_int_int @ ( times_times_int @ ( sgn_sgn_int @ A3 ) @ B2 ) @ ( abs_abs_int @ A3 ) ) )
% 5.41/5.78 @ ( quotient_of @ P5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_inverse_code
% 5.41/5.78 thf(fact_9676_normalize__negative,axiom,
% 5.41/5.78 ! [Q2: int,P5: int] :
% 5.41/5.78 ( ( ord_less_int @ Q2 @ zero_zero_int )
% 5.41/5.78 => ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.41/5.78 = ( normalize @ ( product_Pair_int_int @ ( uminus_uminus_int @ P5 ) @ ( uminus_uminus_int @ Q2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % normalize_negative
% 5.41/5.78 thf(fact_9677_prod__decode__aux_Osimps,axiom,
% 5.41/5.78 ( nat_prod_decode_aux
% 5.41/5.78 = ( ^ [K2: nat,M3: nat] : ( if_Pro6206227464963214023at_nat @ ( ord_less_eq_nat @ M3 @ K2 ) @ ( product_Pair_nat_nat @ M3 @ ( minus_minus_nat @ K2 @ M3 ) ) @ ( nat_prod_decode_aux @ ( suc @ K2 ) @ ( minus_minus_nat @ M3 @ ( suc @ K2 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % prod_decode_aux.simps
% 5.41/5.78 thf(fact_9678_snd__divmod__integer,axiom,
% 5.41/5.78 ! [K: code_integer,L2: code_integer] :
% 5.41/5.78 ( ( produc6174133586879617921nteger @ ( code_divmod_integer @ K @ L2 ) )
% 5.41/5.78 = ( modulo364778990260209775nteger @ K @ L2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % snd_divmod_integer
% 5.41/5.78 thf(fact_9679_snd__divmod__abs,axiom,
% 5.41/5.78 ! [K: code_integer,L2: code_integer] :
% 5.41/5.78 ( ( produc6174133586879617921nteger @ ( code_divmod_abs @ K @ L2 ) )
% 5.41/5.78 = ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K ) @ ( abs_abs_Code_integer @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % snd_divmod_abs
% 5.41/5.78 thf(fact_9680_quotient__of__number_I3_J,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( quotient_of @ ( numeral_numeral_rat @ K ) )
% 5.41/5.78 = ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_number(3)
% 5.41/5.78 thf(fact_9681_normalize__denom__zero,axiom,
% 5.41/5.78 ! [P5: int] :
% 5.41/5.78 ( ( normalize @ ( product_Pair_int_int @ P5 @ zero_zero_int ) )
% 5.41/5.78 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % normalize_denom_zero
% 5.41/5.78 thf(fact_9682_rat__one__code,axiom,
% 5.41/5.78 ( ( quotient_of @ one_one_rat )
% 5.41/5.78 = ( product_Pair_int_int @ one_one_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_one_code
% 5.41/5.78 thf(fact_9683_drop__bit__of__Suc__0,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( bit_se8570568707652914677it_nat @ N @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( zero_n2687167440665602831ol_nat @ ( N = zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_of_Suc_0
% 5.41/5.78 thf(fact_9684_rat__zero__code,axiom,
% 5.41/5.78 ( ( quotient_of @ zero_zero_rat )
% 5.41/5.78 = ( product_Pair_int_int @ zero_zero_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_zero_code
% 5.41/5.78 thf(fact_9685_quotient__of__number_I5_J,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( quotient_of @ ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) ) )
% 5.41/5.78 = ( product_Pair_int_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_number(5)
% 5.41/5.78 thf(fact_9686_quotient__of__number_I4_J,axiom,
% 5.41/5.78 ( ( quotient_of @ ( uminus_uminus_rat @ one_one_rat ) )
% 5.41/5.78 = ( product_Pair_int_int @ ( uminus_uminus_int @ one_one_int ) @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_number(4)
% 5.41/5.78 thf(fact_9687_quotient__of__denom__pos_H,axiom,
% 5.41/5.78 ! [R: rat] : ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ ( quotient_of @ R ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_denom_pos'
% 5.41/5.78 thf(fact_9688_divide__rat__def,axiom,
% 5.41/5.78 ( divide_divide_rat
% 5.41/5.78 = ( ^ [Q5: rat,R5: rat] : ( times_times_rat @ Q5 @ ( inverse_inverse_rat @ R5 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divide_rat_def
% 5.41/5.78 thf(fact_9689_diff__rat__def,axiom,
% 5.41/5.78 ( minus_minus_rat
% 5.41/5.78 = ( ^ [Q5: rat,R5: rat] : ( plus_plus_rat @ Q5 @ ( uminus_uminus_rat @ R5 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % diff_rat_def
% 5.41/5.78 thf(fact_9690_rat__divide__code,axiom,
% 5.41/5.78 ! [P5: rat,Q2: rat] :
% 5.41/5.78 ( ( quotient_of @ ( divide_divide_rat @ P5 @ Q2 ) )
% 5.41/5.78 = ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [A3: int,C3: int] :
% 5.41/5.78 ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) ) )
% 5.41/5.78 @ ( quotient_of @ Q2 ) )
% 5.41/5.78 @ ( quotient_of @ P5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_divide_code
% 5.41/5.78 thf(fact_9691_rat__times__code,axiom,
% 5.41/5.78 ! [P5: rat,Q2: rat] :
% 5.41/5.78 ( ( quotient_of @ ( times_times_rat @ P5 @ Q2 ) )
% 5.41/5.78 = ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [A3: int,C3: int] :
% 5.41/5.78 ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( times_times_int @ A3 @ B2 ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.41/5.78 @ ( quotient_of @ Q2 ) )
% 5.41/5.78 @ ( quotient_of @ P5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_times_code
% 5.41/5.78 thf(fact_9692_drop__bit__nat__eq,axiom,
% 5.41/5.78 ! [N: nat,K: int] :
% 5.41/5.78 ( ( bit_se8570568707652914677it_nat @ N @ ( nat2 @ K ) )
% 5.41/5.78 = ( nat2 @ ( bit_se8568078237143864401it_int @ N @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_nat_eq
% 5.41/5.78 thf(fact_9693_quotient__of__div,axiom,
% 5.41/5.78 ! [R: rat,N: int,D: int] :
% 5.41/5.78 ( ( ( quotient_of @ R )
% 5.41/5.78 = ( product_Pair_int_int @ N @ D ) )
% 5.41/5.78 => ( R
% 5.41/5.78 = ( divide_divide_rat @ ( ring_1_of_int_rat @ N ) @ ( ring_1_of_int_rat @ D ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_div
% 5.41/5.78 thf(fact_9694_rat__plus__code,axiom,
% 5.41/5.78 ! [P5: rat,Q2: rat] :
% 5.41/5.78 ( ( quotient_of @ ( plus_plus_rat @ P5 @ Q2 ) )
% 5.41/5.78 = ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [A3: int,C3: int] :
% 5.41/5.78 ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( plus_plus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.41/5.78 @ ( quotient_of @ Q2 ) )
% 5.41/5.78 @ ( quotient_of @ P5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_plus_code
% 5.41/5.78 thf(fact_9695_rat__minus__code,axiom,
% 5.41/5.78 ! [P5: rat,Q2: rat] :
% 5.41/5.78 ( ( quotient_of @ ( minus_minus_rat @ P5 @ Q2 ) )
% 5.41/5.78 = ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [A3: int,C3: int] :
% 5.41/5.78 ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [B2: int,D2: int] : ( normalize @ ( product_Pair_int_int @ ( minus_minus_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ B2 @ C3 ) ) @ ( times_times_int @ C3 @ D2 ) ) )
% 5.41/5.78 @ ( quotient_of @ Q2 ) )
% 5.41/5.78 @ ( quotient_of @ P5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_minus_code
% 5.41/5.78 thf(fact_9696_quotient__of__denom__pos,axiom,
% 5.41/5.78 ! [R: rat,P5: int,Q2: int] :
% 5.41/5.78 ( ( ( quotient_of @ R )
% 5.41/5.78 = ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.41/5.78 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_denom_pos
% 5.41/5.78 thf(fact_9697_rat__uminus__code,axiom,
% 5.41/5.78 ! [P5: rat] :
% 5.41/5.78 ( ( quotient_of @ ( uminus_uminus_rat @ P5 ) )
% 5.41/5.78 = ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [A3: int] : ( product_Pair_int_int @ ( uminus_uminus_int @ A3 ) )
% 5.41/5.78 @ ( quotient_of @ P5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_uminus_code
% 5.41/5.78 thf(fact_9698_rat__abs__code,axiom,
% 5.41/5.78 ! [P5: rat] :
% 5.41/5.78 ( ( quotient_of @ ( abs_abs_rat @ P5 ) )
% 5.41/5.78 = ( produc4245557441103728435nt_int
% 5.41/5.78 @ ^ [A3: int] : ( product_Pair_int_int @ ( abs_abs_int @ A3 ) )
% 5.41/5.78 @ ( quotient_of @ P5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_abs_code
% 5.41/5.78 thf(fact_9699_normalize__denom__pos,axiom,
% 5.41/5.78 ! [R: product_prod_int_int,P5: int,Q2: int] :
% 5.41/5.78 ( ( ( normalize @ R )
% 5.41/5.78 = ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.41/5.78 => ( ord_less_int @ zero_zero_int @ Q2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % normalize_denom_pos
% 5.41/5.78 thf(fact_9700_normalize__crossproduct,axiom,
% 5.41/5.78 ! [Q2: int,S: int,P5: int,R: int] :
% 5.41/5.78 ( ( Q2 != zero_zero_int )
% 5.41/5.78 => ( ( S != zero_zero_int )
% 5.41/5.78 => ( ( ( normalize @ ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.41/5.78 = ( normalize @ ( product_Pair_int_int @ R @ S ) ) )
% 5.41/5.78 => ( ( times_times_int @ P5 @ S )
% 5.41/5.78 = ( times_times_int @ R @ Q2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % normalize_crossproduct
% 5.41/5.78 thf(fact_9701_drop__bit__nat__def,axiom,
% 5.41/5.78 ( bit_se8570568707652914677it_nat
% 5.41/5.78 = ( ^ [N2: nat,M3: nat] : ( divide_divide_nat @ M3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % drop_bit_nat_def
% 5.41/5.78 thf(fact_9702_rat__less__code,axiom,
% 5.41/5.78 ( ord_less_rat
% 5.41/5.78 = ( ^ [P2: rat,Q5: rat] :
% 5.41/5.78 ( produc4947309494688390418_int_o
% 5.41/5.78 @ ^ [A3: int,C3: int] :
% 5.41/5.78 ( produc4947309494688390418_int_o
% 5.41/5.78 @ ^ [B2: int,D2: int] : ( ord_less_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 5.41/5.78 @ ( quotient_of @ Q5 ) )
% 5.41/5.78 @ ( quotient_of @ P2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_less_code
% 5.41/5.78 thf(fact_9703_rat__less__eq__code,axiom,
% 5.41/5.78 ( ord_less_eq_rat
% 5.41/5.78 = ( ^ [P2: rat,Q5: rat] :
% 5.41/5.78 ( produc4947309494688390418_int_o
% 5.41/5.78 @ ^ [A3: int,C3: int] :
% 5.41/5.78 ( produc4947309494688390418_int_o
% 5.41/5.78 @ ^ [B2: int,D2: int] : ( ord_less_eq_int @ ( times_times_int @ A3 @ D2 ) @ ( times_times_int @ C3 @ B2 ) )
% 5.41/5.78 @ ( quotient_of @ Q5 ) )
% 5.41/5.78 @ ( quotient_of @ P2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_less_eq_code
% 5.41/5.78 thf(fact_9704_prod__decode__aux_Oelims,axiom,
% 5.41/5.78 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.41/5.78 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % prod_decode_aux.elims
% 5.41/5.78 thf(fact_9705_minus__one__mod__numeral,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( modulo_modulo_int @ ( uminus_uminus_int @ one_one_int ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.78 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_one_mod_numeral
% 5.41/5.78 thf(fact_9706_one__mod__minus__numeral,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( modulo_modulo_int @ one_one_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ one @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % one_mod_minus_numeral
% 5.41/5.78 thf(fact_9707_prod__decode__aux_Opelims,axiom,
% 5.41/5.78 ! [X: nat,Xa2: nat,Y: product_prod_nat_nat] :
% 5.41/5.78 ( ( ( nat_prod_decode_aux @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.41/5.78 => ~ ( ( ( ( ord_less_eq_nat @ Xa2 @ X )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( product_Pair_nat_nat @ Xa2 @ ( minus_minus_nat @ X @ Xa2 ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_nat @ Xa2 @ X )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( nat_prod_decode_aux @ ( suc @ X ) @ ( minus_minus_nat @ Xa2 @ ( suc @ X ) ) ) ) ) )
% 5.41/5.78 => ~ ( accp_P4275260045618599050at_nat @ nat_pr5047031295181774490ux_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % prod_decode_aux.pelims
% 5.41/5.78 thf(fact_9708_numeral__mod__minus__numeral,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( modulo_modulo_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.78 = ( uminus_uminus_int @ ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % numeral_mod_minus_numeral
% 5.41/5.78 thf(fact_9709_minus__numeral__mod__numeral,axiom,
% 5.41/5.78 ! [M: num,N: num] :
% 5.41/5.78 ( ( modulo_modulo_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.78 = ( adjust_mod @ ( numeral_numeral_int @ N ) @ ( product_snd_int_int @ ( unique5052692396658037445od_int @ M @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_numeral_mod_numeral
% 5.41/5.78 thf(fact_9710_Divides_Oadjust__mod__def,axiom,
% 5.41/5.78 ( adjust_mod
% 5.41/5.78 = ( ^ [L: int,R5: int] : ( if_int @ ( R5 = zero_zero_int ) @ zero_zero_int @ ( minus_minus_int @ L @ R5 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Divides.adjust_mod_def
% 5.41/5.78 thf(fact_9711_quotient__of__int,axiom,
% 5.41/5.78 ! [A: int] :
% 5.41/5.78 ( ( quotient_of @ ( of_int @ A ) )
% 5.41/5.78 = ( product_Pair_int_int @ A @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_int
% 5.41/5.78 thf(fact_9712_Frct__code__post_I5_J,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ one_one_int @ ( numeral_numeral_int @ K ) ) )
% 5.41/5.78 = ( divide_divide_rat @ one_one_rat @ ( numeral_numeral_rat @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(5)
% 5.41/5.78 thf(fact_9713_bezw_Osimps,axiom,
% 5.41/5.78 ( bezw
% 5.41/5.78 = ( ^ [X3: nat,Y3: nat] : ( if_Pro3027730157355071871nt_int @ ( Y3 = zero_zero_nat ) @ ( product_Pair_int_int @ one_one_int @ zero_zero_int ) @ ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X3 @ Y3 ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezw.simps
% 5.41/5.78 thf(fact_9714_Frct__code__post_I2_J,axiom,
% 5.41/5.78 ! [A: int] :
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ A @ zero_zero_int ) )
% 5.41/5.78 = zero_zero_rat ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(2)
% 5.41/5.78 thf(fact_9715_Frct__code__post_I1_J,axiom,
% 5.41/5.78 ! [A: int] :
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ zero_zero_int @ A ) )
% 5.41/5.78 = zero_zero_rat ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(1)
% 5.41/5.78 thf(fact_9716_Frct__code__post_I7_J,axiom,
% 5.41/5.78 ! [A: int,B: int] :
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ ( uminus_uminus_int @ A ) @ B ) )
% 5.41/5.78 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(7)
% 5.41/5.78 thf(fact_9717_Frct__code__post_I8_J,axiom,
% 5.41/5.78 ! [A: int,B: int] :
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ A @ ( uminus_uminus_int @ B ) ) )
% 5.41/5.78 = ( uminus_uminus_rat @ ( frct @ ( product_Pair_int_int @ A @ B ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(8)
% 5.41/5.78 thf(fact_9718_Frct__code__post_I3_J,axiom,
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ one_one_int @ one_one_int ) )
% 5.41/5.78 = one_one_rat ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(3)
% 5.41/5.78 thf(fact_9719_rat__sgn__code,axiom,
% 5.41/5.78 ! [P5: rat] :
% 5.41/5.78 ( ( quotient_of @ ( sgn_sgn_rat @ P5 ) )
% 5.41/5.78 = ( product_Pair_int_int @ ( sgn_sgn_int @ ( product_fst_int_int @ ( quotient_of @ P5 ) ) ) @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_sgn_code
% 5.41/5.78 thf(fact_9720_Frct__code__post_I4_J,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ one_one_int ) )
% 5.41/5.78 = ( numeral_numeral_rat @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(4)
% 5.41/5.78 thf(fact_9721_Frct__code__post_I6_J,axiom,
% 5.41/5.78 ! [K: num,L2: num] :
% 5.41/5.78 ( ( frct @ ( product_Pair_int_int @ ( numeral_numeral_int @ K ) @ ( numeral_numeral_int @ L2 ) ) )
% 5.41/5.78 = ( divide_divide_rat @ ( numeral_numeral_rat @ K ) @ ( numeral_numeral_rat @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Frct_code_post(6)
% 5.41/5.78 thf(fact_9722_bezw__non__0,axiom,
% 5.41/5.78 ! [Y: nat,X: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ Y )
% 5.41/5.78 => ( ( bezw @ X @ Y )
% 5.41/5.78 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Y ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezw_non_0
% 5.41/5.78 thf(fact_9723_bezw_Oelims,axiom,
% 5.41/5.78 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.41/5.78 ( ( ( bezw @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.41/5.78 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezw.elims
% 5.41/5.78 thf(fact_9724_bezw_Opelims,axiom,
% 5.41/5.78 ! [X: nat,Xa2: nat,Y: product_prod_int_int] :
% 5.41/5.78 ( ( ( bezw @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.41/5.78 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( product_Pair_int_int @ one_one_int @ zero_zero_int ) ) )
% 5.41/5.78 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( product_Pair_int_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( minus_minus_int @ ( product_fst_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) @ ( semiri1314217659103216013at_int @ ( divide_divide_nat @ X @ Xa2 ) ) ) ) ) ) ) )
% 5.41/5.78 => ~ ( accp_P4275260045618599050at_nat @ bezw_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezw.pelims
% 5.41/5.78 thf(fact_9725_fst__divmod__nat,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( product_fst_nat_nat @ ( divmod_nat @ M @ N ) )
% 5.41/5.78 = ( divide_divide_nat @ M @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % fst_divmod_nat
% 5.41/5.78 thf(fact_9726_Suc__0__div__numeral,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( divide_divide_nat @ ( suc @ zero_zero_nat ) @ ( numeral_numeral_nat @ K ) )
% 5.41/5.78 = ( product_fst_nat_nat @ ( unique5055182867167087721od_nat @ one @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Suc_0_div_numeral
% 5.41/5.78 thf(fact_9727_normalize__def,axiom,
% 5.41/5.78 ( normalize
% 5.41/5.78 = ( ^ [P2: product_prod_int_int] :
% 5.41/5.78 ( if_Pro3027730157355071871nt_int @ ( ord_less_int @ zero_zero_int @ ( product_snd_int_int @ P2 ) ) @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P2 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P2 ) @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) )
% 5.41/5.78 @ ( if_Pro3027730157355071871nt_int
% 5.41/5.78 @ ( ( product_snd_int_int @ P2 )
% 5.41/5.78 = zero_zero_int )
% 5.41/5.78 @ ( product_Pair_int_int @ zero_zero_int @ one_one_int )
% 5.41/5.78 @ ( product_Pair_int_int @ ( divide_divide_int @ ( product_fst_int_int @ P2 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) ) @ ( divide_divide_int @ ( product_snd_int_int @ P2 ) @ ( uminus_uminus_int @ ( gcd_gcd_int @ ( product_fst_int_int @ P2 ) @ ( product_snd_int_int @ P2 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % normalize_def
% 5.41/5.78 thf(fact_9728_gcd__1__int,axiom,
% 5.41/5.78 ! [M: int] :
% 5.41/5.78 ( ( gcd_gcd_int @ M @ one_one_int )
% 5.41/5.78 = one_one_int ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_1_int
% 5.41/5.78 thf(fact_9729_gcd__pos__int,axiom,
% 5.41/5.78 ! [M: int,N: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ ( gcd_gcd_int @ M @ N ) )
% 5.41/5.78 = ( ( M != zero_zero_int )
% 5.41/5.78 | ( N != zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_pos_int
% 5.41/5.78 thf(fact_9730_gcd__neg__numeral__1__int,axiom,
% 5.41/5.78 ! [N: num,X: int] :
% 5.41/5.78 ( ( gcd_gcd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ X )
% 5.41/5.78 = ( gcd_gcd_int @ ( numeral_numeral_int @ N ) @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_neg_numeral_1_int
% 5.41/5.78 thf(fact_9731_gcd__neg__numeral__2__int,axiom,
% 5.41/5.78 ! [X: int,N: num] :
% 5.41/5.78 ( ( gcd_gcd_int @ X @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.78 = ( gcd_gcd_int @ X @ ( numeral_numeral_int @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_neg_numeral_2_int
% 5.41/5.78 thf(fact_9732_gcd__0__left__int,axiom,
% 5.41/5.78 ! [X: int] :
% 5.41/5.78 ( ( gcd_gcd_int @ zero_zero_int @ X )
% 5.41/5.78 = ( abs_abs_int @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_0_left_int
% 5.41/5.78 thf(fact_9733_gcd__0__int,axiom,
% 5.41/5.78 ! [X: int] :
% 5.41/5.78 ( ( gcd_gcd_int @ X @ zero_zero_int )
% 5.41/5.78 = ( abs_abs_int @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_0_int
% 5.41/5.78 thf(fact_9734_gcd__mult__distrib__int,axiom,
% 5.41/5.78 ! [K: int,M: int,N: int] :
% 5.41/5.78 ( ( times_times_int @ ( abs_abs_int @ K ) @ ( gcd_gcd_int @ M @ N ) )
% 5.41/5.78 = ( gcd_gcd_int @ ( times_times_int @ K @ M ) @ ( times_times_int @ K @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_mult_distrib_int
% 5.41/5.78 thf(fact_9735_bezout__int,axiom,
% 5.41/5.78 ! [X: int,Y: int] :
% 5.41/5.78 ? [U3: int,V2: int] :
% 5.41/5.78 ( ( plus_plus_int @ ( times_times_int @ U3 @ X ) @ ( times_times_int @ V2 @ Y ) )
% 5.41/5.78 = ( gcd_gcd_int @ X @ Y ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezout_int
% 5.41/5.78 thf(fact_9736_gcd__red__int,axiom,
% 5.41/5.78 ( gcd_gcd_int
% 5.41/5.78 = ( ^ [X3: int,Y3: int] : ( gcd_gcd_int @ Y3 @ ( modulo_modulo_int @ X3 @ Y3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_red_int
% 5.41/5.78 thf(fact_9737_gcd__ge__0__int,axiom,
% 5.41/5.78 ! [X: int,Y: int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_gcd_int @ X @ Y ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_ge_0_int
% 5.41/5.78 thf(fact_9738_gcd__le1__int,axiom,
% 5.41/5.78 ! [A: int,B: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ A )
% 5.41/5.78 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ A ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_le1_int
% 5.41/5.78 thf(fact_9739_gcd__le2__int,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ord_less_eq_int @ ( gcd_gcd_int @ A @ B ) @ B ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_le2_int
% 5.41/5.78 thf(fact_9740_gcd__cases__int,axiom,
% 5.41/5.78 ! [X: int,Y: int,P: int > $o] :
% 5.41/5.78 ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) )
% 5.41/5.78 => ( ( ( ord_less_eq_int @ zero_zero_int @ X )
% 5.41/5.78 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.41/5.78 => ( P @ ( gcd_gcd_int @ X @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.41/5.78 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.41/5.78 => ( ( ord_less_eq_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ Y ) ) ) )
% 5.41/5.78 => ( ( ( ord_less_eq_int @ X @ zero_zero_int )
% 5.41/5.78 => ( ( ord_less_eq_int @ Y @ zero_zero_int )
% 5.41/5.78 => ( P @ ( gcd_gcd_int @ ( uminus_uminus_int @ X ) @ ( uminus_uminus_int @ Y ) ) ) ) )
% 5.41/5.78 => ( P @ ( gcd_gcd_int @ X @ Y ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_cases_int
% 5.41/5.78 thf(fact_9741_gcd__unique__int,axiom,
% 5.41/5.78 ! [D: int,A: int,B: int] :
% 5.41/5.78 ( ( ( ord_less_eq_int @ zero_zero_int @ D )
% 5.41/5.78 & ( dvd_dvd_int @ D @ A )
% 5.41/5.78 & ( dvd_dvd_int @ D @ B )
% 5.41/5.78 & ! [E3: int] :
% 5.41/5.78 ( ( ( dvd_dvd_int @ E3 @ A )
% 5.41/5.78 & ( dvd_dvd_int @ E3 @ B ) )
% 5.41/5.78 => ( dvd_dvd_int @ E3 @ D ) ) )
% 5.41/5.78 = ( D
% 5.41/5.78 = ( gcd_gcd_int @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_unique_int
% 5.41/5.78 thf(fact_9742_gcd__non__0__int,axiom,
% 5.41/5.78 ! [Y: int,X: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ Y )
% 5.41/5.78 => ( ( gcd_gcd_int @ X @ Y )
% 5.41/5.78 = ( gcd_gcd_int @ Y @ ( modulo_modulo_int @ X @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_non_0_int
% 5.41/5.78 thf(fact_9743_gcd__code__int,axiom,
% 5.41/5.78 ( gcd_gcd_int
% 5.41/5.78 = ( ^ [K2: int,L: int] : ( abs_abs_int @ ( if_int @ ( L = zero_zero_int ) @ K2 @ ( gcd_gcd_int @ L @ ( modulo_modulo_int @ ( abs_abs_int @ K2 ) @ ( abs_abs_int @ L ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_code_int
% 5.41/5.78 thf(fact_9744_nat__descend__induct,axiom,
% 5.41/5.78 ! [N: nat,P: nat > $o,M: nat] :
% 5.41/5.78 ( ! [K3: nat] :
% 5.41/5.78 ( ( ord_less_nat @ N @ K3 )
% 5.41/5.78 => ( P @ K3 ) )
% 5.41/5.78 => ( ! [K3: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ K3 @ N )
% 5.41/5.78 => ( ! [I2: nat] :
% 5.41/5.78 ( ( ord_less_nat @ K3 @ I2 )
% 5.41/5.78 => ( P @ I2 ) )
% 5.41/5.78 => ( P @ K3 ) ) )
% 5.41/5.78 => ( P @ M ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_descend_induct
% 5.41/5.78 thf(fact_9745_finite__enumerate,axiom,
% 5.41/5.78 ! [S2: set_nat] :
% 5.41/5.78 ( ( finite_finite_nat @ S2 )
% 5.41/5.78 => ? [R2: nat > nat] :
% 5.41/5.78 ( ( strict1292158309912662752at_nat @ R2 @ ( set_ord_lessThan_nat @ ( finite_card_nat @ S2 ) ) )
% 5.41/5.78 & ! [N7: nat] :
% 5.41/5.78 ( ( ord_less_nat @ N7 @ ( finite_card_nat @ S2 ) )
% 5.41/5.78 => ( member_nat @ ( R2 @ N7 ) @ S2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_enumerate
% 5.41/5.78 thf(fact_9746_divmod__integer__eq__cases,axiom,
% 5.41/5.78 ( code_divmod_integer
% 5.41/5.78 = ( ^ [K2: code_integer,L: code_integer] :
% 5.41/5.78 ( if_Pro6119634080678213985nteger @ ( K2 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ zero_z3403309356797280102nteger )
% 5.41/5.78 @ ( if_Pro6119634080678213985nteger @ ( L = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ zero_z3403309356797280102nteger @ K2 )
% 5.41/5.78 @ ( comp_C1593894019821074884nteger @ ( comp_C8797469213163452608nteger @ produc6499014454317279255nteger @ times_3573771949741848930nteger ) @ sgn_sgn_Code_integer @ L
% 5.41/5.78 @ ( if_Pro6119634080678213985nteger
% 5.41/5.78 @ ( ( sgn_sgn_Code_integer @ K2 )
% 5.41/5.78 = ( sgn_sgn_Code_integer @ L ) )
% 5.41/5.78 @ ( code_divmod_abs @ K2 @ L )
% 5.41/5.78 @ ( produc6916734918728496179nteger
% 5.41/5.78 @ ^ [R5: code_integer,S7: code_integer] : ( if_Pro6119634080678213985nteger @ ( S7 = zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( uminus1351360451143612070nteger @ R5 ) @ zero_z3403309356797280102nteger ) @ ( produc1086072967326762835nteger @ ( minus_8373710615458151222nteger @ ( uminus1351360451143612070nteger @ R5 ) @ one_one_Code_integer ) @ ( minus_8373710615458151222nteger @ ( abs_abs_Code_integer @ L ) @ S7 ) ) )
% 5.41/5.78 @ ( code_divmod_abs @ K2 @ L ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divmod_integer_eq_cases
% 5.41/5.78 thf(fact_9747_gcd__nat_Oeq__neutr__iff,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( ( gcd_gcd_nat @ A @ B )
% 5.41/5.78 = zero_zero_nat )
% 5.41/5.78 = ( ( A = zero_zero_nat )
% 5.41/5.78 & ( B = zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.eq_neutr_iff
% 5.41/5.78 thf(fact_9748_gcd__nat_Oleft__neutral,axiom,
% 5.41/5.78 ! [A: nat] :
% 5.41/5.78 ( ( gcd_gcd_nat @ zero_zero_nat @ A )
% 5.41/5.78 = A ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.left_neutral
% 5.41/5.78 thf(fact_9749_gcd__nat_Oneutr__eq__iff,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( zero_zero_nat
% 5.41/5.78 = ( gcd_gcd_nat @ A @ B ) )
% 5.41/5.78 = ( ( A = zero_zero_nat )
% 5.41/5.78 & ( B = zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.neutr_eq_iff
% 5.41/5.78 thf(fact_9750_gcd__nat_Oright__neutral,axiom,
% 5.41/5.78 ! [A: nat] :
% 5.41/5.78 ( ( gcd_gcd_nat @ A @ zero_zero_nat )
% 5.41/5.78 = A ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.right_neutral
% 5.41/5.78 thf(fact_9751_gcd__0__nat,axiom,
% 5.41/5.78 ! [X: nat] :
% 5.41/5.78 ( ( gcd_gcd_nat @ X @ zero_zero_nat )
% 5.41/5.78 = X ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_0_nat
% 5.41/5.78 thf(fact_9752_gcd__0__left__nat,axiom,
% 5.41/5.78 ! [X: nat] :
% 5.41/5.78 ( ( gcd_gcd_nat @ zero_zero_nat @ X )
% 5.41/5.78 = X ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_0_left_nat
% 5.41/5.78 thf(fact_9753_gcd__1__nat,axiom,
% 5.41/5.78 ! [M: nat] :
% 5.41/5.78 ( ( gcd_gcd_nat @ M @ one_one_nat )
% 5.41/5.78 = one_one_nat ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_1_nat
% 5.41/5.78 thf(fact_9754_gcd__Suc__0,axiom,
% 5.41/5.78 ! [M: nat] :
% 5.41/5.78 ( ( gcd_gcd_nat @ M @ ( suc @ zero_zero_nat ) )
% 5.41/5.78 = ( suc @ zero_zero_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_Suc_0
% 5.41/5.78 thf(fact_9755_gcd__pos__nat,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ ( gcd_gcd_nat @ M @ N ) )
% 5.41/5.78 = ( ( M != zero_zero_nat )
% 5.41/5.78 | ( N != zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_pos_nat
% 5.41/5.78 thf(fact_9756_gcd__mult__distrib__nat,axiom,
% 5.41/5.78 ! [K: nat,M: nat,N: nat] :
% 5.41/5.78 ( ( times_times_nat @ K @ ( gcd_gcd_nat @ M @ N ) )
% 5.41/5.78 = ( gcd_gcd_nat @ ( times_times_nat @ K @ M ) @ ( times_times_nat @ K @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_mult_distrib_nat
% 5.41/5.78 thf(fact_9757_gcd__diff1__nat,axiom,
% 5.41/5.78 ! [N: nat,M: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ N @ M )
% 5.41/5.78 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ M @ N ) @ N )
% 5.41/5.78 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_diff1_nat
% 5.41/5.78 thf(fact_9758_gcd__diff2__nat,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.78 => ( ( gcd_gcd_nat @ ( minus_minus_nat @ N @ M ) @ N )
% 5.41/5.78 = ( gcd_gcd_nat @ M @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_diff2_nat
% 5.41/5.78 thf(fact_9759_gcd__red__nat,axiom,
% 5.41/5.78 ( gcd_gcd_nat
% 5.41/5.78 = ( ^ [X3: nat,Y3: nat] : ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_red_nat
% 5.41/5.78 thf(fact_9760_gcd__nat_Oelims,axiom,
% 5.41/5.78 ! [X: nat,Xa2: nat,Y: nat] :
% 5.41/5.78 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.78 => ( Y = X ) )
% 5.41/5.78 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.elims
% 5.41/5.78 thf(fact_9761_gcd__nat_Osimps,axiom,
% 5.41/5.78 ( gcd_gcd_nat
% 5.41/5.78 = ( ^ [X3: nat,Y3: nat] : ( if_nat @ ( Y3 = zero_zero_nat ) @ X3 @ ( gcd_gcd_nat @ Y3 @ ( modulo_modulo_nat @ X3 @ Y3 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.simps
% 5.41/5.78 thf(fact_9762_gcd__non__0__nat,axiom,
% 5.41/5.78 ! [Y: nat,X: nat] :
% 5.41/5.78 ( ( Y != zero_zero_nat )
% 5.41/5.78 => ( ( gcd_gcd_nat @ X @ Y )
% 5.41/5.78 = ( gcd_gcd_nat @ Y @ ( modulo_modulo_nat @ X @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_non_0_nat
% 5.41/5.78 thf(fact_9763_gcd__le1__nat,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( A != zero_zero_nat )
% 5.41/5.78 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ A ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_le1_nat
% 5.41/5.78 thf(fact_9764_gcd__le2__nat,axiom,
% 5.41/5.78 ! [B: nat,A: nat] :
% 5.41/5.78 ( ( B != zero_zero_nat )
% 5.41/5.78 => ( ord_less_eq_nat @ ( gcd_gcd_nat @ A @ B ) @ B ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_le2_nat
% 5.41/5.78 thf(fact_9765_bezout__nat,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( A != zero_zero_nat )
% 5.41/5.78 => ? [X6: nat,Y5: nat] :
% 5.41/5.78 ( ( times_times_nat @ A @ X6 )
% 5.41/5.78 = ( plus_plus_nat @ ( times_times_nat @ B @ Y5 ) @ ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezout_nat
% 5.41/5.78 thf(fact_9766_bezout__gcd__nat_H,axiom,
% 5.41/5.78 ! [B: nat,A: nat] :
% 5.41/5.78 ? [X6: nat,Y5: nat] :
% 5.41/5.78 ( ( ( ord_less_eq_nat @ ( times_times_nat @ B @ Y5 ) @ ( times_times_nat @ A @ X6 ) )
% 5.41/5.78 & ( ( minus_minus_nat @ ( times_times_nat @ A @ X6 ) @ ( times_times_nat @ B @ Y5 ) )
% 5.41/5.78 = ( gcd_gcd_nat @ A @ B ) ) )
% 5.41/5.78 | ( ( ord_less_eq_nat @ ( times_times_nat @ A @ Y5 ) @ ( times_times_nat @ B @ X6 ) )
% 5.41/5.78 & ( ( minus_minus_nat @ ( times_times_nat @ B @ X6 ) @ ( times_times_nat @ A @ Y5 ) )
% 5.41/5.78 = ( gcd_gcd_nat @ A @ B ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezout_gcd_nat'
% 5.41/5.78 thf(fact_9767_gcd__code__integer,axiom,
% 5.41/5.78 ( gcd_gcd_Code_integer
% 5.41/5.78 = ( ^ [K2: code_integer,L: code_integer] : ( abs_abs_Code_integer @ ( if_Code_integer @ ( L = zero_z3403309356797280102nteger ) @ K2 @ ( gcd_gcd_Code_integer @ L @ ( modulo364778990260209775nteger @ ( abs_abs_Code_integer @ K2 ) @ ( abs_abs_Code_integer @ L ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_code_integer
% 5.41/5.78 thf(fact_9768_bezw__aux,axiom,
% 5.41/5.78 ! [X: nat,Y: nat] :
% 5.41/5.78 ( ( semiri1314217659103216013at_int @ ( gcd_gcd_nat @ X @ Y ) )
% 5.41/5.78 = ( plus_plus_int @ ( times_times_int @ ( product_fst_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ X ) ) @ ( times_times_int @ ( product_snd_int_int @ ( bezw @ X @ Y ) ) @ ( semiri1314217659103216013at_int @ Y ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % bezw_aux
% 5.41/5.78 thf(fact_9769_gcd__nat_Opelims,axiom,
% 5.41/5.78 ! [X: nat,Xa2: nat,Y: nat] :
% 5.41/5.78 ( ( ( gcd_gcd_nat @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) )
% 5.41/5.78 => ~ ( ( ( ( Xa2 = zero_zero_nat )
% 5.41/5.78 => ( Y = X ) )
% 5.41/5.78 & ( ( Xa2 != zero_zero_nat )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( gcd_gcd_nat @ Xa2 @ ( modulo_modulo_nat @ X @ Xa2 ) ) ) ) )
% 5.41/5.78 => ~ ( accp_P4275260045618599050at_nat @ gcd_nat_rel @ ( product_Pair_nat_nat @ X @ Xa2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.pelims
% 5.41/5.78 thf(fact_9770_Code__Numeral_Onegative__def,axiom,
% 5.41/5.78 ( code_negative
% 5.41/5.78 = ( comp_C3531382070062128313er_num @ uminus1351360451143612070nteger @ numera6620942414471956472nteger ) ) ).
% 5.41/5.78
% 5.41/5.78 % Code_Numeral.negative_def
% 5.41/5.78 thf(fact_9771_Code__Target__Int_Onegative__def,axiom,
% 5.41/5.78 ( code_Target_negative
% 5.41/5.78 = ( comp_int_int_num @ uminus_uminus_int @ numeral_numeral_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % Code_Target_Int.negative_def
% 5.41/5.78 thf(fact_9772_card__greaterThanLessThan__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( finite_card_int @ ( set_or5832277885323065728an_int @ L2 @ U ) )
% 5.41/5.78 = ( nat2 @ ( minus_minus_int @ U @ ( plus_plus_int @ L2 @ one_one_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_greaterThanLessThan_int
% 5.41/5.78 thf(fact_9773_finite__greaterThanLessThan__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_greaterThanLessThan_int
% 5.41/5.78 thf(fact_9774_atLeastPlusOneLessThan__greaterThanLessThan__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( set_or4662586982721622107an_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.41/5.78 = ( set_or5832277885323065728an_int @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastPlusOneLessThan_greaterThanLessThan_int
% 5.41/5.78 thf(fact_9775_xor__minus__numerals_I1_J,axiom,
% 5.41/5.78 ! [N: num,K: int] :
% 5.41/5.78 ( ( bit_se6526347334894502574or_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) @ K )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ ( neg_numeral_sub_int @ N @ one ) @ K ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_minus_numerals(1)
% 5.41/5.78 thf(fact_9776_xor__minus__numerals_I2_J,axiom,
% 5.41/5.78 ! [K: int,N: num] :
% 5.41/5.78 ( ( bit_se6526347334894502574or_int @ K @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.78 = ( bit_ri7919022796975470100ot_int @ ( bit_se6526347334894502574or_int @ K @ ( neg_numeral_sub_int @ N @ one ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % xor_minus_numerals(2)
% 5.41/5.78 thf(fact_9777_finite__greaterThanLessThan,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_greaterThanLessThan
% 5.41/5.78 thf(fact_9778_card__greaterThanLessThan,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] :
% 5.41/5.78 ( ( finite_card_nat @ ( set_or5834768355832116004an_nat @ L2 @ U ) )
% 5.41/5.78 = ( minus_minus_nat @ U @ ( suc @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_greaterThanLessThan
% 5.41/5.78 thf(fact_9779_atLeastSucLessThan__greaterThanLessThan,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] :
% 5.41/5.78 ( ( set_or4665077453230672383an_nat @ ( suc @ L2 ) @ U )
% 5.41/5.78 = ( set_or5834768355832116004an_nat @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastSucLessThan_greaterThanLessThan
% 5.41/5.78 thf(fact_9780_tanh__real__bounds,axiom,
% 5.41/5.78 ! [X: real] : ( member_real @ ( tanh_real @ X ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) ).
% 5.41/5.78
% 5.41/5.78 % tanh_real_bounds
% 5.41/5.78 thf(fact_9781_sub__BitM__One__eq,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( neg_numeral_sub_int @ ( bitM @ N ) @ one )
% 5.41/5.78 = ( times_times_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( neg_numeral_sub_int @ N @ one ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sub_BitM_One_eq
% 5.41/5.78 thf(fact_9782_Suc__funpow,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( compow_nat_nat @ N @ suc )
% 5.41/5.78 = ( plus_plus_nat @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % Suc_funpow
% 5.41/5.78 thf(fact_9783_max__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.41/5.78 ( semila1623282765462674594er_nat @ ord_max_nat @ zero_zero_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] : ( ord_less_eq_nat @ Y3 @ X3 )
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] : ( ord_less_nat @ Y3 @ X3 ) ) ).
% 5.41/5.78
% 5.41/5.78 % max_nat.semilattice_neutr_order_axioms
% 5.41/5.78 thf(fact_9784_gcd__nat_Osemilattice__neutr__order__axioms,axiom,
% 5.41/5.78 ( semila1623282765462674594er_nat @ gcd_gcd_nat @ zero_zero_nat @ dvd_dvd_nat
% 5.41/5.78 @ ^ [M3: nat,N2: nat] :
% 5.41/5.78 ( ( dvd_dvd_nat @ M3 @ N2 )
% 5.41/5.78 & ( M3 != N2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % gcd_nat.semilattice_neutr_order_axioms
% 5.41/5.78 thf(fact_9785_Sup__nat__empty,axiom,
% 5.41/5.78 ( ( complete_Sup_Sup_nat @ bot_bot_set_nat )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % Sup_nat_empty
% 5.41/5.78 thf(fact_9786_Gcd__remove0__nat,axiom,
% 5.41/5.78 ! [M5: set_nat] :
% 5.41/5.78 ( ( finite_finite_nat @ M5 )
% 5.41/5.78 => ( ( gcd_Gcd_nat @ M5 )
% 5.41/5.78 = ( gcd_Gcd_nat @ ( minus_minus_set_nat @ M5 @ ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Gcd_remove0_nat
% 5.41/5.78 thf(fact_9787_times__int_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.41/5.78 ( ( times_times_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.41/5.78 = ( abs_Integ
% 5.41/5.78 @ ( produc27273713700761075at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) )
% 5.41/5.78 @ Xa2
% 5.41/5.78 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % times_int.abs_eq
% 5.41/5.78 thf(fact_9788_eq__Abs__Integ,axiom,
% 5.41/5.78 ! [Z: int] :
% 5.41/5.78 ~ ! [X6: nat,Y5: nat] :
% 5.41/5.78 ( Z
% 5.41/5.78 != ( abs_Integ @ ( product_Pair_nat_nat @ X6 @ Y5 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % eq_Abs_Integ
% 5.41/5.78 thf(fact_9789_Gcd__nat__eq__one,axiom,
% 5.41/5.78 ! [N4: set_nat] :
% 5.41/5.78 ( ( member_nat @ one_one_nat @ N4 )
% 5.41/5.78 => ( ( gcd_Gcd_nat @ N4 )
% 5.41/5.78 = one_one_nat ) ) ).
% 5.41/5.78
% 5.41/5.78 % Gcd_nat_eq_one
% 5.41/5.78 thf(fact_9790_nat_Oabs__eq,axiom,
% 5.41/5.78 ! [X: product_prod_nat_nat] :
% 5.41/5.78 ( ( nat2 @ ( abs_Integ @ X ) )
% 5.41/5.78 = ( produc6842872674320459806at_nat @ minus_minus_nat @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat.abs_eq
% 5.41/5.78 thf(fact_9791_zero__int__def,axiom,
% 5.41/5.78 ( zero_zero_int
% 5.41/5.78 = ( abs_Integ @ ( product_Pair_nat_nat @ zero_zero_nat @ zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % zero_int_def
% 5.41/5.78 thf(fact_9792_int__def,axiom,
% 5.41/5.78 ( semiri1314217659103216013at_int
% 5.41/5.78 = ( ^ [N2: nat] : ( abs_Integ @ ( product_Pair_nat_nat @ N2 @ zero_zero_nat ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % int_def
% 5.41/5.78 thf(fact_9793_uminus__int_Oabs__eq,axiom,
% 5.41/5.78 ! [X: product_prod_nat_nat] :
% 5.41/5.78 ( ( uminus_uminus_int @ ( abs_Integ @ X ) )
% 5.41/5.78 = ( abs_Integ
% 5.41/5.78 @ ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 )
% 5.41/5.78 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % uminus_int.abs_eq
% 5.41/5.78 thf(fact_9794_one__int__def,axiom,
% 5.41/5.78 ( one_one_int
% 5.41/5.78 = ( abs_Integ @ ( product_Pair_nat_nat @ one_one_nat @ zero_zero_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % one_int_def
% 5.41/5.78 thf(fact_9795_less__int_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.41/5.78 ( ( ord_less_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.41/5.78 = ( produc8739625826339149834_nat_o
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc6081775807080527818_nat_o
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 5.41/5.78 @ Xa2
% 5.41/5.78 @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_int.abs_eq
% 5.41/5.78 thf(fact_9796_less__eq__int_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.41/5.78 ( ( ord_less_eq_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.41/5.78 = ( produc8739625826339149834_nat_o
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc6081775807080527818_nat_o
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) )
% 5.41/5.78 @ Xa2
% 5.41/5.78 @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_eq_int.abs_eq
% 5.41/5.78 thf(fact_9797_plus__int_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.41/5.78 ( ( plus_plus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.41/5.78 = ( abs_Integ
% 5.41/5.78 @ ( produc27273713700761075at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) )
% 5.41/5.78 @ Xa2
% 5.41/5.78 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_int.abs_eq
% 5.41/5.78 thf(fact_9798_minus__int_Oabs__eq,axiom,
% 5.41/5.78 ! [Xa2: product_prod_nat_nat,X: product_prod_nat_nat] :
% 5.41/5.78 ( ( minus_minus_int @ ( abs_Integ @ Xa2 ) @ ( abs_Integ @ X ) )
% 5.41/5.78 = ( abs_Integ
% 5.41/5.78 @ ( produc27273713700761075at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) )
% 5.41/5.78 @ Xa2
% 5.41/5.78 @ X ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_int.abs_eq
% 5.41/5.78 thf(fact_9799_Gcd__int__greater__eq__0,axiom,
% 5.41/5.78 ! [K5: set_int] : ( ord_less_eq_int @ zero_zero_int @ ( gcd_Gcd_int @ K5 ) ) ).
% 5.41/5.78
% 5.41/5.78 % Gcd_int_greater_eq_0
% 5.41/5.78 thf(fact_9800_less__eq__int_Orep__eq,axiom,
% 5.41/5.78 ( ord_less_eq_int
% 5.41/5.78 = ( ^ [X3: int,Xa4: int] :
% 5.41/5.78 ( produc8739625826339149834_nat_o
% 5.41/5.78 @ ^ [Y3: nat,Z3: nat] :
% 5.41/5.78 ( produc6081775807080527818_nat_o
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 5.41/5.78 @ ( rep_Integ @ X3 )
% 5.41/5.78 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_eq_int.rep_eq
% 5.41/5.78 thf(fact_9801_less__int_Orep__eq,axiom,
% 5.41/5.78 ( ord_less_int
% 5.41/5.78 = ( ^ [X3: int,Xa4: int] :
% 5.41/5.78 ( produc8739625826339149834_nat_o
% 5.41/5.78 @ ^ [Y3: nat,Z3: nat] :
% 5.41/5.78 ( produc6081775807080527818_nat_o
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ Y3 @ V4 ) @ ( plus_plus_nat @ U2 @ Z3 ) ) )
% 5.41/5.78 @ ( rep_Integ @ X3 )
% 5.41/5.78 @ ( rep_Integ @ Xa4 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_int.rep_eq
% 5.41/5.78 thf(fact_9802_nat_Orep__eq,axiom,
% 5.41/5.78 ( nat2
% 5.41/5.78 = ( ^ [X3: int] : ( produc6842872674320459806at_nat @ minus_minus_nat @ ( rep_Integ @ X3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat.rep_eq
% 5.41/5.78 thf(fact_9803_prod__encode__def,axiom,
% 5.41/5.78 ( nat_prod_encode
% 5.41/5.78 = ( produc6842872674320459806at_nat
% 5.41/5.78 @ ^ [M3: nat,N2: nat] : ( plus_plus_nat @ ( nat_triangle @ ( plus_plus_nat @ M3 @ N2 ) ) @ M3 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % prod_encode_def
% 5.41/5.78 thf(fact_9804_le__prod__encode__1,axiom,
% 5.41/5.78 ! [A: nat,B: nat] : ( ord_less_eq_nat @ A @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % le_prod_encode_1
% 5.41/5.78 thf(fact_9805_le__prod__encode__2,axiom,
% 5.41/5.78 ! [B: nat,A: nat] : ( ord_less_eq_nat @ B @ ( nat_prod_encode @ ( product_Pair_nat_nat @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % le_prod_encode_2
% 5.41/5.78 thf(fact_9806_prod__encode__prod__decode__aux,axiom,
% 5.41/5.78 ! [K: nat,M: nat] :
% 5.41/5.78 ( ( nat_prod_encode @ ( nat_prod_decode_aux @ K @ M ) )
% 5.41/5.78 = ( plus_plus_nat @ ( nat_triangle @ K ) @ M ) ) ).
% 5.41/5.78
% 5.41/5.78 % prod_encode_prod_decode_aux
% 5.41/5.78 thf(fact_9807_uminus__int__def,axiom,
% 5.41/5.78 ( uminus_uminus_int
% 5.41/5.78 = ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ
% 5.41/5.78 @ ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] : ( product_Pair_nat_nat @ Y3 @ X3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % uminus_int_def
% 5.41/5.78 thf(fact_9808_times__int__def,axiom,
% 5.41/5.78 ( times_times_int
% 5.41/5.78 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.41/5.78 @ ( produc27273713700761075at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ ( times_times_nat @ X3 @ U2 ) @ ( times_times_nat @ Y3 @ V4 ) ) @ ( plus_plus_nat @ ( times_times_nat @ X3 @ V4 ) @ ( times_times_nat @ Y3 @ U2 ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % times_int_def
% 5.41/5.78 thf(fact_9809_minus__int__def,axiom,
% 5.41/5.78 ( minus_minus_int
% 5.41/5.78 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.41/5.78 @ ( produc27273713700761075at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ Y3 @ U2 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % minus_int_def
% 5.41/5.78 thf(fact_9810_plus__int__def,axiom,
% 5.41/5.78 ( plus_plus_int
% 5.41/5.78 = ( map_fu4960017516451851995nt_int @ rep_Integ @ ( map_fu3667384564859982768at_int @ rep_Integ @ abs_Integ )
% 5.41/5.78 @ ( produc27273713700761075at_nat
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc2626176000494625587at_nat
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( product_Pair_nat_nat @ ( plus_plus_nat @ X3 @ U2 ) @ ( plus_plus_nat @ Y3 @ V4 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % plus_int_def
% 5.41/5.78 thf(fact_9811_num__of__nat_Osimps_I2_J,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( num_of_nat @ ( suc @ N ) )
% 5.41/5.78 = ( inc @ ( num_of_nat @ N ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( num_of_nat @ ( suc @ N ) )
% 5.41/5.78 = one ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % num_of_nat.simps(2)
% 5.41/5.78 thf(fact_9812_num__of__nat__numeral__eq,axiom,
% 5.41/5.78 ! [Q2: num] :
% 5.41/5.78 ( ( num_of_nat @ ( numeral_numeral_nat @ Q2 ) )
% 5.41/5.78 = Q2 ) ).
% 5.41/5.78
% 5.41/5.78 % num_of_nat_numeral_eq
% 5.41/5.78 thf(fact_9813_num__of__nat_Osimps_I1_J,axiom,
% 5.41/5.78 ( ( num_of_nat @ zero_zero_nat )
% 5.41/5.78 = one ) ).
% 5.41/5.78
% 5.41/5.78 % num_of_nat.simps(1)
% 5.41/5.78 thf(fact_9814_numeral__num__of__nat,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( numeral_numeral_nat @ ( num_of_nat @ N ) )
% 5.41/5.78 = N ) ) ).
% 5.41/5.78
% 5.41/5.78 % numeral_num_of_nat
% 5.41/5.78 thf(fact_9815_num__of__nat__One,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ N @ one_one_nat )
% 5.41/5.78 => ( ( num_of_nat @ N )
% 5.41/5.78 = one ) ) ).
% 5.41/5.78
% 5.41/5.78 % num_of_nat_One
% 5.41/5.78 thf(fact_9816_num__of__nat__double,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( num_of_nat @ ( plus_plus_nat @ N @ N ) )
% 5.41/5.78 = ( bit0 @ ( num_of_nat @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % num_of_nat_double
% 5.41/5.78 thf(fact_9817_num__of__nat__plus__distrib,axiom,
% 5.41/5.78 ! [M: nat,N: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ M )
% 5.41/5.78 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( num_of_nat @ ( plus_plus_nat @ M @ N ) )
% 5.41/5.78 = ( plus_plus_num @ ( num_of_nat @ M ) @ ( num_of_nat @ N ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % num_of_nat_plus_distrib
% 5.41/5.78 thf(fact_9818_nth__sorted__list__of__set__greaterThanLessThan,axiom,
% 5.41/5.78 ! [N: nat,J: nat,I: nat] :
% 5.41/5.78 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ ( suc @ I ) ) )
% 5.41/5.78 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) ) @ N )
% 5.41/5.78 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nth_sorted_list_of_set_greaterThanLessThan
% 5.41/5.78 thf(fact_9819_nth__sorted__list__of__set__greaterThanAtMost,axiom,
% 5.41/5.78 ! [N: nat,J: nat,I: nat] :
% 5.41/5.78 ( ( ord_less_nat @ N @ ( minus_minus_nat @ J @ I ) )
% 5.41/5.78 => ( ( nth_nat @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) ) @ N )
% 5.41/5.78 = ( suc @ ( plus_plus_nat @ I @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nth_sorted_list_of_set_greaterThanAtMost
% 5.41/5.78 thf(fact_9820_pow_Osimps_I3_J,axiom,
% 5.41/5.78 ! [X: num,Y: num] :
% 5.41/5.78 ( ( pow @ X @ ( bit1 @ Y ) )
% 5.41/5.78 = ( times_times_num @ ( sqr @ ( pow @ X @ Y ) ) @ X ) ) ).
% 5.41/5.78
% 5.41/5.78 % pow.simps(3)
% 5.41/5.78 thf(fact_9821_finite__greaterThanAtMost,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] : ( finite_finite_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_greaterThanAtMost
% 5.41/5.78 thf(fact_9822_card__greaterThanAtMost,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] :
% 5.41/5.78 ( ( finite_card_nat @ ( set_or6659071591806873216st_nat @ L2 @ U ) )
% 5.41/5.78 = ( minus_minus_nat @ U @ L2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_greaterThanAtMost
% 5.41/5.78 thf(fact_9823_atLeastSucAtMost__greaterThanAtMost,axiom,
% 5.41/5.78 ! [L2: nat,U: nat] :
% 5.41/5.78 ( ( set_or1269000886237332187st_nat @ ( suc @ L2 ) @ U )
% 5.41/5.78 = ( set_or6659071591806873216st_nat @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastSucAtMost_greaterThanAtMost
% 5.41/5.78 thf(fact_9824_sqr_Osimps_I2_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( sqr @ ( bit0 @ N ) )
% 5.41/5.78 = ( bit0 @ ( bit0 @ ( sqr @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sqr.simps(2)
% 5.41/5.78 thf(fact_9825_sqr_Osimps_I1_J,axiom,
% 5.41/5.78 ( ( sqr @ one )
% 5.41/5.78 = one ) ).
% 5.41/5.78
% 5.41/5.78 % sqr.simps(1)
% 5.41/5.78 thf(fact_9826_sqr__conv__mult,axiom,
% 5.41/5.78 ( sqr
% 5.41/5.78 = ( ^ [X3: num] : ( times_times_num @ X3 @ X3 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sqr_conv_mult
% 5.41/5.78 thf(fact_9827_pow_Osimps_I2_J,axiom,
% 5.41/5.78 ! [X: num,Y: num] :
% 5.41/5.78 ( ( pow @ X @ ( bit0 @ Y ) )
% 5.41/5.78 = ( sqr @ ( pow @ X @ Y ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % pow.simps(2)
% 5.41/5.78 thf(fact_9828_sqr_Osimps_I3_J,axiom,
% 5.41/5.78 ! [N: num] :
% 5.41/5.78 ( ( sqr @ ( bit1 @ N ) )
% 5.41/5.78 = ( bit1 @ ( bit0 @ ( plus_plus_num @ ( sqr @ N ) @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sqr.simps(3)
% 5.41/5.78 thf(fact_9829_rat__floor__lemma,axiom,
% 5.41/5.78 ! [A: int,B: int] :
% 5.41/5.78 ( ( ord_less_eq_rat @ ( ring_1_of_int_rat @ ( divide_divide_int @ A @ B ) ) @ ( fract @ A @ B ) )
% 5.41/5.78 & ( ord_less_rat @ ( fract @ A @ B ) @ ( ring_1_of_int_rat @ ( plus_plus_int @ ( divide_divide_int @ A @ B ) @ one_one_int ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_floor_lemma
% 5.41/5.78 thf(fact_9830_finite__greaterThanAtMost__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] : ( finite_finite_int @ ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_greaterThanAtMost_int
% 5.41/5.78 thf(fact_9831_mult__rat,axiom,
% 5.41/5.78 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.78 ( ( times_times_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.41/5.78 = ( fract @ ( times_times_int @ A @ C ) @ ( times_times_int @ B @ D ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % mult_rat
% 5.41/5.78 thf(fact_9832_divide__rat,axiom,
% 5.41/5.78 ! [A: int,B: int,C: int,D: int] :
% 5.41/5.78 ( ( divide_divide_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.41/5.78 = ( fract @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ C ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % divide_rat
% 5.41/5.78 thf(fact_9833_card__greaterThanAtMost__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( finite_card_int @ ( set_or6656581121297822940st_int @ L2 @ U ) )
% 5.41/5.78 = ( nat2 @ ( minus_minus_int @ U @ L2 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_greaterThanAtMost_int
% 5.41/5.78 thf(fact_9834_less__rat,axiom,
% 5.41/5.78 ! [B: int,D: int,A: int,C: int] :
% 5.41/5.78 ( ( B != zero_zero_int )
% 5.41/5.78 => ( ( D != zero_zero_int )
% 5.41/5.78 => ( ( ord_less_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.41/5.78 = ( ord_less_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_rat
% 5.41/5.78 thf(fact_9835_add__rat,axiom,
% 5.41/5.78 ! [B: int,D: int,A: int,C: int] :
% 5.41/5.78 ( ( B != zero_zero_int )
% 5.41/5.78 => ( ( D != zero_zero_int )
% 5.41/5.78 => ( ( plus_plus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.41/5.78 = ( fract @ ( plus_plus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % add_rat
% 5.41/5.78 thf(fact_9836_le__rat,axiom,
% 5.41/5.78 ! [B: int,D: int,A: int,C: int] :
% 5.41/5.78 ( ( B != zero_zero_int )
% 5.41/5.78 => ( ( D != zero_zero_int )
% 5.41/5.78 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.41/5.78 = ( ord_less_eq_int @ ( times_times_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ B @ D ) ) @ ( times_times_int @ ( times_times_int @ C @ B ) @ ( times_times_int @ B @ D ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % le_rat
% 5.41/5.78 thf(fact_9837_diff__rat,axiom,
% 5.41/5.78 ! [B: int,D: int,A: int,C: int] :
% 5.41/5.78 ( ( B != zero_zero_int )
% 5.41/5.78 => ( ( D != zero_zero_int )
% 5.41/5.78 => ( ( minus_minus_rat @ ( fract @ A @ B ) @ ( fract @ C @ D ) )
% 5.41/5.78 = ( fract @ ( minus_minus_int @ ( times_times_int @ A @ D ) @ ( times_times_int @ C @ B ) ) @ ( times_times_int @ B @ D ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % diff_rat
% 5.41/5.78 thf(fact_9838_sgn__rat,axiom,
% 5.41/5.78 ! [A: int,B: int] :
% 5.41/5.78 ( ( sgn_sgn_rat @ ( fract @ A @ B ) )
% 5.41/5.78 = ( ring_1_of_int_rat @ ( times_times_int @ ( sgn_sgn_int @ A ) @ ( sgn_sgn_int @ B ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sgn_rat
% 5.41/5.78 thf(fact_9839_Fract__of__int__eq,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( fract @ K @ one_one_int )
% 5.41/5.78 = ( ring_1_of_int_rat @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % Fract_of_int_eq
% 5.41/5.78 thf(fact_9840_quotient__of__eq,axiom,
% 5.41/5.78 ! [A: int,B: int,P5: int,Q2: int] :
% 5.41/5.78 ( ( ( quotient_of @ ( fract @ A @ B ) )
% 5.41/5.78 = ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.41/5.78 => ( ( fract @ P5 @ Q2 )
% 5.41/5.78 = ( fract @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_eq
% 5.41/5.78 thf(fact_9841_One__rat__def,axiom,
% 5.41/5.78 ( one_one_rat
% 5.41/5.78 = ( fract @ one_one_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % One_rat_def
% 5.41/5.78 thf(fact_9842_rat__number__collapse_I1_J,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( fract @ zero_zero_int @ K )
% 5.41/5.78 = zero_zero_rat ) ).
% 5.41/5.78
% 5.41/5.78 % rat_number_collapse(1)
% 5.41/5.78 thf(fact_9843_rat__number__collapse_I6_J,axiom,
% 5.41/5.78 ! [K: int] :
% 5.41/5.78 ( ( fract @ K @ zero_zero_int )
% 5.41/5.78 = zero_zero_rat ) ).
% 5.41/5.78
% 5.41/5.78 % rat_number_collapse(6)
% 5.41/5.78 thf(fact_9844_mult__rat__cancel,axiom,
% 5.41/5.78 ! [C: int,A: int,B: int] :
% 5.41/5.78 ( ( C != zero_zero_int )
% 5.41/5.78 => ( ( fract @ ( times_times_int @ C @ A ) @ ( times_times_int @ C @ B ) )
% 5.41/5.78 = ( fract @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % mult_rat_cancel
% 5.41/5.78 thf(fact_9845_eq__rat_I1_J,axiom,
% 5.41/5.78 ! [B: int,D: int,A: int,C: int] :
% 5.41/5.78 ( ( B != zero_zero_int )
% 5.41/5.78 => ( ( D != zero_zero_int )
% 5.41/5.78 => ( ( ( fract @ A @ B )
% 5.41/5.78 = ( fract @ C @ D ) )
% 5.41/5.78 = ( ( times_times_int @ A @ D )
% 5.41/5.78 = ( times_times_int @ C @ B ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % eq_rat(1)
% 5.41/5.78 thf(fact_9846_Fract__of__nat__eq,axiom,
% 5.41/5.78 ! [K: nat] :
% 5.41/5.78 ( ( fract @ ( semiri1314217659103216013at_int @ K ) @ one_one_int )
% 5.41/5.78 = ( semiri681578069525770553at_rat @ K ) ) ).
% 5.41/5.78
% 5.41/5.78 % Fract_of_nat_eq
% 5.41/5.78 thf(fact_9847_eq__rat_I2_J,axiom,
% 5.41/5.78 ! [A: int] :
% 5.41/5.78 ( ( fract @ A @ zero_zero_int )
% 5.41/5.78 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % eq_rat(2)
% 5.41/5.78 thf(fact_9848_eq__rat_I3_J,axiom,
% 5.41/5.78 ! [A: int,C: int] :
% 5.41/5.78 ( ( fract @ zero_zero_int @ A )
% 5.41/5.78 = ( fract @ zero_zero_int @ C ) ) ).
% 5.41/5.78
% 5.41/5.78 % eq_rat(3)
% 5.41/5.78 thf(fact_9849_Rat__induct__pos,axiom,
% 5.41/5.78 ! [P: rat > $o,Q2: rat] :
% 5.41/5.78 ( ! [A5: int,B5: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B5 )
% 5.41/5.78 => ( P @ ( fract @ A5 @ B5 ) ) )
% 5.41/5.78 => ( P @ Q2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % Rat_induct_pos
% 5.41/5.78 thf(fact_9850_normalize__eq,axiom,
% 5.41/5.78 ! [A: int,B: int,P5: int,Q2: int] :
% 5.41/5.78 ( ( ( normalize @ ( product_Pair_int_int @ A @ B ) )
% 5.41/5.78 = ( product_Pair_int_int @ P5 @ Q2 ) )
% 5.41/5.78 => ( ( fract @ P5 @ Q2 )
% 5.41/5.78 = ( fract @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % normalize_eq
% 5.41/5.78 thf(fact_9851_Zero__rat__def,axiom,
% 5.41/5.78 ( zero_zero_rat
% 5.41/5.78 = ( fract @ zero_zero_int @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % Zero_rat_def
% 5.41/5.78 thf(fact_9852_rat__number__collapse_I3_J,axiom,
% 5.41/5.78 ! [W: num] :
% 5.41/5.78 ( ( fract @ ( numeral_numeral_int @ W ) @ one_one_int )
% 5.41/5.78 = ( numeral_numeral_rat @ W ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_number_collapse(3)
% 5.41/5.78 thf(fact_9853_rat__number__expand_I3_J,axiom,
% 5.41/5.78 ( numeral_numeral_rat
% 5.41/5.78 = ( ^ [K2: num] : ( fract @ ( numeral_numeral_int @ K2 ) @ one_one_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_number_expand(3)
% 5.41/5.78 thf(fact_9854_atLeastPlusOneAtMost__greaterThanAtMost__int,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( set_or1266510415728281911st_int @ ( plus_plus_int @ L2 @ one_one_int ) @ U )
% 5.41/5.78 = ( set_or6656581121297822940st_int @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastPlusOneAtMost_greaterThanAtMost_int
% 5.41/5.78 thf(fact_9855_quotient__of__Fract,axiom,
% 5.41/5.78 ! [A: int,B: int] :
% 5.41/5.78 ( ( quotient_of @ ( fract @ A @ B ) )
% 5.41/5.78 = ( normalize @ ( product_Pair_int_int @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % quotient_of_Fract
% 5.41/5.78 thf(fact_9856_zero__less__Fract__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.41/5.78 = ( ord_less_int @ zero_zero_int @ A ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % zero_less_Fract_iff
% 5.41/5.78 thf(fact_9857_Fract__less__zero__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.41/5.78 = ( ord_less_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Fract_less_zero_iff
% 5.41/5.78 thf(fact_9858_one__less__Fract__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.41/5.78 = ( ord_less_int @ B @ A ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % one_less_Fract_iff
% 5.41/5.78 thf(fact_9859_Fract__less__one__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.41/5.78 = ( ord_less_int @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Fract_less_one_iff
% 5.41/5.78 thf(fact_9860_rat__number__collapse_I5_J,axiom,
% 5.41/5.78 ( ( fract @ ( uminus_uminus_int @ one_one_int ) @ one_one_int )
% 5.41/5.78 = ( uminus_uminus_rat @ one_one_rat ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_number_collapse(5)
% 5.41/5.78 thf(fact_9861_Fract__add__one,axiom,
% 5.41/5.78 ! [N: int,M: int] :
% 5.41/5.78 ( ( N != zero_zero_int )
% 5.41/5.78 => ( ( fract @ ( plus_plus_int @ M @ N ) @ N )
% 5.41/5.78 = ( plus_plus_rat @ ( fract @ M @ N ) @ one_one_rat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Fract_add_one
% 5.41/5.78 thf(fact_9862_Fract__le__zero__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ zero_zero_rat )
% 5.41/5.78 = ( ord_less_eq_int @ A @ zero_zero_int ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Fract_le_zero_iff
% 5.41/5.78 thf(fact_9863_zero__le__Fract__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_eq_rat @ zero_zero_rat @ ( fract @ A @ B ) )
% 5.41/5.78 = ( ord_less_eq_int @ zero_zero_int @ A ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % zero_le_Fract_iff
% 5.41/5.78 thf(fact_9864_Fract__le__one__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_eq_rat @ ( fract @ A @ B ) @ one_one_rat )
% 5.41/5.78 = ( ord_less_eq_int @ A @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Fract_le_one_iff
% 5.41/5.78 thf(fact_9865_one__le__Fract__iff,axiom,
% 5.41/5.78 ! [B: int,A: int] :
% 5.41/5.78 ( ( ord_less_int @ zero_zero_int @ B )
% 5.41/5.78 => ( ( ord_less_eq_rat @ one_one_rat @ ( fract @ A @ B ) )
% 5.41/5.78 = ( ord_less_eq_int @ B @ A ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % one_le_Fract_iff
% 5.41/5.78 thf(fact_9866_rat__number__collapse_I4_J,axiom,
% 5.41/5.78 ! [W: num] :
% 5.41/5.78 ( ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ W ) ) @ one_one_int )
% 5.41/5.78 = ( uminus_uminus_rat @ ( numeral_numeral_rat @ W ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_number_collapse(4)
% 5.41/5.78 thf(fact_9867_rat__number__expand_I5_J,axiom,
% 5.41/5.78 ! [K: num] :
% 5.41/5.78 ( ( uminus_uminus_rat @ ( numeral_numeral_rat @ K ) )
% 5.41/5.78 = ( fract @ ( uminus_uminus_int @ ( numeral_numeral_int @ K ) ) @ one_one_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % rat_number_expand(5)
% 5.41/5.78 thf(fact_9868_image__minus__const__atLeastLessThan__nat,axiom,
% 5.41/5.78 ! [C: nat,Y: nat,X: nat] :
% 5.41/5.78 ( ( ( ord_less_nat @ C @ Y )
% 5.41/5.78 => ( ( image_nat_nat
% 5.41/5.78 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.41/5.78 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.41/5.78 = ( set_or4665077453230672383an_nat @ ( minus_minus_nat @ X @ C ) @ ( minus_minus_nat @ Y @ C ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_nat @ C @ Y )
% 5.41/5.78 => ( ( ( ord_less_nat @ X @ Y )
% 5.41/5.78 => ( ( image_nat_nat
% 5.41/5.78 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.41/5.78 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.41/5.78 = ( insert_nat @ zero_zero_nat @ bot_bot_set_nat ) ) )
% 5.41/5.78 & ( ~ ( ord_less_nat @ X @ Y )
% 5.41/5.78 => ( ( image_nat_nat
% 5.41/5.78 @ ^ [I5: nat] : ( minus_minus_nat @ I5 @ C )
% 5.41/5.78 @ ( set_or4665077453230672383an_nat @ X @ Y ) )
% 5.41/5.78 = bot_bot_set_nat ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_minus_const_atLeastLessThan_nat
% 5.41/5.78 thf(fact_9869_of__nat__eq__id,axiom,
% 5.41/5.78 semiri1316708129612266289at_nat = id_nat ).
% 5.41/5.78
% 5.41/5.78 % of_nat_eq_id
% 5.41/5.78 thf(fact_9870_bij__betw__Suc,axiom,
% 5.41/5.78 ! [M5: set_nat,N4: set_nat] :
% 5.41/5.78 ( ( bij_betw_nat_nat @ suc @ M5 @ N4 )
% 5.41/5.78 = ( ( image_nat_nat @ suc @ M5 )
% 5.41/5.78 = N4 ) ) ).
% 5.41/5.78
% 5.41/5.78 % bij_betw_Suc
% 5.41/5.78 thf(fact_9871_image__Suc__atLeastAtMost,axiom,
% 5.41/5.78 ! [I: nat,J: nat] :
% 5.41/5.78 ( ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ I @ J ) )
% 5.41/5.78 = ( set_or1269000886237332187st_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_Suc_atLeastAtMost
% 5.41/5.78 thf(fact_9872_image__Suc__atLeastLessThan,axiom,
% 5.41/5.78 ! [I: nat,J: nat] :
% 5.41/5.78 ( ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ I @ J ) )
% 5.41/5.78 = ( set_or4665077453230672383an_nat @ ( suc @ I ) @ ( suc @ J ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_Suc_atLeastLessThan
% 5.41/5.78 thf(fact_9873_less__eq__int__def,axiom,
% 5.41/5.78 ( ord_less_eq_int
% 5.41/5.78 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.41/5.78 @ ( produc8739625826339149834_nat_o
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc6081775807080527818_nat_o
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( ord_less_eq_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_eq_int_def
% 5.41/5.78 thf(fact_9874_zero__notin__Suc__image,axiom,
% 5.41/5.78 ! [A2: set_nat] :
% 5.41/5.78 ~ ( member_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ A2 ) ) ).
% 5.41/5.78
% 5.41/5.78 % zero_notin_Suc_image
% 5.41/5.78 thf(fact_9875_less__int__def,axiom,
% 5.41/5.78 ( ord_less_int
% 5.41/5.78 = ( map_fu434086159418415080_int_o @ rep_Integ @ ( map_fu4826362097070443709at_o_o @ rep_Integ @ id_o )
% 5.41/5.78 @ ( produc8739625826339149834_nat_o
% 5.41/5.78 @ ^ [X3: nat,Y3: nat] :
% 5.41/5.78 ( produc6081775807080527818_nat_o
% 5.41/5.78 @ ^ [U2: nat,V4: nat] : ( ord_less_nat @ ( plus_plus_nat @ X3 @ V4 ) @ ( plus_plus_nat @ U2 @ Y3 ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % less_int_def
% 5.41/5.78 thf(fact_9876_nat__def,axiom,
% 5.41/5.78 ( nat2
% 5.41/5.78 = ( map_fu2345160673673942751at_nat @ rep_Integ @ id_nat @ ( produc6842872674320459806at_nat @ minus_minus_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_def
% 5.41/5.78 thf(fact_9877_image__Suc__lessThan,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.78 = ( set_or1269000886237332187st_nat @ one_one_nat @ N ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_Suc_lessThan
% 5.41/5.78 thf(fact_9878_image__Suc__atMost,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) )
% 5.41/5.78 = ( set_or1269000886237332187st_nat @ one_one_nat @ ( suc @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_Suc_atMost
% 5.41/5.78 thf(fact_9879_atLeast0__atMost__Suc__eq__insert__0,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( set_or1269000886237332187st_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.41/5.78 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or1269000886237332187st_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeast0_atMost_Suc_eq_insert_0
% 5.41/5.78 thf(fact_9880_atLeast0__lessThan__Suc__eq__insert__0,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( suc @ N ) )
% 5.41/5.78 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeast0_lessThan_Suc_eq_insert_0
% 5.41/5.78 thf(fact_9881_lessThan__Suc__eq__insert__0,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( set_ord_lessThan_nat @ ( suc @ N ) )
% 5.41/5.78 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_lessThan_nat @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % lessThan_Suc_eq_insert_0
% 5.41/5.78 thf(fact_9882_atMost__Suc__eq__insert__0,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( set_ord_atMost_nat @ ( suc @ N ) )
% 5.41/5.78 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ ( set_ord_atMost_nat @ N ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atMost_Suc_eq_insert_0
% 5.41/5.78 thf(fact_9883_UN__lessThan__UNIV,axiom,
% 5.41/5.78 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_lessThan_nat @ top_top_set_nat ) )
% 5.41/5.78 = top_top_set_nat ) ).
% 5.41/5.78
% 5.41/5.78 % UN_lessThan_UNIV
% 5.41/5.78 thf(fact_9884_UN__atMost__UNIV,axiom,
% 5.41/5.78 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atMost_nat @ top_top_set_nat ) )
% 5.41/5.78 = top_top_set_nat ) ).
% 5.41/5.78
% 5.41/5.78 % UN_atMost_UNIV
% 5.41/5.78 thf(fact_9885_Inf__real__def,axiom,
% 5.41/5.78 ( comple4887499456419720421f_real
% 5.41/5.78 = ( ^ [X2: set_real] : ( uminus_uminus_real @ ( comple1385675409528146559p_real @ ( image_real_real @ uminus_uminus_real @ X2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % Inf_real_def
% 5.41/5.78 thf(fact_9886_finite__int__iff__bounded__le,axiom,
% 5.41/5.78 ( finite_finite_int
% 5.41/5.78 = ( ^ [S6: set_int] :
% 5.41/5.78 ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_atMost_int @ K2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_int_iff_bounded_le
% 5.41/5.78 thf(fact_9887_finite__int__iff__bounded,axiom,
% 5.41/5.78 ( finite_finite_int
% 5.41/5.78 = ( ^ [S6: set_int] :
% 5.41/5.78 ? [K2: int] : ( ord_less_eq_set_int @ ( image_int_int @ abs_abs_int @ S6 ) @ ( set_ord_lessThan_int @ K2 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % finite_int_iff_bounded
% 5.41/5.78 thf(fact_9888_image__int__atLeastAtMost,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or1269000886237332187st_nat @ A @ B ) )
% 5.41/5.78 = ( set_or1266510415728281911st_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_int_atLeastAtMost
% 5.41/5.78 thf(fact_9889_image__int__atLeastLessThan,axiom,
% 5.41/5.78 ! [A: nat,B: nat] :
% 5.41/5.78 ( ( image_nat_int @ semiri1314217659103216013at_int @ ( set_or4665077453230672383an_nat @ A @ B ) )
% 5.41/5.78 = ( set_or4662586982721622107an_int @ ( semiri1314217659103216013at_int @ A ) @ ( semiri1314217659103216013at_int @ B ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_int_atLeastLessThan
% 5.41/5.78 thf(fact_9890_suminf__eq__SUP__real,axiom,
% 5.41/5.78 ! [X8: nat > real] :
% 5.41/5.78 ( ( summable_real @ X8 )
% 5.41/5.78 => ( ! [I4: nat] : ( ord_less_eq_real @ zero_zero_real @ ( X8 @ I4 ) )
% 5.41/5.78 => ( ( suminf_real @ X8 )
% 5.41/5.78 = ( comple1385675409528146559p_real
% 5.41/5.78 @ ( image_nat_real
% 5.41/5.78 @ ^ [I5: nat] : ( groups6591440286371151544t_real @ X8 @ ( set_ord_lessThan_nat @ I5 ) )
% 5.41/5.78 @ top_top_set_nat ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % suminf_eq_SUP_real
% 5.41/5.78 thf(fact_9891_image__add__int__atLeastLessThan,axiom,
% 5.41/5.78 ! [L2: int,U: int] :
% 5.41/5.78 ( ( image_int_int
% 5.41/5.78 @ ^ [X3: int] : ( plus_plus_int @ X3 @ L2 )
% 5.41/5.78 @ ( set_or4662586982721622107an_int @ zero_zero_int @ ( minus_minus_int @ U @ L2 ) ) )
% 5.41/5.78 = ( set_or4662586982721622107an_int @ L2 @ U ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_add_int_atLeastLessThan
% 5.41/5.78 thf(fact_9892_range__mod,axiom,
% 5.41/5.78 ! [N: nat] :
% 5.41/5.78 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.78 => ( ( image_nat_nat
% 5.41/5.78 @ ^ [M3: nat] : ( modulo_modulo_nat @ M3 @ N )
% 5.41/5.78 @ top_top_set_nat )
% 5.41/5.78 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ N ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % range_mod
% 5.41/5.78 thf(fact_9893_image__atLeastZeroLessThan__int,axiom,
% 5.41/5.78 ! [U: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ zero_zero_int @ U )
% 5.41/5.78 => ( ( set_or4662586982721622107an_int @ zero_zero_int @ U )
% 5.41/5.78 = ( image_nat_int @ semiri1314217659103216013at_int @ ( set_ord_lessThan_nat @ ( nat2 @ U ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % image_atLeastZeroLessThan_int
% 5.41/5.78 thf(fact_9894_UNIV__nat__eq,axiom,
% 5.41/5.78 ( top_top_set_nat
% 5.41/5.78 = ( insert_nat @ zero_zero_nat @ ( image_nat_nat @ suc @ top_top_set_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % UNIV_nat_eq
% 5.41/5.78 thf(fact_9895_card__UNIV__unit,axiom,
% 5.41/5.78 ( ( finite410649719033368117t_unit @ top_to1996260823553986621t_unit )
% 5.41/5.78 = one_one_nat ) ).
% 5.41/5.78
% 5.41/5.78 % card_UNIV_unit
% 5.41/5.78 thf(fact_9896_card__UNIV__bool,axiom,
% 5.41/5.78 ( ( finite_card_o @ top_top_set_o )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_UNIV_bool
% 5.41/5.78 thf(fact_9897_range__mult,axiom,
% 5.41/5.78 ! [A: real] :
% 5.41/5.78 ( ( ( A = zero_zero_real )
% 5.41/5.78 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.41/5.78 = ( insert_real @ zero_zero_real @ bot_bot_set_real ) ) )
% 5.41/5.78 & ( ( A != zero_zero_real )
% 5.41/5.78 => ( ( image_real_real @ ( times_times_real @ A ) @ top_top_set_real )
% 5.41/5.78 = top_top_set_real ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % range_mult
% 5.41/5.78 thf(fact_9898_root__def,axiom,
% 5.41/5.78 ( root
% 5.41/5.78 = ( ^ [N2: nat,X3: real] :
% 5.41/5.78 ( if_real @ ( N2 = zero_zero_nat ) @ zero_zero_real
% 5.41/5.78 @ ( the_in5290026491893676941l_real @ top_top_set_real
% 5.41/5.78 @ ^ [Y3: real] : ( times_times_real @ ( sgn_sgn_real @ Y3 ) @ ( power_power_real @ ( abs_abs_real @ Y3 ) @ N2 ) )
% 5.41/5.78 @ X3 ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % root_def
% 5.41/5.78 thf(fact_9899_card__UNIV__char,axiom,
% 5.41/5.78 ( ( finite_card_char @ top_top_set_char )
% 5.41/5.78 = ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % card_UNIV_char
% 5.41/5.78 thf(fact_9900_UNIV__char__of__nat,axiom,
% 5.41/5.78 ( top_top_set_char
% 5.41/5.78 = ( image_nat_char @ unique3096191561947761185of_nat @ ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % UNIV_char_of_nat
% 5.41/5.78 thf(fact_9901_char_Osize_I2_J,axiom,
% 5.41/5.78 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.41/5.78 ( ( size_size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % char.size(2)
% 5.41/5.78 thf(fact_9902_nat__of__char__less__256,axiom,
% 5.41/5.78 ! [C: char] : ( ord_less_nat @ ( comm_s629917340098488124ar_nat @ C ) @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nat_of_char_less_256
% 5.41/5.78 thf(fact_9903_range__nat__of__char,axiom,
% 5.41/5.78 ( ( image_char_nat @ comm_s629917340098488124ar_nat @ top_top_set_char )
% 5.41/5.78 = ( set_or4665077453230672383an_nat @ zero_zero_nat @ ( numeral_numeral_nat @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ ( bit0 @ one ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % range_nat_of_char
% 5.41/5.78 thf(fact_9904_integer__of__char__code,axiom,
% 5.41/5.78 ! [B0: $o,B1: $o,B22: $o,B32: $o,B42: $o,B52: $o,B62: $o,B72: $o] :
% 5.41/5.78 ( ( integer_of_char @ ( char2 @ B0 @ B1 @ B22 @ B32 @ B42 @ B52 @ B62 @ B72 ) )
% 5.41/5.78 = ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( plus_p5714425477246183910nteger @ ( times_3573771949741848930nteger @ ( zero_n356916108424825756nteger @ B72 ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B62 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B52 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B42 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B32 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B22 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B1 ) ) @ ( numera6620942414471956472nteger @ ( bit0 @ one ) ) ) @ ( zero_n356916108424825756nteger @ B0 ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % integer_of_char_code
% 5.41/5.78 thf(fact_9905_char_Osize__gen,axiom,
% 5.41/5.78 ! [X1: $o,X22: $o,X32: $o,X42: $o,X52: $o,X62: $o,X72: $o,X82: $o] :
% 5.41/5.78 ( ( size_char @ ( char2 @ X1 @ X22 @ X32 @ X42 @ X52 @ X62 @ X72 @ X82 ) )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % char.size_gen
% 5.41/5.78 thf(fact_9906_String_Ochar__of__ascii__of,axiom,
% 5.41/5.78 ! [C: char] :
% 5.41/5.78 ( ( comm_s629917340098488124ar_nat @ ( ascii_of @ C ) )
% 5.41/5.78 = ( bit_se2925701944663578781it_nat @ ( numeral_numeral_nat @ ( bit1 @ ( bit1 @ one ) ) ) @ ( comm_s629917340098488124ar_nat @ C ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % String.char_of_ascii_of
% 5.41/5.78 thf(fact_9907_sorted__list__of__set__lessThan__Suc,axiom,
% 5.41/5.78 ! [K: nat] :
% 5.41/5.78 ( ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ ( suc @ K ) ) )
% 5.41/5.78 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_lessThan_nat @ K ) ) @ ( cons_nat @ K @ nil_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sorted_list_of_set_lessThan_Suc
% 5.41/5.78 thf(fact_9908_sorted__list__of__set__atMost__Suc,axiom,
% 5.41/5.78 ! [K: nat] :
% 5.41/5.78 ( ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ ( suc @ K ) ) )
% 5.41/5.78 = ( append_nat @ ( linord2614967742042102400et_nat @ ( set_ord_atMost_nat @ K ) ) @ ( cons_nat @ ( suc @ K ) @ nil_nat ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sorted_list_of_set_atMost_Suc
% 5.41/5.78 thf(fact_9909_sorted__list__of__set__greaterThanAtMost,axiom,
% 5.41/5.78 ! [I: nat,J: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ ( suc @ I ) @ J )
% 5.41/5.78 => ( ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ I @ J ) )
% 5.41/5.78 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or6659071591806873216st_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sorted_list_of_set_greaterThanAtMost
% 5.41/5.78 thf(fact_9910_sorted__list__of__set__greaterThanLessThan,axiom,
% 5.41/5.78 ! [I: nat,J: nat] :
% 5.41/5.78 ( ( ord_less_nat @ ( suc @ I ) @ J )
% 5.41/5.78 => ( ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ I @ J ) )
% 5.41/5.78 = ( cons_nat @ ( suc @ I ) @ ( linord2614967742042102400et_nat @ ( set_or5834768355832116004an_nat @ ( suc @ I ) @ J ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % sorted_list_of_set_greaterThanLessThan
% 5.41/5.78 thf(fact_9911_list__encode_Oelims,axiom,
% 5.41/5.78 ! [X: list_nat,Y: nat] :
% 5.41/5.78 ( ( ( nat_list_encode @ X )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( ( X = nil_nat )
% 5.41/5.78 => ( Y != zero_zero_nat ) )
% 5.41/5.78 => ~ ! [X6: nat,Xs3: list_nat] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( cons_nat @ X6 @ Xs3 ) )
% 5.41/5.78 => ( Y
% 5.41/5.78 != ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X6 @ ( nat_list_encode @ Xs3 ) ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % list_encode.elims
% 5.41/5.78 thf(fact_9912_upto__aux__rec,axiom,
% 5.41/5.78 ( upto_aux
% 5.41/5.78 = ( ^ [I5: int,J3: int,Js: list_int] : ( if_list_int @ ( ord_less_int @ J3 @ I5 ) @ Js @ ( upto_aux @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) @ ( cons_int @ J3 @ Js ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % upto_aux_rec
% 5.41/5.78 thf(fact_9913_sup__enat__def,axiom,
% 5.41/5.78 sup_su3973961784419623482d_enat = ord_ma741700101516333627d_enat ).
% 5.41/5.78
% 5.41/5.78 % sup_enat_def
% 5.41/5.78 thf(fact_9914_sup__nat__def,axiom,
% 5.41/5.78 sup_sup_nat = ord_max_nat ).
% 5.41/5.78
% 5.41/5.78 % sup_nat_def
% 5.41/5.78 thf(fact_9915_atLeastLessThan__add__Un,axiom,
% 5.41/5.78 ! [I: nat,J: nat,K: nat] :
% 5.41/5.78 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.78 => ( ( set_or4665077453230672383an_nat @ I @ ( plus_plus_nat @ J @ K ) )
% 5.41/5.78 = ( sup_sup_set_nat @ ( set_or4665077453230672383an_nat @ I @ J ) @ ( set_or4665077453230672383an_nat @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % atLeastLessThan_add_Un
% 5.41/5.78 thf(fact_9916_list__encode_Osimps_I1_J,axiom,
% 5.41/5.78 ( ( nat_list_encode @ nil_nat )
% 5.41/5.78 = zero_zero_nat ) ).
% 5.41/5.78
% 5.41/5.78 % list_encode.simps(1)
% 5.41/5.78 thf(fact_9917_list__encode_Osimps_I2_J,axiom,
% 5.41/5.78 ! [X: nat,Xs: list_nat] :
% 5.41/5.78 ( ( nat_list_encode @ ( cons_nat @ X @ Xs ) )
% 5.41/5.78 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X @ ( nat_list_encode @ Xs ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % list_encode.simps(2)
% 5.41/5.78 thf(fact_9918_list__encode_Opelims,axiom,
% 5.41/5.78 ! [X: list_nat,Y: nat] :
% 5.41/5.78 ( ( ( nat_list_encode @ X )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( accp_list_nat @ nat_list_encode_rel @ X )
% 5.41/5.78 => ( ( ( X = nil_nat )
% 5.41/5.78 => ( ( Y = zero_zero_nat )
% 5.41/5.78 => ~ ( accp_list_nat @ nat_list_encode_rel @ nil_nat ) ) )
% 5.41/5.78 => ~ ! [X6: nat,Xs3: list_nat] :
% 5.41/5.78 ( ( X
% 5.41/5.78 = ( cons_nat @ X6 @ Xs3 ) )
% 5.41/5.78 => ( ( Y
% 5.41/5.78 = ( suc @ ( nat_prod_encode @ ( product_Pair_nat_nat @ X6 @ ( nat_list_encode @ Xs3 ) ) ) ) )
% 5.41/5.78 => ~ ( accp_list_nat @ nat_list_encode_rel @ ( cons_nat @ X6 @ Xs3 ) ) ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % list_encode.pelims
% 5.41/5.78 thf(fact_9919_upto_Opelims,axiom,
% 5.41/5.78 ! [X: int,Xa2: int,Y: list_int] :
% 5.41/5.78 ( ( ( upto @ X @ Xa2 )
% 5.41/5.78 = Y )
% 5.41/5.78 => ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) )
% 5.41/5.78 => ~ ( ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.41/5.78 => ( Y
% 5.41/5.78 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.41/5.78 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.41/5.78 => ( Y = nil_int ) ) )
% 5.41/5.78 => ~ ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ X @ Xa2 ) ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % upto.pelims
% 5.41/5.78 thf(fact_9920_upto__Nil,axiom,
% 5.41/5.78 ! [I: int,J: int] :
% 5.41/5.78 ( ( ( upto @ I @ J )
% 5.41/5.78 = nil_int )
% 5.41/5.78 = ( ord_less_int @ J @ I ) ) ).
% 5.41/5.78
% 5.41/5.78 % upto_Nil
% 5.41/5.78 thf(fact_9921_upto__Nil2,axiom,
% 5.41/5.78 ! [I: int,J: int] :
% 5.41/5.78 ( ( nil_int
% 5.41/5.78 = ( upto @ I @ J ) )
% 5.41/5.78 = ( ord_less_int @ J @ I ) ) ).
% 5.41/5.78
% 5.41/5.78 % upto_Nil2
% 5.41/5.78 thf(fact_9922_upto__empty,axiom,
% 5.41/5.78 ! [J: int,I: int] :
% 5.41/5.78 ( ( ord_less_int @ J @ I )
% 5.41/5.78 => ( ( upto @ I @ J )
% 5.41/5.78 = nil_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % upto_empty
% 5.41/5.78 thf(fact_9923_upto__single,axiom,
% 5.41/5.78 ! [I: int] :
% 5.41/5.78 ( ( upto @ I @ I )
% 5.41/5.78 = ( cons_int @ I @ nil_int ) ) ).
% 5.41/5.78
% 5.41/5.78 % upto_single
% 5.41/5.78 thf(fact_9924_nth__upto,axiom,
% 5.41/5.78 ! [I: int,K: nat,J: int] :
% 5.41/5.78 ( ( ord_less_eq_int @ ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) @ J )
% 5.41/5.78 => ( ( nth_int @ ( upto @ I @ J ) @ K )
% 5.41/5.78 = ( plus_plus_int @ I @ ( semiri1314217659103216013at_int @ K ) ) ) ) ).
% 5.41/5.78
% 5.41/5.78 % nth_upto
% 5.41/5.78 thf(fact_9925_length__upto,axiom,
% 5.41/5.78 ! [I: int,J: int] :
% 5.41/5.78 ( ( size_size_list_int @ ( upto @ I @ J ) )
% 5.41/5.78 = ( nat2 @ ( plus_plus_int @ ( minus_minus_int @ J @ I ) @ one_one_int ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % length_upto
% 5.41/5.79 thf(fact_9926_upto__rec__numeral_I1_J,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 = nil_int ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_rec_numeral(1)
% 5.41/5.79 thf(fact_9927_upto__rec__numeral_I2_J,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = ( cons_int @ ( numeral_numeral_int @ M ) @ ( upto @ ( plus_plus_int @ ( numeral_numeral_int @ M ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_eq_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 => ( ( upto @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = nil_int ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_rec_numeral(2)
% 5.41/5.79 thf(fact_9928_upto__rec__numeral_I3_J,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( numeral_numeral_int @ N ) ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 = nil_int ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_rec_numeral(3)
% 5.41/5.79 thf(fact_9929_upto__rec__numeral_I4_J,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = ( cons_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( upto @ ( plus_plus_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ one_one_int ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_eq_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 => ( ( upto @ ( uminus_uminus_int @ ( numeral_numeral_int @ M ) ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = nil_int ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_rec_numeral(4)
% 5.41/5.79 thf(fact_9930_upto__aux__def,axiom,
% 5.41/5.79 ( upto_aux
% 5.41/5.79 = ( ^ [I5: int,J3: int] : ( append_int @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_aux_def
% 5.41/5.79 thf(fact_9931_upto__code,axiom,
% 5.41/5.79 ( upto
% 5.41/5.79 = ( ^ [I5: int,J3: int] : ( upto_aux @ I5 @ J3 @ nil_int ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_code
% 5.41/5.79 thf(fact_9932_distinct__upto,axiom,
% 5.41/5.79 ! [I: int,J: int] : ( distinct_int @ ( upto @ I @ J ) ) ).
% 5.41/5.79
% 5.41/5.79 % distinct_upto
% 5.41/5.79 thf(fact_9933_atLeastAtMost__upto,axiom,
% 5.41/5.79 ( set_or1266510415728281911st_int
% 5.41/5.79 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ J3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % atLeastAtMost_upto
% 5.41/5.79 thf(fact_9934_upto__split2,axiom,
% 5.41/5.79 ! [I: int,J: int,K: int] :
% 5.41/5.79 ( ( ord_less_eq_int @ I @ J )
% 5.41/5.79 => ( ( ord_less_eq_int @ J @ K )
% 5.41/5.79 => ( ( upto @ I @ K )
% 5.41/5.79 = ( append_int @ ( upto @ I @ J ) @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_split2
% 5.41/5.79 thf(fact_9935_upto__split1,axiom,
% 5.41/5.79 ! [I: int,J: int,K: int] :
% 5.41/5.79 ( ( ord_less_eq_int @ I @ J )
% 5.41/5.79 => ( ( ord_less_eq_int @ J @ K )
% 5.41/5.79 => ( ( upto @ I @ K )
% 5.41/5.79 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( upto @ J @ K ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_split1
% 5.41/5.79 thf(fact_9936_atLeastLessThan__upto,axiom,
% 5.41/5.79 ( set_or4662586982721622107an_int
% 5.41/5.79 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ I5 @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % atLeastLessThan_upto
% 5.41/5.79 thf(fact_9937_greaterThanAtMost__upto,axiom,
% 5.41/5.79 ( set_or6656581121297822940st_int
% 5.41/5.79 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % greaterThanAtMost_upto
% 5.41/5.79 thf(fact_9938_upto_Oelims,axiom,
% 5.41/5.79 ! [X: int,Xa2: int,Y: list_int] :
% 5.41/5.79 ( ( ( upto @ X @ Xa2 )
% 5.41/5.79 = Y )
% 5.41/5.79 => ( ( ( ord_less_eq_int @ X @ Xa2 )
% 5.41/5.79 => ( Y
% 5.41/5.79 = ( cons_int @ X @ ( upto @ ( plus_plus_int @ X @ one_one_int ) @ Xa2 ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_eq_int @ X @ Xa2 )
% 5.41/5.79 => ( Y = nil_int ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto.elims
% 5.41/5.79 thf(fact_9939_upto_Osimps,axiom,
% 5.41/5.79 ( upto
% 5.41/5.79 = ( ^ [I5: int,J3: int] : ( if_list_int @ ( ord_less_eq_int @ I5 @ J3 ) @ ( cons_int @ I5 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ J3 ) ) @ nil_int ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto.simps
% 5.41/5.79 thf(fact_9940_upto__rec1,axiom,
% 5.41/5.79 ! [I: int,J: int] :
% 5.41/5.79 ( ( ord_less_eq_int @ I @ J )
% 5.41/5.79 => ( ( upto @ I @ J )
% 5.41/5.79 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_rec1
% 5.41/5.79 thf(fact_9941_upto__rec2,axiom,
% 5.41/5.79 ! [I: int,J: int] :
% 5.41/5.79 ( ( ord_less_eq_int @ I @ J )
% 5.41/5.79 => ( ( upto @ I @ J )
% 5.41/5.79 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ nil_int ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_rec2
% 5.41/5.79 thf(fact_9942_greaterThanLessThan__upto,axiom,
% 5.41/5.79 ( set_or5832277885323065728an_int
% 5.41/5.79 = ( ^ [I5: int,J3: int] : ( set_int2 @ ( upto @ ( plus_plus_int @ I5 @ one_one_int ) @ ( minus_minus_int @ J3 @ one_one_int ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % greaterThanLessThan_upto
% 5.41/5.79 thf(fact_9943_upto__split3,axiom,
% 5.41/5.79 ! [I: int,J: int,K: int] :
% 5.41/5.79 ( ( ord_less_eq_int @ I @ J )
% 5.41/5.79 => ( ( ord_less_eq_int @ J @ K )
% 5.41/5.79 => ( ( upto @ I @ K )
% 5.41/5.79 = ( append_int @ ( upto @ I @ ( minus_minus_int @ J @ one_one_int ) ) @ ( cons_int @ J @ ( upto @ ( plus_plus_int @ J @ one_one_int ) @ K ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto_split3
% 5.41/5.79 thf(fact_9944_upto_Opsimps,axiom,
% 5.41/5.79 ! [I: int,J: int] :
% 5.41/5.79 ( ( accp_P1096762738010456898nt_int @ upto_rel @ ( product_Pair_int_int @ I @ J ) )
% 5.41/5.79 => ( ( ( ord_less_eq_int @ I @ J )
% 5.41/5.79 => ( ( upto @ I @ J )
% 5.41/5.79 = ( cons_int @ I @ ( upto @ ( plus_plus_int @ I @ one_one_int ) @ J ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_eq_int @ I @ J )
% 5.41/5.79 => ( ( upto @ I @ J )
% 5.41/5.79 = nil_int ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upto.psimps
% 5.41/5.79 thf(fact_9945_DERIV__real__root__generic,axiom,
% 5.41/5.79 ! [N: nat,X: real,D4: real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( X != zero_zero_real )
% 5.41/5.79 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.79 => ( D4
% 5.41/5.79 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) )
% 5.41/5.79 => ( ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.79 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.79 => ( D4
% 5.41/5.79 = ( uminus_uminus_real @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) ) ) )
% 5.41/5.79 => ( ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.79 => ( D4
% 5.41/5.79 = ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_real_root_generic
% 5.41/5.79 thf(fact_9946_DERIV__local__const,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real,D: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.41/5.79 => ( ! [Y5: real] :
% 5.41/5.79 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.41/5.79 => ( ( F @ X )
% 5.41/5.79 = ( F @ Y5 ) ) )
% 5.41/5.79 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_local_const
% 5.41/5.79 thf(fact_9947_DERIV__pos__inc__left,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_pos_inc_left
% 5.41/5.79 thf(fact_9948_DERIV__neg__dec__left,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_neg_dec_left
% 5.41/5.79 thf(fact_9949_DERIV__const__ratio__const,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,K: real] :
% 5.41/5.79 ( ( A != B )
% 5.41/5.79 => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.41/5.79 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ K ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_const_ratio_const
% 5.41/5.79 thf(fact_9950_DERIV__const__ratio__const2,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,K: real] :
% 5.41/5.79 ( ( A != B )
% 5.41/5.79 => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 => ( ( divide_divide_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( minus_minus_real @ B @ A ) )
% 5.41/5.79 = K ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_const_ratio_const2
% 5.41/5.79 thf(fact_9951_DERIV__isconst__all,axiom,
% 5.41/5.79 ! [F: real > real,X: real,Y: real] :
% 5.41/5.79 ( ! [X6: real] : ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 => ( ( F @ X )
% 5.41/5.79 = ( F @ Y ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_isconst_all
% 5.41/5.79 thf(fact_9952_DERIV__neg__dec__right,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_neg_dec_right
% 5.41/5.79 thf(fact_9953_DERIV__pos__inc__right,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_pos_inc_right
% 5.41/5.79 thf(fact_9954_DERIV__ln,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( inverse_inverse_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_ln
% 5.41/5.79 thf(fact_9955_DERIV__isconst3,axiom,
% 5.41/5.79 ! [A: real,B: real,X: real,Y: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ( member_real @ X @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.41/5.79 => ( ( member_real @ Y @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 5.41/5.79 => ( ( F @ X )
% 5.41/5.79 = ( F @ Y ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_isconst3
% 5.41/5.79 thf(fact_9956_has__real__derivative__pos__inc__right,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real,S2: set_real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ X ) @ ( F @ ( plus_plus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % has_real_derivative_pos_inc_right
% 5.41/5.79 thf(fact_9957_has__real__derivative__neg__dec__right,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real,S2: set_real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 5.41/5.79 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( member_real @ ( plus_plus_real @ X @ H4 ) @ S2 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ ( plus_plus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % has_real_derivative_neg_dec_right
% 5.41/5.79 thf(fact_9958_has__real__derivative__pos__inc__left,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real,S2: set_real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ ( minus_minus_real @ X @ H4 ) ) @ ( F @ X ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % has_real_derivative_pos_inc_left
% 5.41/5.79 thf(fact_9959_has__real__derivative__neg__dec__left,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real,S2: set_real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ S2 ) )
% 5.41/5.79 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.41/5.79 => ? [D3: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D3 )
% 5.41/5.79 & ! [H4: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H4 )
% 5.41/5.79 => ( ( member_real @ ( minus_minus_real @ X @ H4 ) @ S2 )
% 5.41/5.79 => ( ( ord_less_real @ H4 @ D3 )
% 5.41/5.79 => ( ord_less_real @ ( F @ X ) @ ( F @ ( minus_minus_real @ X @ H4 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % has_real_derivative_neg_dec_left
% 5.41/5.79 thf(fact_9960_MVT2,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,F5: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_eq_real @ X6 @ B )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ? [Z5: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Z5 )
% 5.41/5.79 & ( ord_less_real @ Z5 @ B )
% 5.41/5.79 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.41/5.79 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ ( F5 @ Z5 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % MVT2
% 5.41/5.79 thf(fact_9961_DERIV__neg__imp__decreasing,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_eq_real @ X6 @ B )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 5.41/5.79 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_neg_imp_decreasing
% 5.41/5.79 thf(fact_9962_DERIV__pos__imp__increasing,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_eq_real @ X6 @ B )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 5.41/5.79 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_pos_imp_increasing
% 5.41/5.79 thf(fact_9963_deriv__nonneg__imp__mono,axiom,
% 5.41/5.79 ! [A: real,B: real,G: real > real,G2: real > real] :
% 5.41/5.79 ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.41/5.79 => ( ord_less_eq_real @ zero_zero_real @ ( G2 @ X6 ) ) )
% 5.41/5.79 => ( ( ord_less_eq_real @ A @ B )
% 5.41/5.79 => ( ord_less_eq_real @ ( G @ A ) @ ( G @ B ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % deriv_nonneg_imp_mono
% 5.41/5.79 thf(fact_9964_DERIV__nonpos__imp__nonincreasing,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_eq_real @ X6 @ B )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_eq_real @ Y2 @ zero_zero_real ) ) ) )
% 5.41/5.79 => ( ord_less_eq_real @ ( F @ B ) @ ( F @ A ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_nonpos_imp_nonincreasing
% 5.41/5.79 thf(fact_9965_DERIV__nonneg__imp__nondecreasing,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_eq_real @ X6 @ B )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_eq_real @ zero_zero_real @ Y2 ) ) ) )
% 5.41/5.79 => ( ord_less_eq_real @ ( F @ A ) @ ( F @ B ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_nonneg_imp_nondecreasing
% 5.41/5.79 thf(fact_9966_DERIV__const__average,axiom,
% 5.41/5.79 ! [A: real,B: real,V: real > real,K: real] :
% 5.41/5.79 ( ( A != B )
% 5.41/5.79 => ( ! [X6: real] : ( has_fi5821293074295781190e_real @ V @ K @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 => ( ( V @ ( divide_divide_real @ ( plus_plus_real @ A @ B ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) )
% 5.41/5.79 = ( divide_divide_real @ ( plus_plus_real @ ( V @ A ) @ ( V @ B ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_const_average
% 5.41/5.79 thf(fact_9967_DERIV__local__min,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real,D: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.41/5.79 => ( ! [Y5: real] :
% 5.41/5.79 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.41/5.79 => ( ord_less_eq_real @ ( F @ X ) @ ( F @ Y5 ) ) )
% 5.41/5.79 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_local_min
% 5.41/5.79 thf(fact_9968_DERIV__local__max,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,X: real,D: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ L2 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ D )
% 5.41/5.79 => ( ! [Y5: real] :
% 5.41/5.79 ( ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ X @ Y5 ) ) @ D )
% 5.41/5.79 => ( ord_less_eq_real @ ( F @ Y5 ) @ ( F @ X ) ) )
% 5.41/5.79 => ( L2 = zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_local_max
% 5.41/5.79 thf(fact_9969_DERIV__ln__divide,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ln_ln_real @ ( divide_divide_real @ one_one_real @ X ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_ln_divide
% 5.41/5.79 thf(fact_9970_DERIV__pow,axiom,
% 5.41/5.79 ! [N: nat,X: real,S: set_real] :
% 5.41/5.79 ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X3: real] : ( power_power_real @ X3 @ N )
% 5.41/5.79 @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ X @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ S ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_pow
% 5.41/5.79 thf(fact_9971_DERIV__fun__pow,axiom,
% 5.41/5.79 ! [G: real > real,M: real,X: real,N: nat] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X3: real] : ( power_power_real @ ( G @ X3 ) @ N )
% 5.41/5.79 @ ( times_times_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( G @ X ) @ ( minus_minus_nat @ N @ one_one_nat ) ) ) @ M )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_fun_pow
% 5.41/5.79 thf(fact_9972_has__real__derivative__powr,axiom,
% 5.41/5.79 ! [Z: real,R: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ Z )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [Z3: real] : ( powr_real @ Z3 @ R )
% 5.41/5.79 @ ( times_times_real @ R @ ( powr_real @ Z @ ( minus_minus_real @ R @ one_one_real ) ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ Z @ top_top_set_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % has_real_derivative_powr
% 5.41/5.79 thf(fact_9973_DERIV__log,axiom,
% 5.41/5.79 ! [X: real,B: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( log @ B ) @ ( divide_divide_real @ one_one_real @ ( times_times_real @ ( ln_ln_real @ B ) @ X ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_log
% 5.41/5.79 thf(fact_9974_DERIV__fun__powr,axiom,
% 5.41/5.79 ! [G: real > real,M: real,X: real,R: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ R )
% 5.41/5.79 @ ( times_times_real @ ( times_times_real @ R @ ( powr_real @ ( G @ X ) @ ( minus_minus_real @ R @ ( semiri5074537144036343181t_real @ one_one_nat ) ) ) ) @ M )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_fun_powr
% 5.41/5.79 thf(fact_9975_DERIV__powr,axiom,
% 5.41/5.79 ! [G: real > real,M: real,X: real,F: real > real,R: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ G @ M @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ ( G @ X ) )
% 5.41/5.79 => ( ( has_fi5821293074295781190e_real @ F @ R @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X3: real] : ( powr_real @ ( G @ X3 ) @ ( F @ X3 ) )
% 5.41/5.79 @ ( times_times_real @ ( powr_real @ ( G @ X ) @ ( F @ X ) ) @ ( plus_plus_real @ ( times_times_real @ R @ ( ln_ln_real @ ( G @ X ) ) ) @ ( divide_divide_real @ ( times_times_real @ M @ ( F @ X ) ) @ ( G @ X ) ) ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_powr
% 5.41/5.79 thf(fact_9976_DERIV__real__sqrt,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ sqrt @ ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_real_sqrt
% 5.41/5.79 thf(fact_9977_DERIV__series_H,axiom,
% 5.41/5.79 ! [F: real > nat > real,F5: real > nat > real,X0: real,A: real,B: real,L5: nat > real] :
% 5.41/5.79 ( ! [N3: nat] :
% 5.41/5.79 ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X3: real] : ( F @ X3 @ N3 )
% 5.41/5.79 @ ( F5 @ X0 @ N3 )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.41/5.79 => ( summable_real @ ( F @ X6 ) ) )
% 5.41/5.79 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.41/5.79 => ( ( summable_real @ ( F5 @ X0 ) )
% 5.41/5.79 => ( ( summable_real @ L5 )
% 5.41/5.79 => ( ! [N3: nat,X6: real,Y5: real] :
% 5.41/5.79 ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.41/5.79 => ( ( member_real @ Y5 @ ( set_or1633881224788618240n_real @ A @ B ) )
% 5.41/5.79 => ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ ( F @ X6 @ N3 ) @ ( F @ Y5 @ N3 ) ) ) @ ( times_times_real @ ( L5 @ N3 ) @ ( abs_abs_real @ ( minus_minus_real @ X6 @ Y5 ) ) ) ) ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X3: real] : ( suminf_real @ ( F @ X3 ) )
% 5.41/5.79 @ ( suminf_real @ ( F5 @ X0 ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_series'
% 5.41/5.79 thf(fact_9978_DERIV__arctan,axiom,
% 5.41/5.79 ! [X: real] : ( has_fi5821293074295781190e_real @ arctan @ ( inverse_inverse_real @ ( plus_plus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_arctan
% 5.41/5.79 thf(fact_9979_arsinh__real__has__field__derivative,axiom,
% 5.41/5.79 ! [X: real,A2: set_real] : ( has_fi5821293074295781190e_real @ arsinh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( plus_plus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ).
% 5.41/5.79
% 5.41/5.79 % arsinh_real_has_field_derivative
% 5.41/5.79 thf(fact_9980_DERIV__real__sqrt__generic,axiom,
% 5.41/5.79 ! [X: real,D4: real] :
% 5.41/5.79 ( ( X != zero_zero_real )
% 5.41/5.79 => ( ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.79 => ( D4
% 5.41/5.79 = ( divide_divide_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 => ( ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.79 => ( D4
% 5.41/5.79 = ( divide_divide_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( sqrt @ X ) ) ) @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ sqrt @ D4 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_real_sqrt_generic
% 5.41/5.79 thf(fact_9981_arcosh__real__has__field__derivative,axiom,
% 5.41/5.79 ! [X: real,A2: set_real] :
% 5.41/5.79 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ arcosh_real @ ( divide_divide_real @ one_one_real @ ( sqrt @ ( minus_minus_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_real ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % arcosh_real_has_field_derivative
% 5.41/5.79 thf(fact_9982_artanh__real__has__field__derivative,axiom,
% 5.41/5.79 ! [X: real,A2: set_real] :
% 5.41/5.79 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ artanh_real @ ( divide_divide_real @ one_one_real @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ A2 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % artanh_real_has_field_derivative
% 5.41/5.79 thf(fact_9983_DERIV__power__series_H,axiom,
% 5.41/5.79 ! [R4: real,F: nat > real,X0: real] :
% 5.41/5.79 ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R4 ) @ R4 ) )
% 5.41/5.79 => ( summable_real
% 5.41/5.79 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X6 @ N2 ) ) ) )
% 5.41/5.79 => ( ( member_real @ X0 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ R4 ) @ R4 ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ R4 )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( suminf_real
% 5.41/5.79 @ ^ [N2: nat] : ( times_times_real @ ( F @ N2 ) @ ( power_power_real @ X3 @ ( suc @ N2 ) ) ) )
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [N2: nat] : ( times_times_real @ ( times_times_real @ ( F @ N2 ) @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) @ ( power_power_real @ X0 @ N2 ) ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X0 @ top_top_set_real ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_power_series'
% 5.41/5.79 thf(fact_9984_DERIV__real__root,axiom,
% 5.41/5.79 ! [N: nat,X: real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ X )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_real_root
% 5.41/5.79 thf(fact_9985_DERIV__arccos,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ arccos @ ( inverse_inverse_real @ ( uminus_uminus_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_arccos
% 5.41/5.79 thf(fact_9986_DERIV__arcsin,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ arcsin @ ( inverse_inverse_real @ ( sqrt @ ( minus_minus_real @ one_one_real @ ( power_power_real @ X @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_arcsin
% 5.41/5.79 thf(fact_9987_Maclaurin__all__le__objl,axiom,
% 5.41/5.79 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.41/5.79 ( ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 & ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.79 & ( ( F @ X )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin_all_le_objl
% 5.41/5.79 thf(fact_9988_Maclaurin__all__le,axiom,
% 5.41/5.79 ! [Diff: nat > real > real,F: real > real,X: real,N: nat] :
% 5.41/5.79 ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.79 & ( ( F @ X )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin_all_le
% 5.41/5.79 thf(fact_9989_DERIV__odd__real__root,axiom,
% 5.41/5.79 ! [N: nat,X: real] :
% 5.41/5.79 ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.79 => ( ( X != zero_zero_real )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( semiri5074537144036343181t_real @ N ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_odd_real_root
% 5.41/5.79 thf(fact_9990_Maclaurin__minus,axiom,
% 5.41/5.79 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ H2 @ zero_zero_real )
% 5.41/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ H2 @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ zero_zero_real ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_real @ H2 @ T6 )
% 5.41/5.79 & ( ord_less_real @ T6 @ zero_zero_real )
% 5.41/5.79 & ( ( F @ H2 )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin_minus
% 5.41/5.79 thf(fact_9991_Maclaurin2,axiom,
% 5.41/5.79 ! [H2: real,Diff: nat > real > real,F: real > real,N: nat] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.41/5.79 => ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ H2 )
% 5.41/5.79 & ( ( F @ H2 )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin2
% 5.41/5.79 thf(fact_9992_Maclaurin,axiom,
% 5.41/5.79 ! [H2: real,N: nat,Diff: nat > real > real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ H2 )
% 5.41/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ T6 )
% 5.41/5.79 & ( ord_less_real @ T6 @ H2 )
% 5.41/5.79 & ( ( F @ H2 )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ H2 @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ H2 @ N ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin
% 5.41/5.79 thf(fact_9993_Maclaurin__all__lt,axiom,
% 5.41/5.79 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.41/5.79 ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( X != zero_zero_real )
% 5.41/5.79 => ( ! [M4: nat,X6: real] : ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ ( abs_abs_real @ T6 ) )
% 5.41/5.79 & ( ord_less_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.79 & ( ( F @ X )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin_all_lt
% 5.41/5.79 thf(fact_9994_Maclaurin__bi__le,axiom,
% 5.41/5.79 ! [Diff: nat > real > real,F: real > real,N: nat,X: real] :
% 5.41/5.79 ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ T6 ) @ ( abs_abs_real @ X ) )
% 5.41/5.79 & ( ( F @ X )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ X @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ X @ N ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin_bi_le
% 5.41/5.79 thf(fact_9995_Taylor__down,axiom,
% 5.41/5.79 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ A @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ B ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ( ( ord_less_real @ A @ C )
% 5.41/5.79 => ( ( ord_less_eq_real @ C @ B )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ T6 )
% 5.41/5.79 & ( ord_less_real @ T6 @ C )
% 5.41/5.79 & ( ( F @ A )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ A @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Taylor_down
% 5.41/5.79 thf(fact_9996_Taylor__up,axiom,
% 5.41/5.79 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ A @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ B ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ( ( ord_less_eq_real @ A @ C )
% 5.41/5.79 => ( ( ord_less_real @ C @ B )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ord_less_real @ C @ T6 )
% 5.41/5.79 & ( ord_less_real @ T6 @ B )
% 5.41/5.79 & ( ( F @ B )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ B @ C ) @ N ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Taylor_up
% 5.41/5.79 thf(fact_9997_Taylor,axiom,
% 5.41/5.79 ! [N: nat,Diff: nat > real > real,F: real > real,A: real,B: real,C: real,X: real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( ( Diff @ zero_zero_nat )
% 5.41/5.79 = F )
% 5.41/5.79 => ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ A @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ B ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ( ( ord_less_eq_real @ A @ C )
% 5.41/5.79 => ( ( ord_less_eq_real @ C @ B )
% 5.41/5.79 => ( ( ord_less_eq_real @ A @ X )
% 5.41/5.79 => ( ( ord_less_eq_real @ X @ B )
% 5.41/5.79 => ( ( X != C )
% 5.41/5.79 => ? [T6: real] :
% 5.41/5.79 ( ( ( ord_less_real @ X @ C )
% 5.41/5.79 => ( ( ord_less_real @ X @ T6 )
% 5.41/5.79 & ( ord_less_real @ T6 @ C ) ) )
% 5.41/5.79 & ( ~ ( ord_less_real @ X @ C )
% 5.41/5.79 => ( ( ord_less_real @ C @ T6 )
% 5.41/5.79 & ( ord_less_real @ T6 @ X ) ) )
% 5.41/5.79 & ( ( F @ X )
% 5.41/5.79 = ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [M3: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ M3 @ C ) @ ( semiri2265585572941072030t_real @ M3 ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ M3 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ N ) )
% 5.41/5.79 @ ( times_times_real @ ( divide_divide_real @ ( Diff @ N @ T6 ) @ ( semiri2265585572941072030t_real @ N ) ) @ ( power_power_real @ ( minus_minus_real @ X @ C ) @ N ) ) ) ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Taylor
% 5.41/5.79 thf(fact_9998_Maclaurin__lemma2,axiom,
% 5.41/5.79 ! [N: nat,H2: real,Diff: nat > real > real,K: nat,B3: real] :
% 5.41/5.79 ( ! [M4: nat,T6: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M4 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ zero_zero_real @ T6 )
% 5.41/5.79 & ( ord_less_eq_real @ T6 @ H2 ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( Diff @ M4 ) @ ( Diff @ ( suc @ M4 ) @ T6 ) @ ( topolo2177554685111907308n_real @ T6 @ top_top_set_real ) ) )
% 5.41/5.79 => ( ( N
% 5.41/5.79 = ( suc @ K ) )
% 5.41/5.79 => ! [M2: nat,T7: real] :
% 5.41/5.79 ( ( ( ord_less_nat @ M2 @ N )
% 5.41/5.79 & ( ord_less_eq_real @ zero_zero_real @ T7 )
% 5.41/5.79 & ( ord_less_eq_real @ T7 @ H2 ) )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [U2: real] :
% 5.41/5.79 ( minus_minus_real @ ( Diff @ M2 @ U2 )
% 5.41/5.79 @ ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [P2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ M2 @ P2 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P2 ) ) @ ( power_power_real @ U2 @ P2 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ M2 ) ) )
% 5.41/5.79 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ U2 @ ( minus_minus_nat @ N @ M2 ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ M2 ) ) ) ) ) )
% 5.41/5.79 @ ( minus_minus_real @ ( Diff @ ( suc @ M2 ) @ T7 )
% 5.41/5.79 @ ( plus_plus_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [P2: nat] : ( times_times_real @ ( divide_divide_real @ ( Diff @ ( plus_plus_nat @ ( suc @ M2 ) @ P2 ) @ zero_zero_real ) @ ( semiri2265585572941072030t_real @ P2 ) ) @ ( power_power_real @ T7 @ P2 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) )
% 5.41/5.79 @ ( times_times_real @ B3 @ ( divide_divide_real @ ( power_power_real @ T7 @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) @ ( semiri2265585572941072030t_real @ ( minus_minus_nat @ N @ ( suc @ M2 ) ) ) ) ) ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ T7 @ top_top_set_real ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Maclaurin_lemma2
% 5.41/5.79 thf(fact_9999_DERIV__arctan__series,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.79 => ( has_fi5821293074295781190e_real
% 5.41/5.79 @ ^ [X9: real] :
% 5.41/5.79 ( suminf_real
% 5.41/5.79 @ ^ [K2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ K2 ) @ ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X9 @ ( plus_plus_nat @ ( times_times_nat @ K2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) ) )
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [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 ) ) ) ) ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_arctan_series
% 5.41/5.79 thf(fact_10000_DERIV__even__real__root,axiom,
% 5.41/5.79 ! [N: nat,X: real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.79 => ( ( ord_less_real @ X @ zero_zero_real )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ ( root @ N ) @ ( inverse_inverse_real @ ( times_times_real @ ( uminus_uminus_real @ ( semiri5074537144036343181t_real @ N ) ) @ ( power_power_real @ ( root @ N @ X ) @ ( minus_minus_nat @ N @ ( suc @ zero_zero_nat ) ) ) ) ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_even_real_root
% 5.41/5.79 thf(fact_10001_take__bit__numeral__minus__numeral__int,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = ( case_option_int_num @ zero_zero_int
% 5.41/5.79 @ ^ [Q5: num] : ( bit_se2923211474154528505it_int @ ( numeral_numeral_nat @ M ) @ ( minus_minus_int @ ( power_power_int @ ( numeral_numeral_int @ ( bit0 @ one ) ) @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_int @ Q5 ) ) )
% 5.41/5.79 @ ( bit_take_bit_num @ ( numeral_numeral_nat @ M ) @ N ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_numeral_minus_numeral_int
% 5.41/5.79 thf(fact_10002_take__bit__num__simps_I1_J,axiom,
% 5.41/5.79 ! [M: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ zero_zero_nat @ M )
% 5.41/5.79 = none_num ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_simps(1)
% 5.41/5.79 thf(fact_10003_take__bit__num__simps_I2_J,axiom,
% 5.41/5.79 ! [N: nat] :
% 5.41/5.79 ( ( bit_take_bit_num @ ( suc @ N ) @ one )
% 5.41/5.79 = ( some_num @ one ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_simps(2)
% 5.41/5.79 thf(fact_10004_take__bit__num__simps_I5_J,axiom,
% 5.41/5.79 ! [R: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ one )
% 5.41/5.79 = ( some_num @ one ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_simps(5)
% 5.41/5.79 thf(fact_10005_take__bit__num__simps_I3_J,axiom,
% 5.41/5.79 ! [N: nat,M: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit0 @ M ) )
% 5.41/5.79 = ( case_o6005452278849405969um_num @ none_num
% 5.41/5.79 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.41/5.79 @ ( bit_take_bit_num @ N @ M ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_simps(3)
% 5.41/5.79 thf(fact_10006_take__bit__num__simps_I4_J,axiom,
% 5.41/5.79 ! [N: nat,M: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ ( suc @ N ) @ ( bit1 @ M ) )
% 5.41/5.79 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N @ M ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_simps(4)
% 5.41/5.79 thf(fact_10007_take__bit__num__simps_I6_J,axiom,
% 5.41/5.79 ! [R: num,M: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit0 @ M ) )
% 5.41/5.79 = ( case_o6005452278849405969um_num @ none_num
% 5.41/5.79 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.41/5.79 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_simps(6)
% 5.41/5.79 thf(fact_10008_take__bit__num__simps_I7_J,axiom,
% 5.41/5.79 ! [R: num,M: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ ( numeral_numeral_nat @ R ) @ ( bit1 @ M ) )
% 5.41/5.79 = ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ ( pred_numeral @ R ) @ M ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_simps(7)
% 5.41/5.79 thf(fact_10009_Code__Abstract__Nat_Otake__bit__num__code_I2_J,axiom,
% 5.41/5.79 ! [N: nat,M: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ N @ ( bit0 @ M ) )
% 5.41/5.79 = ( case_nat_option_num @ none_num
% 5.41/5.79 @ ^ [N2: nat] :
% 5.41/5.79 ( case_o6005452278849405969um_num @ none_num
% 5.41/5.79 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.41/5.79 @ ( bit_take_bit_num @ N2 @ M ) )
% 5.41/5.79 @ N ) ) ).
% 5.41/5.79
% 5.41/5.79 % Code_Abstract_Nat.take_bit_num_code(2)
% 5.41/5.79 thf(fact_10010_Code__Abstract__Nat_Otake__bit__num__code_I1_J,axiom,
% 5.41/5.79 ! [N: nat] :
% 5.41/5.79 ( ( bit_take_bit_num @ N @ one )
% 5.41/5.79 = ( case_nat_option_num @ none_num
% 5.41/5.79 @ ^ [N2: nat] : ( some_num @ one )
% 5.41/5.79 @ N ) ) ).
% 5.41/5.79
% 5.41/5.79 % Code_Abstract_Nat.take_bit_num_code(1)
% 5.41/5.79 thf(fact_10011_Code__Abstract__Nat_Otake__bit__num__code_I3_J,axiom,
% 5.41/5.79 ! [N: nat,M: num] :
% 5.41/5.79 ( ( bit_take_bit_num @ N @ ( bit1 @ M ) )
% 5.41/5.79 = ( case_nat_option_num @ none_num
% 5.41/5.79 @ ^ [N2: nat] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ N2 @ M ) ) )
% 5.41/5.79 @ N ) ) ).
% 5.41/5.79
% 5.41/5.79 % Code_Abstract_Nat.take_bit_num_code(3)
% 5.41/5.79 thf(fact_10012_take__bit__num__def,axiom,
% 5.41/5.79 ( bit_take_bit_num
% 5.41/5.79 = ( ^ [N2: nat,M3: num] :
% 5.41/5.79 ( if_option_num
% 5.41/5.79 @ ( ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) )
% 5.41/5.79 = zero_zero_nat )
% 5.41/5.79 @ none_num
% 5.41/5.79 @ ( some_num @ ( num_of_nat @ ( bit_se2925701944663578781it_nat @ N2 @ ( numeral_numeral_nat @ M3 ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % take_bit_num_def
% 5.41/5.79 thf(fact_10013_and__minus__numerals_I7_J,axiom,
% 5.41/5.79 ! [N: num,M: num] :
% 5.41/5.79 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.41/5.79 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_minus_numerals(7)
% 5.41/5.79 thf(fact_10014_and__minus__numerals_I3_J,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit0 @ N ) ) ) )
% 5.41/5.79 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bitM @ N ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_minus_numerals(3)
% 5.41/5.79 thf(fact_10015_and__minus__numerals_I4_J,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) )
% 5.41/5.79 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_minus_numerals(4)
% 5.41/5.79 thf(fact_10016_and__minus__numerals_I8_J,axiom,
% 5.41/5.79 ! [N: num,M: num] :
% 5.41/5.79 ( ( bit_se725231765392027082nd_int @ ( uminus_uminus_int @ ( numeral_numeral_int @ ( bit1 @ N ) ) ) @ ( numeral_numeral_int @ M ) )
% 5.41/5.79 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ ( bit0 @ N ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_minus_numerals(8)
% 5.41/5.79 thf(fact_10017_and__not__num_Osimps_I3_J,axiom,
% 5.41/5.79 ! [N: num] :
% 5.41/5.79 ( ( bit_and_not_num @ one @ ( bit1 @ N ) )
% 5.41/5.79 = none_num ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num.simps(3)
% 5.41/5.79 thf(fact_10018_and__not__num_Osimps_I1_J,axiom,
% 5.41/5.79 ( ( bit_and_not_num @ one @ one )
% 5.41/5.79 = none_num ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num.simps(1)
% 5.41/5.79 thf(fact_10019_and__not__num_Osimps_I4_J,axiom,
% 5.41/5.79 ! [M: num] :
% 5.41/5.79 ( ( bit_and_not_num @ ( bit0 @ M ) @ one )
% 5.41/5.79 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num.simps(4)
% 5.41/5.79 thf(fact_10020_and__not__num_Osimps_I2_J,axiom,
% 5.41/5.79 ! [N: num] :
% 5.41/5.79 ( ( bit_and_not_num @ one @ ( bit0 @ N ) )
% 5.41/5.79 = ( some_num @ one ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num.simps(2)
% 5.41/5.79 thf(fact_10021_and__not__num_Osimps_I7_J,axiom,
% 5.41/5.79 ! [M: num] :
% 5.41/5.79 ( ( bit_and_not_num @ ( bit1 @ M ) @ one )
% 5.41/5.79 = ( some_num @ ( bit0 @ M ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num.simps(7)
% 5.41/5.79 thf(fact_10022_and__not__num__eq__Some__iff,axiom,
% 5.41/5.79 ! [M: num,N: num,Q2: num] :
% 5.41/5.79 ( ( ( bit_and_not_num @ M @ N )
% 5.41/5.79 = ( some_num @ Q2 ) )
% 5.41/5.79 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = ( numeral_numeral_int @ Q2 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num_eq_Some_iff
% 5.41/5.79 thf(fact_10023_and__not__num_Osimps_I8_J,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( bit_and_not_num @ ( bit1 @ M ) @ ( bit0 @ N ) )
% 5.41/5.79 = ( case_o6005452278849405969um_num @ ( some_num @ one )
% 5.41/5.79 @ ^ [N9: num] : ( some_num @ ( bit1 @ N9 ) )
% 5.41/5.79 @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num.simps(8)
% 5.41/5.79 thf(fact_10024_and__not__num__eq__None__iff,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( ( bit_and_not_num @ M @ N )
% 5.41/5.79 = none_num )
% 5.41/5.79 = ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = zero_zero_int ) ) ).
% 5.41/5.79
% 5.41/5.79 % and_not_num_eq_None_iff
% 5.41/5.79 thf(fact_10025_int__numeral__not__and__num,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( bit_se725231765392027082nd_int @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ M ) ) @ ( numeral_numeral_int @ N ) )
% 5.41/5.79 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ N @ M ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % int_numeral_not_and_num
% 5.41/5.79 thf(fact_10026_int__numeral__and__not__num,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( bit_se725231765392027082nd_int @ ( numeral_numeral_int @ M ) @ ( bit_ri7919022796975470100ot_int @ ( numeral_numeral_int @ N ) ) )
% 5.41/5.79 = ( case_option_int_num @ zero_zero_int @ numeral_numeral_int @ ( bit_and_not_num @ M @ N ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % int_numeral_and_not_num
% 5.41/5.79 thf(fact_10027_Bit__Operations_Otake__bit__num__code,axiom,
% 5.41/5.79 ( bit_take_bit_num
% 5.41/5.79 = ( ^ [N2: nat,M3: num] :
% 5.41/5.79 ( produc478579273971653890on_num
% 5.41/5.79 @ ^ [A3: nat,X3: num] :
% 5.41/5.79 ( case_nat_option_num @ none_num
% 5.41/5.79 @ ^ [O: nat] :
% 5.41/5.79 ( case_num_option_num @ ( some_num @ one )
% 5.41/5.79 @ ^ [P2: num] :
% 5.41/5.79 ( case_o6005452278849405969um_num @ none_num
% 5.41/5.79 @ ^ [Q5: num] : ( some_num @ ( bit0 @ Q5 ) )
% 5.41/5.79 @ ( bit_take_bit_num @ O @ P2 ) )
% 5.41/5.79 @ ^ [P2: num] : ( some_num @ ( case_option_num_num @ one @ bit1 @ ( bit_take_bit_num @ O @ P2 ) ) )
% 5.41/5.79 @ X3 )
% 5.41/5.79 @ A3 )
% 5.41/5.79 @ ( product_Pair_nat_num @ N2 @ M3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Bit_Operations.take_bit_num_code
% 5.41/5.79 thf(fact_10028_isCont__Lb__Ub,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 & ( ord_less_eq_real @ X6 @ B ) )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ F ) )
% 5.41/5.79 => ? [L6: real,M9: real] :
% 5.41/5.79 ( ! [X4: real] :
% 5.41/5.79 ( ( ( ord_less_eq_real @ A @ X4 )
% 5.41/5.79 & ( ord_less_eq_real @ X4 @ B ) )
% 5.41/5.79 => ( ( ord_less_eq_real @ L6 @ ( F @ X4 ) )
% 5.41/5.79 & ( ord_less_eq_real @ ( F @ X4 ) @ M9 ) ) )
% 5.41/5.79 & ! [Y2: real] :
% 5.41/5.79 ( ( ( ord_less_eq_real @ L6 @ Y2 )
% 5.41/5.79 & ( ord_less_eq_real @ Y2 @ M9 ) )
% 5.41/5.79 => ? [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 & ( ord_less_eq_real @ X6 @ B )
% 5.41/5.79 & ( ( F @ X6 )
% 5.41/5.79 = Y2 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_Lb_Ub
% 5.41/5.79 thf(fact_10029_isCont__real__sqrt,axiom,
% 5.41/5.79 ! [X: real] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ sqrt ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_real_sqrt
% 5.41/5.79 thf(fact_10030_isCont__real__root,axiom,
% 5.41/5.79 ! [X: real,N: nat] : ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ( root @ N ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_real_root
% 5.41/5.79 thf(fact_10031_isCont__inverse__function2,axiom,
% 5.41/5.79 ! [A: real,X: real,B: real,G: real > real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ B )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ Z5 )
% 5.41/5.79 => ( ( ord_less_eq_real @ Z5 @ B )
% 5.41/5.79 => ( ( G @ ( F @ Z5 ) )
% 5.41/5.79 = Z5 ) ) )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ Z5 )
% 5.41/5.79 => ( ( ord_less_eq_real @ Z5 @ B )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) ) )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_inverse_function2
% 5.41/5.79 thf(fact_10032_isCont__ln,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( X != zero_zero_real )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ ln_ln_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_ln
% 5.41/5.79 thf(fact_10033_isCont__arcosh,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcosh_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_arcosh
% 5.41/5.79 thf(fact_10034_DERIV__inverse__function,axiom,
% 5.41/5.79 ! [F: real > real,D4: real,G: real > real,X: real,A: real,B: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ D4 @ ( topolo2177554685111907308n_real @ ( G @ X ) @ top_top_set_real ) )
% 5.41/5.79 => ( ( D4 != zero_zero_real )
% 5.41/5.79 => ( ( ord_less_real @ A @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ B )
% 5.41/5.79 => ( ! [Y5: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Y5 )
% 5.41/5.79 => ( ( ord_less_real @ Y5 @ B )
% 5.41/5.79 => ( ( F @ ( G @ Y5 ) )
% 5.41/5.79 = Y5 ) ) )
% 5.41/5.79 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ G )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ G @ ( inverse_inverse_real @ D4 ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_inverse_function
% 5.41/5.79 thf(fact_10035_isCont__arccos,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arccos ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_arccos
% 5.41/5.79 thf(fact_10036_isCont__arcsin,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ arcsin ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_arcsin
% 5.41/5.79 thf(fact_10037_LIM__less__bound,axiom,
% 5.41/5.79 ! [B: real,X: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ B @ X )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ ( set_or1633881224788618240n_real @ B @ X ) )
% 5.41/5.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X6 ) ) )
% 5.41/5.79 => ( ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ F )
% 5.41/5.79 => ( ord_less_eq_real @ zero_zero_real @ ( F @ X ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIM_less_bound
% 5.41/5.79 thf(fact_10038_isCont__artanh,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ ( uminus_uminus_real @ one_one_real ) @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) @ artanh_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_artanh
% 5.41/5.79 thf(fact_10039_isCont__inverse__function,axiom,
% 5.41/5.79 ! [D: real,X: real,G: real > real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ D )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z5 @ X ) ) @ D )
% 5.41/5.79 => ( ( G @ ( F @ Z5 ) )
% 5.41/5.79 = Z5 ) )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ ( minus_minus_real @ Z5 @ X ) ) @ D )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ ( F @ X ) @ top_top_set_real ) @ G ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % isCont_inverse_function
% 5.41/5.79 thf(fact_10040_GMVT_H,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,G: real > real,G2: real > real,F5: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ Z5 )
% 5.41/5.79 => ( ( ord_less_eq_real @ Z5 @ B )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ F ) ) )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ Z5 )
% 5.41/5.79 => ( ( ord_less_eq_real @ Z5 @ B )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) @ G ) ) )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Z5 )
% 5.41/5.79 => ( ( ord_less_real @ Z5 @ B )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ G @ ( G2 @ Z5 ) @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ( ! [Z5: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Z5 )
% 5.41/5.79 => ( ( ord_less_real @ Z5 @ B )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ F @ ( F5 @ Z5 ) @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ? [C2: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ C2 )
% 5.41/5.79 & ( ord_less_real @ C2 @ B )
% 5.41/5.79 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ ( G2 @ C2 ) )
% 5.41/5.79 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ ( F5 @ C2 ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % GMVT'
% 5.41/5.79 thf(fact_10041_Gcd__eq__Max,axiom,
% 5.41/5.79 ! [M5: set_nat] :
% 5.41/5.79 ( ( finite_finite_nat @ M5 )
% 5.41/5.79 => ( ( M5 != bot_bot_set_nat )
% 5.41/5.79 => ( ~ ( member_nat @ zero_zero_nat @ M5 )
% 5.41/5.79 => ( ( gcd_Gcd_nat @ M5 )
% 5.41/5.79 = ( lattic8265883725875713057ax_nat
% 5.41/5.79 @ ( comple7806235888213564991et_nat
% 5.41/5.79 @ ( image_nat_set_nat
% 5.41/5.79 @ ^ [M3: nat] :
% 5.41/5.79 ( collect_nat
% 5.41/5.79 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ M3 ) )
% 5.41/5.79 @ M5 ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Gcd_eq_Max
% 5.41/5.79 thf(fact_10042_Max__divisors__self__nat,axiom,
% 5.41/5.79 ! [N: nat] :
% 5.41/5.79 ( ( N != zero_zero_nat )
% 5.41/5.79 => ( ( lattic8265883725875713057ax_nat
% 5.41/5.79 @ ( collect_nat
% 5.41/5.79 @ ^ [D2: nat] : ( dvd_dvd_nat @ D2 @ N ) ) )
% 5.41/5.79 = N ) ) ).
% 5.41/5.79
% 5.41/5.79 % Max_divisors_self_nat
% 5.41/5.79 thf(fact_10043_LIM__fun__less__zero,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,C: real] :
% 5.41/5.79 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ L2 @ zero_zero_real )
% 5.41/5.79 => ? [R2: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.41/5.79 & ! [X4: real] :
% 5.41/5.79 ( ( ( X4 != C )
% 5.41/5.79 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 5.41/5.79 => ( ord_less_real @ ( F @ X4 ) @ zero_zero_real ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIM_fun_less_zero
% 5.41/5.79 thf(fact_10044_LIM__fun__not__zero,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,C: real] :
% 5.41/5.79 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.41/5.79 => ( ( L2 != zero_zero_real )
% 5.41/5.79 => ? [R2: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.41/5.79 & ! [X4: real] :
% 5.41/5.79 ( ( ( X4 != C )
% 5.41/5.79 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 5.41/5.79 => ( ( F @ X4 )
% 5.41/5.79 != zero_zero_real ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIM_fun_not_zero
% 5.41/5.79 thf(fact_10045_LIM__fun__gt__zero,axiom,
% 5.41/5.79 ! [F: real > real,L2: real,C: real] :
% 5.41/5.79 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ ( topolo2177554685111907308n_real @ C @ top_top_set_real ) )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ L2 )
% 5.41/5.79 => ? [R2: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ R2 )
% 5.41/5.79 & ! [X4: real] :
% 5.41/5.79 ( ( ( X4 != C )
% 5.41/5.79 & ( ord_less_real @ ( abs_abs_real @ ( minus_minus_real @ C @ X4 ) ) @ R2 ) )
% 5.41/5.79 => ( ord_less_real @ zero_zero_real @ ( F @ X4 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIM_fun_gt_zero
% 5.41/5.79 thf(fact_10046_card__le__Suc__Max,axiom,
% 5.41/5.79 ! [S2: set_nat] :
% 5.41/5.79 ( ( finite_finite_nat @ S2 )
% 5.41/5.79 => ( ord_less_eq_nat @ ( finite_card_nat @ S2 ) @ ( suc @ ( lattic8265883725875713057ax_nat @ S2 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % card_le_Suc_Max
% 5.41/5.79 thf(fact_10047_Sup__nat__def,axiom,
% 5.41/5.79 ( complete_Sup_Sup_nat
% 5.41/5.79 = ( ^ [X2: set_nat] : ( if_nat @ ( X2 = bot_bot_set_nat ) @ zero_zero_nat @ ( lattic8265883725875713057ax_nat @ X2 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Sup_nat_def
% 5.41/5.79 thf(fact_10048_divide__nat__def,axiom,
% 5.41/5.79 ( divide_divide_nat
% 5.41/5.79 = ( ^ [M3: nat,N2: nat] :
% 5.41/5.79 ( if_nat @ ( N2 = zero_zero_nat ) @ zero_zero_nat
% 5.41/5.79 @ ( lattic8265883725875713057ax_nat
% 5.41/5.79 @ ( collect_nat
% 5.41/5.79 @ ^ [K2: nat] : ( ord_less_eq_nat @ ( times_times_nat @ K2 @ N2 ) @ M3 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % divide_nat_def
% 5.41/5.79 thf(fact_10049_gcd__is__Max__divisors__nat,axiom,
% 5.41/5.79 ! [N: nat,M: nat] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( gcd_gcd_nat @ M @ N )
% 5.41/5.79 = ( lattic8265883725875713057ax_nat
% 5.41/5.79 @ ( collect_nat
% 5.41/5.79 @ ^ [D2: nat] :
% 5.41/5.79 ( ( dvd_dvd_nat @ D2 @ M )
% 5.41/5.79 & ( dvd_dvd_nat @ D2 @ N ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % gcd_is_Max_divisors_nat
% 5.41/5.79 thf(fact_10050_LIM__cos__div__sin,axiom,
% 5.41/5.79 ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( cos_real @ X3 ) @ ( sin_real @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ top_top_set_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIM_cos_div_sin
% 5.41/5.79 thf(fact_10051_summable__Leibniz_I3_J,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ( topolo6980174941875973593q_real @ A )
% 5.41/5.79 => ( ( ord_less_real @ ( A @ zero_zero_nat ) @ zero_zero_real )
% 5.41/5.79 => ! [N7: nat] :
% 5.41/5.79 ( member_real
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.41/5.79 @ ( set_or1222579329274155063t_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) )
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz(3)
% 5.41/5.79 thf(fact_10052_summable__Leibniz_I2_J,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ( topolo6980174941875973593q_real @ A )
% 5.41/5.79 => ( ( ord_less_real @ zero_zero_real @ ( A @ zero_zero_nat ) )
% 5.41/5.79 => ! [N7: nat] :
% 5.41/5.79 ( member_real
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.41/5.79 @ ( set_or1222579329274155063t_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz(2)
% 5.41/5.79 thf(fact_10053_Max__divisors__self__int,axiom,
% 5.41/5.79 ! [N: int] :
% 5.41/5.79 ( ( N != zero_zero_int )
% 5.41/5.79 => ( ( lattic8263393255366662781ax_int
% 5.41/5.79 @ ( collect_int
% 5.41/5.79 @ ^ [D2: int] : ( dvd_dvd_int @ D2 @ N ) ) )
% 5.41/5.79 = ( abs_abs_int @ N ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Max_divisors_self_int
% 5.41/5.79 thf(fact_10054_mult__nat__right__at__top,axiom,
% 5.41/5.79 ! [C: nat] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.79 => ( filterlim_nat_nat
% 5.41/5.79 @ ^ [X3: nat] : ( times_times_nat @ X3 @ C )
% 5.41/5.79 @ at_top_nat
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % mult_nat_right_at_top
% 5.41/5.79 thf(fact_10055_mult__nat__left__at__top,axiom,
% 5.41/5.79 ! [C: nat] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ C )
% 5.41/5.79 => ( filterlim_nat_nat @ ( times_times_nat @ C ) @ at_top_nat @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % mult_nat_left_at_top
% 5.41/5.79 thf(fact_10056_monoseq__convergent,axiom,
% 5.41/5.79 ! [X8: nat > real,B3: real] :
% 5.41/5.79 ( ( topolo6980174941875973593q_real @ X8 )
% 5.41/5.79 => ( ! [I4: nat] : ( ord_less_eq_real @ ( abs_abs_real @ ( X8 @ I4 ) ) @ B3 )
% 5.41/5.79 => ~ ! [L6: real] :
% 5.41/5.79 ~ ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % monoseq_convergent
% 5.41/5.79 thf(fact_10057_LIMSEQ__root,axiom,
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( root @ N2 @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.41/5.79 @ at_top_nat ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_root
% 5.41/5.79 thf(fact_10058_gcd__is__Max__divisors__int,axiom,
% 5.41/5.79 ! [N: int,M: int] :
% 5.41/5.79 ( ( N != zero_zero_int )
% 5.41/5.79 => ( ( gcd_gcd_int @ M @ N )
% 5.41/5.79 = ( lattic8263393255366662781ax_int
% 5.41/5.79 @ ( collect_int
% 5.41/5.79 @ ^ [D2: int] :
% 5.41/5.79 ( ( dvd_dvd_int @ D2 @ M )
% 5.41/5.79 & ( dvd_dvd_int @ D2 @ N ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % gcd_is_Max_divisors_int
% 5.41/5.79 thf(fact_10059_nested__sequence__unique,axiom,
% 5.41/5.79 ! [F: nat > real,G: nat > real] :
% 5.41/5.79 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( G @ ( suc @ N3 ) ) @ ( G @ N3 ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( G @ N3 ) )
% 5.41/5.79 => ( ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( minus_minus_real @ ( F @ N2 ) @ ( G @ N2 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat )
% 5.41/5.79 => ? [L4: real] :
% 5.41/5.79 ( ! [N7: nat] : ( ord_less_eq_real @ ( F @ N7 ) @ L4 )
% 5.41/5.79 & ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat )
% 5.41/5.79 & ! [N7: nat] : ( ord_less_eq_real @ L4 @ ( G @ N7 ) )
% 5.41/5.79 & ( filterlim_nat_real @ G @ ( topolo2815343760600316023s_real @ L4 ) @ at_top_nat ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % nested_sequence_unique
% 5.41/5.79 thf(fact_10060_LIMSEQ__inverse__zero,axiom,
% 5.41/5.79 ! [X8: nat > real] :
% 5.41/5.79 ( ! [R2: real] :
% 5.41/5.79 ? [N8: nat] :
% 5.41/5.79 ! [N3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ N8 @ N3 )
% 5.41/5.79 => ( ord_less_real @ R2 @ ( X8 @ N3 ) ) )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( inverse_inverse_real @ ( X8 @ N2 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_inverse_zero
% 5.41/5.79 thf(fact_10061_lim__inverse__n_H,axiom,
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ N2 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat ) ).
% 5.41/5.79
% 5.41/5.79 % lim_inverse_n'
% 5.41/5.79 thf(fact_10062_LIMSEQ__root__const,axiom,
% 5.41/5.79 ! [C: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ C )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( root @ N2 @ C )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_root_const
% 5.41/5.79 thf(fact_10063_LIMSEQ__inverse__real__of__nat,axiom,
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_inverse_real_of_nat
% 5.41/5.79 thf(fact_10064_LIMSEQ__inverse__real__of__nat__add,axiom,
% 5.41/5.79 ! [R: real] :
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( plus_plus_real @ R @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ R )
% 5.41/5.79 @ at_top_nat ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_inverse_real_of_nat_add
% 5.41/5.79 thf(fact_10065_increasing__LIMSEQ,axiom,
% 5.41/5.79 ! [F: nat > real,L2: real] :
% 5.41/5.79 ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ ( F @ ( suc @ N3 ) ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( F @ N3 ) @ L2 )
% 5.41/5.79 => ( ! [E2: real] :
% 5.41/5.79 ( ( ord_less_real @ zero_zero_real @ E2 )
% 5.41/5.79 => ? [N7: nat] : ( ord_less_eq_real @ L2 @ ( plus_plus_real @ ( F @ N7 ) @ E2 ) ) )
% 5.41/5.79 => ( filterlim_nat_real @ F @ ( topolo2815343760600316023s_real @ L2 ) @ at_top_nat ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % increasing_LIMSEQ
% 5.41/5.79 thf(fact_10066_LIMSEQ__realpow__zero,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.79 => ( ( ord_less_real @ X @ one_one_real )
% 5.41/5.79 => ( filterlim_nat_real @ ( power_power_real @ X ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_realpow_zero
% 5.41/5.79 thf(fact_10067_LIMSEQ__divide__realpow__zero,axiom,
% 5.41/5.79 ! [X: real,A: real] :
% 5.41/5.79 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( divide_divide_real @ A @ ( power_power_real @ X @ N2 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_divide_realpow_zero
% 5.41/5.79 thf(fact_10068_LIMSEQ__abs__realpow__zero,axiom,
% 5.41/5.79 ! [C: real] :
% 5.41/5.79 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.41/5.79 => ( filterlim_nat_real @ ( power_power_real @ ( abs_abs_real @ C ) ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_abs_realpow_zero
% 5.41/5.79 thf(fact_10069_LIMSEQ__abs__realpow__zero2,axiom,
% 5.41/5.79 ! [C: real] :
% 5.41/5.79 ( ( ord_less_real @ ( abs_abs_real @ C ) @ one_one_real )
% 5.41/5.79 => ( filterlim_nat_real @ ( power_power_real @ C ) @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_abs_realpow_zero2
% 5.41/5.79 thf(fact_10070_LIMSEQ__inverse__realpow__zero,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_real @ one_one_real @ X )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( inverse_inverse_real @ ( power_power_real @ X @ N2 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_inverse_realpow_zero
% 5.41/5.79 thf(fact_10071_LIMSEQ__inverse__real__of__nat__add__minus,axiom,
% 5.41/5.79 ! [R: real] :
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( plus_plus_real @ R @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ R )
% 5.41/5.79 @ at_top_nat ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_inverse_real_of_nat_add_minus
% 5.41/5.79 thf(fact_10072_tendsto__exp__limit__sequentially,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( power_power_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ ( semiri5074537144036343181t_real @ N2 ) ) ) @ N2 )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.41/5.79 @ at_top_nat ) ).
% 5.41/5.79
% 5.41/5.79 % tendsto_exp_limit_sequentially
% 5.41/5.79 thf(fact_10073_LIMSEQ__inverse__real__of__nat__add__minus__mult,axiom,
% 5.41/5.79 ! [R: real] :
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( times_times_real @ R @ ( plus_plus_real @ one_one_real @ ( uminus_uminus_real @ ( inverse_inverse_real @ ( semiri5074537144036343181t_real @ ( suc @ N2 ) ) ) ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ R )
% 5.41/5.79 @ at_top_nat ) ).
% 5.41/5.79
% 5.41/5.79 % LIMSEQ_inverse_real_of_nat_add_minus_mult
% 5.41/5.79 thf(fact_10074_summable__Leibniz_I1_J,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ( topolo6980174941875973593q_real @ A )
% 5.41/5.79 => ( summable_real
% 5.41/5.79 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz(1)
% 5.41/5.79 thf(fact_10075_summable,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.41/5.79 => ( summable_real
% 5.41/5.79 @ ^ [N2: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ N2 ) @ ( A @ N2 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable
% 5.41/5.79 thf(fact_10076_cos__diff__limit__1,axiom,
% 5.41/5.79 ! [Theta: nat > real,Theta2: real] :
% 5.41/5.79 ( ( filterlim_nat_real
% 5.41/5.79 @ ^ [J3: nat] : ( cos_real @ ( minus_minus_real @ ( Theta @ J3 ) @ Theta2 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.41/5.79 @ at_top_nat )
% 5.41/5.79 => ~ ! [K3: nat > int] :
% 5.41/5.79 ~ ( filterlim_nat_real
% 5.41/5.79 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ Theta2 )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % cos_diff_limit_1
% 5.41/5.79 thf(fact_10077_cos__limit__1,axiom,
% 5.41/5.79 ! [Theta: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real
% 5.41/5.79 @ ^ [J3: nat] : ( cos_real @ ( Theta @ J3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ one_one_real )
% 5.41/5.79 @ at_top_nat )
% 5.41/5.79 => ? [K3: nat > int] :
% 5.41/5.79 ( filterlim_nat_real
% 5.41/5.79 @ ^ [J3: nat] : ( minus_minus_real @ ( Theta @ J3 ) @ ( times_times_real @ ( ring_1_of_int_real @ ( K3 @ J3 ) ) @ ( times_times_real @ ( numeral_numeral_real @ ( bit0 @ one ) ) @ pi ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % cos_limit_1
% 5.41/5.79 thf(fact_10078_summable__Leibniz_I4_J,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ( topolo6980174941875973593q_real @ A )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] :
% 5.41/5.79 ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.41/5.79 @ at_top_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz(4)
% 5.41/5.79 thf(fact_10079_zeroseq__arctan__series,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ ( abs_abs_real @ X ) @ one_one_real )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] : ( times_times_real @ ( divide_divide_real @ one_one_real @ ( semiri5074537144036343181t_real @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) ) @ ( power_power_real @ X @ ( plus_plus_nat @ ( times_times_nat @ N2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ one_one_nat ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % zeroseq_arctan_series
% 5.41/5.79 thf(fact_10080_summable__Leibniz_H_I2_J,axiom,
% 5.41/5.79 ! [A: nat > real,N: nat] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.41/5.79 => ( ord_less_eq_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) ) )
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz'(2)
% 5.41/5.79 thf(fact_10081_summable__Leibniz_H_I3_J,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] :
% 5.41/5.79 ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.41/5.79 @ at_top_nat ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz'(3)
% 5.41/5.79 thf(fact_10082_sums__alternating__upper__lower,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.41/5.79 => ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ? [L4: real] :
% 5.41/5.79 ( ! [N7: nat] :
% 5.41/5.79 ( ord_less_eq_real
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) ) )
% 5.41/5.79 @ L4 )
% 5.41/5.79 & ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] :
% 5.41/5.79 ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ L4 )
% 5.41/5.79 @ at_top_nat )
% 5.41/5.79 & ! [N7: nat] :
% 5.41/5.79 ( ord_less_eq_real @ L4
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N7 ) @ one_one_nat ) ) ) )
% 5.41/5.79 & ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] :
% 5.41/5.79 ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ L4 )
% 5.41/5.79 @ at_top_nat ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % sums_alternating_upper_lower
% 5.41/5.79 thf(fact_10083_summable__Leibniz_I5_J,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ( topolo6980174941875973593q_real @ A )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] :
% 5.41/5.79 ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.41/5.79 @ at_top_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz(5)
% 5.41/5.79 thf(fact_10084_summable__Leibniz_H_I4_J,axiom,
% 5.41/5.79 ! [A: nat > real,N: nat] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.41/5.79 => ( ord_less_eq_real
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) )
% 5.41/5.79 @ ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N ) @ one_one_nat ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz'(4)
% 5.41/5.79 thf(fact_10085_summable__Leibniz_H_I5_J,axiom,
% 5.41/5.79 ! [A: nat > real] :
% 5.41/5.79 ( ( filterlim_nat_real @ A @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_top_nat )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ zero_zero_real @ ( A @ N3 ) )
% 5.41/5.79 => ( ! [N3: nat] : ( ord_less_eq_real @ ( A @ ( suc @ N3 ) ) @ ( A @ N3 ) )
% 5.41/5.79 => ( filterlim_nat_real
% 5.41/5.79 @ ^ [N2: nat] :
% 5.41/5.79 ( groups6591440286371151544t_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) )
% 5.41/5.79 @ ( set_ord_lessThan_nat @ ( plus_plus_nat @ ( times_times_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N2 ) @ one_one_nat ) ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real
% 5.41/5.79 @ ( suminf_real
% 5.41/5.79 @ ^ [I5: nat] : ( times_times_real @ ( power_power_real @ ( uminus_uminus_real @ one_one_real ) @ I5 ) @ ( A @ I5 ) ) ) )
% 5.41/5.79 @ at_top_nat ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % summable_Leibniz'(5)
% 5.41/5.79 thf(fact_10086_real__bounded__linear,axiom,
% 5.41/5.79 ( real_V5970128139526366754l_real
% 5.41/5.79 = ( ^ [F6: real > real] :
% 5.41/5.79 ? [C3: real] :
% 5.41/5.79 ( F6
% 5.41/5.79 = ( ^ [X3: real] : ( times_times_real @ X3 @ C3 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % real_bounded_linear
% 5.41/5.79 thf(fact_10087_tendsto__exp__limit__at__right,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( filterlim_real_real
% 5.41/5.79 @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( times_times_real @ X @ Y3 ) ) @ ( divide_divide_real @ one_one_real @ Y3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % tendsto_exp_limit_at_right
% 5.41/5.79 thf(fact_10088_dist__real__def,axiom,
% 5.41/5.79 ( real_V975177566351809787t_real
% 5.41/5.79 = ( ^ [X3: real,Y3: real] : ( abs_abs_real @ ( minus_minus_real @ X3 @ Y3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % dist_real_def
% 5.41/5.79 thf(fact_10089_dist__complex__def,axiom,
% 5.41/5.79 ( real_V3694042436643373181omplex
% 5.41/5.79 = ( ^ [X3: complex,Y3: complex] : ( real_V1022390504157884413omplex @ ( minus_minus_complex @ X3 @ Y3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % dist_complex_def
% 5.41/5.79 thf(fact_10090_tendsto__arcosh__at__left__1,axiom,
% 5.41/5.79 filterlim_real_real @ arcosh_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5849166863359141190n_real @ one_one_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % tendsto_arcosh_at_left_1
% 5.41/5.79 thf(fact_10091_greaterThan__0,axiom,
% 5.41/5.79 ( ( set_or1210151606488870762an_nat @ zero_zero_nat )
% 5.41/5.79 = ( image_nat_nat @ suc @ top_top_set_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % greaterThan_0
% 5.41/5.79 thf(fact_10092_greaterThan__Suc,axiom,
% 5.41/5.79 ! [K: nat] :
% 5.41/5.79 ( ( set_or1210151606488870762an_nat @ ( suc @ K ) )
% 5.41/5.79 = ( minus_minus_set_nat @ ( set_or1210151606488870762an_nat @ K ) @ ( insert_nat @ ( suc @ K ) @ bot_bot_set_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % greaterThan_Suc
% 5.41/5.79 thf(fact_10093_INT__greaterThan__UNIV,axiom,
% 5.41/5.79 ( ( comple7806235888213564991et_nat @ ( image_nat_set_nat @ set_or1210151606488870762an_nat @ top_top_set_nat ) )
% 5.41/5.79 = bot_bot_set_nat ) ).
% 5.41/5.79
% 5.41/5.79 % INT_greaterThan_UNIV
% 5.41/5.79 thf(fact_10094_filterlim__tan__at__right,axiom,
% 5.41/5.79 filterlim_real_real @ tan_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % filterlim_tan_at_right
% 5.41/5.79 thf(fact_10095_atLeast__0,axiom,
% 5.41/5.79 ( ( set_ord_atLeast_nat @ zero_zero_nat )
% 5.41/5.79 = top_top_set_nat ) ).
% 5.41/5.79
% 5.41/5.79 % atLeast_0
% 5.41/5.79 thf(fact_10096_atLeast__Suc__greaterThan,axiom,
% 5.41/5.79 ! [K: nat] :
% 5.41/5.79 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.41/5.79 = ( set_or1210151606488870762an_nat @ K ) ) ).
% 5.41/5.79
% 5.41/5.79 % atLeast_Suc_greaterThan
% 5.41/5.79 thf(fact_10097_exp__at__bot,axiom,
% 5.41/5.79 filterlim_real_real @ exp_real @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ at_bot_real ).
% 5.41/5.79
% 5.41/5.79 % exp_at_bot
% 5.41/5.79 thf(fact_10098_filterlim__inverse__at__bot__neg,axiom,
% 5.41/5.79 filterlim_real_real @ inverse_inverse_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5984915006950818249n_real @ zero_zero_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % filterlim_inverse_at_bot_neg
% 5.41/5.79 thf(fact_10099_UN__atLeast__UNIV,axiom,
% 5.41/5.79 ( ( comple7399068483239264473et_nat @ ( image_nat_set_nat @ set_ord_atLeast_nat @ top_top_set_nat ) )
% 5.41/5.79 = top_top_set_nat ) ).
% 5.41/5.79
% 5.41/5.79 % UN_atLeast_UNIV
% 5.41/5.79 thf(fact_10100_atLeast__Suc,axiom,
% 5.41/5.79 ! [K: nat] :
% 5.41/5.79 ( ( set_ord_atLeast_nat @ ( suc @ K ) )
% 5.41/5.79 = ( minus_minus_set_nat @ ( set_ord_atLeast_nat @ K ) @ ( insert_nat @ K @ bot_bot_set_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % atLeast_Suc
% 5.41/5.79 thf(fact_10101_tanh__real__at__bot,axiom,
% 5.41/5.79 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ one_one_real ) ) @ at_bot_real ).
% 5.41/5.79
% 5.41/5.79 % tanh_real_at_bot
% 5.41/5.79 thf(fact_10102_ln__at__0,axiom,
% 5.41/5.79 filterlim_real_real @ ln_ln_real @ at_bot_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % ln_at_0
% 5.41/5.79 thf(fact_10103_artanh__real__at__right__1,axiom,
% 5.41/5.79 filterlim_real_real @ artanh_real @ at_bot_real @ ( topolo2177554685111907308n_real @ ( uminus_uminus_real @ one_one_real ) @ ( set_or5849166863359141190n_real @ ( uminus_uminus_real @ one_one_real ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % artanh_real_at_right_1
% 5.41/5.79 thf(fact_10104_DERIV__pos__imp__increasing__at__bot,axiom,
% 5.41/5.79 ! [B: real,F: real > real,Flim: real] :
% 5.41/5.79 ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ X6 @ B )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_real @ zero_zero_real @ Y2 ) ) )
% 5.41/5.79 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_bot_real )
% 5.41/5.79 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_pos_imp_increasing_at_bot
% 5.41/5.79 thf(fact_10105_filterlim__pow__at__bot__odd,axiom,
% 5.41/5.79 ! [N: nat,F: real > real,F3: filter_real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 5.41/5.79 => ( ~ ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.41/5.79 @ at_bot_real
% 5.41/5.79 @ F3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % filterlim_pow_at_bot_odd
% 5.41/5.79 thf(fact_10106_tendsto__arctan__at__bot,axiom,
% 5.41/5.79 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( uminus_uminus_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) @ at_bot_real ).
% 5.41/5.79
% 5.41/5.79 % tendsto_arctan_at_bot
% 5.41/5.79 thf(fact_10107_filterlim__pow__at__bot__even,axiom,
% 5.41/5.79 ! [N: nat,F: real > real,F3: filter_real] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( ( filterlim_real_real @ F @ at_bot_real @ F3 )
% 5.41/5.79 => ( ( dvd_dvd_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ N )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( power_power_real @ ( F @ X3 ) @ N )
% 5.41/5.79 @ at_top_real
% 5.41/5.79 @ F3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % filterlim_pow_at_bot_even
% 5.41/5.79 thf(fact_10108_at__bot__le__at__infinity,axiom,
% 5.41/5.79 ord_le4104064031414453916r_real @ at_bot_real @ at_infinity_real ).
% 5.41/5.79
% 5.41/5.79 % at_bot_le_at_infinity
% 5.41/5.79 thf(fact_10109_at__top__le__at__infinity,axiom,
% 5.41/5.79 ord_le4104064031414453916r_real @ at_top_real @ at_infinity_real ).
% 5.41/5.79
% 5.41/5.79 % at_top_le_at_infinity
% 5.41/5.79 thf(fact_10110_sqrt__at__top,axiom,
% 5.41/5.79 filterlim_real_real @ sqrt @ at_top_real @ at_top_real ).
% 5.41/5.79
% 5.41/5.79 % sqrt_at_top
% 5.41/5.79 thf(fact_10111_tanh__real__at__top,axiom,
% 5.41/5.79 filterlim_real_real @ tanh_real @ ( topolo2815343760600316023s_real @ one_one_real ) @ at_top_real ).
% 5.41/5.79
% 5.41/5.79 % tanh_real_at_top
% 5.41/5.79 thf(fact_10112_artanh__real__at__left__1,axiom,
% 5.41/5.79 filterlim_real_real @ artanh_real @ at_top_real @ ( topolo2177554685111907308n_real @ one_one_real @ ( set_or5984915006950818249n_real @ one_one_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % artanh_real_at_left_1
% 5.41/5.79 thf(fact_10113_ln__x__over__x__tendsto__0,axiom,
% 5.41/5.79 ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( ln_ln_real @ X3 ) @ X3 )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_real ) ).
% 5.41/5.79
% 5.41/5.79 % ln_x_over_x_tendsto_0
% 5.41/5.79 thf(fact_10114_filterlim__inverse__at__top__right,axiom,
% 5.41/5.79 filterlim_real_real @ inverse_inverse_real @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % filterlim_inverse_at_top_right
% 5.41/5.79 thf(fact_10115_filterlim__inverse__at__right__top,axiom,
% 5.41/5.79 filterlim_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) @ at_top_real ).
% 5.41/5.79
% 5.41/5.79 % filterlim_inverse_at_right_top
% 5.41/5.79 thf(fact_10116_tendsto__power__div__exp__0,axiom,
% 5.41/5.79 ! [K: nat] :
% 5.41/5.79 ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( power_power_real @ X3 @ K ) @ ( exp_real @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ zero_zero_real )
% 5.41/5.79 @ at_top_real ) ).
% 5.41/5.79
% 5.41/5.79 % tendsto_power_div_exp_0
% 5.41/5.79 thf(fact_10117_tendsto__exp__limit__at__top,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( filterlim_real_real
% 5.41/5.79 @ ^ [Y3: real] : ( powr_real @ ( plus_plus_real @ one_one_real @ ( divide_divide_real @ X @ Y3 ) ) @ Y3 )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ ( exp_real @ X ) )
% 5.41/5.79 @ at_top_real ) ).
% 5.41/5.79
% 5.41/5.79 % tendsto_exp_limit_at_top
% 5.41/5.79 thf(fact_10118_filterlim__tan__at__left,axiom,
% 5.41/5.79 filterlim_real_real @ tan_real @ at_top_real @ ( topolo2177554685111907308n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) @ ( set_or5984915006950818249n_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % filterlim_tan_at_left
% 5.41/5.79 thf(fact_10119_DERIV__neg__imp__decreasing__at__top,axiom,
% 5.41/5.79 ! [B: real,F: real > real,Flim: real] :
% 5.41/5.79 ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ B @ X6 )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_real @ Y2 @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ Flim ) @ at_top_real )
% 5.41/5.79 => ( ord_less_real @ Flim @ ( F @ B ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_neg_imp_decreasing_at_top
% 5.41/5.79 thf(fact_10120_tendsto__arctan__at__top,axiom,
% 5.41/5.79 filterlim_real_real @ arctan @ ( topolo2815343760600316023s_real @ ( divide_divide_real @ pi @ ( numeral_numeral_real @ ( bit0 @ one ) ) ) ) @ at_top_real ).
% 5.41/5.79
% 5.41/5.79 % tendsto_arctan_at_top
% 5.41/5.79 thf(fact_10121_lhopital__left__at__top,axiom,
% 5.41/5.79 ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 5.41/5.79 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ Y )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ Y )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital_left_at_top
% 5.41/5.79 thf(fact_10122_eventually__sequentially__seg,axiom,
% 5.41/5.79 ! [P: nat > $o,K: nat] :
% 5.41/5.79 ( ( eventually_nat
% 5.41/5.79 @ ^ [N2: nat] : ( P @ ( plus_plus_nat @ N2 @ K ) )
% 5.41/5.79 @ at_top_nat )
% 5.41/5.79 = ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % eventually_sequentially_seg
% 5.41/5.79 thf(fact_10123_eventually__sequentiallyI,axiom,
% 5.41/5.79 ! [C: nat,P: nat > $o] :
% 5.41/5.79 ( ! [X6: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ C @ X6 )
% 5.41/5.79 => ( P @ X6 ) )
% 5.41/5.79 => ( eventually_nat @ P @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % eventually_sequentiallyI
% 5.41/5.79 thf(fact_10124_eventually__sequentially,axiom,
% 5.41/5.79 ! [P: nat > $o] :
% 5.41/5.79 ( ( eventually_nat @ P @ at_top_nat )
% 5.41/5.79 = ( ? [N6: nat] :
% 5.41/5.79 ! [N2: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.41/5.79 => ( P @ N2 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % eventually_sequentially
% 5.41/5.79 thf(fact_10125_le__sequentially,axiom,
% 5.41/5.79 ! [F3: filter_nat] :
% 5.41/5.79 ( ( ord_le2510731241096832064er_nat @ F3 @ at_top_nat )
% 5.41/5.79 = ( ! [N6: nat] : ( eventually_nat @ ( ord_less_eq_nat @ N6 ) @ F3 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % le_sequentially
% 5.41/5.79 thf(fact_10126_sequentially__offset,axiom,
% 5.41/5.79 ! [P: nat > $o,K: nat] :
% 5.41/5.79 ( ( eventually_nat @ P @ at_top_nat )
% 5.41/5.79 => ( eventually_nat
% 5.41/5.79 @ ^ [I5: nat] : ( P @ ( plus_plus_nat @ I5 @ K ) )
% 5.41/5.79 @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % sequentially_offset
% 5.41/5.79 thf(fact_10127_eventually__at__right__to__0,axiom,
% 5.41/5.79 ! [P: real > $o,A: real] :
% 5.41/5.79 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.41/5.79 = ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( P @ ( plus_plus_real @ X3 @ A ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % eventually_at_right_to_0
% 5.41/5.79 thf(fact_10128_eventually__at__top__to__right,axiom,
% 5.41/5.79 ! [P: real > $o] :
% 5.41/5.79 ( ( eventually_real @ P @ at_top_real )
% 5.41/5.79 = ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % eventually_at_top_to_right
% 5.41/5.79 thf(fact_10129_eventually__at__right__to__top,axiom,
% 5.41/5.79 ! [P: real > $o] :
% 5.41/5.79 ( ( eventually_real @ P @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 = ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( P @ ( inverse_inverse_real @ X3 ) )
% 5.41/5.79 @ at_top_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % eventually_at_right_to_top
% 5.41/5.79 thf(fact_10130_lhopital,axiom,
% 5.41/5.79 ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.41/5.79 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital
% 5.41/5.79 thf(fact_10131_lhopital__at__top,axiom,
% 5.41/5.79 ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 5.41/5.79 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ Y )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ Y )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital_at_top
% 5.41/5.79 thf(fact_10132_lhospital__at__top__at__top,axiom,
% 5.41/5.79 ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X: real] :
% 5.41/5.79 ( ( filterlim_real_real @ G @ at_top_real @ at_top_real )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ at_top_real )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ at_top_real )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ at_top_real )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ X )
% 5.41/5.79 @ at_top_real )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ X )
% 5.41/5.79 @ at_top_real ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhospital_at_top_at_top
% 5.41/5.79 thf(fact_10133_lhopital__right,axiom,
% 5.41/5.79 ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.41/5.79 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital_right
% 5.41/5.79 thf(fact_10134_lhopital__right__0,axiom,
% 5.41/5.79 ! [F0: real > real,G0: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.41/5.79 ( ( filterlim_real_real @ F0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( filterlim_real_real @ G0 @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G0 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F0 @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G0 @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F0 @ X3 ) @ ( G0 @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital_right_0
% 5.41/5.79 thf(fact_10135_lhopital__left,axiom,
% 5.41/5.79 ! [F: real > real,X: real,G: real > real,G2: real > real,F5: real > real,F3: filter_real] :
% 5.41/5.79 ( ( filterlim_real_real @ F @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( filterlim_real_real @ G @ ( topolo2815343760600316023s_real @ zero_zero_real ) @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ F3
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5984915006950818249n_real @ X ) ) ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital_left
% 5.41/5.79 thf(fact_10136_lhopital__right__at__top,axiom,
% 5.41/5.79 ! [G: real > real,X: real,G2: real > real,F: real > real,F5: real > real,Y: real] :
% 5.41/5.79 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ Y )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ Y )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ X @ ( set_or5849166863359141190n_real @ X ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital_right_at_top
% 5.41/5.79 thf(fact_10137_lhopital__right__0__at__top,axiom,
% 5.41/5.79 ! [G: real > real,G2: real > real,F: real > real,F5: real > real,X: real] :
% 5.41/5.79 ( ( filterlim_real_real @ G @ at_top_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] :
% 5.41/5.79 ( ( G2 @ X3 )
% 5.41/5.79 != zero_zero_real )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ F @ ( F5 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( eventually_real
% 5.41/5.79 @ ^ [X3: real] : ( has_fi5821293074295781190e_real @ G @ ( G2 @ X3 ) @ ( topolo2177554685111907308n_real @ X3 @ top_top_set_real ) )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F5 @ X3 ) @ ( G2 @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ X )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 => ( filterlim_real_real
% 5.41/5.79 @ ^ [X3: real] : ( divide_divide_real @ ( F @ X3 ) @ ( G @ X3 ) )
% 5.41/5.79 @ ( topolo2815343760600316023s_real @ X )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % lhopital_right_0_at_top
% 5.41/5.79 thf(fact_10138_GreatestI__nat,axiom,
% 5.41/5.79 ! [P: nat > $o,K: nat,B: nat] :
% 5.41/5.79 ( ( P @ K )
% 5.41/5.79 => ( ! [Y5: nat] :
% 5.41/5.79 ( ( P @ Y5 )
% 5.41/5.79 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.41/5.79 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % GreatestI_nat
% 5.41/5.79 thf(fact_10139_Greatest__le__nat,axiom,
% 5.41/5.79 ! [P: nat > $o,K: nat,B: nat] :
% 5.41/5.79 ( ( P @ K )
% 5.41/5.79 => ( ! [Y5: nat] :
% 5.41/5.79 ( ( P @ Y5 )
% 5.41/5.79 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.41/5.79 => ( ord_less_eq_nat @ K @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Greatest_le_nat
% 5.41/5.79 thf(fact_10140_GreatestI__ex__nat,axiom,
% 5.41/5.79 ! [P: nat > $o,B: nat] :
% 5.41/5.79 ( ? [X_12: nat] : ( P @ X_12 )
% 5.41/5.79 => ( ! [Y5: nat] :
% 5.41/5.79 ( ( P @ Y5 )
% 5.41/5.79 => ( ord_less_eq_nat @ Y5 @ B ) )
% 5.41/5.79 => ( P @ ( order_Greatest_nat @ P ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % GreatestI_ex_nat
% 5.41/5.79 thf(fact_10141_Bseq__eq__bounded,axiom,
% 5.41/5.79 ! [F: nat > real,A: real,B: real] :
% 5.41/5.79 ( ( ord_less_eq_set_real @ ( image_nat_real @ F @ top_top_set_nat ) @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.41/5.79 => ( bfun_nat_real @ F @ at_top_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % Bseq_eq_bounded
% 5.41/5.79 thf(fact_10142_Bseq__realpow,axiom,
% 5.41/5.79 ! [X: real] :
% 5.41/5.79 ( ( ord_less_eq_real @ zero_zero_real @ X )
% 5.41/5.79 => ( ( ord_less_eq_real @ X @ one_one_real )
% 5.41/5.79 => ( bfun_nat_real @ ( power_power_real @ X ) @ at_top_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Bseq_realpow
% 5.41/5.79 thf(fact_10143_VEBT__internal_Ovalid_H_Oelims_I3_J,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.79 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.41/5.79 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.41/5.79 ( X
% 5.41/5.79 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.79 => ( Xa2 = one_one_nat ) )
% 5.41/5.79 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.79 => ( ( Deg2 = Xa2 )
% 5.41/5.79 & ! [X6: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 & ( case_o184042715313410164at_nat
% 5.41/5.79 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 @ ( produc6081775807080527818_nat_o
% 5.41/5.79 @ ^ [Mi3: nat,Ma3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.79 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 & ! [I5: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 5.41/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.41/5.79 & ( ( Mi3 = Ma3 )
% 5.41/5.79 => ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 & ( ( Mi3 != Ma3 )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.41/5.79 & ! [X3: nat] :
% 5.41/5.79 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 5.41/5.79 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.79 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.41/5.79 @ Mima ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % VEBT_internal.valid'.elims(3)
% 5.41/5.79 thf(fact_10144_decseq__bounded,axiom,
% 5.41/5.79 ! [X8: nat > real,B3: real] :
% 5.41/5.79 ( ( order_9091379641038594480t_real @ X8 )
% 5.41/5.79 => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 5.41/5.79 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % decseq_bounded
% 5.41/5.79 thf(fact_10145_decseq__convergent,axiom,
% 5.41/5.79 ! [X8: nat > real,B3: real] :
% 5.41/5.79 ( ( order_9091379641038594480t_real @ X8 )
% 5.41/5.79 => ( ! [I4: nat] : ( ord_less_eq_real @ B3 @ ( X8 @ I4 ) )
% 5.41/5.79 => ~ ! [L6: real] :
% 5.41/5.79 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.41/5.79 => ~ ! [I2: nat] : ( ord_less_eq_real @ L6 @ ( X8 @ I2 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % decseq_convergent
% 5.41/5.79 thf(fact_10146_VEBT__internal_Ovalid_H_Osimps_I2_J,axiom,
% 5.41/5.79 ! [Mima2: option4927543243414619207at_nat,Deg: nat,TreeList2: list_VEBT_VEBT,Summary: vEBT_VEBT,Deg4: nat] :
% 5.41/5.79 ( ( vEBT_VEBT_valid @ ( vEBT_Node @ Mima2 @ Deg @ TreeList2 @ Summary ) @ Deg4 )
% 5.41/5.79 = ( ( Deg = Deg4 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.79 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( vEBT_VEBT_valid @ Summary @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList2 )
% 5.41/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 & ( case_o184042715313410164at_nat
% 5.41/5.79 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary @ X2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 @ ( produc6081775807080527818_nat_o
% 5.41/5.79 @ ^ [Mi3: nat,Ma3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.79 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.41/5.79 & ! [I5: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList2 @ I5 ) @ X2 ) )
% 5.41/5.79 = ( vEBT_V8194947554948674370ptions @ Summary @ I5 ) ) )
% 5.41/5.79 & ( ( Mi3 = Ma3 )
% 5.41/5.79 => ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList2 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 & ( ( Mi3 != Ma3 )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ Ma3 )
% 5.41/5.79 & ! [X3: nat] :
% 5.41/5.79 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg ) )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList2 @ X3 )
% 5.41/5.79 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.79 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.41/5.79 @ Mima2 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % VEBT_internal.valid'.simps(2)
% 5.41/5.79 thf(fact_10147_VEBT__internal_Ovalid_H_Oelims_I1_J,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.79 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.41/5.79 = Y )
% 5.41/5.79 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.41/5.79 ( X
% 5.41/5.79 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.79 => ( Y
% 5.41/5.79 = ( Xa2 != one_one_nat ) ) )
% 5.41/5.79 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.79 => ( Y
% 5.41/5.79 = ( ~ ( ( Deg2 = Xa2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 & ( case_o184042715313410164at_nat
% 5.41/5.79 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 @ ( produc6081775807080527818_nat_o
% 5.41/5.79 @ ^ [Mi3: nat,Ma3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.79 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 & ! [I5: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 5.41/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.41/5.79 & ( ( Mi3 = Ma3 )
% 5.41/5.79 => ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 & ( ( Mi3 != Ma3 )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.41/5.79 & ! [X3: nat] :
% 5.41/5.79 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 5.41/5.79 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.79 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.41/5.79 @ Mima ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % VEBT_internal.valid'.elims(1)
% 5.41/5.79 thf(fact_10148_VEBT__internal_Ovalid_H_Oelims_I2_J,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.79 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.41/5.79 => ( ( ? [Uu2: $o,Uv2: $o] :
% 5.41/5.79 ( X
% 5.41/5.79 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.79 => ( Xa2 != one_one_nat ) )
% 5.41/5.79 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.79 => ~ ( ( Deg2 = Xa2 )
% 5.41/5.79 & ! [X4: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 & ( case_o184042715313410164at_nat
% 5.41/5.79 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 @ ( produc6081775807080527818_nat_o
% 5.41/5.79 @ ^ [Mi3: nat,Ma3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.79 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 & ! [I5: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 5.41/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.41/5.79 & ( ( Mi3 = Ma3 )
% 5.41/5.79 => ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 & ( ( Mi3 != Ma3 )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.41/5.79 & ! [X3: nat] :
% 5.41/5.79 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 5.41/5.79 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.79 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.41/5.79 @ Mima ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % VEBT_internal.valid'.elims(2)
% 5.41/5.79 thf(fact_10149_VEBT__internal_Ovalid_H_Opelims_I3_J,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.79 ( ~ ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.41/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.79 => ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.41/5.79 => ( Xa2 = one_one_nat ) ) )
% 5.41/5.79 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.41/5.79 => ( ( Deg2 = Xa2 )
% 5.41/5.79 & ! [X6: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X6 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ( vEBT_VEBT_valid @ X6 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 & ( case_o184042715313410164at_nat
% 5.41/5.79 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 @ ( produc6081775807080527818_nat_o
% 5.41/5.79 @ ^ [Mi3: nat,Ma3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.79 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 & ! [I5: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 5.41/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.41/5.79 & ( ( Mi3 = Ma3 )
% 5.41/5.79 => ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 & ( ( Mi3 != Ma3 )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.41/5.79 & ! [X3: nat] :
% 5.41/5.79 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 5.41/5.79 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.79 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.41/5.79 @ Mima ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % VEBT_internal.valid'.pelims(3)
% 5.41/5.79 thf(fact_10150_VEBT__internal_Ovalid_H_Opelims_I2_J,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Xa2: nat] :
% 5.41/5.79 ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.41/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.79 => ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) )
% 5.41/5.79 => ( Xa2 != one_one_nat ) ) )
% 5.41/5.79 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) )
% 5.41/5.79 => ~ ( ( Deg2 = Xa2 )
% 5.41/5.79 & ! [X4: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X4 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ( vEBT_VEBT_valid @ X4 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 & ( case_o184042715313410164at_nat
% 5.41/5.79 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 @ ( produc6081775807080527818_nat_o
% 5.41/5.79 @ ^ [Mi3: nat,Ma3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.79 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 & ! [I5: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 5.41/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.41/5.79 & ( ( Mi3 = Ma3 )
% 5.41/5.79 => ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 & ( ( Mi3 != Ma3 )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.41/5.79 & ! [X3: nat] :
% 5.41/5.79 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 5.41/5.79 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.79 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.41/5.79 @ Mima ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % VEBT_internal.valid'.pelims(2)
% 5.41/5.79 thf(fact_10151_Sup__int__def,axiom,
% 5.41/5.79 ( complete_Sup_Sup_int
% 5.41/5.79 = ( ^ [X2: set_int] :
% 5.41/5.79 ( the_int
% 5.41/5.79 @ ^ [X3: int] :
% 5.41/5.79 ( ( member_int @ X3 @ X2 )
% 5.41/5.79 & ! [Y3: int] :
% 5.41/5.79 ( ( member_int @ Y3 @ X2 )
% 5.41/5.79 => ( ord_less_eq_int @ Y3 @ X3 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Sup_int_def
% 5.41/5.79 thf(fact_10152_VEBT__internal_Ovalid_H_Opelims_I1_J,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Xa2: nat,Y: $o] :
% 5.41/5.79 ( ( ( vEBT_VEBT_valid @ X @ Xa2 )
% 5.41/5.79 = Y )
% 5.41/5.79 => ( ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ X @ Xa2 ) )
% 5.41/5.79 => ( ! [Uu2: $o,Uv2: $o] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Leaf @ Uu2 @ Uv2 ) )
% 5.41/5.79 => ( ( Y
% 5.41/5.79 = ( Xa2 = one_one_nat ) )
% 5.41/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Leaf @ Uu2 @ Uv2 ) @ Xa2 ) ) ) )
% 5.41/5.79 => ~ ! [Mima: option4927543243414619207at_nat,Deg2: nat,TreeList3: list_VEBT_VEBT,Summary2: vEBT_VEBT] :
% 5.41/5.79 ( ( X
% 5.41/5.79 = ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) )
% 5.41/5.79 => ( ( Y
% 5.41/5.79 = ( ( Deg2 = Xa2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ( vEBT_VEBT_valid @ X3 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( vEBT_VEBT_valid @ Summary2 @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) )
% 5.41/5.79 & ( ( size_s6755466524823107622T_VEBT @ TreeList3 )
% 5.41/5.79 = ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 & ( case_o184042715313410164at_nat
% 5.41/5.79 @ ( ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ Summary2 @ X2 )
% 5.41/5.79 & ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 @ ( produc6081775807080527818_nat_o
% 5.41/5.79 @ ^ [Mi3: nat,Ma3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ Mi3 @ Ma3 )
% 5.41/5.79 & ( ord_less_nat @ Ma3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 & ! [I5: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I5 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ ( minus_minus_nat @ Deg2 @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) ) ) )
% 5.41/5.79 => ( ( ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ TreeList3 @ I5 ) @ X2 ) )
% 5.41/5.79 = ( vEBT_V8194947554948674370ptions @ Summary2 @ I5 ) ) )
% 5.41/5.79 & ( ( Mi3 = Ma3 )
% 5.41/5.79 => ! [X3: vEBT_VEBT] :
% 5.41/5.79 ( ( member_VEBT_VEBT @ X3 @ ( set_VEBT_VEBT2 @ TreeList3 ) )
% 5.41/5.79 => ~ ? [X2: nat] : ( vEBT_V8194947554948674370ptions @ X3 @ X2 ) ) )
% 5.41/5.79 & ( ( Mi3 != Ma3 )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ Ma3 )
% 5.41/5.79 & ! [X3: nat] :
% 5.41/5.79 ( ( ord_less_nat @ X3 @ ( power_power_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ Deg2 ) )
% 5.41/5.79 => ( ( vEBT_V5917875025757280293ildren @ ( divide_divide_nat @ Deg2 @ ( numeral_numeral_nat @ ( bit0 @ one ) ) ) @ TreeList3 @ X3 )
% 5.41/5.79 => ( ( ord_less_nat @ Mi3 @ X3 )
% 5.41/5.79 & ( ord_less_eq_nat @ X3 @ Ma3 ) ) ) ) ) ) ) )
% 5.41/5.79 @ Mima ) ) )
% 5.41/5.79 => ~ ( accp_P2887432264394892906BT_nat @ vEBT_VEBT_valid_rel @ ( produc738532404422230701BT_nat @ ( vEBT_Node @ Mima @ Deg2 @ TreeList3 @ Summary2 ) @ Xa2 ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % VEBT_internal.valid'.pelims(1)
% 5.41/5.79 thf(fact_10153_GMVT,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,G: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 & ( ord_less_eq_real @ X6 @ B ) )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ F ) )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 & ( ord_less_real @ X6 @ B ) )
% 5.41/5.79 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ( ord_less_eq_real @ A @ X6 )
% 5.41/5.79 & ( ord_less_eq_real @ X6 @ B ) )
% 5.41/5.79 => ( topolo4422821103128117721l_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) @ G ) )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 & ( ord_less_real @ X6 @ B ) )
% 5.41/5.79 => ( differ6690327859849518006l_real @ G @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) )
% 5.41/5.79 => ? [G_c: real,F_c: real,C2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ G @ G_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.41/5.79 & ( has_fi5821293074295781190e_real @ F @ F_c @ ( topolo2177554685111907308n_real @ C2 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_real @ A @ C2 )
% 5.41/5.79 & ( ord_less_real @ C2 @ B )
% 5.41/5.79 & ( ( times_times_real @ ( minus_minus_real @ ( F @ B ) @ ( F @ A ) ) @ G_c )
% 5.41/5.79 = ( times_times_real @ ( minus_minus_real @ ( G @ B ) @ ( G @ A ) ) @ F_c ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % GMVT
% 5.41/5.79 thf(fact_10154_MVT,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ? [L4: real,Z5: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Z5 )
% 5.41/5.79 & ( ord_less_real @ Z5 @ B )
% 5.41/5.79 & ( has_fi5821293074295781190e_real @ F @ L4 @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) )
% 5.41/5.79 & ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.41/5.79 = ( times_times_real @ ( minus_minus_real @ B @ A ) @ L4 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % MVT
% 5.41/5.79 thf(fact_10155_continuous__on__arcosh_H,axiom,
% 5.41/5.79 ! [A2: set_real,F: real > real] :
% 5.41/5.79 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ A2 )
% 5.41/5.79 => ( ord_less_eq_real @ one_one_real @ ( F @ X6 ) ) )
% 5.41/5.79 => ( topolo5044208981011980120l_real @ A2
% 5.41/5.79 @ ^ [X3: real] : ( arcosh_real @ ( F @ X3 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % continuous_on_arcosh'
% 5.41/5.79 thf(fact_10156_continuous__image__closed__interval,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_eq_real @ A @ B )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ? [C2: real,D3: real] :
% 5.41/5.79 ( ( ( image_real_real @ F @ ( set_or1222579329274155063t_real @ A @ B ) )
% 5.41/5.79 = ( set_or1222579329274155063t_real @ C2 @ D3 ) )
% 5.41/5.79 & ( ord_less_eq_real @ C2 @ D3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % continuous_image_closed_interval
% 5.41/5.79 thf(fact_10157_continuous__on__arcosh,axiom,
% 5.41/5.79 ! [A2: set_real] :
% 5.41/5.79 ( ( ord_less_eq_set_real @ A2 @ ( set_ord_atLeast_real @ one_one_real ) )
% 5.41/5.79 => ( topolo5044208981011980120l_real @ A2 @ arcosh_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % continuous_on_arcosh
% 5.41/5.79 thf(fact_10158_continuous__on__arccos_H,axiom,
% 5.41/5.79 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arccos ).
% 5.41/5.79
% 5.41/5.79 % continuous_on_arccos'
% 5.41/5.79 thf(fact_10159_continuous__on__arcsin_H,axiom,
% 5.41/5.79 topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) @ arcsin ).
% 5.41/5.79
% 5.41/5.79 % continuous_on_arcsin'
% 5.41/5.79 thf(fact_10160_continuous__on__artanh_H,axiom,
% 5.41/5.79 ! [A2: set_real,F: real > real] :
% 5.41/5.79 ( ( topolo5044208981011980120l_real @ A2 @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( member_real @ X6 @ A2 )
% 5.41/5.79 => ( member_real @ ( F @ X6 ) @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) ) )
% 5.41/5.79 => ( topolo5044208981011980120l_real @ A2
% 5.41/5.79 @ ^ [X3: real] : ( artanh_real @ ( F @ X3 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % continuous_on_artanh'
% 5.41/5.79 thf(fact_10161_Rolle__deriv,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ( ( F @ A )
% 5.41/5.79 = ( F @ B ) )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ( has_de1759254742604945161l_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ? [Z5: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Z5 )
% 5.41/5.79 & ( ord_less_real @ Z5 @ B )
% 5.41/5.79 & ( ( F5 @ Z5 )
% 5.41/5.79 = ( ^ [V4: real] : zero_zero_real ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Rolle_deriv
% 5.41/5.79 thf(fact_10162_mvt,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,F5: real > real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ( has_de1759254742604945161l_real @ F @ ( F5 @ X6 ) @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ~ ! [Xi: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Xi )
% 5.41/5.79 => ( ( ord_less_real @ Xi @ B )
% 5.41/5.79 => ( ( minus_minus_real @ ( F @ B ) @ ( F @ A ) )
% 5.41/5.79 != ( F5 @ Xi @ ( minus_minus_real @ B @ A ) ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % mvt
% 5.41/5.79 thf(fact_10163_DERIV__isconst__end,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ( ( F @ B )
% 5.41/5.79 = ( F @ A ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_isconst_end
% 5.41/5.79 thf(fact_10164_DERIV__neg__imp__decreasing__open,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_real @ Y2 @ zero_zero_real ) ) ) )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ord_less_real @ ( F @ B ) @ ( F @ A ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_neg_imp_decreasing_open
% 5.41/5.79 thf(fact_10165_DERIV__pos__imp__increasing__open,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ? [Y2: real] :
% 5.41/5.79 ( ( has_fi5821293074295781190e_real @ F @ Y2 @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) )
% 5.41/5.79 & ( ord_less_real @ zero_zero_real @ Y2 ) ) ) )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ord_less_real @ ( F @ A ) @ ( F @ B ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_pos_imp_increasing_open
% 5.41/5.79 thf(fact_10166_continuous__on__artanh,axiom,
% 5.41/5.79 ! [A2: set_real] :
% 5.41/5.79 ( ( ord_less_eq_set_real @ A2 @ ( set_or1633881224788618240n_real @ ( uminus_uminus_real @ one_one_real ) @ one_one_real ) )
% 5.41/5.79 => ( topolo5044208981011980120l_real @ A2 @ artanh_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % continuous_on_artanh
% 5.41/5.79 thf(fact_10167_DERIV__isconst2,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real,X: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ( ( ord_less_eq_real @ A @ X )
% 5.41/5.79 => ( ( ord_less_eq_real @ X @ B )
% 5.41/5.79 => ( ( F @ X )
% 5.41/5.79 = ( F @ A ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % DERIV_isconst2
% 5.41/5.79 thf(fact_10168_Rolle,axiom,
% 5.41/5.79 ! [A: real,B: real,F: real > real] :
% 5.41/5.79 ( ( ord_less_real @ A @ B )
% 5.41/5.79 => ( ( ( F @ A )
% 5.41/5.79 = ( F @ B ) )
% 5.41/5.79 => ( ( topolo5044208981011980120l_real @ ( set_or1222579329274155063t_real @ A @ B ) @ F )
% 5.41/5.79 => ( ! [X6: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ X6 )
% 5.41/5.79 => ( ( ord_less_real @ X6 @ B )
% 5.41/5.79 => ( differ6690327859849518006l_real @ F @ ( topolo2177554685111907308n_real @ X6 @ top_top_set_real ) ) ) )
% 5.41/5.79 => ? [Z5: real] :
% 5.41/5.79 ( ( ord_less_real @ A @ Z5 )
% 5.41/5.79 & ( ord_less_real @ Z5 @ B )
% 5.41/5.79 & ( has_fi5821293074295781190e_real @ F @ zero_zero_real @ ( topolo2177554685111907308n_real @ Z5 @ top_top_set_real ) ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % Rolle
% 5.41/5.79 thf(fact_10169_uniformity__real__def,axiom,
% 5.41/5.79 ( topolo1511823702728130853y_real
% 5.41/5.79 = ( comple2936214249959783750l_real
% 5.41/5.79 @ ( image_2178119161166701260l_real
% 5.41/5.79 @ ^ [E3: real] :
% 5.41/5.79 ( princi6114159922880469582l_real
% 5.41/5.79 @ ( collec3799799289383736868l_real
% 5.41/5.79 @ ( produc5414030515140494994real_o
% 5.41/5.79 @ ^ [X3: real,Y3: real] : ( ord_less_real @ ( real_V975177566351809787t_real @ X3 @ Y3 ) @ E3 ) ) ) )
% 5.41/5.79 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % uniformity_real_def
% 5.41/5.79 thf(fact_10170_uniformity__complex__def,axiom,
% 5.41/5.79 ( topolo896644834953643431omplex
% 5.41/5.79 = ( comple8358262395181532106omplex
% 5.41/5.79 @ ( image_5971271580939081552omplex
% 5.41/5.79 @ ^ [E3: real] :
% 5.41/5.79 ( princi3496590319149328850omplex
% 5.41/5.79 @ ( collec8663557070575231912omplex
% 5.41/5.79 @ ( produc6771430404735790350plex_o
% 5.41/5.79 @ ^ [X3: complex,Y3: complex] : ( ord_less_real @ ( real_V3694042436643373181omplex @ X3 @ Y3 ) @ E3 ) ) ) )
% 5.41/5.79 @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % uniformity_complex_def
% 5.41/5.79 thf(fact_10171_eventually__prod__sequentially,axiom,
% 5.41/5.79 ! [P: product_prod_nat_nat > $o] :
% 5.41/5.79 ( ( eventu1038000079068216329at_nat @ P @ ( prod_filter_nat_nat @ at_top_nat @ at_top_nat ) )
% 5.41/5.79 = ( ? [N6: nat] :
% 5.41/5.79 ! [M3: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ N6 @ M3 )
% 5.41/5.79 => ! [N2: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ N6 @ N2 )
% 5.41/5.79 => ( P @ ( product_Pair_nat_nat @ N2 @ M3 ) ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % eventually_prod_sequentially
% 5.41/5.79 thf(fact_10172_mono__times__nat,axiom,
% 5.41/5.79 ! [N: nat] :
% 5.41/5.79 ( ( ord_less_nat @ zero_zero_nat @ N )
% 5.41/5.79 => ( order_mono_nat_nat @ ( times_times_nat @ N ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % mono_times_nat
% 5.41/5.79 thf(fact_10173_mono__Suc,axiom,
% 5.41/5.79 order_mono_nat_nat @ suc ).
% 5.41/5.79
% 5.41/5.79 % mono_Suc
% 5.41/5.79 thf(fact_10174_incseq__bounded,axiom,
% 5.41/5.79 ! [X8: nat > real,B3: real] :
% 5.41/5.79 ( ( order_mono_nat_real @ X8 )
% 5.41/5.79 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 5.41/5.79 => ( bfun_nat_real @ X8 @ at_top_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % incseq_bounded
% 5.41/5.79 thf(fact_10175_filtermap__at__right__shift,axiom,
% 5.41/5.79 ! [D: real,A: real] :
% 5.41/5.79 ( ( filtermap_real_real
% 5.41/5.79 @ ^ [X3: real] : ( minus_minus_real @ X3 @ D )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) ) )
% 5.41/5.79 = ( topolo2177554685111907308n_real @ ( minus_minus_real @ A @ D ) @ ( set_or5849166863359141190n_real @ ( minus_minus_real @ A @ D ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % filtermap_at_right_shift
% 5.41/5.79 thf(fact_10176_incseq__convergent,axiom,
% 5.41/5.79 ! [X8: nat > real,B3: real] :
% 5.41/5.79 ( ( order_mono_nat_real @ X8 )
% 5.41/5.79 => ( ! [I4: nat] : ( ord_less_eq_real @ ( X8 @ I4 ) @ B3 )
% 5.41/5.79 => ~ ! [L6: real] :
% 5.41/5.79 ( ( filterlim_nat_real @ X8 @ ( topolo2815343760600316023s_real @ L6 ) @ at_top_nat )
% 5.41/5.79 => ~ ! [I2: nat] : ( ord_less_eq_real @ ( X8 @ I2 ) @ L6 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % incseq_convergent
% 5.41/5.79 thf(fact_10177_at__right__to__0,axiom,
% 5.41/5.79 ! [A: real] :
% 5.41/5.79 ( ( topolo2177554685111907308n_real @ A @ ( set_or5849166863359141190n_real @ A ) )
% 5.41/5.79 = ( filtermap_real_real
% 5.41/5.79 @ ^ [X3: real] : ( plus_plus_real @ X3 @ A )
% 5.41/5.79 @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % at_right_to_0
% 5.41/5.79 thf(fact_10178_at__right__to__top,axiom,
% 5.41/5.79 ( ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) )
% 5.41/5.79 = ( filtermap_real_real @ inverse_inverse_real @ at_top_real ) ) ).
% 5.41/5.79
% 5.41/5.79 % at_right_to_top
% 5.41/5.79 thf(fact_10179_at__top__to__right,axiom,
% 5.41/5.79 ( at_top_real
% 5.41/5.79 = ( filtermap_real_real @ inverse_inverse_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % at_top_to_right
% 5.41/5.79 thf(fact_10180_filtermap__ln__at__right,axiom,
% 5.41/5.79 ( ( filtermap_real_real @ ln_ln_real @ ( topolo2177554685111907308n_real @ zero_zero_real @ ( set_or5849166863359141190n_real @ zero_zero_real ) ) )
% 5.41/5.79 = at_bot_real ) ).
% 5.41/5.79
% 5.41/5.79 % filtermap_ln_at_right
% 5.41/5.79 thf(fact_10181_mono__ge2__power__minus__self,axiom,
% 5.41/5.79 ! [K: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ ( numeral_numeral_nat @ ( bit0 @ one ) ) @ K )
% 5.41/5.79 => ( order_mono_nat_nat
% 5.41/5.79 @ ^ [M3: nat] : ( minus_minus_nat @ ( power_power_nat @ K @ M3 ) @ M3 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % mono_ge2_power_minus_self
% 5.41/5.79 thf(fact_10182_remdups__upt,axiom,
% 5.41/5.79 ! [M: nat,N: nat] :
% 5.41/5.79 ( ( remdups_nat @ ( upt @ M @ N ) )
% 5.41/5.79 = ( upt @ M @ N ) ) ).
% 5.41/5.79
% 5.41/5.79 % remdups_upt
% 5.41/5.79 thf(fact_10183_length__upt,axiom,
% 5.41/5.79 ! [I: nat,J: nat] :
% 5.41/5.79 ( ( size_size_list_nat @ ( upt @ I @ J ) )
% 5.41/5.79 = ( minus_minus_nat @ J @ I ) ) ).
% 5.41/5.79
% 5.41/5.79 % length_upt
% 5.41/5.79 thf(fact_10184_upt__conv__Nil,axiom,
% 5.41/5.79 ! [J: nat,I: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ J @ I )
% 5.41/5.79 => ( ( upt @ I @ J )
% 5.41/5.79 = nil_nat ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_conv_Nil
% 5.41/5.79 thf(fact_10185_sorted__list__of__set__range,axiom,
% 5.41/5.79 ! [M: nat,N: nat] :
% 5.41/5.79 ( ( linord2614967742042102400et_nat @ ( set_or4665077453230672383an_nat @ M @ N ) )
% 5.41/5.79 = ( upt @ M @ N ) ) ).
% 5.41/5.79
% 5.41/5.79 % sorted_list_of_set_range
% 5.41/5.79 thf(fact_10186_upt__eq__Nil__conv,axiom,
% 5.41/5.79 ! [I: nat,J: nat] :
% 5.41/5.79 ( ( ( upt @ I @ J )
% 5.41/5.79 = nil_nat )
% 5.41/5.79 = ( ( J = zero_zero_nat )
% 5.41/5.79 | ( ord_less_eq_nat @ J @ I ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_eq_Nil_conv
% 5.41/5.79 thf(fact_10187_nth__upt,axiom,
% 5.41/5.79 ! [I: nat,K: nat,J: nat] :
% 5.41/5.79 ( ( ord_less_nat @ ( plus_plus_nat @ I @ K ) @ J )
% 5.41/5.79 => ( ( nth_nat @ ( upt @ I @ J ) @ K )
% 5.41/5.79 = ( plus_plus_nat @ I @ K ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % nth_upt
% 5.41/5.79 thf(fact_10188_upt__rec__numeral,axiom,
% 5.41/5.79 ! [M: num,N: num] :
% 5.41/5.79 ( ( ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.79 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.79 = ( cons_nat @ ( numeral_numeral_nat @ M ) @ ( upt @ ( suc @ ( numeral_numeral_nat @ M ) ) @ ( numeral_numeral_nat @ N ) ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_nat @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.79 => ( ( upt @ ( numeral_numeral_nat @ M ) @ ( numeral_numeral_nat @ N ) )
% 5.41/5.79 = nil_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_rec_numeral
% 5.41/5.79 thf(fact_10189_atLeast__upt,axiom,
% 5.41/5.79 ( set_ord_lessThan_nat
% 5.41/5.79 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ N2 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % atLeast_upt
% 5.41/5.79 thf(fact_10190_atMost__upto,axiom,
% 5.41/5.79 ( set_ord_atMost_nat
% 5.41/5.79 = ( ^ [N2: nat] : ( set_nat2 @ ( upt @ zero_zero_nat @ ( suc @ N2 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % atMost_upto
% 5.41/5.79 thf(fact_10191_atLeastAtMost__upt,axiom,
% 5.41/5.79 ( set_or1269000886237332187st_nat
% 5.41/5.79 = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ N2 @ ( suc @ M3 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % atLeastAtMost_upt
% 5.41/5.79 thf(fact_10192_greaterThanLessThan__upt,axiom,
% 5.41/5.79 ( set_or5834768355832116004an_nat
% 5.41/5.79 = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ M3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % greaterThanLessThan_upt
% 5.41/5.79 thf(fact_10193_greaterThanAtMost__upt,axiom,
% 5.41/5.79 ( set_or6659071591806873216st_nat
% 5.41/5.79 = ( ^ [N2: nat,M3: nat] : ( set_nat2 @ ( upt @ ( suc @ N2 ) @ ( suc @ M3 ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % greaterThanAtMost_upt
% 5.41/5.79 thf(fact_10194_atLeastLessThan__upt,axiom,
% 5.41/5.79 ( set_or4665077453230672383an_nat
% 5.41/5.79 = ( ^ [I5: nat,J3: nat] : ( set_nat2 @ ( upt @ I5 @ J3 ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % atLeastLessThan_upt
% 5.41/5.79 thf(fact_10195_upt__0,axiom,
% 5.41/5.79 ! [I: nat] :
% 5.41/5.79 ( ( upt @ I @ zero_zero_nat )
% 5.41/5.79 = nil_nat ) ).
% 5.41/5.79
% 5.41/5.79 % upt_0
% 5.41/5.79 thf(fact_10196_upt__conv__Cons__Cons,axiom,
% 5.41/5.79 ! [M: nat,N: nat,Ns: list_nat,Q2: nat] :
% 5.41/5.79 ( ( ( cons_nat @ M @ ( cons_nat @ N @ Ns ) )
% 5.41/5.79 = ( upt @ M @ Q2 ) )
% 5.41/5.79 = ( ( cons_nat @ N @ Ns )
% 5.41/5.79 = ( upt @ ( suc @ M ) @ Q2 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_conv_Cons_Cons
% 5.41/5.79 thf(fact_10197_upt__conv__Cons,axiom,
% 5.41/5.79 ! [I: nat,J: nat] :
% 5.41/5.79 ( ( ord_less_nat @ I @ J )
% 5.41/5.79 => ( ( upt @ I @ J )
% 5.41/5.79 = ( cons_nat @ I @ ( upt @ ( suc @ I ) @ J ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_conv_Cons
% 5.41/5.79 thf(fact_10198_distinct__upt,axiom,
% 5.41/5.79 ! [I: nat,J: nat] : ( distinct_nat @ ( upt @ I @ J ) ) ).
% 5.41/5.79
% 5.41/5.79 % distinct_upt
% 5.41/5.79 thf(fact_10199_map__add__upt,axiom,
% 5.41/5.79 ! [N: nat,M: nat] :
% 5.41/5.79 ( ( map_nat_nat
% 5.41/5.79 @ ^ [I5: nat] : ( plus_plus_nat @ I5 @ N )
% 5.41/5.79 @ ( upt @ zero_zero_nat @ M ) )
% 5.41/5.79 = ( upt @ N @ ( plus_plus_nat @ M @ N ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % map_add_upt
% 5.41/5.79 thf(fact_10200_map__Suc__upt,axiom,
% 5.41/5.79 ! [M: nat,N: nat] :
% 5.41/5.79 ( ( map_nat_nat @ suc @ ( upt @ M @ N ) )
% 5.41/5.79 = ( upt @ ( suc @ M ) @ ( suc @ N ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % map_Suc_upt
% 5.41/5.79 thf(fact_10201_map__decr__upt,axiom,
% 5.41/5.79 ! [M: nat,N: nat] :
% 5.41/5.79 ( ( map_nat_nat
% 5.41/5.79 @ ^ [N2: nat] : ( minus_minus_nat @ N2 @ ( suc @ zero_zero_nat ) )
% 5.41/5.79 @ ( upt @ ( suc @ M ) @ ( suc @ N ) ) )
% 5.41/5.79 = ( upt @ M @ N ) ) ).
% 5.41/5.79
% 5.41/5.79 % map_decr_upt
% 5.41/5.79 thf(fact_10202_upt__add__eq__append,axiom,
% 5.41/5.79 ! [I: nat,J: nat,K: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.79 => ( ( upt @ I @ ( plus_plus_nat @ J @ K ) )
% 5.41/5.79 = ( append_nat @ ( upt @ I @ J ) @ ( upt @ J @ ( plus_plus_nat @ J @ K ) ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_add_eq_append
% 5.41/5.79 thf(fact_10203_upt__eq__Cons__conv,axiom,
% 5.41/5.79 ! [I: nat,J: nat,X: nat,Xs: list_nat] :
% 5.41/5.79 ( ( ( upt @ I @ J )
% 5.41/5.79 = ( cons_nat @ X @ Xs ) )
% 5.41/5.79 = ( ( ord_less_nat @ I @ J )
% 5.41/5.79 & ( I = X )
% 5.41/5.79 & ( ( upt @ ( plus_plus_nat @ I @ one_one_nat ) @ J )
% 5.41/5.79 = Xs ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_eq_Cons_conv
% 5.41/5.79 thf(fact_10204_upt__rec,axiom,
% 5.41/5.79 ( upt
% 5.41/5.79 = ( ^ [I5: nat,J3: nat] : ( if_list_nat @ ( ord_less_nat @ I5 @ J3 ) @ ( cons_nat @ I5 @ ( upt @ ( suc @ I5 ) @ J3 ) ) @ nil_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_rec
% 5.41/5.79 thf(fact_10205_upt__Suc__append,axiom,
% 5.41/5.79 ! [I: nat,J: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.79 => ( ( upt @ I @ ( suc @ J ) )
% 5.41/5.79 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_Suc_append
% 5.41/5.79 thf(fact_10206_upt__Suc,axiom,
% 5.41/5.79 ! [I: nat,J: nat] :
% 5.41/5.79 ( ( ( ord_less_eq_nat @ I @ J )
% 5.41/5.79 => ( ( upt @ I @ ( suc @ J ) )
% 5.41/5.79 = ( append_nat @ ( upt @ I @ J ) @ ( cons_nat @ J @ nil_nat ) ) ) )
% 5.41/5.79 & ( ~ ( ord_less_eq_nat @ I @ J )
% 5.41/5.79 => ( ( upt @ I @ ( suc @ J ) )
% 5.41/5.79 = nil_nat ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % upt_Suc
% 5.41/5.79 thf(fact_10207_sum__list__upt,axiom,
% 5.41/5.79 ! [M: nat,N: nat] :
% 5.41/5.79 ( ( ord_less_eq_nat @ M @ N )
% 5.41/5.79 => ( ( groups4561878855575611511st_nat @ ( upt @ M @ N ) )
% 5.41/5.79 = ( groups3542108847815614940at_nat
% 5.41/5.79 @ ^ [X3: nat] : X3
% 5.41/5.79 @ ( set_or4665077453230672383an_nat @ M @ N ) ) ) ) ).
% 5.41/5.79
% 5.41/5.79 % sum_list_upt
% 5.41/5.79
% 5.41/5.79 % Helper facts (40)
% 5.41/5.79 thf(help_If_2_1_If_001t__Int__Oint_T,axiom,
% 5.41/5.79 ! [X: int,Y: int] :
% 5.41/5.79 ( ( if_int @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Int__Oint_T,axiom,
% 5.41/5.79 ! [X: int,Y: int] :
% 5.41/5.79 ( ( if_int @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Nat__Onat_T,axiom,
% 5.41/5.79 ! [X: nat,Y: nat] :
% 5.41/5.79 ( ( if_nat @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Nat__Onat_T,axiom,
% 5.41/5.79 ! [X: nat,Y: nat] :
% 5.41/5.79 ( ( if_nat @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Num__Onum_T,axiom,
% 5.41/5.79 ! [X: num,Y: num] :
% 5.41/5.79 ( ( if_num @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Num__Onum_T,axiom,
% 5.41/5.79 ! [X: num,Y: num] :
% 5.41/5.79 ( ( if_num @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Rat__Orat_T,axiom,
% 5.41/5.79 ! [X: rat,Y: rat] :
% 5.41/5.79 ( ( if_rat @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Rat__Orat_T,axiom,
% 5.41/5.79 ! [X: rat,Y: rat] :
% 5.41/5.79 ( ( if_rat @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Real__Oreal_T,axiom,
% 5.41/5.79 ! [X: real,Y: real] :
% 5.41/5.79 ( ( if_real @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Real__Oreal_T,axiom,
% 5.41/5.79 ! [X: real,Y: real] :
% 5.41/5.79 ( ( if_real @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_fChoice_1_1_fChoice_001t__Real__Oreal_T,axiom,
% 5.41/5.79 ! [P: real > $o] :
% 5.41/5.79 ( ( P @ ( fChoice_real @ P ) )
% 5.41/5.79 = ( ? [X2: real] : ( P @ X2 ) ) ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.41/5.79 ! [X: complex,Y: complex] :
% 5.41/5.79 ( ( if_complex @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Complex__Ocomplex_T,axiom,
% 5.41/5.79 ! [X: complex,Y: complex] :
% 5.41/5.79 ( ( if_complex @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.41/5.79 ! [X: extended_enat,Y: extended_enat] :
% 5.41/5.79 ( ( if_Extended_enat @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Extended____Nat__Oenat_T,axiom,
% 5.41/5.79 ! [X: extended_enat,Y: extended_enat] :
% 5.41/5.79 ( ( if_Extended_enat @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.41/5.79 ! [X: code_integer,Y: code_integer] :
% 5.41/5.79 ( ( if_Code_integer @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Code____Numeral__Ointeger_T,axiom,
% 5.41/5.79 ! [X: code_integer,Y: code_integer] :
% 5.41/5.79 ( ( if_Code_integer @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: set_int,Y: set_int] :
% 5.41/5.79 ( ( if_set_int @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Set__Oset_It__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: set_int,Y: set_int] :
% 5.41/5.79 ( ( if_set_int @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.41/5.79 ( ( if_VEBT_VEBT @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__VEBT____Definitions__OVEBT_T,axiom,
% 5.41/5.79 ! [X: vEBT_VEBT,Y: vEBT_VEBT] :
% 5.41/5.79 ( ( if_VEBT_VEBT @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: list_int,Y: list_int] :
% 5.41/5.79 ( ( if_list_int @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__List__Olist_It__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: list_int,Y: list_int] :
% 5.41/5.79 ( ( if_list_int @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.41/5.79 ! [X: list_nat,Y: list_nat] :
% 5.41/5.79 ( ( if_list_nat @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__List__Olist_It__Nat__Onat_J_T,axiom,
% 5.41/5.79 ! [X: list_nat,Y: list_nat] :
% 5.41/5.79 ( ( if_list_nat @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: int > int,Y: int > int] :
% 5.41/5.79 ( ( if_int_int @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001_062_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: int > int,Y: int > int] :
% 5.41/5.79 ( ( if_int_int @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.41/5.79 ! [X: option_nat,Y: option_nat] :
% 5.41/5.79 ( ( if_option_nat @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Option__Ooption_It__Nat__Onat_J_T,axiom,
% 5.41/5.79 ! [X: option_nat,Y: option_nat] :
% 5.41/5.79 ( ( if_option_nat @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.41/5.79 ! [X: option_num,Y: option_num] :
% 5.41/5.79 ( ( if_option_num @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Option__Ooption_It__Num__Onum_J_T,axiom,
% 5.41/5.79 ! [X: option_num,Y: option_num] :
% 5.41/5.79 ( ( if_option_num @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.41/5.79 ( ( if_Pro3027730157355071871nt_int @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Int__Oint_Mt__Int__Oint_J_T,axiom,
% 5.41/5.79 ! [X: product_prod_int_int,Y: product_prod_int_int] :
% 5.41/5.79 ( ( if_Pro3027730157355071871nt_int @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.41/5.79 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.41/5.79 ( ( if_Pro6206227464963214023at_nat @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Nat__Onat_Mt__Nat__Onat_J_T,axiom,
% 5.41/5.79 ! [X: product_prod_nat_nat,Y: product_prod_nat_nat] :
% 5.41/5.79 ( ( if_Pro6206227464963214023at_nat @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.41/5.79 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.41/5.79 ( ( if_Pro5737122678794959658eger_o @ $false @ X @ Y )
% 5.41/5.79 = Y ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_M_Eo_J_T,axiom,
% 5.41/5.79 ! [X: produc6271795597528267376eger_o,Y: produc6271795597528267376eger_o] :
% 5.41/5.79 ( ( if_Pro5737122678794959658eger_o @ $true @ X @ Y )
% 5.41/5.79 = X ) ).
% 5.41/5.79
% 5.41/5.79 thf(help_If_3_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 5.41/5.79 ! [P: $o] :
% 5.41/5.79 ( ( P = $true )
% 5.41/5.79 | ( P = $false ) ) ).
% 6.60/6.96
% 6.60/6.96 thf(help_If_2_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.60/6.96 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.60/6.96 ( ( if_Pro6119634080678213985nteger @ $false @ X @ Y )
% 6.60/6.96 = Y ) ).
% 6.60/6.96
% 6.60/6.96 thf(help_If_1_1_If_001t__Product____Type__Oprod_It__Code____Numeral__Ointeger_Mt__Code____Numeral__Ointeger_J_T,axiom,
% 6.60/6.96 ! [X: produc8923325533196201883nteger,Y: produc8923325533196201883nteger] :
% 6.60/6.96 ( ( if_Pro6119634080678213985nteger @ $true @ X @ Y )
% 6.60/6.96 = X ) ).
% 6.60/6.96
% 6.60/6.96 % Conjectures (1)
% 6.60/6.96 thf(conj_0,conjecture,
% 6.60/6.96 ? [Y2: nat] : ( vEBT_V8194947554948674370ptions @ ( nth_VEBT_VEBT @ ( list_u1324408373059187874T_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) @ ( vEBT_vebt_delete @ ( nth_VEBT_VEBT @ treeList @ ( vEBT_VEBT_high @ xa @ na ) ) @ ( vEBT_VEBT_low @ xa @ na ) ) ) @ maxs ) @ Y2 ) ).
% 6.60/6.96
% 6.60/6.96 %------------------------------------------------------------------------------
% 6.60/6.96 ------- convert to smt2 : /export/starexec/sandbox2/tmp/tmp.L9WiwseROQ/cvc5---1.0.5_17604.p...
% 6.60/6.96 (declare-sort $$unsorted 0)
% 6.60/6.96 (declare-sort tptp.produc5542196010084753463at_nat 0)
% 6.60/6.96 (declare-sort tptp.produc1908205239877642774nteger 0)
% 6.60/6.96 (declare-sort tptp.produc5491161045314408544at_nat 0)
% 6.60/6.96 (declare-sort tptp.produc2285326912895808259nt_int 0)
% 6.60/6.96 (declare-sort tptp.produc8763457246119570046nteger 0)
% 6.60/6.96 (declare-sort tptp.produc7773217078559923341nt_int 0)
% 6.60/6.96 (declare-sort tptp.produc1193250871479095198on_num 0)
% 6.60/6.96 (declare-sort tptp.produc8306885398267862888on_nat 0)
% 6.60/6.96 (declare-sort tptp.produc6121120109295599847at_nat 0)
% 6.60/6.96 (declare-sort tptp.produc7036089656553540234on_num 0)
% 6.60/6.96 (declare-sort tptp.produc2233624965454879586on_nat 0)
% 6.60/6.96 (declare-sort tptp.produc6241069584506657477e_term 0)
% 6.60/6.96 (declare-sort tptp.set_fi4554929511873752355omplex 0)
% 6.60/6.96 (declare-sort tptp.list_P7413028617227757229T_VEBT 0)
% 6.60/6.96 (declare-sort tptp.produc8551481072490612790e_term 0)
% 6.60/6.96 (declare-sort tptp.option6357759511663192854e_term 0)
% 6.60/6.96 (declare-sort tptp.produc3447558737645232053on_num 0)
% 6.60/6.96 (declare-sort tptp.produc4953844613479565601on_nat 0)
% 6.60/6.96 (declare-sort tptp.set_fi7789364187291644575l_real 0)
% 6.60/6.96 (declare-sort tptp.filter6041513312241820739omplex 0)
% 6.60/6.96 (declare-sort tptp.list_P7037539587688870467BT_nat 0)
% 6.60/6.96 (declare-sort tptp.list_P4547456442757143711BT_int 0)
% 6.60/6.96 (declare-sort tptp.list_P5647936690300460905T_VEBT 0)
% 6.60/6.96 (declare-sort tptp.produc8243902056947475879T_VEBT 0)
% 6.60/6.96 (declare-sort tptp.set_Pr5085853215250843933omplex 0)
% 6.60/6.96 (declare-sort tptp.produc8923325533196201883nteger 0)
% 6.60/6.96 (declare-sort tptp.list_P3126845725202233233VEBT_o 0)
% 6.60/6.96 (declare-sort tptp.list_P7495141550334521929T_VEBT 0)
% 6.60/6.96 (declare-sort tptp.filter2146258269922977983l_real 0)
% 6.60/6.96 (declare-sort tptp.option4927543243414619207at_nat 0)
% 6.60/6.96 (declare-sort tptp.filter1242075044329608583at_nat 0)
% 6.60/6.96 (declare-sort tptp.set_Pr6218003697084177305l_real 0)
% 6.60/6.96 (declare-sort tptp.produc9072475918466114483BT_nat 0)
% 6.60/6.96 (declare-sort tptp.produc4894624898956917775BT_int 0)
% 6.60/6.96 (declare-sort tptp.produc8025551001238799321T_VEBT 0)
% 6.60/6.96 (declare-sort tptp.set_Pr958786334691620121nt_int 0)
% 6.60/6.96 (declare-sort tptp.produc4411394909380815293omplex 0)
% 6.60/6.96 (declare-sort tptp.list_P7333126701944960589_nat_o 0)
% 6.60/6.96 (declare-sort tptp.list_P6285523579766656935_o_nat 0)
% 6.60/6.96 (declare-sort tptp.list_P3795440434834930179_o_int 0)
% 6.60/6.96 (declare-sort tptp.set_list_VEBT_VEBT 0)
% 6.60/6.96 (declare-sort tptp.produc334124729049499915VEBT_o 0)
% 6.60/6.96 (declare-sort tptp.produc2504756804600209347T_VEBT 0)
% 6.60/6.96 (declare-sort tptp.produc6271795597528267376eger_o 0)
% 6.60/6.96 (declare-sort tptp.produc2422161461964618553l_real 0)
% 6.60/6.96 (declare-sort tptp.product_prod_num_num 0)
% 6.60/6.96 (declare-sort tptp.product_prod_nat_num 0)
% 6.60/6.96 (declare-sort tptp.product_prod_nat_nat 0)
% 6.60/6.96 (declare-sort tptp.product_prod_int_int 0)
% 6.60/6.96 (declare-sort tptp.list_P4002435161011370285od_o_o 0)
% 6.60/6.96 (declare-sort tptp.set_list_complex 0)
% 6.60/6.96 (declare-sort tptp.set_set_complex 0)
% 6.60/6.96 (declare-sort tptp.list_VEBT_VEBT 0)
% 6.60/6.96 (declare-sort tptp.set_list_nat 0)
% 6.60/6.96 (declare-sort tptp.set_list_int 0)
% 6.60/6.96 (declare-sort tptp.product_prod_nat_o 0)
% 6.60/6.96 (declare-sort tptp.product_prod_o_nat 0)
% 6.60/6.96 (declare-sort tptp.product_prod_o_int 0)
% 6.60/6.96 (declare-sort tptp.list_set_nat 0)
% 6.60/6.96 (declare-sort tptp.set_VEBT_VEBT 0)
% 6.60/6.96 (declare-sort tptp.set_set_nat 0)
% 6.60/6.96 (declare-sort tptp.set_set_int 0)
% 6.60/6.96 (declare-sort tptp.set_Code_integer 0)
% 6.60/6.96 (declare-sort tptp.set_Product_unit 0)
% 6.60/6.96 (declare-sort tptp.set_Extended_enat 0)
% 6.60/6.96 (declare-sort tptp.list_complex 0)
% 6.60/6.96 (declare-sort tptp.set_list_o 0)
% 6.60/6.96 (declare-sort tptp.product_prod_o_o 0)
% 6.60/6.96 (declare-sort tptp.set_complex 0)
% 6.60/6.96 (declare-sort tptp.filter_real 0)
% 6.60/6.96 (declare-sort tptp.option_num 0)
% 6.60/6.96 (declare-sort tptp.option_nat 0)
% 6.60/6.96 (declare-sort tptp.filter_nat 0)
% 6.60/6.96 (declare-sort tptp.set_char 0)
% 6.60/6.96 (declare-sort tptp.list_real 0)
% 6.60/6.96 (declare-sort tptp.set_real 0)
% 6.60/6.96 (declare-sort tptp.list_nat 0)
% 6.60/6.96 (declare-sort tptp.list_int 0)
% 6.60/6.96 (declare-sort tptp.vEBT_VEBT 0)
% 6.60/6.96 (declare-sort tptp.set_rat 0)
% 6.60/6.96 (declare-sort tptp.set_num 0)
% 6.60/6.96 (declare-sort tptp.set_nat 0)
% 6.60/6.96 (declare-sort tptp.set_int 0)
% 6.60/6.96 (declare-sort tptp.code_integer 0)
% 6.60/6.96 (declare-sort tptp.extended_enat 0)
% 6.60/6.96 (declare-sort tptp.list_o 0)
% 6.60/6.96 (declare-sort tptp.complex 0)
% 6.60/6.96 (declare-sort tptp.set_o 0)
% 6.60/6.96 (declare-sort tptp.char 0)
% 6.60/6.96 (declare-sort tptp.real 0)
% 6.60/6.96 (declare-sort tptp.rat 0)
% 6.60/6.96 (declare-sort tptp.num 0)
% 6.60/6.96 (declare-sort tptp.nat 0)
% 6.60/6.96 (declare-sort tptp.int 0)
% 6.60/6.96 (declare-fun tptp.archim7802044766580827645g_real (tptp.real) tptp.int)
% 6.60/6.96 (declare-fun tptp.archim3151403230148437115or_rat (tptp.rat) tptp.int)
% 6.60/6.96 (declare-fun tptp.archim6058952711729229775r_real (tptp.real) tptp.int)
% 6.60/6.96 (declare-fun tptp.archim7778729529865785530nd_rat (tptp.rat) tptp.int)
% 6.60/6.96 (declare-fun tptp.archim8280529875227126926d_real (tptp.real) tptp.int)
% 6.60/6.96 (declare-fun tptp.binomial (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_and_int_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.60/6.96 (declare-fun tptp.bit_and_not_num (tptp.num tptp.num) tptp.option_num)
% 6.60/6.96 (declare-fun tptp.bit_concat_bit (tptp.nat tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_or_not_num_neg (tptp.num tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.bit_or3848514188828904588eg_rel (tptp.product_prod_num_num tptp.product_prod_num_num) Bool)
% 6.60/6.96 (declare-fun tptp.bit_ri7919022796975470100ot_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_ri6519982836138164636nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.bit_ri631733984087533419it_int (tptp.nat tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se3949692690581998587nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.bit_se725231765392027082nd_int (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se727722235901077358nd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se8568078237143864401it_int (tptp.nat tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se8570568707652914677it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se1345352211410354436nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.bit_se2159334234014336723it_int (tptp.nat tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se2161824704523386999it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se2119862282449309892nteger (tptp.nat) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.bit_se2000444600071755411sk_int (tptp.nat) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se2002935070580805687sk_nat (tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se1409905431419307370or_int (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se1412395901928357646or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se545348938243370406it_int (tptp.nat tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se547839408752420682it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se2793503036327961859nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.bit_se7879613467334960850it_int (tptp.nat tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se7882103937844011126it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se1745604003318907178nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.bit_se2923211474154528505it_int (tptp.nat tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se2925701944663578781it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se8260200283734997820nteger (tptp.nat tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.bit_se4203085406695923979it_int (tptp.nat tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se4205575877204974255it_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se6526347334894502574or_int (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit_se6528837805403552850or_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bit_se1146084159140164899it_int (tptp.int tptp.nat) Bool)
% 6.60/6.96 (declare-fun tptp.bit_se1148574629649215175it_nat (tptp.nat tptp.nat) Bool)
% 6.60/6.96 (declare-fun tptp.bit_take_bit_num (tptp.nat tptp.num) tptp.option_num)
% 6.60/6.96 (declare-fun tptp.code_bit_cut_integer (tptp.code_integer) tptp.produc6271795597528267376eger_o)
% 6.60/6.96 (declare-fun tptp.code_divmod_abs (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.60/6.96 (declare-fun tptp.code_divmod_integer (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.60/6.96 (declare-fun tptp.code_int_of_integer (tptp.code_integer) tptp.int)
% 6.60/6.96 (declare-fun tptp.code_integer_of_int (tptp.int) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.code_integer_of_num (tptp.num) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.code_nat_of_integer (tptp.code_integer) tptp.nat)
% 6.60/6.96 (declare-fun tptp.code_negative (tptp.num) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.code_num_of_integer (tptp.code_integer) tptp.num)
% 6.60/6.96 (declare-fun tptp.code_positive (tptp.num) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.code_Target_negative (tptp.num) tptp.int)
% 6.60/6.96 (declare-fun tptp.code_Target_positive (tptp.num) tptp.int)
% 6.60/6.96 (declare-fun tptp.comple8358262395181532106omplex (tptp.set_fi4554929511873752355omplex) tptp.filter6041513312241820739omplex)
% 6.60/6.96 (declare-fun tptp.comple2936214249959783750l_real (tptp.set_fi7789364187291644575l_real) tptp.filter2146258269922977983l_real)
% 6.60/6.96 (declare-fun tptp.comple4887499456419720421f_real (tptp.set_real) tptp.real)
% 6.60/6.96 (declare-fun tptp.comple7806235888213564991et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.complete_Sup_Sup_int (tptp.set_int) tptp.int)
% 6.60/6.96 (declare-fun tptp.complete_Sup_Sup_nat (tptp.set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.comple1385675409528146559p_real (tptp.set_real) tptp.real)
% 6.60/6.96 (declare-fun tptp.comple7399068483239264473et_nat (tptp.set_set_nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.arg (tptp.complex) tptp.real)
% 6.60/6.96 (declare-fun tptp.cis (tptp.real) tptp.complex)
% 6.60/6.96 (declare-fun tptp.cnj (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.complex2 (tptp.real tptp.real) tptp.complex)
% 6.60/6.96 (declare-fun tptp.im (tptp.complex) tptp.real)
% 6.60/6.96 (declare-fun tptp.re (tptp.complex) tptp.real)
% 6.60/6.96 (declare-fun tptp.csqrt (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.imaginary_unit () tptp.complex)
% 6.60/6.96 (declare-fun tptp.differ6690327859849518006l_real ((-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.60/6.96 (declare-fun tptp.has_de1759254742604945161l_real ((-> tptp.real tptp.real) (-> tptp.real tptp.real) tptp.filter_real) Bool)
% 6.60/6.96 (declare-fun tptp.has_fi5821293074295781190e_real ((-> tptp.real tptp.real) tptp.real tptp.filter_real) Bool)
% 6.60/6.96 (declare-fun tptp.adjust_div (tptp.product_prod_int_int) tptp.int)
% 6.60/6.96 (declare-fun tptp.adjust_mod (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.divmod_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.60/6.96 (declare-fun tptp.eucl_rel_int (tptp.int tptp.int tptp.product_prod_int_int) Bool)
% 6.60/6.96 (declare-fun tptp.unique5706413561485394159nteger (tptp.produc8923325533196201883nteger) Bool)
% 6.60/6.96 (declare-fun tptp.unique6319869463603278526ux_int (tptp.product_prod_int_int) Bool)
% 6.60/6.96 (declare-fun tptp.unique6322359934112328802ux_nat (tptp.product_prod_nat_nat) Bool)
% 6.60/6.96 (declare-fun tptp.unique3479559517661332726nteger (tptp.num tptp.num) tptp.produc8923325533196201883nteger)
% 6.60/6.96 (declare-fun tptp.unique5052692396658037445od_int (tptp.num tptp.num) tptp.product_prod_int_int)
% 6.60/6.96 (declare-fun tptp.unique5055182867167087721od_nat (tptp.num tptp.num) tptp.product_prod_nat_nat)
% 6.60/6.96 (declare-fun tptp.unique4921790084139445826nteger (tptp.num tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.60/6.96 (declare-fun tptp.unique5024387138958732305ep_int (tptp.num tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.60/6.96 (declare-fun tptp.unique5026877609467782581ep_nat (tptp.num tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.60/6.96 (declare-fun tptp.semiri5044797733671781792omplex (tptp.nat) tptp.complex)
% 6.60/6.96 (declare-fun tptp.semiri1408675320244567234ct_nat (tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.semiri2265585572941072030t_real (tptp.nat) tptp.real)
% 6.60/6.96 (declare-fun tptp.invers8013647133539491842omplex (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.inverse_inverse_rat (tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.inverse_inverse_real (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.at_bot_real () tptp.filter_real)
% 6.60/6.96 (declare-fun tptp.at_top_nat () tptp.filter_nat)
% 6.60/6.96 (declare-fun tptp.at_top_real () tptp.filter_real)
% 6.60/6.96 (declare-fun tptp.eventually_nat ((-> tptp.nat Bool) tptp.filter_nat) Bool)
% 6.60/6.96 (declare-fun tptp.eventu1038000079068216329at_nat ((-> tptp.product_prod_nat_nat Bool) tptp.filter1242075044329608583at_nat) Bool)
% 6.60/6.96 (declare-fun tptp.eventually_real ((-> tptp.real Bool) tptp.filter_real) Bool)
% 6.60/6.96 (declare-fun tptp.filterlim_nat_nat ((-> tptp.nat tptp.nat) tptp.filter_nat tptp.filter_nat) Bool)
% 6.60/6.96 (declare-fun tptp.filterlim_nat_real ((-> tptp.nat tptp.real) tptp.filter_real tptp.filter_nat) Bool)
% 6.60/6.96 (declare-fun tptp.filterlim_real_real ((-> tptp.real tptp.real) tptp.filter_real tptp.filter_real) Bool)
% 6.60/6.96 (declare-fun tptp.filtermap_real_real ((-> tptp.real tptp.real) tptp.filter_real) tptp.filter_real)
% 6.60/6.96 (declare-fun tptp.princi3496590319149328850omplex (tptp.set_Pr5085853215250843933omplex) tptp.filter6041513312241820739omplex)
% 6.60/6.96 (declare-fun tptp.princi6114159922880469582l_real (tptp.set_Pr6218003697084177305l_real) tptp.filter2146258269922977983l_real)
% 6.60/6.96 (declare-fun tptp.prod_filter_nat_nat (tptp.filter_nat tptp.filter_nat) tptp.filter1242075044329608583at_nat)
% 6.60/6.96 (declare-fun tptp.finite_card_o (tptp.set_o) tptp.nat)
% 6.60/6.96 (declare-fun tptp.finite_card_complex (tptp.set_complex) tptp.nat)
% 6.60/6.96 (declare-fun tptp.finite_card_int (tptp.set_int) tptp.nat)
% 6.60/6.96 (declare-fun tptp.finite_card_nat (tptp.set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.finite410649719033368117t_unit (tptp.set_Product_unit) tptp.nat)
% 6.60/6.96 (declare-fun tptp.finite_card_set_nat (tptp.set_set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.finite_card_char (tptp.set_char) tptp.nat)
% 6.60/6.96 (declare-fun tptp.finite_finite_o (tptp.set_o) Bool)
% 6.60/6.96 (declare-fun tptp.finite3207457112153483333omplex (tptp.set_complex) Bool)
% 6.60/6.96 (declare-fun tptp.finite_finite_int (tptp.set_int) Bool)
% 6.60/6.96 (declare-fun tptp.finite_finite_list_o (tptp.set_list_o) Bool)
% 6.60/6.96 (declare-fun tptp.finite8712137658972009173omplex (tptp.set_list_complex) Bool)
% 6.60/6.96 (declare-fun tptp.finite3922522038869484883st_int (tptp.set_list_int) Bool)
% 6.60/6.96 (declare-fun tptp.finite8100373058378681591st_nat (tptp.set_list_nat) Bool)
% 6.60/6.96 (declare-fun tptp.finite3004134309566078307T_VEBT (tptp.set_list_VEBT_VEBT) Bool)
% 6.60/6.96 (declare-fun tptp.finite_finite_nat (tptp.set_nat) Bool)
% 6.60/6.96 (declare-fun tptp.finite_finite_num (tptp.set_num) Bool)
% 6.60/6.96 (declare-fun tptp.finite_finite_rat (tptp.set_rat) Bool)
% 6.60/6.96 (declare-fun tptp.finite_finite_real (tptp.set_real) Bool)
% 6.60/6.96 (declare-fun tptp.finite6551019134538273531omplex (tptp.set_set_complex) Bool)
% 6.60/6.96 (declare-fun tptp.finite6197958912794628473et_int (tptp.set_set_int) Bool)
% 6.60/6.96 (declare-fun tptp.finite1152437895449049373et_nat (tptp.set_set_nat) Bool)
% 6.60/6.96 (declare-fun tptp.finite5795047828879050333T_VEBT (tptp.set_VEBT_VEBT) Bool)
% 6.60/6.96 (declare-fun tptp.bij_be1856998921033663316omplex ((-> tptp.complex tptp.complex) tptp.set_complex tptp.set_complex) Bool)
% 6.60/6.96 (declare-fun tptp.bij_betw_nat_complex ((-> tptp.nat tptp.complex) tptp.set_nat tptp.set_complex) Bool)
% 6.60/6.96 (declare-fun tptp.bij_betw_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat tptp.set_nat) Bool)
% 6.60/6.96 (declare-fun tptp.comp_C8797469213163452608nteger ((-> (-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.60/6.96 (declare-fun tptp.comp_C1593894019821074884nteger ((-> tptp.code_integer tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) (-> tptp.code_integer tptp.code_integer) tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.60/6.96 (declare-fun tptp.comp_C3531382070062128313er_num ((-> tptp.code_integer tptp.code_integer) (-> tptp.num tptp.code_integer) tptp.num) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.comp_int_int_num ((-> tptp.int tptp.int) (-> tptp.num tptp.int) tptp.num) tptp.int)
% 6.60/6.96 (declare-fun tptp.id_o (Bool) Bool)
% 6.60/6.96 (declare-fun tptp.id_nat (tptp.nat) tptp.nat)
% 6.60/6.96 (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)
% 6.60/6.96 (declare-fun tptp.map_fu4960017516451851995nt_int ((-> tptp.int tptp.product_prod_nat_nat) (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int tptp.int) tptp.int)
% 6.60/6.96 (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)
% 6.60/6.96 (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)
% 6.60/6.96 (declare-fun tptp.map_fu3667384564859982768at_int ((-> tptp.int tptp.product_prod_nat_nat) (-> tptp.product_prod_nat_nat tptp.int) (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.strict1292158309912662752at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) Bool)
% 6.60/6.96 (declare-fun tptp.the_in5290026491893676941l_real (tptp.set_real (-> tptp.real tptp.real) tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.gcd_Gcd_int (tptp.set_int) tptp.int)
% 6.60/6.96 (declare-fun tptp.gcd_Gcd_nat (tptp.set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bezw (tptp.nat tptp.nat) tptp.product_prod_int_int)
% 6.60/6.96 (declare-fun tptp.bezw_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.60/6.96 (declare-fun tptp.gcd_gcd_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.gcd_gcd_int (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.gcd_gcd_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.gcd_nat_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.60/6.96 (declare-fun tptp.abs_abs_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.abs_abs_complex (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.abs_abs_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.abs_abs_rat (tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.abs_abs_real (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.minus_8727706125548526216plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool) tptp.complex) Bool)
% 6.60/6.96 (declare-fun tptp.minus_minus_int_o ((-> tptp.int Bool) (-> tptp.int Bool) tptp.int) Bool)
% 6.60/6.96 (declare-fun tptp.minus_minus_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool) tptp.nat) Bool)
% 6.60/6.96 (declare-fun tptp.minus_711738161318947805_int_o ((-> tptp.product_prod_int_int Bool) (-> tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.60/6.96 (declare-fun tptp.minus_minus_real_o ((-> tptp.real Bool) (-> tptp.real Bool) tptp.real) Bool)
% 6.60/6.96 (declare-fun tptp.minus_6910147592129066416_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool) tptp.set_nat) Bool)
% 6.60/6.96 (declare-fun tptp.minus_8373710615458151222nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.minus_minus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.minus_3235023915231533773d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.minus_minus_int (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.minus_minus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.minus_minus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.minus_minus_real (tptp.real tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.minus_811609699411566653omplex (tptp.set_complex tptp.set_complex) tptp.set_complex)
% 6.60/6.96 (declare-fun tptp.minus_minus_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.60/6.96 (declare-fun tptp.minus_minus_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.minus_1052850069191792384nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) tptp.set_Pr958786334691620121nt_int)
% 6.60/6.96 (declare-fun tptp.minus_minus_set_real (tptp.set_real tptp.set_real) tptp.set_real)
% 6.60/6.96 (declare-fun tptp.minus_2163939370556025621et_nat (tptp.set_set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.60/6.96 (declare-fun tptp.one_one_Code_integer () tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.one_one_complex () tptp.complex)
% 6.60/6.96 (declare-fun tptp.one_on7984719198319812577d_enat () tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.one_one_int () tptp.int)
% 6.60/6.96 (declare-fun tptp.one_one_nat () tptp.nat)
% 6.60/6.96 (declare-fun tptp.one_one_rat () tptp.rat)
% 6.60/6.96 (declare-fun tptp.one_one_real () tptp.real)
% 6.60/6.96 (declare-fun tptp.plus_p5714425477246183910nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.plus_plus_complex (tptp.complex tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.plus_p3455044024723400733d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.plus_plus_int (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.plus_plus_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.plus_plus_num (tptp.num tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.plus_plus_rat (tptp.rat tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.plus_plus_real (tptp.real tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.sgn_sgn_Code_integer (tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.sgn_sgn_complex (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.sgn_sgn_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.sgn_sgn_rat (tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.sgn_sgn_real (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.times_3573771949741848930nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.times_times_complex (tptp.complex tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.times_7803423173614009249d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.times_times_int (tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.times_times_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.times_times_num (tptp.num tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.times_times_rat (tptp.rat tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.times_times_real (tptp.real tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.uminus1351360451143612070nteger (tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.uminus1482373934393186551omplex (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.uminus_uminus_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.uminus_uminus_rat (tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.uminus_uminus_real (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.uminus8566677241136511917omplex (tptp.set_complex) tptp.set_complex)
% 6.60/6.96 (declare-fun tptp.uminus1532241313380277803et_int (tptp.set_int) tptp.set_int)
% 6.60/6.96 (declare-fun tptp.uminus5710092332889474511et_nat (tptp.set_nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.uminus612125837232591019t_real (tptp.set_real) tptp.set_real)
% 6.60/6.96 (declare-fun tptp.uminus613421341184616069et_nat (tptp.set_set_nat) tptp.set_set_nat)
% 6.60/6.96 (declare-fun tptp.zero_z3403309356797280102nteger () tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.zero_zero_complex () tptp.complex)
% 6.60/6.96 (declare-fun tptp.zero_z5237406670263579293d_enat () tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.zero_zero_int () tptp.int)
% 6.60/6.96 (declare-fun tptp.zero_zero_nat () tptp.nat)
% 6.60/6.96 (declare-fun tptp.zero_zero_rat () tptp.rat)
% 6.60/6.96 (declare-fun tptp.zero_zero_real () tptp.real)
% 6.60/6.96 (declare-fun tptp.groups6621422865394947399nteger ((-> tptp.complex tptp.code_integer) tptp.set_complex) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.groups7754918857620584856omplex ((-> tptp.complex tptp.complex) tptp.set_complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.groups5690904116761175830ex_int ((-> tptp.complex tptp.int) tptp.set_complex) tptp.int)
% 6.60/6.96 (declare-fun tptp.groups5693394587270226106ex_nat ((-> tptp.complex tptp.nat) tptp.set_complex) tptp.nat)
% 6.60/6.96 (declare-fun tptp.groups5058264527183730370ex_rat ((-> tptp.complex tptp.rat) tptp.set_complex) tptp.rat)
% 6.60/6.96 (declare-fun tptp.groups5808333547571424918x_real ((-> tptp.complex tptp.real) tptp.set_complex) tptp.real)
% 6.60/6.96 (declare-fun tptp.groups7873554091576472773nteger ((-> tptp.int tptp.code_integer) tptp.set_int) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.groups3049146728041665814omplex ((-> tptp.int tptp.complex) tptp.set_int) tptp.complex)
% 6.60/6.96 (declare-fun tptp.groups4538972089207619220nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.60/6.96 (declare-fun tptp.groups4541462559716669496nt_nat ((-> tptp.int tptp.nat) tptp.set_int) tptp.nat)
% 6.60/6.96 (declare-fun tptp.groups3906332499630173760nt_rat ((-> tptp.int tptp.rat) tptp.set_int) tptp.rat)
% 6.60/6.96 (declare-fun tptp.groups8778361861064173332t_real ((-> tptp.int tptp.real) tptp.set_int) tptp.real)
% 6.60/6.96 (declare-fun tptp.groups7501900531339628137nteger ((-> tptp.nat tptp.code_integer) tptp.set_nat) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.groups2073611262835488442omplex ((-> tptp.nat tptp.complex) tptp.set_nat) tptp.complex)
% 6.60/6.96 (declare-fun tptp.groups3539618377306564664at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.60/6.96 (declare-fun tptp.groups3542108847815614940at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.groups2906978787729119204at_rat ((-> tptp.nat tptp.rat) tptp.set_nat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.groups6591440286371151544t_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.real)
% 6.60/6.96 (declare-fun tptp.groups7713935264441627589nteger ((-> tptp.real tptp.code_integer) tptp.set_real) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.groups5754745047067104278omplex ((-> tptp.real tptp.complex) tptp.set_real) tptp.complex)
% 6.60/6.96 (declare-fun tptp.groups1932886352136224148al_int ((-> tptp.real tptp.int) tptp.set_real) tptp.int)
% 6.60/6.96 (declare-fun tptp.groups1935376822645274424al_nat ((-> tptp.real tptp.nat) tptp.set_real) tptp.nat)
% 6.60/6.96 (declare-fun tptp.groups1300246762558778688al_rat ((-> tptp.real tptp.rat) tptp.set_real) tptp.rat)
% 6.60/6.96 (declare-fun tptp.groups8097168146408367636l_real ((-> tptp.real tptp.real) tptp.set_real) tptp.real)
% 6.60/6.96 (declare-fun tptp.groups8255218700646806128omplex ((-> tptp.set_nat tptp.complex) tptp.set_set_nat) tptp.complex)
% 6.60/6.96 (declare-fun tptp.groups8294997508430121362at_nat ((-> tptp.set_nat tptp.nat) tptp.set_set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.groups5107569545109728110t_real ((-> tptp.set_nat tptp.real) tptp.set_set_nat) tptp.real)
% 6.60/6.96 (declare-fun tptp.groups1705073143266064639nt_int ((-> tptp.int tptp.int) tptp.set_int) tptp.int)
% 6.60/6.96 (declare-fun tptp.groups705719431365010083at_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.int)
% 6.60/6.96 (declare-fun tptp.groups708209901874060359at_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.groups9116527308978886569_o_int ((-> Bool tptp.int) tptp.int tptp.list_o) tptp.int)
% 6.60/6.96 (declare-fun tptp.groups4561878855575611511st_nat (tptp.list_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.the_int ((-> tptp.int Bool)) tptp.int)
% 6.60/6.96 (declare-fun tptp.the_real ((-> tptp.real Bool)) tptp.real)
% 6.60/6.96 (declare-fun tptp.if_int_int (Bool (-> tptp.int tptp.int) (-> tptp.int tptp.int) tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.if_Code_integer (Bool tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.if_complex (Bool tptp.complex tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.if_Extended_enat (Bool tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.if_int (Bool tptp.int tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.if_list_int (Bool tptp.list_int tptp.list_int) tptp.list_int)
% 6.60/6.96 (declare-fun tptp.if_list_nat (Bool tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.if_nat (Bool tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.if_num (Bool tptp.num tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.if_option_nat (Bool tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.60/6.96 (declare-fun tptp.if_option_num (Bool tptp.option_num tptp.option_num) tptp.option_num)
% 6.60/6.96 (declare-fun tptp.if_Pro5737122678794959658eger_o (Bool tptp.produc6271795597528267376eger_o tptp.produc6271795597528267376eger_o) tptp.produc6271795597528267376eger_o)
% 6.60/6.96 (declare-fun tptp.if_Pro6119634080678213985nteger (Bool tptp.produc8923325533196201883nteger tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.60/6.96 (declare-fun tptp.if_Pro3027730157355071871nt_int (Bool tptp.product_prod_int_int tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.60/6.96 (declare-fun tptp.if_Pro6206227464963214023at_nat (Bool tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.60/6.96 (declare-fun tptp.if_rat (Bool tptp.rat tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.if_real (Bool tptp.real tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.if_set_int (Bool tptp.set_int tptp.set_int) tptp.set_int)
% 6.60/6.96 (declare-fun tptp.if_VEBT_VEBT (Bool tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.60/6.96 (declare-fun tptp.abs_Integ (tptp.product_prod_nat_nat) tptp.int)
% 6.60/6.96 (declare-fun tptp.rep_Integ (tptp.int) tptp.product_prod_nat_nat)
% 6.60/6.96 (declare-fun tptp.int_ge_less_than (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.60/6.96 (declare-fun tptp.int_ge_less_than2 (tptp.int) tptp.set_Pr958786334691620121nt_int)
% 6.60/6.96 (declare-fun tptp.nat2 (tptp.int) tptp.nat)
% 6.60/6.96 (declare-fun tptp.ring_1_Ints_complex () tptp.set_complex)
% 6.60/6.96 (declare-fun tptp.ring_1_Ints_real () tptp.set_real)
% 6.60/6.96 (declare-fun tptp.ring_18347121197199848620nteger (tptp.int) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.ring_17405671764205052669omplex (tptp.int) tptp.complex)
% 6.60/6.96 (declare-fun tptp.ring_1_of_int_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.ring_1_of_int_rat (tptp.int) tptp.rat)
% 6.60/6.96 (declare-fun tptp.ring_1_of_int_real (tptp.int) tptp.real)
% 6.60/6.96 (declare-fun tptp.semila1623282765462674594er_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat (-> tptp.nat tptp.nat Bool) (-> tptp.nat tptp.nat Bool)) Bool)
% 6.60/6.96 (declare-fun tptp.sup_su3973961784419623482d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.sup_sup_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.sup_sup_set_nat (tptp.set_nat tptp.set_nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.lattic8263393255366662781ax_int (tptp.set_int) tptp.int)
% 6.60/6.96 (declare-fun tptp.lattic8265883725875713057ax_nat (tptp.set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.bfun_nat_real ((-> tptp.nat tptp.real) tptp.filter_nat) Bool)
% 6.60/6.96 (declare-fun tptp.at_infinity_real () tptp.filter_real)
% 6.60/6.96 (declare-fun tptp.append_int (tptp.list_int tptp.list_int) tptp.list_int)
% 6.60/6.96 (declare-fun tptp.append_nat (tptp.list_nat tptp.list_nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.distinct_int (tptp.list_int) Bool)
% 6.60/6.96 (declare-fun tptp.distinct_nat (tptp.list_nat) Bool)
% 6.60/6.96 (declare-fun tptp.linord2614967742042102400et_nat (tptp.set_nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.cons_int (tptp.int tptp.list_int) tptp.list_int)
% 6.60/6.96 (declare-fun tptp.cons_nat (tptp.nat tptp.list_nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.nil_int () tptp.list_int)
% 6.60/6.96 (declare-fun tptp.nil_nat () tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.map_nat_nat ((-> tptp.nat tptp.nat) tptp.list_nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.set_o2 (tptp.list_o) tptp.set_o)
% 6.60/6.96 (declare-fun tptp.set_complex2 (tptp.list_complex) tptp.set_complex)
% 6.60/6.96 (declare-fun tptp.set_int2 (tptp.list_int) tptp.set_int)
% 6.60/6.96 (declare-fun tptp.set_nat2 (tptp.list_nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.set_real2 (tptp.list_real) tptp.set_real)
% 6.60/6.96 (declare-fun tptp.set_set_nat2 (tptp.list_set_nat) tptp.set_set_nat)
% 6.60/6.96 (declare-fun tptp.set_VEBT_VEBT2 (tptp.list_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.60/6.96 (declare-fun tptp.size_list_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.nat) tptp.list_VEBT_VEBT) tptp.nat)
% 6.60/6.96 (declare-fun tptp.list_update_o (tptp.list_o tptp.nat Bool) tptp.list_o)
% 6.60/6.96 (declare-fun tptp.list_update_complex (tptp.list_complex tptp.nat tptp.complex) tptp.list_complex)
% 6.60/6.96 (declare-fun tptp.list_update_int (tptp.list_int tptp.nat tptp.int) tptp.list_int)
% 6.60/6.96 (declare-fun tptp.list_update_nat (tptp.list_nat tptp.nat tptp.nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.list_update_real (tptp.list_real tptp.nat tptp.real) tptp.list_real)
% 6.60/6.96 (declare-fun tptp.list_update_set_nat (tptp.list_set_nat tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.60/6.96 (declare-fun tptp.list_u1324408373059187874T_VEBT (tptp.list_VEBT_VEBT tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.60/6.96 (declare-fun tptp.nth_o (tptp.list_o tptp.nat) Bool)
% 6.60/6.96 (declare-fun tptp.nth_complex (tptp.list_complex tptp.nat) tptp.complex)
% 6.60/6.96 (declare-fun tptp.nth_int (tptp.list_int tptp.nat) tptp.int)
% 6.60/6.96 (declare-fun tptp.nth_nat (tptp.list_nat tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.nth_Product_prod_o_o (tptp.list_P4002435161011370285od_o_o tptp.nat) tptp.product_prod_o_o)
% 6.60/6.96 (declare-fun tptp.nth_Pr1649062631805364268_o_int (tptp.list_P3795440434834930179_o_int tptp.nat) tptp.product_prod_o_int)
% 6.60/6.96 (declare-fun tptp.nth_Pr5826913651314560976_o_nat (tptp.list_P6285523579766656935_o_nat tptp.nat) tptp.product_prod_o_nat)
% 6.60/6.96 (declare-fun tptp.nth_Pr6777367263587873994T_VEBT (tptp.list_P7495141550334521929T_VEBT tptp.nat) tptp.produc2504756804600209347T_VEBT)
% 6.60/6.96 (declare-fun tptp.nth_Pr112076138515278198_nat_o (tptp.list_P7333126701944960589_nat_o tptp.nat) tptp.product_prod_nat_o)
% 6.60/6.96 (declare-fun tptp.nth_Pr744662078594809490T_VEBT (tptp.list_P5647936690300460905T_VEBT tptp.nat) tptp.produc8025551001238799321T_VEBT)
% 6.60/6.96 (declare-fun tptp.nth_Pr4606735188037164562VEBT_o (tptp.list_P3126845725202233233VEBT_o tptp.nat) tptp.produc334124729049499915VEBT_o)
% 6.60/6.96 (declare-fun tptp.nth_Pr6837108013167703752BT_int (tptp.list_P4547456442757143711BT_int tptp.nat) tptp.produc4894624898956917775BT_int)
% 6.60/6.96 (declare-fun tptp.nth_Pr1791586995822124652BT_nat (tptp.list_P7037539587688870467BT_nat tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.60/6.96 (declare-fun tptp.nth_Pr4953567300277697838T_VEBT (tptp.list_P7413028617227757229T_VEBT tptp.nat) tptp.produc8243902056947475879T_VEBT)
% 6.60/6.96 (declare-fun tptp.nth_real (tptp.list_real tptp.nat) tptp.real)
% 6.60/6.96 (declare-fun tptp.nth_set_nat (tptp.list_set_nat tptp.nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.nth_VEBT_VEBT (tptp.list_VEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.60/6.96 (declare-fun tptp.product_o_o (tptp.list_o tptp.list_o) tptp.list_P4002435161011370285od_o_o)
% 6.60/6.96 (declare-fun tptp.product_o_int (tptp.list_o tptp.list_int) tptp.list_P3795440434834930179_o_int)
% 6.60/6.96 (declare-fun tptp.product_o_nat (tptp.list_o tptp.list_nat) tptp.list_P6285523579766656935_o_nat)
% 6.60/6.96 (declare-fun tptp.product_o_VEBT_VEBT (tptp.list_o tptp.list_VEBT_VEBT) tptp.list_P7495141550334521929T_VEBT)
% 6.60/6.96 (declare-fun tptp.product_nat_o (tptp.list_nat tptp.list_o) tptp.list_P7333126701944960589_nat_o)
% 6.60/6.96 (declare-fun tptp.produc7156399406898700509T_VEBT (tptp.list_nat tptp.list_VEBT_VEBT) tptp.list_P5647936690300460905T_VEBT)
% 6.60/6.96 (declare-fun tptp.product_VEBT_VEBT_o (tptp.list_VEBT_VEBT tptp.list_o) tptp.list_P3126845725202233233VEBT_o)
% 6.60/6.96 (declare-fun tptp.produc7292646706713671643BT_int (tptp.list_VEBT_VEBT tptp.list_int) tptp.list_P4547456442757143711BT_int)
% 6.60/6.96 (declare-fun tptp.produc7295137177222721919BT_nat (tptp.list_VEBT_VEBT tptp.list_nat) tptp.list_P7037539587688870467BT_nat)
% 6.60/6.96 (declare-fun tptp.produc4743750530478302277T_VEBT (tptp.list_VEBT_VEBT tptp.list_VEBT_VEBT) tptp.list_P7413028617227757229T_VEBT)
% 6.60/6.96 (declare-fun tptp.remdups_nat (tptp.list_nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.replicate_o (tptp.nat Bool) tptp.list_o)
% 6.60/6.96 (declare-fun tptp.replicate_complex (tptp.nat tptp.complex) tptp.list_complex)
% 6.60/6.96 (declare-fun tptp.replicate_int (tptp.nat tptp.int) tptp.list_int)
% 6.60/6.96 (declare-fun tptp.replicate_nat (tptp.nat tptp.nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.replicate_real (tptp.nat tptp.real) tptp.list_real)
% 6.60/6.96 (declare-fun tptp.replicate_set_nat (tptp.nat tptp.set_nat) tptp.list_set_nat)
% 6.60/6.96 (declare-fun tptp.replicate_VEBT_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.list_VEBT_VEBT)
% 6.60/6.96 (declare-fun tptp.upt (tptp.nat tptp.nat) tptp.list_nat)
% 6.60/6.96 (declare-fun tptp.upto (tptp.int tptp.int) tptp.list_int)
% 6.60/6.96 (declare-fun tptp.upto_aux (tptp.int tptp.int tptp.list_int) tptp.list_int)
% 6.60/6.96 (declare-fun tptp.upto_rel (tptp.product_prod_int_int tptp.product_prod_int_int) Bool)
% 6.60/6.96 (declare-fun tptp.suc (tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.compow_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.case_nat_o (Bool (-> tptp.nat Bool) tptp.nat) Bool)
% 6.60/6.96 (declare-fun tptp.case_nat_nat (tptp.nat (-> tptp.nat tptp.nat) tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.case_nat_option_num (tptp.option_num (-> tptp.nat tptp.option_num) tptp.nat) tptp.option_num)
% 6.60/6.96 (declare-fun tptp.pred (tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.semiri4939895301339042750nteger (tptp.nat) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.semiri8010041392384452111omplex (tptp.nat) tptp.complex)
% 6.60/6.96 (declare-fun tptp.semiri4216267220026989637d_enat (tptp.nat) tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.semiri1314217659103216013at_int (tptp.nat) tptp.int)
% 6.60/6.96 (declare-fun tptp.semiri1316708129612266289at_nat (tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.semiri681578069525770553at_rat (tptp.nat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.semiri5074537144036343181t_real (tptp.nat) tptp.real)
% 6.60/6.96 (declare-fun tptp.size_size_list_o (tptp.list_o) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s3451745648224563538omplex (tptp.list_complex) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_list_int (tptp.list_int) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_list_nat (tptp.list_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s1515746228057227161od_o_o (tptp.list_P4002435161011370285od_o_o) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s2953683556165314199_o_int (tptp.list_P3795440434834930179_o_int) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s5443766701097040955_o_nat (tptp.list_P6285523579766656935_o_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s4313452262239582901T_VEBT (tptp.list_P7495141550334521929T_VEBT) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s6491369823275344609_nat_o (tptp.list_P7333126701944960589_nat_o) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s4762443039079500285T_VEBT (tptp.list_P5647936690300460905T_VEBT) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s9168528473962070013VEBT_o (tptp.list_P3126845725202233233VEBT_o) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s3661962791536183091BT_int (tptp.list_P4547456442757143711BT_int) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s6152045936467909847BT_nat (tptp.list_P7037539587688870467BT_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s7466405169056248089T_VEBT (tptp.list_P7413028617227757229T_VEBT) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_list_real (tptp.list_real) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s3254054031482475050et_nat (tptp.list_set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s6755466524823107622T_VEBT (tptp.list_VEBT_VEBT) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_num (tptp.num) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_option_nat (tptp.option_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_option_num (tptp.option_num) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_s170228958280169651at_nat (tptp.option4927543243414619207at_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_char (tptp.char) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_size_VEBT_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.60/6.96 (declare-fun tptp.nat_list_encode (tptp.list_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.nat_list_encode_rel (tptp.list_nat tptp.list_nat) Bool)
% 6.60/6.96 (declare-fun tptp.nat_prod_decode_aux (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.60/6.96 (declare-fun tptp.nat_pr5047031295181774490ux_rel (tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.60/6.96 (declare-fun tptp.nat_prod_encode (tptp.product_prod_nat_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.nat_set_decode (tptp.nat) tptp.set_nat)
% 6.60/6.96 (declare-fun tptp.nat_set_encode (tptp.set_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.nat_triangle (tptp.nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.root (tptp.nat tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.sqrt (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.bitM (tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.inc (tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.neg_nu8804712462038260780nteger (tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.neg_nu7009210354673126013omplex (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.neg_numeral_dbl_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.neg_numeral_dbl_rat (tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.neg_numeral_dbl_real (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.neg_nu7757733837767384882nteger (tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.neg_nu6511756317524482435omplex (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.neg_nu3811975205180677377ec_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.neg_nu3179335615603231917ec_rat (tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.neg_nu6075765906172075777c_real (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.neg_nu5831290666863070958nteger (tptp.code_integer) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.neg_nu8557863876264182079omplex (tptp.complex) tptp.complex)
% 6.60/6.96 (declare-fun tptp.neg_nu5851722552734809277nc_int (tptp.int) tptp.int)
% 6.60/6.96 (declare-fun tptp.neg_nu5219082963157363817nc_rat (tptp.rat) tptp.rat)
% 6.60/6.96 (declare-fun tptp.neg_nu8295874005876285629c_real (tptp.real) tptp.real)
% 6.60/6.96 (declare-fun tptp.neg_numeral_sub_int (tptp.num tptp.num) tptp.int)
% 6.60/6.96 (declare-fun tptp.bit0 (tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.bit1 (tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.one () tptp.num)
% 6.60/6.96 (declare-fun tptp.case_num_option_num (tptp.option_num (-> tptp.num tptp.option_num) (-> tptp.num tptp.option_num) tptp.num) tptp.option_num)
% 6.60/6.96 (declare-fun tptp.size_num (tptp.num) tptp.nat)
% 6.60/6.96 (declare-fun tptp.num_of_nat (tptp.nat) tptp.num)
% 6.60/6.96 (declare-fun tptp.numera6620942414471956472nteger (tptp.num) tptp.code_integer)
% 6.60/6.96 (declare-fun tptp.numera6690914467698888265omplex (tptp.num) tptp.complex)
% 6.60/6.96 (declare-fun tptp.numera1916890842035813515d_enat (tptp.num) tptp.extended_enat)
% 6.60/6.96 (declare-fun tptp.numeral_numeral_int (tptp.num) tptp.int)
% 6.60/6.96 (declare-fun tptp.numeral_numeral_nat (tptp.num) tptp.nat)
% 6.60/6.96 (declare-fun tptp.numeral_numeral_rat (tptp.num) tptp.rat)
% 6.60/6.96 (declare-fun tptp.numeral_numeral_real (tptp.num) tptp.real)
% 6.60/6.96 (declare-fun tptp.pow (tptp.num tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.pred_numeral (tptp.num) tptp.nat)
% 6.60/6.96 (declare-fun tptp.sqr (tptp.num) tptp.num)
% 6.60/6.96 (declare-fun tptp.none_nat () tptp.option_nat)
% 6.60/6.96 (declare-fun tptp.none_num () tptp.option_num)
% 6.60/6.96 (declare-fun tptp.none_P5556105721700978146at_nat () tptp.option4927543243414619207at_nat)
% 6.60/6.96 (declare-fun tptp.some_nat (tptp.nat) tptp.option_nat)
% 6.60/6.96 (declare-fun tptp.some_num (tptp.num) tptp.option_num)
% 6.60/6.96 (declare-fun tptp.some_P7363390416028606310at_nat (tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat)
% 6.60/6.96 (declare-fun tptp.case_o184042715313410164at_nat (Bool (-> tptp.product_prod_nat_nat Bool) tptp.option4927543243414619207at_nat) Bool)
% 6.60/6.96 (declare-fun tptp.case_option_int_num (tptp.int (-> tptp.num tptp.int) tptp.option_num) tptp.int)
% 6.60/6.96 (declare-fun tptp.case_option_num_num (tptp.num (-> tptp.num tptp.num) tptp.option_num) tptp.num)
% 6.60/6.96 (declare-fun tptp.case_o6005452278849405969um_num (tptp.option_num (-> tptp.num tptp.option_num) tptp.option_num) tptp.option_num)
% 6.60/6.96 (declare-fun tptp.size_option_nat ((-> tptp.nat tptp.nat) tptp.option_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_option_num ((-> tptp.num tptp.nat) tptp.option_num) tptp.nat)
% 6.60/6.96 (declare-fun tptp.size_o8335143837870341156at_nat ((-> tptp.product_prod_nat_nat tptp.nat) tptp.option4927543243414619207at_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.the_nat (tptp.option_nat) tptp.nat)
% 6.60/6.96 (declare-fun tptp.the_num (tptp.option_num) tptp.num)
% 6.60/6.96 (declare-fun tptp.the_Pr8591224930841456533at_nat (tptp.option4927543243414619207at_nat) tptp.product_prod_nat_nat)
% 6.60/6.97 (declare-fun tptp.bot_bo4199563552545308370d_enat () tptp.extended_enat)
% 6.60/6.97 (declare-fun tptp.bot_bot_nat () tptp.nat)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_complex () tptp.set_complex)
% 6.60/6.97 (declare-fun tptp.bot_bo7653980558646680370d_enat () tptp.set_Extended_enat)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_int () tptp.set_int)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_nat () tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_num () tptp.set_num)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_rat () tptp.set_rat)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_real () tptp.set_real)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_set_int () tptp.set_set_int)
% 6.60/6.97 (declare-fun tptp.bot_bot_set_set_nat () tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.bot_bo8194388402131092736T_VEBT () tptp.set_VEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.ord_le6747313008572928689nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le72135733267957522d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_int (tptp.int tptp.int) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_nat (tptp.nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_num (tptp.num tptp.num) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_rat (tptp.rat tptp.rat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_real (tptp.real tptp.real) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le1307284697595431911nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_complex (tptp.set_complex tptp.set_complex) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_int (tptp.set_int tptp.set_int) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_num (tptp.set_num tptp.set_num) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_real (tptp.set_real tptp.set_real) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_set_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_set_set_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le4573692005234683329plex_o ((-> tptp.complex Bool) (-> tptp.complex Bool)) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le6741204236512500942_int_o ((-> tptp.int tptp.int Bool) (-> tptp.int tptp.int Bool)) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_int_o ((-> tptp.int Bool) (-> tptp.int Bool)) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_nat_o ((-> tptp.nat Bool) (-> tptp.nat Bool)) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_real_o ((-> tptp.real Bool) (-> tptp.real Bool)) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le3964352015994296041_nat_o ((-> tptp.set_nat Bool) (-> tptp.set_nat Bool)) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le3102999989581377725nteger (tptp.code_integer tptp.code_integer) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le2932123472753598470d_enat (tptp.extended_enat tptp.extended_enat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le2510731241096832064er_nat (tptp.filter_nat tptp.filter_nat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le4104064031414453916r_real (tptp.filter_real tptp.filter_real) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_int (tptp.int tptp.int) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_nat (tptp.nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_num (tptp.num tptp.num) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_rat (tptp.rat tptp.rat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_real (tptp.real tptp.real) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_set_o (tptp.set_o tptp.set_o) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le7084787975880047091nteger (tptp.set_Code_integer tptp.set_Code_integer) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le211207098394363844omplex (tptp.set_complex tptp.set_complex) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_set_int (tptp.set_int tptp.set_int) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_set_nat (tptp.set_nat tptp.set_nat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_set_num (tptp.set_num tptp.set_num) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le2843351958646193337nt_int (tptp.set_Pr958786334691620121nt_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_set_rat (tptp.set_rat tptp.set_rat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_less_eq_set_real (tptp.set_real tptp.set_real) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le4403425263959731960et_int (tptp.set_set_int tptp.set_set_int) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le6893508408891458716et_nat (tptp.set_set_nat tptp.set_set_nat) Bool)
% 6.60/6.97 (declare-fun tptp.ord_le4337996190870823476T_VEBT (tptp.set_VEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.ord_max_Code_integer (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.97 (declare-fun tptp.ord_ma741700101516333627d_enat (tptp.extended_enat tptp.extended_enat) tptp.extended_enat)
% 6.60/6.97 (declare-fun tptp.ord_max_int (tptp.int tptp.int) tptp.int)
% 6.60/6.97 (declare-fun tptp.ord_max_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.ord_max_num (tptp.num tptp.num) tptp.num)
% 6.60/6.97 (declare-fun tptp.ord_max_rat (tptp.rat tptp.rat) tptp.rat)
% 6.60/6.97 (declare-fun tptp.ord_max_real (tptp.real tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.ord_max_set_int (tptp.set_int tptp.set_int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.order_Greatest_nat ((-> tptp.nat Bool)) tptp.nat)
% 6.60/6.97 (declare-fun tptp.order_9091379641038594480t_real ((-> tptp.nat tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.order_mono_nat_nat ((-> tptp.nat tptp.nat)) Bool)
% 6.60/6.97 (declare-fun tptp.order_mono_nat_real ((-> tptp.nat tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.top_top_set_o () tptp.set_o)
% 6.60/6.97 (declare-fun tptp.top_top_set_nat () tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.top_to1996260823553986621t_unit () tptp.set_Product_unit)
% 6.60/6.97 (declare-fun tptp.top_top_set_real () tptp.set_real)
% 6.60/6.97 (declare-fun tptp.top_top_set_char () tptp.set_char)
% 6.60/6.97 (declare-fun tptp.power_8256067586552552935nteger (tptp.code_integer tptp.nat) tptp.code_integer)
% 6.60/6.97 (declare-fun tptp.power_power_complex (tptp.complex tptp.nat) tptp.complex)
% 6.60/6.97 (declare-fun tptp.power_power_int (tptp.int tptp.nat) tptp.int)
% 6.60/6.97 (declare-fun tptp.power_power_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.power_power_rat (tptp.rat tptp.nat) tptp.rat)
% 6.60/6.97 (declare-fun tptp.power_power_real (tptp.real tptp.nat) tptp.real)
% 6.60/6.97 (declare-fun tptp.produc6137756002093451184nteger ((-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc8763457246119570046nteger)
% 6.60/6.97 (declare-fun tptp.produc4305682042979456191nt_int ((-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc7773217078559923341nt_int)
% 6.60/6.97 (declare-fun tptp.produc4035269172776083154on_nat ((-> tptp.nat tptp.nat Bool) tptp.produc4953844613479565601on_nat) tptp.produc2233624965454879586on_nat)
% 6.60/6.97 (declare-fun tptp.produc8929957630744042906on_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.produc4953844613479565601on_nat) tptp.produc8306885398267862888on_nat)
% 6.60/6.97 (declare-fun tptp.produc3576312749637752826on_num ((-> tptp.num tptp.num Bool) tptp.produc3447558737645232053on_num) tptp.produc7036089656553540234on_num)
% 6.60/6.97 (declare-fun tptp.produc5778274026573060048on_num ((-> tptp.num tptp.num tptp.num) tptp.produc3447558737645232053on_num) tptp.produc1193250871479095198on_num)
% 6.60/6.97 (declare-fun tptp.produc8603105652947943368nteger ((-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger) tptp.produc1908205239877642774nteger)
% 6.60/6.97 (declare-fun tptp.produc5700946648718959541nt_int ((-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int) tptp.produc2285326912895808259nt_int)
% 6.60/6.97 (declare-fun tptp.produc3994169339658061776at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.produc6121120109295599847at_nat) tptp.produc5491161045314408544at_nat)
% 6.60/6.97 (declare-fun tptp.produc2899441246263362727at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.produc6121120109295599847at_nat) tptp.produc5542196010084753463at_nat)
% 6.60/6.97 (declare-fun tptp.product_Pair_o_o (Bool Bool) tptp.product_prod_o_o)
% 6.60/6.97 (declare-fun tptp.product_Pair_o_int (Bool tptp.int) tptp.product_prod_o_int)
% 6.60/6.97 (declare-fun tptp.product_Pair_o_nat (Bool tptp.nat) tptp.product_prod_o_nat)
% 6.60/6.97 (declare-fun tptp.produc2982872950893828659T_VEBT (Bool tptp.vEBT_VEBT) tptp.produc2504756804600209347T_VEBT)
% 6.60/6.97 (declare-fun tptp.produc6677183202524767010eger_o (tptp.code_integer Bool) tptp.produc6271795597528267376eger_o)
% 6.60/6.97 (declare-fun tptp.produc1086072967326762835nteger (tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger)
% 6.60/6.97 (declare-fun tptp.product_Pair_int_int (tptp.int tptp.int) tptp.product_prod_int_int)
% 6.60/6.97 (declare-fun tptp.product_Pair_nat_o (tptp.nat Bool) tptp.product_prod_nat_o)
% 6.60/6.97 (declare-fun tptp.product_Pair_nat_nat (tptp.nat tptp.nat) tptp.product_prod_nat_nat)
% 6.60/6.97 (declare-fun tptp.product_Pair_nat_num (tptp.nat tptp.num) tptp.product_prod_nat_num)
% 6.60/6.97 (declare-fun tptp.produc599794634098209291T_VEBT (tptp.nat tptp.vEBT_VEBT) tptp.produc8025551001238799321T_VEBT)
% 6.60/6.97 (declare-fun tptp.product_Pair_num_num (tptp.num tptp.num) tptp.product_prod_num_num)
% 6.60/6.97 (declare-fun tptp.produc5098337634421038937on_nat (tptp.option_nat tptp.option_nat) tptp.produc4953844613479565601on_nat)
% 6.60/6.97 (declare-fun tptp.produc8585076106096196333on_num (tptp.option_num tptp.option_num) tptp.produc3447558737645232053on_num)
% 6.60/6.97 (declare-fun tptp.produc488173922507101015at_nat (tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.produc6121120109295599847at_nat)
% 6.60/6.97 (declare-fun tptp.produc8721562602347293563VEBT_o (tptp.vEBT_VEBT Bool) tptp.produc334124729049499915VEBT_o)
% 6.60/6.97 (declare-fun tptp.produc736041933913180425BT_int (tptp.vEBT_VEBT tptp.int) tptp.produc4894624898956917775BT_int)
% 6.60/6.97 (declare-fun tptp.produc738532404422230701BT_nat (tptp.vEBT_VEBT tptp.nat) tptp.produc9072475918466114483BT_nat)
% 6.60/6.97 (declare-fun tptp.produc537772716801021591T_VEBT (tptp.vEBT_VEBT tptp.vEBT_VEBT) tptp.produc8243902056947475879T_VEBT)
% 6.60/6.97 (declare-fun tptp.produc6499014454317279255nteger ((-> tptp.code_integer tptp.code_integer) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.60/6.97 (declare-fun tptp.produc127349428274296955eger_o ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) tptp.produc8763457246119570046nteger) Bool)
% 6.60/6.97 (declare-fun tptp.produc2592262431452330817omplex ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex) tptp.produc8763457246119570046nteger) tptp.set_complex)
% 6.60/6.97 (declare-fun tptp.produc8604463032469472703et_int ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int) tptp.produc8763457246119570046nteger) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.produc3558942015123893603et_nat ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat) tptp.produc8763457246119570046nteger) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.produc815715089573277247t_real ((-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real) tptp.produc8763457246119570046nteger) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.produc2558449545302689196_int_o ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc7773217078559923341nt_int) Bool)
% 6.60/6.97 (declare-fun tptp.produc7959293469001253456omplex ((-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_complex) tptp.produc7773217078559923341nt_int) tptp.set_complex)
% 6.60/6.97 (declare-fun tptp.produc6253627499356882019eger_o ((-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool) tptp.produc1908205239877642774nteger) Bool)
% 6.60/6.97 (declare-fun tptp.produc1573362020775583542_int_o ((-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool) tptp.produc2285326912895808259nt_int) Bool)
% 6.60/6.97 (declare-fun tptp.produc1553301316500091796er_int ((-> tptp.code_integer tptp.code_integer tptp.int) tptp.produc8923325533196201883nteger) tptp.int)
% 6.60/6.97 (declare-fun tptp.produc1555791787009142072er_nat ((-> tptp.code_integer tptp.code_integer tptp.nat) tptp.produc8923325533196201883nteger) tptp.nat)
% 6.60/6.97 (declare-fun tptp.produc7336495610019696514er_num ((-> tptp.code_integer tptp.code_integer tptp.num) tptp.produc8923325533196201883nteger) tptp.num)
% 6.60/6.97 (declare-fun tptp.produc9125791028180074456eger_o ((-> tptp.code_integer tptp.code_integer tptp.produc6271795597528267376eger_o) tptp.produc8923325533196201883nteger) tptp.produc6271795597528267376eger_o)
% 6.60/6.97 (declare-fun tptp.produc6916734918728496179nteger ((-> tptp.code_integer tptp.code_integer tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger) tptp.produc8923325533196201883nteger)
% 6.60/6.97 (declare-fun tptp.produc6771430404735790350plex_o ((-> tptp.complex tptp.complex Bool) tptp.produc4411394909380815293omplex) Bool)
% 6.60/6.97 (declare-fun tptp.produc4947309494688390418_int_o ((-> tptp.int tptp.int Bool) tptp.product_prod_int_int) Bool)
% 6.60/6.97 (declare-fun tptp.produc8211389475949308722nt_int ((-> tptp.int tptp.int tptp.int) tptp.product_prod_int_int) tptp.int)
% 6.60/6.97 (declare-fun tptp.produc4245557441103728435nt_int ((-> tptp.int tptp.int tptp.product_prod_int_int) tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.60/6.97 (declare-fun tptp.produc8580519160106071146omplex ((-> tptp.int tptp.int tptp.set_complex) tptp.product_prod_int_int) tptp.set_complex)
% 6.60/6.97 (declare-fun tptp.produc73460835934605544et_int ((-> tptp.int tptp.int tptp.set_int) tptp.product_prod_int_int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.produc4251311855443802252et_nat ((-> tptp.int tptp.int tptp.set_nat) tptp.product_prod_int_int) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.produc6452406959799940328t_real ((-> tptp.int tptp.int tptp.set_real) tptp.product_prod_int_int) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.produc5233655623923918146et_nat ((-> tptp.int tptp.int tptp.set_set_nat) tptp.product_prod_int_int) tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.produc8739625826339149834_nat_o ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)
% 6.60/6.97 (declare-fun tptp.produc27273713700761075at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.60/6.97 (declare-fun tptp.produc6081775807080527818_nat_o ((-> tptp.nat tptp.nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.60/6.97 (declare-fun tptp.produc1917071388513777916omplex ((-> tptp.nat tptp.nat tptp.complex) tptp.product_prod_nat_nat) tptp.complex)
% 6.60/6.97 (declare-fun tptp.produc6840382203811409530at_int ((-> tptp.nat tptp.nat tptp.int) tptp.product_prod_nat_nat) tptp.int)
% 6.60/6.97 (declare-fun tptp.produc6842872674320459806at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.product_prod_nat_nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.produc2626176000494625587at_nat ((-> tptp.nat tptp.nat tptp.product_prod_nat_nat) tptp.product_prod_nat_nat) tptp.product_prod_nat_nat)
% 6.60/6.97 (declare-fun tptp.produc6207742614233964070at_rat ((-> tptp.nat tptp.nat tptp.rat) tptp.product_prod_nat_nat) tptp.rat)
% 6.60/6.97 (declare-fun tptp.produc1703576794950452218t_real ((-> tptp.nat tptp.nat tptp.real) tptp.product_prod_nat_nat) tptp.real)
% 6.60/6.97 (declare-fun tptp.produc478579273971653890on_num ((-> tptp.nat tptp.num tptp.option_num) tptp.product_prod_nat_num) tptp.option_num)
% 6.60/6.97 (declare-fun tptp.produc5414030515140494994real_o ((-> tptp.real tptp.real Bool) tptp.produc2422161461964618553l_real) Bool)
% 6.60/6.97 (declare-fun tptp.product_fst_int_int (tptp.product_prod_int_int) tptp.int)
% 6.60/6.97 (declare-fun tptp.product_fst_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.produc6174133586879617921nteger (tptp.produc8923325533196201883nteger) tptp.code_integer)
% 6.60/6.97 (declare-fun tptp.product_snd_int_int (tptp.product_prod_int_int) tptp.int)
% 6.60/6.97 (declare-fun tptp.product_snd_nat_nat (tptp.product_prod_nat_nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.fract (tptp.int tptp.int) tptp.rat)
% 6.60/6.97 (declare-fun tptp.frct (tptp.product_prod_int_int) tptp.rat)
% 6.60/6.97 (declare-fun tptp.normalize (tptp.product_prod_int_int) tptp.product_prod_int_int)
% 6.60/6.97 (declare-fun tptp.of_int (tptp.int) tptp.rat)
% 6.60/6.97 (declare-fun tptp.quotient_of (tptp.rat) tptp.product_prod_int_int)
% 6.60/6.97 (declare-fun tptp.real_V2521375963428798218omplex () tptp.set_complex)
% 6.60/6.97 (declare-fun tptp.real_V5970128139526366754l_real ((-> tptp.real tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.real_V3694042436643373181omplex (tptp.complex tptp.complex) tptp.real)
% 6.60/6.97 (declare-fun tptp.real_V975177566351809787t_real (tptp.real tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.real_V1022390504157884413omplex (tptp.complex) tptp.real)
% 6.60/6.97 (declare-fun tptp.real_V7735802525324610683m_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.real_V4546457046886955230omplex (tptp.real) tptp.complex)
% 6.60/6.97 (declare-fun tptp.real_V2046097035970521341omplex (tptp.real tptp.complex) tptp.complex)
% 6.60/6.97 (declare-fun tptp.real_V1485227260804924795R_real (tptp.real tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.divide6298287555418463151nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.97 (declare-fun tptp.divide1717551699836669952omplex (tptp.complex tptp.complex) tptp.complex)
% 6.60/6.97 (declare-fun tptp.divide_divide_int (tptp.int tptp.int) tptp.int)
% 6.60/6.97 (declare-fun tptp.divide_divide_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.divide_divide_rat (tptp.rat tptp.rat) tptp.rat)
% 6.60/6.97 (declare-fun tptp.divide_divide_real (tptp.real tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.dvd_dvd_Code_integer (tptp.code_integer tptp.code_integer) Bool)
% 6.60/6.97 (declare-fun tptp.dvd_dvd_complex (tptp.complex tptp.complex) Bool)
% 6.60/6.97 (declare-fun tptp.dvd_dvd_int (tptp.int tptp.int) Bool)
% 6.60/6.97 (declare-fun tptp.dvd_dvd_nat (tptp.nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.dvd_dvd_rat (tptp.rat tptp.rat) Bool)
% 6.60/6.97 (declare-fun tptp.dvd_dvd_real (tptp.real tptp.real) Bool)
% 6.60/6.97 (declare-fun tptp.modulo364778990260209775nteger (tptp.code_integer tptp.code_integer) tptp.code_integer)
% 6.60/6.97 (declare-fun tptp.modulo_modulo_int (tptp.int tptp.int) tptp.int)
% 6.60/6.97 (declare-fun tptp.modulo_modulo_nat (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.zero_n356916108424825756nteger (Bool) tptp.code_integer)
% 6.60/6.97 (declare-fun tptp.zero_n1201886186963655149omplex (Bool) tptp.complex)
% 6.60/6.97 (declare-fun tptp.zero_n2684676970156552555ol_int (Bool) tptp.int)
% 6.60/6.97 (declare-fun tptp.zero_n2687167440665602831ol_nat (Bool) tptp.nat)
% 6.60/6.97 (declare-fun tptp.zero_n2052037380579107095ol_rat (Bool) tptp.rat)
% 6.60/6.97 (declare-fun tptp.zero_n3304061248610475627l_real (Bool) tptp.real)
% 6.60/6.97 (declare-fun tptp.suminf_complex ((-> tptp.nat tptp.complex)) tptp.complex)
% 6.60/6.97 (declare-fun tptp.suminf_real ((-> tptp.nat tptp.real)) tptp.real)
% 6.60/6.97 (declare-fun tptp.summable_real ((-> tptp.nat tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.sums_real ((-> tptp.nat tptp.real) tptp.real) Bool)
% 6.60/6.97 (declare-fun tptp.collect_Code_integer ((-> tptp.code_integer Bool)) tptp.set_Code_integer)
% 6.60/6.97 (declare-fun tptp.collect_complex ((-> tptp.complex Bool)) tptp.set_complex)
% 6.60/6.97 (declare-fun tptp.collect_int ((-> tptp.int Bool)) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.collect_list_o ((-> tptp.list_o Bool)) tptp.set_list_o)
% 6.60/6.97 (declare-fun tptp.collect_list_complex ((-> tptp.list_complex Bool)) tptp.set_list_complex)
% 6.60/6.97 (declare-fun tptp.collect_list_int ((-> tptp.list_int Bool)) tptp.set_list_int)
% 6.60/6.97 (declare-fun tptp.collect_list_nat ((-> tptp.list_nat Bool)) tptp.set_list_nat)
% 6.60/6.97 (declare-fun tptp.collec5608196760682091941T_VEBT ((-> tptp.list_VEBT_VEBT Bool)) tptp.set_list_VEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.collect_nat ((-> tptp.nat Bool)) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.collect_num ((-> tptp.num Bool)) tptp.set_num)
% 6.60/6.97 (declare-fun tptp.collec8663557070575231912omplex ((-> tptp.produc4411394909380815293omplex Bool)) tptp.set_Pr5085853215250843933omplex)
% 6.60/6.97 (declare-fun tptp.collec213857154873943460nt_int ((-> tptp.product_prod_int_int Bool)) tptp.set_Pr958786334691620121nt_int)
% 6.60/6.97 (declare-fun tptp.collec3799799289383736868l_real ((-> tptp.produc2422161461964618553l_real Bool)) tptp.set_Pr6218003697084177305l_real)
% 6.60/6.97 (declare-fun tptp.collect_rat ((-> tptp.rat Bool)) tptp.set_rat)
% 6.60/6.97 (declare-fun tptp.collect_real ((-> tptp.real Bool)) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.collect_set_complex ((-> tptp.set_complex Bool)) tptp.set_set_complex)
% 6.60/6.97 (declare-fun tptp.collect_set_int ((-> tptp.set_int Bool)) tptp.set_set_int)
% 6.60/6.97 (declare-fun tptp.collect_set_nat ((-> tptp.set_nat Bool)) tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.pow_nat (tptp.set_nat) tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.image_int_int ((-> tptp.int tptp.int) tptp.set_int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.image_nat_int ((-> tptp.nat tptp.int) tptp.set_nat) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.image_nat_nat ((-> tptp.nat tptp.nat) tptp.set_nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.image_nat_real ((-> tptp.nat tptp.real) tptp.set_nat) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.image_nat_set_nat ((-> tptp.nat tptp.set_nat) tptp.set_nat) tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.image_nat_char ((-> tptp.nat tptp.char) tptp.set_nat) tptp.set_char)
% 6.60/6.97 (declare-fun tptp.image_5971271580939081552omplex ((-> tptp.real tptp.filter6041513312241820739omplex) tptp.set_real) tptp.set_fi4554929511873752355omplex)
% 6.60/6.97 (declare-fun tptp.image_2178119161166701260l_real ((-> tptp.real tptp.filter2146258269922977983l_real) tptp.set_real) tptp.set_fi7789364187291644575l_real)
% 6.60/6.97 (declare-fun tptp.image_real_real ((-> tptp.real tptp.real) tptp.set_real) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.image_char_nat ((-> tptp.char tptp.nat) tptp.set_char) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.insert_complex (tptp.complex tptp.set_complex) tptp.set_complex)
% 6.60/6.97 (declare-fun tptp.insert_int (tptp.int tptp.set_int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.insert_nat (tptp.nat tptp.set_nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.insert_num (tptp.num tptp.set_num) tptp.set_num)
% 6.60/6.97 (declare-fun tptp.insert_rat (tptp.rat tptp.set_rat) tptp.set_rat)
% 6.60/6.97 (declare-fun tptp.insert_real (tptp.real tptp.set_real) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.insert_set_nat (tptp.set_nat tptp.set_set_nat) tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.insert_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) tptp.set_VEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.set_fo2584398358068434914at_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.set_or1266510415728281911st_int (tptp.int tptp.int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.set_or1269000886237332187st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_or7049704709247886629st_num (tptp.num tptp.num) tptp.set_num)
% 6.60/6.97 (declare-fun tptp.set_or633870826150836451st_rat (tptp.rat tptp.rat) tptp.set_rat)
% 6.60/6.97 (declare-fun tptp.set_or1222579329274155063t_real (tptp.real tptp.real) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.set_or370866239135849197et_int (tptp.set_int tptp.set_int) tptp.set_set_int)
% 6.60/6.97 (declare-fun tptp.set_or4548717258645045905et_nat (tptp.set_nat tptp.set_nat) tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.set_or4662586982721622107an_int (tptp.int tptp.int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.set_or4665077453230672383an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_ord_atLeast_nat (tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_ord_atLeast_real (tptp.real) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.set_ord_atMost_int (tptp.int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.set_ord_atMost_nat (tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_or6656581121297822940st_int (tptp.int tptp.int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.set_or6659071591806873216st_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_or5832277885323065728an_int (tptp.int tptp.int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.set_or5834768355832116004an_nat (tptp.nat tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_or1633881224788618240n_real (tptp.real tptp.real) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.set_or1210151606488870762an_nat (tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_or5849166863359141190n_real (tptp.real) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.set_or8419480210114673929d_enat (tptp.extended_enat) tptp.set_Extended_enat)
% 6.60/6.97 (declare-fun tptp.set_ord_lessThan_int (tptp.int) tptp.set_int)
% 6.60/6.97 (declare-fun tptp.set_ord_lessThan_nat (tptp.nat) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.set_ord_lessThan_num (tptp.num) tptp.set_num)
% 6.60/6.97 (declare-fun tptp.set_ord_lessThan_rat (tptp.rat) tptp.set_rat)
% 6.60/6.97 (declare-fun tptp.set_or5984915006950818249n_real (tptp.real) tptp.set_real)
% 6.60/6.97 (declare-fun tptp.set_or890127255671739683et_nat (tptp.set_nat) tptp.set_set_nat)
% 6.60/6.97 (declare-fun tptp.ascii_of (tptp.char) tptp.char)
% 6.60/6.97 (declare-fun tptp.char2 (Bool Bool Bool Bool Bool Bool Bool Bool) tptp.char)
% 6.60/6.97 (declare-fun tptp.size_char (tptp.char) tptp.nat)
% 6.60/6.97 (declare-fun tptp.comm_s629917340098488124ar_nat (tptp.char) tptp.nat)
% 6.60/6.97 (declare-fun tptp.integer_of_char (tptp.char) tptp.code_integer)
% 6.60/6.97 (declare-fun tptp.unique3096191561947761185of_nat (tptp.nat) tptp.char)
% 6.60/6.97 (declare-fun tptp.topolo4422821103128117721l_real (tptp.filter_real (-> tptp.real tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.topolo5044208981011980120l_real (tptp.set_real (-> tptp.real tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.topolo6980174941875973593q_real ((-> tptp.nat tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.topolo2177554685111907308n_real (tptp.real tptp.set_real) tptp.filter_real)
% 6.60/6.97 (declare-fun tptp.topolo2815343760600316023s_real (tptp.real) tptp.filter_real)
% 6.60/6.97 (declare-fun tptp.topolo4055970368930404560y_real ((-> tptp.nat tptp.real)) Bool)
% 6.60/6.97 (declare-fun tptp.topolo896644834953643431omplex () tptp.filter6041513312241820739omplex)
% 6.60/6.97 (declare-fun tptp.topolo1511823702728130853y_real () tptp.filter2146258269922977983l_real)
% 6.60/6.97 (declare-fun tptp.arccos (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.arcosh_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.arcsin (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.arctan (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.arsinh_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.artanh_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.cos_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.cos_coeff (tptp.nat) tptp.real)
% 6.60/6.97 (declare-fun tptp.cosh_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.cot_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.exp_complex (tptp.complex) tptp.complex)
% 6.60/6.97 (declare-fun tptp.exp_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.ln_ln_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.log (tptp.real tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.pi () tptp.real)
% 6.60/6.97 (declare-fun tptp.powr_real (tptp.real tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.sin_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.sin_coeff (tptp.nat) tptp.real)
% 6.60/6.97 (declare-fun tptp.sinh_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.tan_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.tanh_complex (tptp.complex) tptp.complex)
% 6.60/6.97 (declare-fun tptp.tanh_real (tptp.real) tptp.real)
% 6.60/6.97 (declare-fun tptp.vEBT_Leaf (Bool Bool) tptp.vEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.vEBT_Node (tptp.option4927543243414619207at_nat tptp.nat tptp.list_VEBT_VEBT tptp.vEBT_VEBT) tptp.vEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.vEBT_size_VEBT (tptp.vEBT_VEBT) tptp.nat)
% 6.60/6.97 (declare-fun tptp.vEBT_V8194947554948674370ptions (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_high (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.vEBT_V5917875025757280293ildren (tptp.nat tptp.list_VEBT_VEBT tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_low (tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_membermima (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_V4351362008482014158ma_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_V5719532721284313246member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_V5765760719290551771er_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_valid (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_valid_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_invar_vebt (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_buildup (tptp.nat) tptp.vEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.vEBT_v4011308405150292612up_rel (tptp.nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_delete (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_delete_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_insert (tptp.vEBT_VEBT tptp.nat) tptp.vEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_insert_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_bit_concat (tptp.nat tptp.nat tptp.nat) tptp.nat)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_minNull (tptp.vEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_V6963167321098673237ll_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_set_vebt (tptp.vEBT_VEBT) tptp.set_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_member (tptp.vEBT_VEBT tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_member_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_add (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_greater (tptp.option_nat tptp.option_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_less (tptp.option_nat tptp.option_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_lesseq (tptp.option_nat tptp.option_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_max_in_set (tptp.set_nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_min_in_set (tptp.set_nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_mul (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_V4262088993061758097ft_nat ((-> tptp.nat tptp.nat tptp.nat) tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_V819420779217536731ft_num ((-> tptp.num tptp.num tptp.num) tptp.option_num tptp.option_num) tptp.option_num)
% 6.60/6.97 (declare-fun tptp.vEBT_V1502963449132264192at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat) tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat) tptp.option4927543243414619207at_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_VEBT_power (tptp.option_nat tptp.option_nat) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_maxt (tptp.vEBT_VEBT) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_maxt_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_mint (tptp.vEBT_VEBT) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_mint_rel (tptp.vEBT_VEBT tptp.vEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_is_pred_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_pred (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_pred_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_is_succ_in_set (tptp.set_nat tptp.nat tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_succ (tptp.vEBT_VEBT tptp.nat) tptp.option_nat)
% 6.60/6.97 (declare-fun tptp.vEBT_vebt_succ_rel (tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.accp_list_nat ((-> tptp.list_nat tptp.list_nat Bool) tptp.list_nat) Bool)
% 6.60/6.97 (declare-fun tptp.accp_nat ((-> tptp.nat tptp.nat Bool) tptp.nat) Bool)
% 6.60/6.97 (declare-fun tptp.accp_P1096762738010456898nt_int ((-> tptp.product_prod_int_int tptp.product_prod_int_int Bool) tptp.product_prod_int_int) Bool)
% 6.60/6.97 (declare-fun tptp.accp_P4275260045618599050at_nat ((-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool) tptp.product_prod_nat_nat) Bool)
% 6.60/6.97 (declare-fun tptp.accp_P3113834385874906142um_num ((-> tptp.product_prod_num_num tptp.product_prod_num_num Bool) tptp.product_prod_num_num) Bool)
% 6.60/6.97 (declare-fun tptp.accp_P2887432264394892906BT_nat ((-> tptp.produc9072475918466114483BT_nat tptp.produc9072475918466114483BT_nat Bool) tptp.produc9072475918466114483BT_nat) Bool)
% 6.60/6.97 (declare-fun tptp.accp_VEBT_VEBT ((-> tptp.vEBT_VEBT tptp.vEBT_VEBT Bool) tptp.vEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.fChoice_real ((-> tptp.real Bool)) tptp.real)
% 6.60/6.97 (declare-fun tptp.member_o (Bool tptp.set_o) Bool)
% 6.60/6.97 (declare-fun tptp.member_complex (tptp.complex tptp.set_complex) Bool)
% 6.60/6.97 (declare-fun tptp.member_int (tptp.int tptp.set_int) Bool)
% 6.60/6.97 (declare-fun tptp.member_list_o (tptp.list_o tptp.set_list_o) Bool)
% 6.60/6.97 (declare-fun tptp.member_list_int (tptp.list_int tptp.set_list_int) Bool)
% 6.60/6.97 (declare-fun tptp.member_list_nat (tptp.list_nat tptp.set_list_nat) Bool)
% 6.60/6.97 (declare-fun tptp.member2936631157270082147T_VEBT (tptp.list_VEBT_VEBT tptp.set_list_VEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.member_nat (tptp.nat tptp.set_nat) Bool)
% 6.60/6.97 (declare-fun tptp.member_num (tptp.num tptp.set_num) Bool)
% 6.60/6.97 (declare-fun tptp.member5262025264175285858nt_int (tptp.product_prod_int_int tptp.set_Pr958786334691620121nt_int) Bool)
% 6.60/6.97 (declare-fun tptp.member_rat (tptp.rat tptp.set_rat) Bool)
% 6.60/6.97 (declare-fun tptp.member_real (tptp.real tptp.set_real) Bool)
% 6.60/6.97 (declare-fun tptp.member_set_int (tptp.set_int tptp.set_set_int) Bool)
% 6.60/6.97 (declare-fun tptp.member_set_nat (tptp.set_nat tptp.set_set_nat) Bool)
% 6.60/6.97 (declare-fun tptp.member_VEBT_VEBT (tptp.vEBT_VEBT tptp.set_VEBT_VEBT) Bool)
% 6.60/6.97 (declare-fun tptp.deg () tptp.nat)
% 6.60/6.97 (declare-fun tptp.m () tptp.nat)
% 6.60/6.97 (declare-fun tptp.ma () tptp.nat)
% 6.60/6.97 (declare-fun tptp.maxs () tptp.nat)
% 6.60/6.97 (declare-fun tptp.mi () tptp.nat)
% 6.60/6.97 (declare-fun tptp.na () tptp.nat)
% 6.60/6.97 (declare-fun tptp.summary () tptp.vEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.treeList () tptp.list_VEBT_VEBT)
% 6.60/6.97 (declare-fun tptp.xa () tptp.nat)
% 6.60/6.97 (assert (@ (@ tptp.vEBT_invar_vebt tptp.summary) tptp.m))
% 6.60/6.97 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) tptp.maxs))
% 6.60/6.97 (assert (= tptp.na tptp.m))
% 6.60/6.97 (assert (forall ((X tptp.nat) (D tptp.nat)) (= (@ (@ (@ tptp.vEBT_VEBT_bit_concat (@ (@ tptp.vEBT_VEBT_high X) D)) (@ (@ tptp.vEBT_VEBT_low X) D)) D) X)))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete T) X)) Y) (and (not (= X Y)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) Y))))))
% 6.60/6.97 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)))) tptp.maxs)) tptp.na)))
% 6.60/6.97 (assert (not (= tptp.xa tptp.mi)))
% 6.60/6.97 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)))) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) _let_2)) _let_1) _let_2))))
% 6.60/6.97 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na))) tptp.na))
% 6.60/6.97 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na))))
% 6.60/6.97 (assert (and (not (= tptp.maxs (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ (@ tptp.ord_less_nat tptp.maxs) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m))))
% 6.60/6.97 (assert (= tptp.xa tptp.ma))
% 6.60/6.97 (assert (forall ((I tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT tptp.treeList))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (=> (not (= I _let_2)) (=> (@ (@ tptp.ord_less_nat I) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ _let_1 _let_2)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)))) I) (@ _let_1 I))))))))
% 6.60/6.97 (assert (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions tptp.summary) I2)))))
% 6.60/6.97 (assert (= tptp.vEBT_V5917875025757280293ildren (lambda ((N2 tptp.nat) (TreeList tptp.list_VEBT_VEBT) (X3 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) (@ (@ tptp.vEBT_VEBT_high X3) N2))) (@ (@ tptp.vEBT_VEBT_low X3) N2)))))
% 6.60/6.97 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) tptp.m))
% 6.60/6.97 (assert (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (and (@ (@ tptp.vEBT_invar_vebt X4) tptp.na) (forall ((Xa tptp.nat)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete X4) Xa)) tptp.na))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_nat) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_nat Xs) I) (@ (@ tptp.nth_nat Xs) I)) Xs)))
% 6.60/6.97 (assert (forall ((Xs tptp.list_int) (I tptp.nat)) (= (@ (@ (@ tptp.list_update_int Xs) I) (@ (@ tptp.nth_int Xs) I)) Xs)))
% 6.60/6.97 (assert (forall ((Xs tptp.list_VEBT_VEBT) (I tptp.nat)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) I) (@ (@ tptp.nth_VEBT_VEBT Xs) I)) Xs)))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ tptp.set_VEBT_VEBT2 tptp.treeList)))
% 6.60/6.97 (assert (forall ((X4 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na))))) (@ (@ tptp.vEBT_invar_vebt X4) tptp.na)))))
% 6.60/6.97 (assert (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na))) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na)))
% 6.60/6.97 (assert (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (= (exists ((X2 tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)))) I2)) X2))) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_delete tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) I2)))))
% 6.60/6.97 (assert (forall ((X tptp.nat)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_vebt_delete tptp.summary) X)) tptp.m)))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull T)) (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X_1)))))
% 6.60/6.97 (assert (=> (= tptp.mi tptp.ma) (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))))
% 6.60/6.97 (assert (or (not (= tptp.xa tptp.mi)) (not (= tptp.xa tptp.ma))))
% 6.60/6.97 (assert (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 tptp.treeList)) (@ (@ tptp.vEBT_invar_vebt X4) tptp.na))))
% 6.60/6.97 (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.xa) tptp.na)) (@ _let_1 tptp.m)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)) (@ _let_1 tptp.na)))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg)))
% 6.60/6.97 (assert (= (@ tptp.size_s6755466524823107622T_VEBT tptp.treeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)))
% 6.60/6.97 (assert (=> (not (= tptp.mi tptp.ma)) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y2) (@ (@ tptp.ord_less_eq_nat Y2) tptp.ma)))))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (I3 tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT) (X5 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.list_u1324408373059187874T_VEBT Xs))) (=> (not (= I I3)) (= (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I) X)) I3) X5) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT (@ (@ _let_1 I3) X5)) I) X))))))
% 6.60/6.97 (assert (forall ((Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_low Y) tptp.na))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Y) tptp.na))) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_3)) _let_2) (=> (@ (@ tptp.ord_less_nat _let_3) (@ _let_1 tptp.m)) (and (@ (@ tptp.ord_less_nat tptp.mi) Y) (@ (@ tptp.ord_less_eq_nat Y) tptp.ma) (@ (@ tptp.ord_less_nat _let_2) (@ _let_1 tptp.na))))))))))
% 6.60/6.97 (assert (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high tptp.ma) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low tptp.ma) tptp.na))) (forall ((Y2 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high Y2) tptp.na) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) I2)) (@ (@ tptp.vEBT_VEBT_low Y2) tptp.na))) (and (@ (@ tptp.ord_less_nat tptp.mi) Y2) (@ (@ tptp.ord_less_eq_nat Y2) tptp.ma))))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) Y)) X))))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.vEBT_vebt_insert T) X)) X)))))
% 6.60/6.97 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)))) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.m))))
% 6.60/6.97 (assert (and (not (= tptp.mi tptp.ma)) (@ (@ tptp.ord_less_nat tptp.xa) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))))
% 6.60/6.97 (assert (forall ((Tree tptp.vEBT_VEBT) (X tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.60/6.97 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit0 M) tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit0 N)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (P (-> tptp.real Bool))) (= (@ (@ tptp.member_real A) (@ tptp.collect_real P)) (@ P A))))
% 6.60/6.97 (assert (forall ((A tptp.product_prod_int_int) (P (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.member5262025264175285858nt_int A) (@ tptp.collec213857154873943460nt_int P)) (@ P A))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (P (-> tptp.complex Bool))) (= (@ (@ tptp.member_complex A) (@ tptp.collect_complex P)) (@ P A))))
% 6.60/6.97 (assert (forall ((A tptp.set_nat) (P (-> tptp.set_nat Bool))) (= (@ (@ tptp.member_set_nat A) (@ tptp.collect_set_nat P)) (@ P A))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (P (-> tptp.nat Bool))) (= (@ (@ tptp.member_nat A) (@ tptp.collect_nat P)) (@ P A))))
% 6.60/6.97 (assert (forall ((A tptp.int) (P (-> tptp.int Bool))) (= (@ (@ tptp.member_int A) (@ tptp.collect_int P)) (@ P A))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real)) (= (@ tptp.collect_real (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A2))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_Pr958786334691620121nt_int)) (= (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X3) A2))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_complex)) (= (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A2))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_set_nat)) (= (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A2))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat)) (= (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A2))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int)) (= (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A2))) A2)))
% 6.60/6.97 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X6 tptp.product_prod_int_int)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collec213857154873943460nt_int P) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X6 tptp.complex)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_complex P) (@ tptp.collect_complex Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X6 tptp.set_nat)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_set_nat P) (@ tptp.collect_set_nat Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X6 tptp.nat)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_nat P) (@ tptp.collect_nat Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int)) (= (@ P X6) (@ Q X6))) (= (@ tptp.collect_int P) (@ tptp.collect_int Q)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num M) N))))
% 6.60/6.97 (assert (forall ((Ma tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high Ma) N)) (@ _let_1 M))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (@ tptp.vEBT_VEBT_minNull T) (not (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.60/6.97 (assert (= tptp.deg (@ (@ tptp.plus_plus_nat tptp.na) tptp.m)))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions T) X) (@ (@ tptp.vEBT_vebt_member T) X)))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_min_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) Xs2) (@ (@ tptp.ord_less_eq_nat X3) Y3)))))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_max_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) Xs2) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) Xs2) (@ (@ tptp.ord_less_eq_nat Y3) X3)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (N tptp.nat)) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ tptp.set_complex2 Xs)) (@ P X6))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) N))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_real) (P (-> tptp.real Bool)) (N tptp.nat)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ tptp.set_real2 Xs)) (@ P X6))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ P (@ (@ tptp.nth_real Xs) N))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_set_nat) (P (-> tptp.set_nat Bool)) (N tptp.nat)) (=> (forall ((X6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X6) (@ tptp.set_set_nat2 Xs)) (@ P X6))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ P (@ (@ tptp.nth_set_nat Xs) N))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool)) (N tptp.nat)) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X6))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (N tptp.nat)) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) (@ tptp.set_o2 Xs)) (@ P X6))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ tptp.set_nat2 Xs)) (@ P X6))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool)) (N tptp.nat)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ tptp.set_int2 Xs)) (@ P X6))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.numera6690914467698888265omplex N)) (= M N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_real M) (@ tptp.numeral_numeral_real N)) (= M N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_rat M) (@ tptp.numeral_numeral_rat N)) (= M N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_nat M) (@ tptp.numeral_numeral_nat N)) (= M N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.numeral_numeral_int M) (@ tptp.numeral_numeral_int N)) (= M N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit0 M) (@ tptp.bit0 N)) (= M N))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))
% 6.60/6.97 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.xa) (@ (@ tptp.ord_less_eq_nat tptp.xa) tptp.ma)))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.ord_less_nat X) _let_1) (=> (@ (@ tptp.ord_less_nat Y) _let_1) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_vebt_insert T) X)) Y) (or (@ (@ tptp.vEBT_vebt_member T) Y) (= X Y)))))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.member_nat X) (@ tptp.vEBT_set_vebt T))))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ (@ tptp.list_update_o Xs) I) X)) (@ tptp.size_size_list_o Xs))))
% 6.60/6.97 (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))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.60/6.97 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_num M) tptp.one))))
% 6.60/6.97 (assert (and (@ (@ tptp.ord_less_eq_nat tptp.mi) tptp.ma) (@ (@ tptp.ord_less_nat tptp.ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.deg))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_o) (I tptp.nat) (X Bool)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs)) I) (= (@ (@ (@ tptp.list_update_o Xs) I) X) Xs))))
% 6.60/6.97 (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))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit0 N))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I) X)) I) X))))
% 6.60/6.97 (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))))
% 6.60/6.97 (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))))
% 6.60/6.97 (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))))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (J tptp.nat)) (let ((_let_1 (@ tptp.nth_o Xs))) (let ((_let_2 (@ tptp.size_size_list_o Xs))) (=> (@ (@ tptp.ord_less_nat I) _let_2) (=> (@ (@ tptp.ord_less_nat J) _let_2) (= (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o (@ (@ (@ tptp.list_update_o Xs) I) (@ _let_1 J))) J) (@ _let_1 I))) (@ tptp.set_o2 Xs))))))))
% 6.60/6.97 (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))))))))
% 6.60/6.97 (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))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT Xs3) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_o)) (= (@ tptp.size_size_list_o Xs3) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.size_size_list_nat Xs3) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (exists ((Xs3 tptp.list_int)) (= (@ tptp.size_size_list_int Xs3) N))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys))) (not (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys))) (not (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys))) (not (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys))) (not (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.list_VEBT_VEBT Bool)) (Xs tptp.list_VEBT_VEBT)) (=> (forall ((Xs3 tptp.list_VEBT_VEBT)) (=> (forall ((Ys2 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT Ys2)) (@ tptp.size_s6755466524823107622T_VEBT Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs))))
% 6.60/6.97 (assert (forall ((P (-> tptp.list_o Bool)) (Xs tptp.list_o)) (=> (forall ((Xs3 tptp.list_o)) (=> (forall ((Ys2 tptp.list_o)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o Ys2)) (@ tptp.size_size_list_o Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs))))
% 6.60/6.97 (assert (forall ((P (-> tptp.list_nat Bool)) (Xs tptp.list_nat)) (=> (forall ((Xs3 tptp.list_nat)) (=> (forall ((Ys2 tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat Ys2)) (@ tptp.size_size_list_nat Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs))))
% 6.60/6.97 (assert (forall ((P (-> tptp.list_int Bool)) (Xs tptp.list_int)) (=> (forall ((Xs3 tptp.list_int)) (=> (forall ((Ys2 tptp.list_int)) (=> (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int Ys2)) (@ tptp.size_size_list_int Xs3)) (@ P Ys2))) (@ P Xs3))) (@ P Xs))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) (@ tptp.size_s6755466524823107622T_VEBT Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I4) (@ (@ tptp.nth_VEBT_VEBT Ys) I4)))) (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (=> (= (@ tptp.size_size_list_o Xs) (@ tptp.size_size_list_o Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I4) (@ (@ tptp.nth_o Ys) I4)))) (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_nat)) (=> (= (@ tptp.size_size_list_nat Xs) (@ tptp.size_size_list_nat Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I4) (@ (@ tptp.nth_nat Ys) I4)))) (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_int) (Ys tptp.list_int)) (=> (= (@ tptp.size_size_list_int Xs) (@ tptp.size_size_list_int Ys)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I4) (@ (@ tptp.nth_int Ys) I4)))) (= Xs Ys)))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.vEBT_VEBT Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X2 tptp.vEBT_VEBT)) (@ (@ P I5) X2)))) (exists ((Xs2 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_VEBT_VEBT Xs2) I5)))))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (P (-> tptp.nat Bool Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X2 Bool)) (@ (@ P I5) X2)))) (exists ((Xs2 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_o Xs2) I5)))))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X2 tptp.nat)) (@ (@ P I5) X2)))) (exists ((Xs2 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_nat Xs2) I5)))))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (P (-> tptp.nat tptp.int Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (exists ((X2 tptp.int)) (@ (@ P I5) X2)))) (exists ((Xs2 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) K) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) K) (@ (@ P I5) (@ (@ tptp.nth_int Xs2) I5)))))))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.list_VEBT_VEBT) (Z2 tptp.list_VEBT_VEBT)) (= Y4 Z2)) (lambda ((Xs2 tptp.list_VEBT_VEBT) (Ys3 tptp.list_VEBT_VEBT)) (and (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) (@ tptp.size_s6755466524823107622T_VEBT Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs2)) (= (@ (@ tptp.nth_VEBT_VEBT Xs2) I5) (@ (@ tptp.nth_VEBT_VEBT Ys3) I5))))))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.list_o) (Z2 tptp.list_o)) (= Y4 Z2)) (lambda ((Xs2 tptp.list_o) (Ys3 tptp.list_o)) (and (= (@ tptp.size_size_list_o Xs2) (@ tptp.size_size_list_o Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs2)) (= (@ (@ tptp.nth_o Xs2) I5) (@ (@ tptp.nth_o Ys3) I5))))))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.list_nat) (Z2 tptp.list_nat)) (= Y4 Z2)) (lambda ((Xs2 tptp.list_nat) (Ys3 tptp.list_nat)) (and (= (@ tptp.size_size_list_nat Xs2) (@ tptp.size_size_list_nat Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs2)) (= (@ (@ tptp.nth_nat Xs2) I5) (@ (@ tptp.nth_nat Ys3) I5))))))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.list_int) (Z2 tptp.list_int)) (= Y4 Z2)) (lambda ((Xs2 tptp.list_int) (Ys3 tptp.list_int)) (and (= (@ tptp.size_size_list_int Xs2) (@ tptp.size_size_list_int Ys3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs2)) (= (@ (@ tptp.nth_int Xs2) I5) (@ (@ tptp.nth_int Ys3) I5))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat M) _let_1)) (@ (@ tptp.power_power_nat N) _let_1)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat K) M)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X3))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) I5)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool))) (= (forall ((X3 Bool)) (=> (@ (@ tptp.member_o X3) (@ tptp.set_o2 Xs)) (@ P X3))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I5)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 Xs)) (@ P X3))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (@ P (@ (@ tptp.nth_nat Xs) I5)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_int) (P (-> tptp.int Bool))) (= (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 Xs)) (@ P X3))) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (@ P (@ (@ tptp.nth_int Xs) I5)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_complex) (P (-> tptp.complex Bool)) (X tptp.complex)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_s3451745648224563538omplex Xs)) (@ P (@ (@ tptp.nth_complex Xs) I4)))) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs)) (@ P X)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_o) (P (-> Bool Bool)) (X Bool)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ tptp.size_size_list_o Xs)) (@ P (@ (@ tptp.nth_o Xs) I4)))) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ P X)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Xs tptp.list_complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3451745648224563538omplex Xs)) (= (@ (@ tptp.nth_complex Xs) I5) X))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Xs tptp.list_real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_real Xs)) (= (@ (@ tptp.nth_real Xs) I5) X))))))
% 6.60/6.97 (assert (forall ((X tptp.set_nat) (Xs tptp.list_set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s3254054031482475050et_nat Xs)) (= (@ (@ tptp.nth_set_nat Xs) I5) X))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xs tptp.list_VEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (= (@ (@ tptp.nth_VEBT_VEBT Xs) I5) X))))))
% 6.60/6.97 (assert (forall ((X Bool) (Xs tptp.list_o)) (= (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o Xs) I5) X))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Xs tptp.list_nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_nat Xs)) (= (@ (@ tptp.nth_nat Xs) I5) X))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Xs tptp.list_int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 Xs)) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.size_size_list_int Xs)) (= (@ (@ tptp.nth_int Xs) I5) X))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 Xs)) (@ P X6))) (@ P (@ (@ tptp.nth_VEBT_VEBT Xs) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (P (-> Bool Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) (@ tptp.set_o2 Xs)) (@ P X6))) (@ P (@ (@ tptp.nth_o Xs) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ tptp.set_nat2 Xs)) (@ P X6))) (@ P (@ (@ tptp.nth_nat Xs) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ tptp.set_int2 Xs)) (@ P X6))) (@ P (@ (@ tptp.nth_int Xs) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex (@ (@ tptp.nth_complex Xs) N)) (@ tptp.set_complex2 Xs)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real (@ (@ tptp.nth_real Xs) N)) (@ tptp.set_real2 Xs)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat (@ (@ tptp.nth_set_nat Xs) N)) (@ tptp.set_set_nat2 Xs)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) N)) (@ tptp.set_VEBT_VEBT2 Xs)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_o)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o (@ (@ tptp.nth_o Xs) N)) (@ tptp.set_o2 Xs)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat (@ (@ tptp.nth_nat Xs) N)) (@ tptp.set_nat2 Xs)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int (@ (@ tptp.nth_int Xs) N)) (@ tptp.set_int2 Xs)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_complex) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3451745648224563538omplex Xs)) (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) N) X))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_real Xs)) (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ (@ tptp.list_update_real Xs) N) X))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_set_nat) (X tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s3254054031482475050et_nat Xs)) (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ (@ tptp.list_update_set_nat Xs) N) X))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT Xs) N) X))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_o Xs)) (@ (@ tptp.member_o X) (@ tptp.set_o2 (@ (@ (@ tptp.list_update_o Xs) N) X))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_nat Xs)) (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ (@ tptp.list_update_nat Xs) N) X))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Xs tptp.list_int) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.size_size_list_int Xs)) (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ (@ tptp.list_update_int Xs) N) X))))))
% 6.60/6.97 (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)))))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (X Bool) (J tptp.nat)) (let ((_let_1 (= I J))) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (@ (@ tptp.nth_o (@ (@ (@ tptp.list_update_o Xs) I) X)) J) (and (=> _let_1 X) (=> (not _let_1) (@ (@ tptp.nth_o Xs) J))))))))
% 6.60/6.97 (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)))))))))
% 6.60/6.97 (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)))))))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (Xs tptp.list_o) (X Bool)) (=> (@ (@ tptp.ord_less_nat I) (@ tptp.size_size_list_o Xs)) (= (= (@ (@ (@ tptp.list_update_o Xs) I) X) Xs) (= (@ (@ tptp.nth_o Xs) I) X)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N))) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N)))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_bit_concat (lambda ((H tptp.nat) (L tptp.nat) (D2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) D2))) L))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_low (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) X)))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat X) _let_1) (= (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat Y) _let_1)) X)) N) Y)))))
% 6.60/6.97 (assert (= (@ (@ tptp.divide_divide_nat tptp.deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.na))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.na))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (@ _let_1 A)) (@ _let_1 B)))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_high (lambda ((X3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Z)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Z)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Z)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat W)) Z)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num) (Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Z)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Z))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.one_one_rat) N) tptp.one_one_rat)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.one_one_nat) N) tptp.one_one_nat)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.one_one_real) N) tptp.one_one_real)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.one_one_int) N) tptp.one_one_int)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.one_one_complex) N) tptp.one_one_complex)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= tptp.one_one_nat (@ (@ tptp.times_times_nat M) N)) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.one_one_nat) (and (= M tptp.one_one_nat) (= N tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_num tptp.one) N)))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex A) B)) _let_1) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) _let_1) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) _let_1)) (@ (@ tptp.times_times_nat B) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_complex B) C)) (@ (@ tptp.plus_plus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= (@ tptp.numera6690914467698888265omplex N) tptp.one_one_complex) (= N tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_real N) tptp.one_one_real) (= N tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_rat N) tptp.one_one_rat) (= N tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_nat N) tptp.one_one_nat) (= N tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= (@ tptp.numeral_numeral_int N) tptp.one_one_int) (= N tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= tptp.one_one_complex (@ tptp.numera6690914467698888265omplex N)) (= tptp.one N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= tptp.one_one_real (@ tptp.numeral_numeral_real N)) (= tptp.one N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= tptp.one_one_rat (@ tptp.numeral_numeral_rat N)) (= tptp.one N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= tptp.one_one_nat (@ tptp.numeral_numeral_nat N)) (= tptp.one N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (= tptp.one_one_int (@ tptp.numeral_numeral_int N)) (= tptp.one N))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.60/6.97 (assert (= (@ (@ tptp.plus_plus_num tptp.one) tptp.one) (@ tptp.bit0 tptp.one)))
% 6.60/6.97 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) tptp.one))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ tptp.numera1916890842035813515d_enat M)) (@ tptp.numera1916890842035813515d_enat N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ _let_1 (@ tptp.numeral_numeral_nat N))) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num) (B tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_complex (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num) (B tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (M tptp.num) (N tptp.num) (B tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_rat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num) (B tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_nat (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num) (B tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat N))) B)) (@ (@ tptp.times_times_int (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num M) N)))) B)))))
% 6.60/6.97 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (forall ((B tptp.real) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) B) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) B) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) B) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex N)) tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_num N) tptp.one))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.numeral_numeral_int N)) (@ (@ tptp.ord_less_num tptp.one) N))))
% 6.60/6.97 (assert (forall ((P (-> tptp.extended_enat Bool)) (N tptp.extended_enat)) (=> (forall ((N3 tptp.extended_enat)) (=> (forall ((M2 tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.one_one_complex) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.one_one_real) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.one_one_rat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.one_one_int) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ (@ tptp.times_times_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.times_times_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.times_times_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.60/6.97 (assert (= tptp.times_times_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.times_times_real B2) A3))))
% 6.60/6.97 (assert (= tptp.times_times_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.times_times_rat B2) A3))))
% 6.60/6.97 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.times_times_nat B2) A3))))
% 6.60/6.97 (assert (= tptp.times_times_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.times_times_int B2) A3))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.one_one_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.one_one_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.one_one_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.one_one_int) A)))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.one_one_nat) N) N)))
% 6.60/6.97 (assert (forall ((X tptp.complex)) (= (= tptp.one_one_complex X) (= X tptp.one_one_complex))))
% 6.60/6.97 (assert (forall ((X tptp.real)) (= (= tptp.one_one_real X) (= X tptp.one_one_real))))
% 6.60/6.97 (assert (forall ((X tptp.rat)) (= (= tptp.one_one_rat X) (= X tptp.one_one_rat))))
% 6.60/6.97 (assert (forall ((X tptp.nat)) (= (= tptp.one_one_nat X) (= X tptp.one_one_nat))))
% 6.60/6.97 (assert (forall ((X tptp.int)) (= (= tptp.one_one_int X) (= X tptp.one_one_int))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat N) tptp.one_one_nat) N)))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_complex A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat (@ _let_1 A)) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_complex X) Y) tptp.one_one_complex) (= (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) N)) tptp.one_one_complex))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_real X) Y) tptp.one_one_real) (= (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) N)) tptp.one_one_real))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_rat X) Y) tptp.one_one_rat) (= (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) tptp.one_one_rat))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_nat X) Y) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)) tptp.one_one_nat))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (= (@ (@ tptp.times_times_int X) Y) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) tptp.one_one_int))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (@ (@ tptp.ord_less_eq_nat M) (@ _let_1 (@ _let_1 M))))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.times_times_nat M) M))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat I) K)) (@ (@ tptp.times_times_nat J) L2))))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat M) N)) K) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real A) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat A) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat A) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int A) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat _let_1) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat _let_1) (@ (@ tptp.times_times_nat A) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int _let_1) (@ (@ tptp.times_times_int A) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) N) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real A) B)) N) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.divide_divide_rat A) B)) N) (@ (@ tptp.divide_divide_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) N) (@ (@ tptp.plus_plus_num N) tptp.one))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (= (@ (@ tptp.ord_less_eq_num X) tptp.one) (= X tptp.one))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (= (@ (@ tptp.times_times_complex _let_1) A) (@ (@ tptp.times_times_complex A) _let_1)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (= (@ (@ tptp.times_times_real _let_1) A) (@ (@ tptp.times_times_real A) _let_1)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (= (@ (@ tptp.times_times_rat _let_1) A) (@ (@ tptp.times_times_rat A) _let_1)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (= (@ (@ tptp.times_times_nat _let_1) A) (@ (@ tptp.times_times_nat A) _let_1)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (= (@ (@ tptp.times_times_int _let_1) A) (@ (@ tptp.times_times_int A) _let_1)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ (@ tptp.times_times_complex A) B)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex A) N)) (@ (@ tptp.power_power_complex B) N)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real A) B)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ (@ tptp.times_times_rat A) B)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.times_times_nat A) B)) N) (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ (@ tptp.times_times_int A) B)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex X) N))) (let ((_let_2 (@ tptp.times_times_complex Y))) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ _let_2 _let_1)))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real X) N))) (let ((_let_2 (@ tptp.times_times_real Y))) (=> (= (@ (@ tptp.times_times_real X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_real _let_1) Y) (@ _let_2 _let_1)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat X) N))) (let ((_let_2 (@ tptp.times_times_rat Y))) (=> (= (@ (@ tptp.times_times_rat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat X) N))) (let ((_let_2 (@ tptp.times_times_nat Y))) (=> (= (@ (@ tptp.times_times_nat X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ _let_2 _let_1)))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int X) N))) (let ((_let_2 (@ tptp.times_times_int Y))) (=> (= (@ (@ tptp.times_times_int X) Y) (@ _let_2 X)) (= (@ (@ tptp.times_times_int _let_1) Y) (@ _let_2 _let_1)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_nat (@ _let_1 M)) N)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_real (@ _let_1 M)) N)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_int (@ _let_1 M)) N)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.power_power_complex (@ _let_1 M)) N)))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.one_one_real))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.one_one_int))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.one_one_real)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.one_one_int)))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) B3) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ _let_1 (@ tptp.set_complex2 Xs)) (@ _let_1 B3)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_real2 Xs)) B3) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 (@ tptp.set_real2 Xs)) (@ _let_1 B3)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_set_nat) (B3 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.set_set_nat2 Xs)) B3) (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 (@ tptp.set_set_nat2 Xs)) (@ _let_1 B3)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_VEBT_VEBT) (B3 tptp.set_VEBT_VEBT)) (= (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs)) B3) (forall ((X3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.member_VEBT_VEBT X3))) (=> (@ _let_1 (@ tptp.set_VEBT_VEBT2 Xs)) (@ _let_1 B3)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs)) B3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 (@ tptp.set_nat2 Xs)) (@ _let_1 B3)))))))
% 6.60/6.97 (assert (forall ((Xs tptp.list_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs)) B3) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 (@ tptp.set_int2 Xs)) (@ _let_1 B3)))))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex tptp.one)) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real tptp.one)) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat tptp.one)) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat tptp.one)) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int tptp.one)) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) (@ tptp.numeral_numeral_real tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) (@ tptp.numeral_numeral_rat tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) (@ tptp.numeral_numeral_nat tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) (@ tptp.numeral_numeral_int tptp.one)) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.numeral_numeral_real N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.numeral_numeral_int N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.one_one_real))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.one_one_rat))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.one_one_nat))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.one_one_int))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex X))) (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)))))
% 6.60/6.97 (assert (= (@ tptp.numera6690914467698888265omplex tptp.one) tptp.one_one_complex))
% 6.60/6.97 (assert (= (@ tptp.numeral_numeral_real tptp.one) tptp.one_one_real))
% 6.60/6.97 (assert (= (@ tptp.numeral_numeral_rat tptp.one) tptp.one_one_rat))
% 6.60/6.97 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.60/6.97 (assert (= (@ tptp.numeral_numeral_int tptp.one) tptp.one_one_int))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.60/6.97 (assert (= (@ tptp.numeral_numeral_nat tptp.one) tptp.one_one_nat))
% 6.60/6.97 (assert (forall ((Xs tptp.list_complex) (A2 tptp.set_complex) (X tptp.complex) (I tptp.nat)) (=> (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs)) A2) (=> (@ (@ tptp.member_complex X) A2) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 (@ (@ (@ tptp.list_update_complex Xs) I) X))) A2)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (@ (@ tptp.ord_less_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (@ (@ tptp.ord_less_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_real I) K) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_rat I) K) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_nat I) K) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (= K L2)) (= (@ (@ tptp.plus_plus_int I) K) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_real A2) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_rat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_nat A2) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.plus_plus_int A2) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.60/6.97 (assert (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (let ((_let_2 (@ tptp.plus_plus_real K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (let ((_let_2 (@ tptp.plus_plus_rat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((B3 tptp.nat) (K tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (let ((_let_2 (@ tptp.plus_plus_int K))) (=> (= B3 (@ _let_2 B)) (= (@ _let_1 B3) (@ _let_2 (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ (@ tptp.plus_plus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ (@ tptp.plus_plus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.plus_plus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.plus_plus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.60/6.97 (assert (= tptp.plus_plus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real B2) A3))))
% 6.60/6.97 (assert (= tptp.plus_plus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat B2) A3))))
% 6.60/6.97 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.plus_plus_nat B2) A3))))
% 6.60/6.97 (assert (= tptp.plus_plus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int B2) A3))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real B))) (let ((_let_2 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat B))) (let ((_let_2 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat B))) (let ((_let_2 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int B))) (let ((_let_2 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (=> (= (@ _let_1 B) (@ _let_1 C)) (= B C)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (= (@ (@ tptp.plus_plus_real B) A) (@ (@ tptp.plus_plus_real C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat B) A) (@ (@ tptp.plus_plus_rat C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat B) A) (@ (@ tptp.plus_plus_nat C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (= (@ (@ tptp.plus_plus_int B) A) (@ (@ tptp.plus_plus_int C) A)) (= B C))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) (@ _let_1 N4)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (= M N)) (or (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat N) M)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) M) (not (= M N)))))
% 6.60/6.97 (assert (forall ((S tptp.nat) (T tptp.nat)) (=> (@ (@ tptp.ord_less_nat S) T) (not (= S T)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) N))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M2) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2)))))) (@ P N))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) N)))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= M N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (exists ((X6 tptp.nat)) (and (@ P X6) (forall ((Y2 tptp.nat)) (=> (@ P Y2) (@ (@ tptp.ord_less_eq_nat Y2) X6)))))))))
% 6.60/6.97 (assert (forall ((X tptp.list_VEBT_VEBT) (Y tptp.list_VEBT_VEBT)) (=> (not (= (@ tptp.size_s6755466524823107622T_VEBT X) (@ tptp.size_s6755466524823107622T_VEBT Y))) (not (= X Y)))))
% 6.60/6.97 (assert (forall ((X tptp.list_o) (Y tptp.list_o)) (=> (not (= (@ tptp.size_size_list_o X) (@ tptp.size_size_list_o Y))) (not (= X Y)))))
% 6.60/6.97 (assert (forall ((X tptp.list_nat) (Y tptp.list_nat)) (=> (not (= (@ tptp.size_size_list_nat X) (@ tptp.size_size_list_nat Y))) (not (= X Y)))))
% 6.60/6.97 (assert (forall ((X tptp.list_int) (Y tptp.list_int)) (=> (not (= (@ tptp.size_size_list_int X) (@ tptp.size_size_list_int Y))) (not (= X Y)))))
% 6.60/6.97 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= (@ tptp.size_size_num X) (@ tptp.size_size_num Y))) (not (= X Y)))))
% 6.60/6.97 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Z) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_complex Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_rat Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.nat)) (= (@ (@ tptp.times_times_nat Z) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_nat Z) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_int Z) Z))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.plus_plus_complex A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ _let_1 B)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) B)))))
% 6.60/6.97 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex X) X)) X)) X))))
% 6.60/6.97 (assert (forall ((X tptp.real)) (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real X) X)) X)) X))))
% 6.60/6.97 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat X) X)) X)) X))))
% 6.60/6.97 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.power_power_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat X) X)) X)) X))))
% 6.60/6.97 (assert (forall ((X tptp.int)) (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int X) X)) X)) X))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_complex A) A))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_real A) A))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_rat A) A))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_nat A) A))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.times_times_int A) A))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ (@ tptp.times_times_nat _let_1) N)) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_rat tptp.one_one_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_real tptp.one_one_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_int tptp.one_one_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_complex tptp.one_one_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex))
% 6.60/6.97 (assert (= (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex X) Y)) _let_2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) Y)) _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat X) Y)) _let_2) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat X) Y)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat _let_1) X)) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int X) Y)) _let_2) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (= K L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (= K L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (= K L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (= K L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (not (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.plus_plus_nat A) C2))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (exists ((C3 tptp.nat)) (= B2 (@ (@ tptp.plus_plus_nat A3) C3))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (= I J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (= I J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (= I J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (= I J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (= K L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (= K L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (= K L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (= K L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.ord_less_real A) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.ord_less_rat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.ord_less_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.ord_less_int A) B))))
% 6.60/6.97 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N2) (not (= M3 N2))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (or (@ (@ tptp.ord_less_nat M3) N2) (= M3 N2)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat M) N) (= M N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (not (= M N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.nat)) (I tptp.nat) (J tptp.nat)) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) J2) (@ (@ tptp.ord_less_nat (@ F I4)) (@ F J2)))) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ F J))))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J) (=> (@ (@ tptp.ord_less_nat K) L2) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) J)) I))))
% 6.60/6.97 (assert (forall ((J tptp.nat) (I tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat J) I)) I))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (L2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) L2) (=> (= (@ (@ tptp.plus_plus_nat M) L2) (@ (@ tptp.plus_plus_nat K) N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (not (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (@ (@ tptp.ord_less_eq_nat K) N)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat N) M))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat M) K)) N) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (exists ((N3 tptp.nat)) (= L2 (@ (@ tptp.plus_plus_nat K) N3))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (=> (@ (@ tptp.ord_less_eq_nat K) L2) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2))))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat J) M))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat I))) (=> (@ _let_1 J) (@ _let_1 (@ (@ tptp.plus_plus_nat M) J))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ (@ tptp.plus_plus_nat M3) K2))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat))))))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ _let_1 B) (=> (@ _let_1 K) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (and (@ (@ tptp.ord_less_nat (@ _let_1 N3)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N3) tptp.one_one_nat)))))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D))))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real I) J) (@ (@ tptp.ord_less_eq_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_rat I) J) (@ (@ tptp.ord_less_eq_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_nat I) J) (@ (@ tptp.ord_less_eq_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_int I) J) (@ (@ tptp.ord_less_eq_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.real) (J tptp.real) (K tptp.real) (L2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real I) J) (@ (@ tptp.ord_less_real K) L2)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real I) K)) (@ (@ tptp.plus_plus_real J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (J tptp.rat) (K tptp.rat) (L2 tptp.rat)) (=> (and (@ (@ tptp.ord_less_eq_rat I) J) (@ (@ tptp.ord_less_rat K) L2)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat I) K)) (@ (@ tptp.plus_plus_rat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (K tptp.nat) (L2 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_nat K) L2)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat I) K)) (@ (@ tptp.plus_plus_nat J) L2)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (J tptp.int) (K tptp.int) (L2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int I) J) (@ (@ tptp.ord_less_int K) L2)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int I) K)) (@ (@ tptp.plus_plus_int J) L2)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M4) N3) (@ (@ tptp.ord_less_nat (@ F M4)) (@ F N3)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ F M)) K)) (@ F (@ (@ tptp.plus_plus_nat M) K))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (@ tptp.vEBT_set_vebt T) (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))
% 6.60/6.97 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N 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) N) (=> (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat _let_2) Deg)) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (@ (@ tptp.vEBT_VEBT_low X) _let_3)) (@ (@ tptp.vEBT_V8194947554948674370ptions _let_1) X)))))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_2 (@ _let_1 M))) (@ _let_1 N)) (@ _let_2 (@ _let_1 (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.one_one_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.one_one_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.one_one_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.one_one_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.one_one_int) A)))
% 6.60/6.97 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex B) A)) C))))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real B) A)) C))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat B) A)) C))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((Info tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node Info) Deg) TreeList2) Summary)) N) (= Deg N))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ (@ tptp.times_times_num M) N))))))
% 6.60/6.97 (assert (forall ((M tptp.num)) (= (@ (@ tptp.times_times_num M) tptp.one) M)))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num tptp.one) N) N)))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit0 tptp.one)) N) (@ tptp.bit0 N))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ (@ tptp.power_power_nat (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ (@ tptp.power_power_real (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ (@ tptp.power_power_int (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ (@ tptp.power_power_complex (@ _let_1 (@ tptp.numeral_numeral_nat M))) (@ tptp.numeral_numeral_nat N)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num M) N)))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat X) Y) (forall ((Z3 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z3) (@ (@ tptp.ord_less_nat X) Z3)) (@ (@ tptp.ord_less_eq_nat Y) Z3)))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Y) (and (@ (@ tptp.vEBT_vebt_member T) Y) (@ (@ tptp.ord_less_nat Y) X) (forall ((Z3 tptp.nat)) (=> (and (@ (@ tptp.vEBT_vebt_member T) Z3) (@ (@ tptp.ord_less_nat Z3) X)) (@ (@ tptp.ord_less_eq_nat Z3) Y)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.60/6.97 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) _let_2))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ (@ tptp.times_times_real A) C))) (@ (@ tptp.times_times_real B) D))) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real A) _let_2)) (@ (@ tptp.power_power_real D) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real B) _let_2)) (@ (@ tptp.power_power_real C) _let_2))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat L2)) (@ _let_1 (@ tptp.numeral_numeral_nat (@ (@ tptp.times_times_num K) L2)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (K tptp.num) (L2 tptp.num)) (let ((_let_1 (@ tptp.divide_divide_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int L2)) (@ _let_1 (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num K) L2)))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.60/6.97 (assert (forall ((X4 tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X4) X_1))))
% 6.60/6.97 (assert (forall ((X4 tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X4) X_1))))
% 6.60/6.97 (assert (forall ((X4 tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X4))))
% 6.60/6.97 (assert (forall ((X4 tptp.rat)) (exists ((Y5 tptp.rat)) (@ (@ tptp.ord_less_rat Y5) X4))))
% 6.60/6.97 (assert (forall ((A tptp.real) (E tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) E)) C))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (E tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) E)) C))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (E tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) E)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) E)) C)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) E)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (E tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) E)) C))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.plus_plus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.plus_plus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.plus_plus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.plus_plus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_complex C) B))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ (@ tptp.divide_divide_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_real C) B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ (@ tptp.divide_divide_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.times_times_rat C) B))))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) W)) (@ (@ tptp.times_times_complex Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) W)) (@ (@ tptp.times_times_real Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) W)) (@ (@ tptp.times_times_rat Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Y tptp.complex) (Z tptp.complex) (W tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex Z) W)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex Y) W)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real) (W tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real Z) W)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) W)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat) (W tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat Z) W)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) W)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) B)) C) (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) M)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) K)) (@ (@ tptp.divide_divide_nat N) K)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ (@ tptp.times_times_nat N) Q2)) (@ (@ tptp.divide_divide_nat (@ _let_1 N)) Q2)))))
% 6.60/6.97 (assert (forall ((M tptp.real) (N tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_real M) N)))))))
% 6.60/6.97 (assert (forall ((M tptp.rat) (N tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_rat M) N)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.60/6.97 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.times_times_int M) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) tptp.one_one_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) tptp.one_one_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) tptp.one_one_real)) (@ (@ tptp.plus_plus_real B) tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat B) tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat B) tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (@ (@ tptp.plus_plus_int B) tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (I tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat I) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) I))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N)) M)))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N))) M)))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real))) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat))) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.60/6.97 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) X))))
% 6.60/6.97 (assert (forall ((X tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat X) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) X))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ _let_1 (@ (@ tptp.minus_minus_nat A) B)) (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A3) tptp.one_one_nat)) __flatten_var_0))))
% 6.60/6.97 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A3) tptp.one_one_int)) __flatten_var_0))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_low (lambda ((X3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.modulo_modulo_nat X3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.60/6.97 (assert (= (@ tptp.some_nat tptp.maxs) (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_vebt_delete tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na)))))
% 6.60/6.97 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (= (@ tptp.neg_numeral_dbl_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (= (@ tptp.neg_numeral_dbl_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.pow K) L2)))))
% 6.60/6.97 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_real (@ (@ tptp.pow K) L2)))))
% 6.60/6.97 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_rat (@ (@ tptp.pow K) L2)))))
% 6.60/6.97 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ (@ tptp.pow K) L2)))))
% 6.60/6.97 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ (@ tptp.pow K) L2)))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (=> (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_2)) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))))))))
% 6.60/6.97 (assert (forall ((U tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_real X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.60/6.97 (assert (forall ((U tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat U) (@ tptp.numeral_numeral_nat _let_1)) (@ (@ tptp.times_times_rat X) Y)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ tptp.numeral_numeral_rat _let_1))))))))))
% 6.60/6.97 (assert (not (= (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_vebt_delete tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT)) (not (@ (@ tptp.vEBT_invar_vebt T) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (X tptp.nat)) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_V8194947554948674370ptions T) X))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.power_power_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_power (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat M) N) tptp.zero_zero_nat) (and (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.plus_plus_nat M) tptp.zero_zero_nat) M)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) B))) (= (@ (@ tptp.modulo_modulo_nat _let_1) B) _let_1))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (= (@ (@ tptp.modulo_modulo_int _let_1) B) _let_1))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) B))) (= (@ (@ tptp.modulo364778990260209775nteger _let_1) B) _let_1))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) M) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) N) tptp.zero_zero_nat) (or (= M tptp.zero_zero_nat) (= N tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.times_times_nat M) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= M N) (= K tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.times_times_nat M) K) (@ (@ tptp.times_times_nat N) K)) (or (= M N) (= K tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((X tptp.real)) (= (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real X) X))) (= X tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((R tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 R)) (@ (@ tptp.divide_divide_real A) R)))))
% 6.60/6.97 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat) N) (not (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat Maxi)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat X) Maxi))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_max_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_maxt T) (@ tptp.some_nat X))))))
% 6.60/6.97 (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 ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_12))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.times_times_complex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.times_times_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.times_times_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.times_times_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.times_times_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_nat) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (= A B))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (or (= C tptp.zero_zero_nat) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.plus_plus_real A) A)) (= A tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.plus_plus_rat A) A)) (= A tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ (@ tptp.plus_plus_int A) A)) (= A tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex B) A) A) (= B tptp.zero_zero_complex))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real B) A) A) (= B tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat B) A) A) (= B tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat B) A) A) (= B tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (= (= (@ (@ tptp.plus_plus_int B) A) A) (= B tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) A) (= B tptp.zero_zero_complex))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) A) (= B tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) A) (= B tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat A) B) A) (= B tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) A) (= B tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex B) A)) (= B tptp.zero_zero_complex))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real B) A)) (= B tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat B) A)) (= B tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat B) A)) (= B tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int B) A)) (= B tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ (@ tptp.plus_plus_complex A) B)) (= B tptp.zero_zero_complex))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.plus_plus_real A) B)) (= B tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.plus_plus_rat A) B)) (= B tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= A (@ (@ tptp.plus_plus_nat A) B)) (= B tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.plus_plus_int A) B)) (= B tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.plus_plus_nat X) Y)) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) tptp.zero_zero_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.minus_minus_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) tptp.zero_zero_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) tptp.zero_zero_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) tptp.zero_zero_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) tptp.zero_zero_int) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) A) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real A) A) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) A) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int A) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex tptp.zero_zero_complex) A) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.zero_zero_real) A) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat tptp.zero_zero_rat) A) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (= (= (@ _let_1 A) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (= A B))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (or (= C tptp.zero_zero_complex) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (or (= C tptp.zero_zero_real) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (or (= C tptp.zero_zero_rat) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.divide_divide_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) tptp.zero_zero_complex) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.divide_divide_real A) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.divide_divide_rat A) tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ _let_1 K)))))
% 6.60/6.97 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int K) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A)))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real C))) (= (@ (@ tptp.minus_minus_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat C))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_nat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int C))) (= (@ (@ tptp.minus_minus_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.minus_minus_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) A) B)))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) A) B)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) A) B)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) A) B)))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real A) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) C)) (@ (@ tptp.plus_plus_nat B) C)) (@ (@ tptp.minus_minus_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int A) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) B) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) A) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.zero_zero_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.zero_zero_int) A)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.zero_z3403309356797280102nteger) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.zero_z3403309356797280102nteger) A) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_insert _let_1) X) _let_1))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (@ _let_1 M) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat N) M)) (@ (@ tptp.ord_less_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_nat M) N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (=> (@ (@ tptp.ord_less_eq_nat I) N) (= (@ _let_1 (@ _let_1 I)) I)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) tptp.one_one_nat) (= N tptp.zero_zero_nat))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat X) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (= K tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat M) N)))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (= (@ (@ tptp.modulo_modulo_nat M) N) M))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))))
% 6.60/6.97 (assert (= (@ tptp.neg_nu7009210354673126013omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.60/6.97 (assert (= (@ tptp.neg_numeral_dbl_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.60/6.97 (assert (= (@ tptp.neg_numeral_dbl_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.60/6.97 (assert (= (@ tptp.neg_numeral_dbl_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.60/6.97 (assert (not (forall ((Maxs tptp.nat)) (not (= (@ tptp.some_nat Maxs) (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_vebt_delete tptp.summary) (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N) (and (@ (@ tptp.ord_less_eq_nat Mi) Ma) (@ (@ tptp.ord_less_nat Ma) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real B) A)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat B) A)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat B) A)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int B) A)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat A) (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real B) A)) B) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat B) A)) B) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.ord_less_real B) A))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.ord_less_rat B) A))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.ord_less_int B) A))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex C) B)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real C) B)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat C) B)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int C) B)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex)) (= (= (@ (@ tptp.times_times_complex C) A) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real)) (= (= (@ (@ tptp.times_times_real C) A) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.times_times_rat C) A) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int)) (= (= (@ (@ tptp.times_times_int C) A) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (B tptp.complex)) (= (= C (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (= B tptp.one_one_complex)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real)) (= (= C (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (= B tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (= C (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (= B tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int)) (= (= C (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (= B tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (C tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) C) C) (or (= C tptp.zero_zero_complex) (= A tptp.one_one_complex)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real)) (= (= (@ (@ tptp.times_times_real A) C) C) (or (= C tptp.zero_zero_real) (= A tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) C) C) (or (= C tptp.zero_zero_rat) (= A tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int)) (= (= (@ (@ tptp.times_times_int A) C) C) (or (= C tptp.zero_zero_int) (= A tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (let ((_let_2 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_complex))) (and (=> _let_3 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex A) B)))))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (let ((_let_2 (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_real))) (and (=> _let_3 (= _let_2 tptp.zero_zero_real)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real A) B)))))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (let ((_let_2 (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_rat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat A) B)))))))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_real A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_rat A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) A) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) A) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) A) B))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex C) A)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real C) A)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat C) A)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) B)) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) B)) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) B)) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) B)) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) B)) B) A))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex C) B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real C) B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat C) B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_nat))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat A) B)))))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 A)) (@ _let_1 B)))) (let ((_let_3 (= C tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int A) B)))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat A) B)) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) B) A))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.60/6.97 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) tptp.one_one_real) tptp.zero_zero_real))
% 6.60/6.97 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.60/6.97 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) tptp.one_one_int) tptp.zero_zero_int))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat A) A) tptp.one_one_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int A) A) tptp.one_one_int))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= tptp.one_one_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (and (not (= B tptp.zero_zero_complex)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real A) B)) (and (not (= B tptp.zero_zero_real)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat A) B)) (and (not (= B tptp.zero_zero_rat)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) A) tptp.one_one_complex))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) A) tptp.one_one_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) A) tptp.one_one_rat))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ (@ tptp.divide1717551699836669952omplex A) A))) (let ((_let_2 (= A tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 tptp.zero_zero_complex)) (=> (not _let_2) (= _let_1 tptp.one_one_complex)))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real A) A))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 tptp.zero_zero_real)) (=> (not _let_2) (= _let_1 tptp.one_one_real)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.divide_divide_rat A) A))) (let ((_let_2 (= A tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 tptp.zero_zero_rat)) (=> (not _let_2) (= _let_1 tptp.one_one_rat)))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (= (= (@ (@ tptp.divide_divide_real B) A) tptp.one_one_real) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat B) A) tptp.one_one_rat) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (= (= tptp.one_one_real (@ (@ tptp.divide_divide_real B) A)) (and (not (= A tptp.zero_zero_real)) (= A B)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= tptp.one_one_rat (@ (@ tptp.divide_divide_rat B) A)) (and (not (= A tptp.zero_zero_rat)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.divide_divide_real tptp.one_one_real) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (= A tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (= A tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_complex B) C)) (@ (@ tptp.minus_minus_complex (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (V tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex V))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex A) B)) _let_1) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) _let_1)) (@ (@ tptp.times_times_complex B) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real V))) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) _let_1) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real B) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat V))) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) _let_1) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) _let_1)) (@ (@ tptp.times_times_rat B) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int V))) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) _let_1)) (@ (@ tptp.times_times_int B) _let_1))))))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat K)) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat) (and (= A tptp.zero_zero_rat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (= (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real) (and (= A tptp.zero_zero_real) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (= (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int) (and (= A tptp.zero_zero_int) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex) (and (= A tptp.zero_zero_complex) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) B) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) B) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat B) A)) B) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int B) A)) B) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) B) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat A) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) tptp.one_one_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) B)) B) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) B)) B) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) C)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) B)) A)) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger B) C))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) B))) B) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat M) N)) N) M))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) M)) N) M))))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 K)))))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit0 K)))))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 K)))))
% 6.60/6.97 (assert (forall ((K tptp.num)) (= (@ tptp.neg_numeral_dbl_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) Deg) (=> (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (or (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) (@ (@ tptp.vEBT_VEBT_high X) _let_1))) (@ (@ tptp.vEBT_VEBT_low X) _let_1)) (= X Mi) (= X Ma)))))))
% 6.60/6.97 (assert (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat tptp.mi) tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.deg))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (and (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (or (= X Mi) (= X Ma) (and (@ (@ tptp.ord_less_nat X) Ma) (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))))))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_real B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_rat B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_real A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) C)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) C)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) B)) A)) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) B)) A)) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat B) C))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int B) C))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat C) B))) B) (@ (@ tptp.plus_plus_nat C) (@ (@ tptp.divide_divide_nat A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) B))) B) (@ (@ tptp.plus_plus_int C) (@ (@ tptp.divide_divide_int A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex A) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real A) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat A) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) B)))))
% 6.60/6.97 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex B) (@ (@ tptp.times_times_complex A) B)) (@ (@ tptp.divide1717551699836669952omplex tptp.one_one_complex) A)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real B) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) A)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat B) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (@ (@ tptp.ord_less_eq_real A) B))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (@ (@ tptp.ord_less_eq_rat A) B))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.ord_less_eq_nat A) B))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.ord_less_eq_int A) B))))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_lesseq (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat N) M)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.60/6.97 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.60/6.97 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.60/6.97 (assert (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.60/6.97 (assert (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat M) M)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.60/6.97 (assert (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (= X Y))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (= X Y))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_nat X) _let_1) (@ (@ tptp.power_power_nat Y) _let_1)) (= X Y))))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (= X Y))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_real B) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_rat B) tptp.one_one_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat B) tptp.one_one_nat) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int B) tptp.one_one_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat N) M)))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (= A tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (= _let_1 tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.power_power_real X) N3))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y3) (= X3 Y3)))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) N3)) Y))))))
% 6.60/6.97 (assert (forall ((S2 tptp.set_real)) (=> (exists ((X4 tptp.real)) (@ (@ tptp.member_real X4) S2)) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (@ (@ tptp.ord_less_eq_real X6) Z4)))) (exists ((Y5 tptp.real)) (and (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) S2) (@ (@ tptp.ord_less_eq_real X4) Y5))) (forall ((Z4 tptp.real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (@ (@ tptp.ord_less_eq_real X6) Z4))) (@ (@ tptp.ord_less_eq_real Y5) Z4)))))))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) A))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat A) B)) A))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int A) B)) A))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (D tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) D) tptp.zero_zero_nat) (exists ((Q3 tptp.nat)) (= M (@ (@ tptp.times_times_nat D) Q3))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.minus_minus_nat M) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.minus_minus_nat N) M) tptp.zero_zero_nat) (= M N)))))
% 6.60/6.97 (assert (forall ((X tptp.complex)) (= (= tptp.zero_zero_complex X) (= X tptp.zero_zero_complex))))
% 6.60/6.97 (assert (forall ((X tptp.real)) (= (= tptp.zero_zero_real X) (= X tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((X tptp.rat)) (= (= tptp.zero_zero_rat X) (= X tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((X tptp.nat)) (= (= tptp.zero_zero_nat X) (= X tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((X tptp.int)) (= (= tptp.zero_zero_int X) (= X tptp.zero_zero_int))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 C)) B) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 C)) B) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 C)) B) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.complex) (Z2 tptp.complex)) (= Y4 Z2)) (lambda ((A3 tptp.complex) (B2 tptp.complex)) (= (@ (@ tptp.minus_minus_complex A3) B2) tptp.zero_zero_complex))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.real) (Z2 tptp.real)) (= Y4 Z2)) (lambda ((A3 tptp.real) (B2 tptp.real)) (= (@ (@ tptp.minus_minus_real A3) B2) tptp.zero_zero_real))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.minus_minus_rat A3) B2) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.minus_minus_int A3) B2) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (= A B) (= C D)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (= A B) (= C D)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (= A B) (= C D)))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.minus_minus_nat M) tptp.zero_zero_nat) M)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) B)) B))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) B)) B))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) B))))
% 6.60/6.97 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_nat M3) N2)) M3) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M3) N2)) N2)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.modulo_modulo_nat M) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) A) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) A) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) A) (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A3) B2)) tptp.zero_zero_real))))
% 6.60/6.97 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A3) B2)) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A3) B2)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) M))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.plus_plus_nat N) M)) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((X6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X6) (= (@ (@ tptp.power_power_real X6) N) A) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2) (= (@ (@ tptp.power_power_real Y2) N) A)) (= Y2 X6)))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (= (@ (@ tptp.power_power_real R2) N) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.modulo364778990260209775nteger A) B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.modulo_modulo_nat A) B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.modulo_modulo_int A) B) A)))))
% 6.60/6.97 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat tptp.one)) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int tptp.one)) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger tptp.one)) tptp.zero_z3403309356797280102nteger)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.60/6.97 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.60/6.97 (assert (= tptp.modulo_modulo_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.minus_minus_nat M3) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M3) N2)) N2)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) N))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (not (or (and (@ (@ tptp.ord_less_nat A) B) (not (@ P tptp.zero_zero_nat))) (exists ((D2 tptp.nat)) (and (= A (@ (@ tptp.plus_plus_nat B) D2)) (not (@ P D2)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ P (@ (@ tptp.minus_minus_nat A) B)) (and (=> (@ (@ tptp.ord_less_nat A) B) (@ P tptp.zero_zero_nat)) (forall ((D2 tptp.nat)) (=> (= A (@ (@ tptp.plus_plus_nat B) D2)) (@ P D2)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_rat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_nat)) (=> (not _let_2) (= _let_1 tptp.zero_zero_nat)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real tptp.zero_zero_real) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int tptp.zero_zero_int) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_int)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.one_one_complex)) (=> (not _let_2) (= _let_1 tptp.zero_zero_complex)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) N) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) N) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) N) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N) tptp.zero_zero_complex))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) C))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.modulo_modulo_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (A4 tptp.nat) (B tptp.nat) (B4 tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) C) (@ (@ tptp.modulo_modulo_nat A4) C)) (=> (= (@ (@ tptp.modulo_modulo_nat B) C) (@ (@ tptp.modulo_modulo_nat B4) C)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (A4 tptp.int) (B tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int A4) C)) (=> (= (@ (@ tptp.modulo_modulo_int B) C) (@ (@ tptp.modulo_modulo_int B4) C)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (A4 tptp.code_integer) (B tptp.code_integer) (B4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger A4) C)) (=> (= (@ (@ tptp.modulo364778990260209775nteger B) C) (@ (@ tptp.modulo364778990260209775nteger B4) C)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A4) B4)) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) B)) C) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) B)) C) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) B)) C) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat A))) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C) (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C) (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger A))) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C) (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat (@ (@ tptp.modulo_modulo_nat A) B)) N)) B) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.power_power_nat A) N)) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int (@ (@ tptp.modulo_modulo_int A) B)) N)) B) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.power_power_int A) N)) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) N)) B) (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real D) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat D) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int D) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real C) D)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat C) D)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int C) D)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (D tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real D) C) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (D tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat D) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int D) C) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (= (@ (@ tptp.minus_minus_real A) B) (@ (@ tptp.minus_minus_real C) D)) (= (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real C) D)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (= (@ (@ tptp.minus_minus_rat A) B) (@ (@ tptp.minus_minus_rat C) D)) (= (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat C) D)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.minus_minus_int A) B) (@ (@ tptp.minus_minus_int C) D)) (= (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int C) D)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real C))) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int C))) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) C)) (@ (@ tptp.minus_minus_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) C)) (@ (@ tptp.minus_minus_int B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) C)) A) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real B) A)) (@ (@ tptp.times_times_real C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) C)) A) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat B) A)) (@ (@ tptp.times_times_rat C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat B) C)) A) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) C)) A) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) C)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) (@ _let_1 C))))))
% 6.60/6.97 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_real A2) B) (@ _let_1 (@ (@ tptp.minus_minus_real A) B)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_rat A2) B) (@ _let_1 (@ (@ tptp.minus_minus_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (=> (= A2 (@ _let_1 A)) (= (@ (@ tptp.minus_minus_int A2) B) (@ _let_1 (@ (@ tptp.minus_minus_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.minus_minus_real A) B) C) (= A (@ (@ tptp.plus_plus_real C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (= (@ (@ tptp.minus_minus_rat A) B) C) (= A (@ (@ tptp.plus_plus_rat C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.minus_minus_int A) B) C) (= A (@ (@ tptp.plus_plus_int C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (= A (@ (@ tptp.minus_minus_real C) B)) (= (@ (@ tptp.plus_plus_real A) B) C))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (= A (@ (@ tptp.minus_minus_rat C) B)) (= (@ (@ tptp.plus_plus_rat A) B) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= A (@ (@ tptp.minus_minus_int C) B)) (= (@ (@ tptp.plus_plus_int A) B) C))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real A))) (= (@ _let_1 (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat A))) (= (@ _let_1 (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 B)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ (@ tptp.minus_minus_real B) C)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.minus_minus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ (@ tptp.minus_minus_int B) C)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ (@ tptp.minus_minus_real (@ _let_1 C)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ (@ tptp.minus_minus_rat (@ _let_1 C)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ (@ tptp.minus_minus_int (@ _let_1 C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (= (@ (@ tptp.plus_plus_real C) B) A) (= C (@ (@ tptp.minus_minus_real A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat C) B) A) (= C (@ (@ tptp.minus_minus_rat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat C) B) A) (= C (@ (@ tptp.minus_minus_nat A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (= (@ (@ tptp.plus_plus_int C) B) A) (= C (@ (@ tptp.minus_minus_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (= (@ (@ tptp.minus_minus_real (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat A))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (= (@ (@ tptp.minus_minus_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)) (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real C) D)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) C)) (@ (@ tptp.plus_plus_rat B) D)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat C) D)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) C)) (@ (@ tptp.plus_plus_int B) D)) (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int C) D)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) N)) M)))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) B)) C) (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) C)) (@ (@ tptp.divide1717551699836669952omplex B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (let ((_let_2 (@ tptp.ord_less_nat M))) (=> (@ _let_2 N) (=> (@ _let_2 L2) (@ (@ tptp.ord_less_nat (@ _let_1 N)) (@ _let_1 M))))))))
% 6.60/6.97 (assert (forall ((J tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat J) K) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat J) N)) K))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (= (@ (@ tptp.minus_minus_nat M) K) (@ (@ tptp.minus_minus_nat N) K)) (= M N)))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (let ((_let_2 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_2 M) (=> (@ _let_2 N) (= (@ (@ tptp.minus_minus_nat (@ _let_1 K)) (@ (@ tptp.minus_minus_nat N) K)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) L2)) (@ (@ tptp.minus_minus_nat N) L2)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) M)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (let ((_let_2 (@ tptp.minus_minus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) C) (=> (@ _let_1 C) (= (@ (@ tptp.ord_less_eq_nat (@ _let_2 A)) (@ _let_2 B)) (@ _let_1 A))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (L2 tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat L2))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.minus_minus_nat M) N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) M)) N) M)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) N) M)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M) N)) K) (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat M) K)) (@ (@ tptp.times_times_nat N) K)))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X)))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (not (= N tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((D1 tptp.real) (D22 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real E2))) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.60/6.97 (assert (forall ((D1 tptp.rat) (D22 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 D1) (=> (@ _let_1 D22) (exists ((E2 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat E2))) (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ _let_1 D1) (@ _let_1 D22)))))))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.numera6690914467698888265omplex N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.numeral_numeral_real N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.numeral_numeral_rat N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_nat (@ tptp.numeral_numeral_nat N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.numeral_numeral_int N)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat tptp.one))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int tptp.one))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))
% 6.60/6.97 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger tptp.one))) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex)) (and (not (= A tptp.zero_zero_complex)) (not (= B tptp.zero_zero_complex))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real)) (and (not (= A tptp.zero_zero_real)) (not (= B tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat)) (and (not (= A tptp.zero_zero_rat)) (not (= B tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat)) (and (not (= A tptp.zero_zero_nat)) (not (= B tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int)) (and (not (= A tptp.zero_zero_int)) (not (= B tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex) (or (= A tptp.zero_zero_complex) (= B tptp.zero_zero_complex)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real) (or (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat) (or (= A tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat) (or (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int) (or (= A tptp.zero_zero_int) (= B tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (not (= A tptp.zero_zero_complex)) (=> (not (= B tptp.zero_zero_complex)) (not (= (@ (@ tptp.times_times_complex A) B) tptp.zero_zero_complex))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A tptp.zero_zero_real)) (=> (not (= B tptp.zero_zero_real)) (not (= (@ (@ tptp.times_times_real A) B) tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A tptp.zero_zero_rat)) (=> (not (= B tptp.zero_zero_rat)) (not (= (@ (@ tptp.times_times_rat A) B) tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= B tptp.zero_zero_nat)) (not (= (@ (@ tptp.times_times_nat A) B) tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= B tptp.zero_zero_int)) (not (= (@ (@ tptp.times_times_int A) B) tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (not (= C tptp.zero_zero_real)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (= (@ _let_1 A) (@ _let_1 B)) (= A B))))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.times_times_complex A) C) (@ (@ tptp.times_times_complex B) C)) (= A B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.times_times_real A) C) (@ (@ tptp.times_times_real B) C)) (= A B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.times_times_rat A) C) (@ (@ tptp.times_times_rat B) C)) (= A B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (= (= (@ (@ tptp.times_times_nat A) C) (@ (@ tptp.times_times_nat B) C)) (= A B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (not (= C tptp.zero_zero_int)) (= (= (@ (@ tptp.times_times_int A) C) (@ (@ tptp.times_times_int B) C)) (= A B)))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex tptp.zero_zero_complex) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real tptp.zero_zero_real) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat tptp.zero_zero_rat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) A) A)))
% 6.60/6.97 (assert (not (= tptp.zero_zero_complex tptp.one_one_complex)))
% 6.60/6.97 (assert (not (= tptp.zero_zero_real tptp.one_one_real)))
% 6.60/6.97 (assert (not (= tptp.zero_zero_rat tptp.one_one_rat)))
% 6.60/6.97 (assert (not (= tptp.zero_zero_nat tptp.one_one_nat)))
% 6.60/6.97 (assert (not (= tptp.zero_zero_int tptp.one_one_int)))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_rat)) (not (= (@ (@ tptp.power_power_rat A) N) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (not (= (@ (@ tptp.power_power_nat A) N) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (not (= A tptp.zero_zero_real)) (not (= (@ (@ tptp.power_power_real A) N) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (not (= A tptp.zero_zero_int)) (not (= (@ (@ tptp.power_power_int A) N) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (=> (not (= A tptp.zero_zero_complex)) (not (= (@ (@ tptp.power_power_complex A) N) tptp.zero_zero_complex)))))
% 6.60/6.97 (assert (= (@ tptp.size_size_num tptp.one) tptp.zero_zero_nat))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)) (= N tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_nat N) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (= N tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (not (@ P N3)) (exists ((M2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M2) N3) (not (@ P M2))))))) (@ P N)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) N)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (= A tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat tptp.zero_zero_nat) N) N)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.plus_plus_nat M) N) M) (= N tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (= (@ _let_1 M) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (= M N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.times_times_nat tptp.zero_zero_nat) N) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (exists ((Q1 tptp.nat) (Q22 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (= (@ (@ tptp.plus_plus_nat X) (@ _let_1 Q1)) (@ (@ tptp.plus_plus_nat Y) (@ _let_1 Q22))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z))) tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z))) tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C))) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) B)) C))) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((N tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat N) tptp.zero_z5237406670263579293d_enat))))
% 6.60/6.97 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat tptp.zero_z5237406670263579293d_enat))) (= (@ _let_1 (@ (@ tptp.times_7803423173614009249d_enat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (not (= A tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 M)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (not (= A tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_real (@ _let_1 M)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (not (= A tptp.zero_zero_rat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_rat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.modulo_modulo_nat M) N)) (and (=> _let_1 (@ P M)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I5)) J3)) (@ P J3))))))))))
% 6.60/6.97 (assert (forall ((N tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.zero_z5237406670263579293d_enat) N)))
% 6.60/6.97 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat N) tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) _let_2) (= (@ (@ tptp.minus_8373710615458151222nteger _let_2) B) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) _let_2) (= (@ (@ tptp.minus_minus_nat _let_2) B) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) _let_2) (= (@ (@ tptp.minus_minus_int _let_2) B) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (= A B))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (= A B))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (= A B))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (= (@ (@ tptp.power_power_real A) N) (@ (@ tptp.power_power_real B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (= (@ (@ tptp.power_power_rat A) N) (@ (@ tptp.power_power_rat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (= (@ (@ tptp.power_power_nat A) N) (@ (@ tptp.power_power_nat B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (= (@ (@ tptp.power_power_int A) N) (@ (@ tptp.power_power_int B) N)) (=> (@ _let_1 A) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))))
% 6.60/6.97 (assert (= tptp.times_times_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat N2) (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N2))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_2 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) B) (= _let_2 (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1))))))
% 6.60/6.97 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1))))))
% 6.60/6.97 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1))))))
% 6.60/6.97 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.60/6.97 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.60/6.97 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 6.60/6.97 (assert (forall ((U tptp.real) (V tptp.real) (R tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real U) V) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) R) (=> (@ (@ tptp.ord_less_eq_real R) S) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real U) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real R) (@ (@ tptp.minus_minus_real V) U))) S))) V))))))
% 6.60/6.97 (assert (forall ((U tptp.rat) (V tptp.rat) (R tptp.rat) (S tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat U) V) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) R) (=> (@ (@ tptp.ord_less_eq_rat R) S) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat U) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat R) (@ (@ tptp.minus_minus_rat V) U))) S))) V))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (not (forall ((D3 tptp.int)) (not (= B (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int C) D3)))))))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (not (forall ((D3 tptp.code_integer)) (not (= B (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.times_3573771949741848930nteger C) D3)))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) C)) (@ (@ tptp.modulo_modulo_nat B) C))) C)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) C)) (@ (@ tptp.modulo_modulo_int B) C))) C)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) C)) (@ (@ tptp.modulo364778990260209775nteger B) C))) C)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_nat)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 N) tptp.zero_zero_int)) (not (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (let ((_let_2 (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_nat)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ _let_1 M)) (@ _let_1 N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat N) M))) (=> (not (= A tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M))))))))))))
% 6.60/6.97 (assert (= tptp.power_power_complex (lambda ((P2 tptp.complex) (M3 tptp.nat)) (@ (@ (@ tptp.if_complex (= M3 tptp.zero_zero_nat)) tptp.one_one_complex) (@ (@ tptp.times_times_complex P2) (@ (@ tptp.power_power_complex P2) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.60/6.97 (assert (= tptp.power_power_real (lambda ((P2 tptp.real) (M3 tptp.nat)) (@ (@ (@ tptp.if_real (= M3 tptp.zero_zero_nat)) tptp.one_one_real) (@ (@ tptp.times_times_real P2) (@ (@ tptp.power_power_real P2) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.60/6.97 (assert (= tptp.power_power_rat (lambda ((P2 tptp.rat) (M3 tptp.nat)) (@ (@ (@ tptp.if_rat (= M3 tptp.zero_zero_nat)) tptp.one_one_rat) (@ (@ tptp.times_times_rat P2) (@ (@ tptp.power_power_rat P2) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.60/6.97 (assert (= tptp.power_power_nat (lambda ((P2 tptp.nat) (M3 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) tptp.one_one_nat) (@ (@ tptp.times_times_nat P2) (@ (@ tptp.power_power_nat P2) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.60/6.97 (assert (= tptp.power_power_int (lambda ((P2 tptp.int) (M3 tptp.nat)) (@ (@ (@ tptp.if_int (= M3 tptp.zero_zero_nat)) tptp.one_one_int) (@ (@ tptp.times_times_int P2) (@ (@ tptp.power_power_int P2) (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) A) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_less_eq_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ _let_1 B)) A) (@ _let_1 (@ (@ tptp.minus_minus_nat B) A)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat B) C)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat B) A)) C)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.minus_minus_nat C) (@ (@ tptp.minus_minus_nat B) A)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat C) A)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.minus_minus_nat B) A)) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat A) B))) (=> _let_1 (=> _let_1 (= (= (@ (@ tptp.minus_minus_nat B) A) C) (= B (@ (@ tptp.plus_plus_nat C) A))))))))
% 6.60/6.97 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N) (@ (@ tptp.ord_less_eq_real I) (@ (@ tptp.minus_minus_real N) K)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N) (@ (@ tptp.ord_less_eq_rat I) (@ (@ tptp.minus_minus_rat N) K)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N) (@ (@ tptp.ord_less_eq_nat I) (@ (@ tptp.minus_minus_nat N) K)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N) (@ (@ tptp.ord_less_eq_int I) (@ (@ tptp.minus_minus_int N) K)))))
% 6.60/6.97 (assert (forall ((I tptp.real) (K tptp.real) (N tptp.real) (J tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_eq_real N) (@ (@ tptp.plus_plus_real J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real N) K)) J)))))))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (K tptp.rat) (N tptp.rat) (J tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_rat N) (@ (@ tptp.plus_plus_rat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat N) K)) J)))))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (K tptp.nat) (N tptp.nat) (J tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.plus_plus_nat J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat N) K)) J)))))))))
% 6.60/6.97 (assert (forall ((I tptp.int) (K tptp.int) (N tptp.int) (J tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int N) (@ (@ tptp.plus_plus_int J) K)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int I) K)) N))) (=> _let_2 (=> _let_1 (=> _let_2 (=> _let_1 (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int N) K)) J)))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_complex (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_rat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_nat (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_int (@ _let_1 (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.minus_minus_real C) B)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.minus_minus_rat C) B)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ (@ tptp.minus_minus_int C) B)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) C))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) B)) C) (@ (@ tptp.ord_less_real A) (@ (@ tptp.plus_plus_real C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) B)) C) (@ (@ tptp.ord_less_rat A) (@ (@ tptp.plus_plus_rat C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.ord_less_int A) (@ (@ tptp.plus_plus_int C) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.ord_less_real A) B)) (= (@ (@ tptp.plus_plus_real B) (@ (@ tptp.minus_minus_real A) B)) A))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat A) B)) (= (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.minus_minus_rat A) B)) A))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat A) B)) (= (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.minus_minus_nat A) B)) A))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.ord_less_int A) B)) (= (@ (@ tptp.plus_plus_int B) (@ (@ tptp.minus_minus_int A) B)) A))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 Y)) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_real Y) B))) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) A)) B))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 Y)) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_rat Y) B))) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) A)) B))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 Y)) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_int Y) B))) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) A)) B))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real X) Y)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) Y)) (@ (@ tptp.minus_minus_rat X) Y)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) Y)) (@ (@ tptp.minus_minus_int X) Y)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= C (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= C (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= C (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C) D))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C) D))))
% 6.60/6.97 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C) D))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (not (forall ((S3 tptp.nat)) (not (= M (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (not (forall ((S3 tptp.nat)) (not (= N (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat Q2) S3))))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat X) N) (@ (@ tptp.modulo_modulo_nat Y) N)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (exists ((Q3 tptp.nat)) (= X (@ (@ tptp.plus_plus_nat Y) (@ (@ tptp.times_times_nat N) Q3))))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (@ _let_1 (@ (@ tptp.divide_divide_nat A) B)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 (@ (@ tptp.divide_divide_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat A) C)) (@ (@ tptp.minus_minus_nat B) C))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) K)) (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.ord_less_nat M) N)))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat M) N)) M))))
% 6.60/6.97 (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))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (= tptp.neg_numeral_dbl_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real X3) X3))))
% 6.60/6.97 (assert (= tptp.neg_numeral_dbl_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat X3) X3))))
% 6.60/6.97 (assert (= tptp.neg_numeral_dbl_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) X3))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat)) (and (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (@ _let_1 (@ (@ tptp.times_times_rat A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (@ _let_1 (@ (@ tptp.times_times_int A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) A))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) A))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) A))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.numeral_numeral_real N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_rat N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int N))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat N)) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat))))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (= (@ (@ tptp.plus_plus_real X) Y) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (= (= (@ (@ tptp.plus_plus_rat X) Y) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat Y) tptp.zero_zero_nat) (= (= (@ (@ tptp.plus_plus_nat X) Y) tptp.zero_zero_nat) (and (= X tptp.zero_zero_nat) (= Y tptp.zero_zero_nat)))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int) (= (= (@ (@ tptp.plus_plus_int X) Y) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.one_one_real))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.one_one_int))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.times_times_int A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) A)) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) A)) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) A)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real B) A)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat B) A)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat B) A)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int B) A)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.times_times_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.zero_zero_int)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int A) B)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.times_times_real B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.times_times_rat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 (@ (@ tptp.times_times_nat B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.times_times_int B) A)) (=> (@ _let_1 A) (@ _let_1 B))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real B) A))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat B) A))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int B) A))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_rat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_int A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (and (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (and (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (and (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (forall ((C2 tptp.nat)) (=> (= B (@ (@ tptp.plus_plus_nat A) C2)) (= C2 tptp.zero_zero_nat)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat X) Y)) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X) Y)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int X) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Y) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.one_one_real))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) tptp.one_one_nat))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.one_one_int))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) tptp.zero_zero_real)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_nat tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.divide_divide_real A) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.divide_divide_rat A) C))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) B)) tptp.zero_zero_real) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) B)) tptp.zero_zero_rat) (or (and (@ _let_1 A) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)) (not (= C tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)) (not (= C tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) B)) (or (and (@ _let_1 A) (@ _let_1 B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) N))))))
% 6.60/6.97 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex X) Y) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (= (@ (@ tptp.times_times_complex X) Z) (@ (@ tptp.times_times_complex W) Y)))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real X) Y) (@ (@ tptp.divide_divide_real W) Z)) (= (@ (@ tptp.times_times_real X) Z) (@ (@ tptp.times_times_real W) Y)))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat X) Y) (@ (@ tptp.divide_divide_rat W) Z)) (= (@ (@ tptp.times_times_rat X) Z) (@ (@ tptp.times_times_rat W) Y)))))))
% 6.60/6.97 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (and (=> (not _let_1) (= B (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) B)) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) B)) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) B)) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= B (@ (@ tptp.times_times_complex A) C)) (= (@ (@ tptp.divide1717551699836669952omplex B) C) A)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= B (@ (@ tptp.times_times_real A) C)) (= (@ (@ tptp.divide_divide_real B) C) A)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= B (@ (@ tptp.times_times_rat A) C)) (= (@ (@ tptp.divide_divide_rat B) C) A)))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (=> (= (@ (@ tptp.times_times_complex A) C) B) (= A (@ (@ tptp.divide1717551699836669952omplex B) C))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (=> (= (@ (@ tptp.times_times_real A) C) B) (= A (@ (@ tptp.divide_divide_real B) C))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (=> (= (@ (@ tptp.times_times_rat A) C) B) (= A (@ (@ tptp.divide_divide_rat B) C))))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (B tptp.complex) (A tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) A) (= B (@ (@ tptp.times_times_complex A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real B) C) A) (= B (@ (@ tptp.times_times_real A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat B) C) A) (= B (@ (@ tptp.times_times_rat A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (=> (not (= C tptp.zero_zero_complex)) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) C)) (= (@ (@ tptp.times_times_complex A) C) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (not (= C tptp.zero_zero_real)) (= (= A (@ (@ tptp.divide_divide_real B) C)) (= (@ (@ tptp.times_times_real A) C) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (not (= C tptp.zero_zero_rat)) (= (= A (@ (@ tptp.divide_divide_rat B) C)) (= (@ (@ tptp.times_times_rat A) C) B)))))
% 6.60/6.97 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.one_one_complex) (= A B)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.one_one_real) (= A B)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.one_one_rat) (= A B)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) tptp.zero_zero_nat) tptp.one_one_rat)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) tptp.zero_zero_nat) tptp.one_one_real)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) tptp.zero_zero_nat) tptp.one_one_int)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) tptp.zero_zero_nat) tptp.one_one_complex)))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.modulo_modulo_nat A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) B) (= (@ _let_2 (@ _let_1 _let_3)) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat K3) N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) K3) (not (@ P I2)))) (@ P K3)))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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)))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ (@ tptp.divide_divide_nat M) N) tptp.zero_zero_nat) (or (@ (@ tptp.ord_less_nat M) N) (= N tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) I) (=> (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (= (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.modulo_modulo_nat A) _let_1)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.modulo_modulo_int A) _let_1)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) tptp.zero_z3403309356797280102nteger)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (= M (@ (@ tptp.times_times_nat M) N)) (or (= N tptp.one_one_nat) (= M tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (= (@ (@ tptp.pow X) tptp.one) X)))
% 6.60/6.97 (assert (forall ((M tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) M) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_p5714425477246183910nteger _let_2) M))))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_nat _let_2) M))))))))))
% 6.60/6.97 (assert (forall ((M tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int X))) (let ((_let_2 (@ _let_1 M))) (let ((_let_3 (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) M)))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (or (= _let_3 _let_2) (= _let_3 (@ (@ tptp.plus_plus_int _let_2) M))))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.times_times_nat A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.times_times_int A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.times_3573771949741848930nteger A) _let_2)) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))) _let_2)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (= (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.divide_divide_nat B) C))) (@ (@ tptp.divide_divide_nat (@ _let_1 (@ (@ tptp.modulo_modulo_nat B) C))) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ (@ tptp.divide_divide_int (@ _let_1 B)) C) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.divide_divide_int B) C))) (@ (@ tptp.divide_divide_int (@ _let_1 (@ (@ tptp.modulo_modulo_int B) C))) C))))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C))) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger B) C))) C))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) A)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) A)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) A)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) B)) (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) A)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)) A)))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)) A)))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) B)) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) B)) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) B)) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat A) B))) (@ (@ tptp.modulo_modulo_nat A) B))) C) (@ (@ tptp.plus_plus_nat A) C))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int A) B))) (@ (@ tptp.modulo_modulo_int A) B))) C) (@ (@ tptp.plus_plus_int A) C))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger A) B))) (@ (@ tptp.modulo364778990260209775nteger A) B))) C) (@ (@ tptp.plus_p5714425477246183910nteger A) C))))
% 6.60/6.97 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.60/6.97 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.60/6.97 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real C) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat C) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int C) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int B) A)) E)) D)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (E tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) E)) C)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real B) E)) D)) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real A) B)) E)) C)) D))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (E tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) E)) C)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat B) E)) D)) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat A) B)) E)) C)) D))))
% 6.60/6.97 (assert (forall ((A tptp.int) (E tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) E)) C)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) E)) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int A) B)) E)) C)) D))))
% 6.60/6.97 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex X) X)) tptp.one_one_complex) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex X) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))
% 6.60/6.97 (assert (forall ((X tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real X) X)) tptp.one_one_real) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat X) X)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat X) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int X) X)) tptp.one_one_int) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) (@ (@ tptp.minus_minus_int X) tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (let ((_let_2 (@ tptp.times_times_nat N))) (= (@ _let_1 (@ _let_2 Q2)) (@ (@ tptp.plus_plus_nat (@ _let_2 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat M) N)) Q2))) (@ _let_1 N)))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M) N)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.60/6.97 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.60/6.97 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) D) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) D) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat C) D) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_int C) D) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ _let_1 A) (=> (@ _let_1 C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) C)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) A)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) D) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) D) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_nat C) D) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_int C) D) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (=> (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat C))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) C) (@ (@ tptp.ord_less_nat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (@ (@ tptp.ord_less_int (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A)))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A)))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 A)) (@ _let_1 B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) A)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real B))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat B))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int A) C)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ (@ tptp.ord_less_real B) (@ (@ tptp.plus_plus_real A) C))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.plus_plus_rat A) C))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_nat B) (@ (@ tptp.plus_plus_nat A) C))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_int B) (@ (@ tptp.plus_plus_int A) C))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_real A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real A) B)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat A) B)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) tptp.zero_zero_nat) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat A) B)) tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real Y) E2)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat Y) E2)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (@ _let_1 (@ (@ tptp.divide_divide_rat X) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real Y) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat Y) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) C)) (@ (@ tptp.divide_divide_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) C)) (@ (@ tptp.divide_divide_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W)))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ _let_1 W) (=> (@ (@ tptp.ord_less_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W)))))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (X tptp.real) (W tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) W) (=> (@ (@ tptp.ord_less_eq_real W) Z) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Z)) (@ (@ tptp.divide_divide_real Y) W))))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (X tptp.rat) (W tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) W) (=> (@ (@ tptp.ord_less_eq_rat W) Z) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Z)) (@ (@ tptp.divide_divide_rat Y) W))))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) A)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) A)))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) C)) A)))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (=> (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) B)) tptp.one_one_real))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (=> (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) B)) tptp.one_one_rat))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Y)) X)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Y)) X)))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Y)) X)))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Y) X)) X)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Y) X)) X)))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int Y) X)) X)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) X)) (@ (@ tptp.times_times_rat Y) Y))) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int X) X)) (@ (@ tptp.times_times_int Y) Y))) tptp.zero_zero_int))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) tptp.one_one_real)))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) tptp.one_one_rat)))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.one_one_nat)))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) tptp.one_one_int)))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_4 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_2) (@ _let_1 A))))))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_2 C) (=> (@ _let_2 (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B)))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_real B) A)) (and (@ _let_1 tptp.zero_zero_real) (@ _let_1 B)) (= A tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_rat B) A)) (and (@ _let_1 tptp.zero_zero_rat) (@ _let_1 B)) (= A tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ _let_1 B)) (and (@ _let_1 tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) A)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.60/6.97 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.60/6.97 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.60/6.97 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Z)) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Z)) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Z)) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.divide1717551699836669952omplex Y) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real Y) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat Y) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real Z) (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat Z) (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.60/6.97 (assert (forall ((Y tptp.complex) (X tptp.complex) (Z tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) Z) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex X) (@ (@ tptp.times_times_complex Z) Y))) Y)))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) Z) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real Z) Y))) Y)))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) Z) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.times_times_rat Z) Y))) Y)))))
% 6.60/6.97 (assert (forall ((Y tptp.complex) (Z tptp.complex) (X tptp.complex) (W tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide1717551699836669952omplex W) Z)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex X) Z)) (@ (@ tptp.times_times_complex W) Y))) (@ (@ tptp.times_times_complex Y) Z)))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real) (W tptp.real)) (=> (not (= Y tptp.zero_zero_real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real W) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real W) Y))) (@ (@ tptp.times_times_real Y) Z)))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat) (W tptp.rat)) (=> (not (= Y tptp.zero_zero_rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat X) Y)) (@ (@ tptp.divide_divide_rat W) Z)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat W) Y))) (@ (@ tptp.times_times_rat Y) Z)))))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.divide1717551699836669952omplex B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ (@ tptp.times_times_complex A) Z)) B)) Z))))))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real A) (@ (@ tptp.divide_divide_real B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real A) Z)) B)) Z))))))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.divide_divide_rat B) Z)))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 A)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat A) Z)) B)) Z))))))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat B) A)) B) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (not (= B tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int B) A)) B) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (X tptp.nat) (M5 tptp.nat)) (=> (@ P X) (=> (forall ((X6 tptp.nat)) (=> (@ P X6) (@ (@ tptp.ord_less_eq_nat X6) M5))) (not (forall ((M4 tptp.nat)) (=> (@ P M4) (not (forall ((X4 tptp.nat)) (=> (@ P X4) (@ (@ tptp.ord_less_eq_nat X4) M4)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Xs tptp.list_complex)) (=> (@ (@ tptp.member_complex X) (@ tptp.set_complex2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_s3451745648224563538omplex Xs)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((X Bool) (Xs tptp.list_o)) (=> (@ (@ tptp.member_o X) (@ tptp.set_o2 Xs)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.size_size_list_o Xs)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.divide_divide_nat M) N)) (and (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) (@ _let_1 M)))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.divide_divide_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.divide_divide_nat M) N))))))
% 6.60/6.97 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) Q2)) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.times_times_nat N) Q2))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat M) N)) M)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (= (@ (@ tptp.divide_divide_nat M) N) M) (= N tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.modulo364778990260209775nteger A) _let_3)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_Code_integer) (@ _let_1 B))))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) B) (=> (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.modulo_modulo_nat A) _let_3)) (= (@ (@ tptp.plus_plus_nat (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_nat) (@ _let_1 B))))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ _let_2 B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (=> (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.modulo_modulo_int A) _let_3)) (= (@ (@ tptp.plus_plus_int (@ _let_2 (@ _let_1 _let_3))) tptp.one_one_int) (@ _let_1 B))))))))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_1) (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex Y) X)) _let_1)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_1) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real Y) X)) _let_1)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_1) (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat Y) X)) _let_1)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_1) (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int Y) X)) _let_1)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (J tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat J) I)) U)) N))))))
% 6.60/6.97 (assert (forall ((J tptp.nat) (I tptp.nat) (U tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat I) U)) M)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat J) U)) N)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.minus_minus_nat I) J)) U)) M)) N)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z5) (=> (@ (@ tptp.ord_less_real Z5) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z5) X)) Y)))) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (forall ((Z5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z5) (=> (@ (@ tptp.ord_less_rat Z5) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z5) X)) Y)))) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.one_one_real) A))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.one_one_rat) A))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) A))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_real B) tptp.one_one_real))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat B) tptp.one_one_rat))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_eq_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_int B) tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (C tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (C tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (C tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A) C)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real B) C)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat B) C)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int B) C)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real C) A)) C) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat C) A)) C) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int C) A)) C) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real C) (@ (@ tptp.times_times_real C) B)) (and (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) B)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) tptp.one_one_real))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat C) (@ (@ tptp.times_times_rat C) B)) (and (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) B)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) tptp.one_one_rat))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int C) (@ (@ tptp.times_times_int C) B)) (and (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) C) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) B)) (=> (@ (@ tptp.ord_less_int C) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int B) tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real C) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat C) tptp.zero_zero_rat) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (Z tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real Z) Y)) X) (@ (@ tptp.ord_less_eq_real Z) (@ (@ tptp.divide_divide_real X) Y))))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (Z tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat Z) Y)) X) (@ (@ tptp.ord_less_eq_rat Z) (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.60/6.97 (assert (forall ((Y tptp.real) (X tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.times_times_real Z) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real X) Y)) Z)))))
% 6.60/6.97 (assert (forall ((Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (=> (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.times_times_rat Z) Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat X) Y)) Z)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) C)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) C)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) C))))))
% 6.60/6.97 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) B)))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) B)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) C) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) C) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A)) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real))))))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat))))))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.times_times_real A) C))) (let ((_let_3 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A)))))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.times_times_rat A) C))) (let ((_let_3 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_2)) (=> (not _let_3) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_2) B)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A)))))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.divide_divide_real B) A)) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real B) A))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.divide_divide_rat B) A)) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat B) A))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) A)) tptp.one_one_real) (or (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real B) A)) (and (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real A) B)) (= A tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) A)) tptp.one_one_rat) (or (and (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (@ (@ tptp.ord_less_eq_rat B) A)) (and (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat A) B)) (= A tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_eq_real X) A) (=> (@ (@ tptp.ord_less_eq_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_eq_rat X) A) (=> (@ (@ tptp.ord_less_eq_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int X) A) (=> (@ (@ tptp.ord_less_eq_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.60/6.97 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.60/6.97 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat A) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.times_times_nat A) _let_1)) _let_1))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A) _let_1)) _let_1))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (N4 tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ _let_1 N4)) (@ _let_1 N))))))))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_rat))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_real))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.60/6.97 (assert (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_complex))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.power_power_real A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.power_power_rat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.power_power_nat A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.one_one_int) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int A) N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_real A) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_rat A) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_nat A) N)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ _let_1 (@ (@ tptp.power_power_int A) N)))))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (forall ((Q2 tptp.nat) (M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Q2) (= (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.divide_divide_nat N) Q2)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat M) Q2)) N)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat N) (@ (@ tptp.divide_divide_nat M) N)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat M) N)) N))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (= N tptp.zero_zero_nat))) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (and (=> _let_1 (@ P tptp.zero_zero_nat)) (=> (not _let_1) (forall ((I5 tptp.nat) (J3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat J3) N) (=> (= M (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) I5)) J3)) (@ P I5))))))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ _let_1 M)) (@ _let_1 N)))))))
% 6.60/6.97 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.60/6.97 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.60/6.97 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (A tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real X) A) (=> (@ (@ tptp.ord_less_real Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_real U) V) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real U) X)) (@ (@ tptp.times_times_real V) Y))) A)))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (A tptp.rat) (Y tptp.rat) (U tptp.rat) (V tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ (@ tptp.ord_less_rat X) A) (=> (@ (@ tptp.ord_less_rat Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_rat U) V) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat U) X)) (@ (@ tptp.times_times_rat V) Y))) A)))))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (A tptp.int) (Y tptp.int) (U tptp.int) (V tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int X) A) (=> (@ (@ tptp.ord_less_int Y) A) (=> (@ _let_1 U) (=> (@ _let_1 V) (=> (= (@ (@ tptp.plus_plus_int U) V) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U) X)) (@ (@ tptp.times_times_int V) Y))) A)))))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_real X) _let_2) (@ (@ tptp.power_power_real Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_rat X) _let_2) (@ (@ tptp.power_power_rat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_nat X) _let_2) (@ (@ tptp.power_power_nat Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.power_power_int X) _let_2) (@ (@ tptp.power_power_int Y) _let_2)) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= X Y))))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 M) tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 M) tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_nat)) (not (= (@ _let_1 N) tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (= (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)) tptp.zero_zero_int)) (not (= (@ _let_1 N) tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.modulo_modulo_nat A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide_divide_int (@ (@ tptp.modulo_modulo_int A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 N))) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_2)) (@ _let_1 M)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M)))) _let_2))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (@ (@ tptp.ord_less_real X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (@ (@ tptp.ord_less_rat X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat X) _let_1)) (@ (@ tptp.power_power_nat Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) Y) (@ (@ tptp.ord_less_nat X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_int X) Y))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real) (and (= X tptp.zero_zero_real) (= Y tptp.zero_zero_real))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat) (and (= X tptp.zero_zero_rat) (= Y tptp.zero_zero_rat))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int) (and (= X tptp.zero_zero_int) (= Y tptp.zero_zero_int))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) tptp.zero_zero_real)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) tptp.zero_zero_rat)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (or (not (= X tptp.zero_zero_real)) (not (= Y tptp.zero_zero_real)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))) (or (not (= X tptp.zero_zero_rat)) (not (= Y tptp.zero_zero_rat)))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))) (or (not (= X tptp.zero_zero_int)) (not (= Y tptp.zero_zero_int)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.60/6.97 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_complex (@ (@ tptp.minus_minus_complex X) Y)) _let_2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex (@ (@ tptp.power_power_complex X) _let_2)) (@ (@ tptp.power_power_complex Y) _let_2))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) Y)) _let_2) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_rat (@ (@ tptp.minus_minus_rat X) Y)) _let_2) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat (@ (@ tptp.power_power_rat X) _let_2)) (@ (@ tptp.power_power_rat Y) _let_2))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (= (@ (@ tptp.power_power_int (@ (@ tptp.minus_minus_int X) Y)) _let_2) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int (@ (@ tptp.power_power_int X) _let_2)) (@ (@ tptp.power_power_int Y) _let_2))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int _let_1)) X)) Y)))))))
% 6.60/6.97 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X6 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X6) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X6) N))) (and (@ (@ tptp.ord_less_nat Mi) X6) (@ (@ tptp.ord_less_eq_nat X6) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (@ (@ tptp.vEBT_VEBT_high X) (@ (@ tptp.divide_divide_nat Deg) _let_1))) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) tptp.none_nat)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_nat)) (= _let_1 tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_zero_int)) (= _let_1 tptp.one_one_int)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.zero_z3403309356797280102nteger)) (= _let_1 tptp.one_one_Code_integer)))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_nat)) (= _let_1 tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_int)) (= _let_1 tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 tptp.one_one_Code_integer)) (= _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Ma))))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (=> (@ (@ tptp.ord_less_nat X) Mi) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ tptp.some_nat Mi))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_4 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_2) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_3 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) (@ (@ tptp.power_power_nat _let_1) _let_2))) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))
% 6.60/6.97 (assert (= tptp.ord_less_nat (lambda ((Y3 tptp.nat) (X3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))
% 6.60/6.97 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat X3)) (@ tptp.some_nat Y3)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.60/6.97 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (Y11 tptp.option4927543243414619207at_nat) (Y12 tptp.nat) (Y13 tptp.list_VEBT_VEBT) (Y14 tptp.vEBT_VEBT)) (= (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ (@ (@ tptp.vEBT_Node Y11) Y12) Y13) Y14)) (and (= X11 Y11) (= X12 Y12) (= X13 Y13) (= X14 Y14)))))
% 6.60/6.97 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat N) tptp.zero_z5237406670263579293d_enat) N)))
% 6.60/6.97 (assert (forall ((N tptp.extended_enat)) (= (@ (@ tptp.minus_3235023915231533773d_enat tptp.zero_z5237406670263579293d_enat) N) tptp.zero_z5237406670263579293d_enat)))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Sx)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Px tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Px)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) Px)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_succ_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Sx tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Sx)) (@ (@ (@ tptp.vEBT_is_pred_in_set (@ tptp.vEBT_set_vebt T)) X) Sx)))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (=> (@ (@ tptp.vEBT_invar_vebt _let_1) N) (=> (@ (@ tptp.ord_less_eq_nat Ma) X) (= (@ (@ tptp.vEBT_vebt_succ _let_1) X) tptp.none_nat))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ (@ tptp.vEBT_vebt_pred T) X) (@ tptp.some_nat Y)) (@ (@ tptp.ord_less_nat Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg) (=> (not (= Mi Ma)) (= (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt Summary)) (@ (@ tptp.vEBT_VEBT_high Ma) (@ (@ tptp.divide_divide_nat Deg) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.60/6.97 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.60/6.97 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.modulo_modulo_int K) L2) K)))))
% 6.60/6.97 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W))))))
% 6.60/6.97 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) L2) (= (@ (@ tptp.divide_divide_int K) L2) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_power (@ tptp.vEBT_V4262088993061758097ft_nat tptp.power_power_nat)))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.divide_divide_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P tptp.zero_zero_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P I5)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P I5))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (N tptp.int) (K tptp.int)) (= (@ P (@ (@ tptp.modulo_modulo_int N) K)) (and (=> (= K tptp.zero_zero_int) (@ P N)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P J3)))) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ P J3))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int A4) B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B)) (@ _let_1 B4))))))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int K) L2)) L2)) tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (=> (@ (@ tptp.ord_less_eq_int L2) K) (= (@ (@ tptp.modulo_modulo_int K) L2) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) L2)) L2))))))
% 6.60/6.97 (assert (forall ((B4 tptp.int) (Q4 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q4)) R3)) (=> (@ (@ tptp.ord_less_int R3) B4) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (@ _let_1 Q4)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ tptp.ord_less_int B))) (=> (@ _let_2 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (@ _let_2 _let_1)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) _let_1) (@ (@ tptp.ord_less_int _let_1) B))))))
% 6.60/6.97 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.divide_divide_int I) K) tptp.zero_zero_int) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.divide_divide_int A) B) Q2))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int B) R) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (=> (@ (@ tptp.ord_less_int R) B) (= (@ (@ tptp.modulo_modulo_int A) B) R))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (A4 tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) A4) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A4) B)) (@ (@ tptp.divide_divide_int A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B4 tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int (@ _let_1 B4)) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)) (or (= K tptp.zero_zero_int) (= L2 tptp.zero_zero_int) (and (@ _let_1 K) (@ _let_1 L2)) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))))
% 6.60/6.97 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_int K) J3) (@ (@ tptp.ord_less_eq_int J3) tptp.zero_zero_int) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ (@ P I5) J3)))))))
% 6.60/6.97 (assert (forall ((K tptp.int) (P (-> tptp.int tptp.int Bool)) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ P (@ (@ tptp.divide_divide_int N) K)) (@ (@ tptp.modulo_modulo_int N) K)) (forall ((I5 tptp.int) (J3 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) J3) (@ (@ tptp.ord_less_int J3) K) (= N (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int K) I5)) J3))) (@ (@ P I5) J3)))))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int L2) K) (=> (@ _let_1 L2) (@ _let_1 (@ (@ tptp.divide_divide_int K) L2)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B4 tptp.int) (Q4 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q4)) R3))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R) _let_2) (=> (@ _let_1 _let_2) (=> (@ (@ tptp.ord_less_int R3) B4) (=> (@ _let_1 R) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q2) Q4)))))))))))
% 6.60/6.97 (assert (forall ((I tptp.int) (K tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int I) K) I) (or (= K tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I) (@ (@ tptp.ord_less_int I) K)) (and (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) I))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int tptp.one_one_int) K) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int X) K)) X)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A) B)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((K tptp.int) (I tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 K) (= (@ _let_1 (@ (@ tptp.divide_divide_int I) K)) (@ (@ tptp.ord_less_eq_int K) I))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (Q2 tptp.int) (R tptp.int) (B4 tptp.int) (Q4 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B4) Q4)) R3))) (=> (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int B) Q2)) R) _let_1) (=> (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int) (=> (@ (@ tptp.ord_less_int R) B) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B4) (=> (@ (@ tptp.ord_less_eq_int B4) B) (@ (@ tptp.ord_less_eq_int Q4) Q2))))))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (Q4 tptp.int) (R3 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_1 Q4)) R3)) (@ (@ tptp.plus_plus_int (@ _let_1 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R3) (=> (@ (@ tptp.ord_less_int R3) B) (=> (@ (@ tptp.ord_less_int R) B) (@ (@ tptp.ord_less_eq_int Q4) Q2))))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) tptp.zero_zero_int) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (@ _let_1 A))))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int K) L2)) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (@ _let_1 B)))))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (=> (@ _let_1 tptp.zero_zero_int) (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2))))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_int (@ (@ tptp.modulo_modulo_int K) L2)) L2))))
% 6.60/6.97 (assert (forall ((B tptp.int) (Q4 tptp.int) (R3 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_int B))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ _let_2 Q4)) R3)) (@ (@ tptp.plus_plus_int (@ _let_2 Q2)) R)) (=> (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int) (=> (@ _let_1 R) (=> (@ _let_1 R3) (@ (@ tptp.ord_less_eq_int Q2) Q4)))))))))
% 6.60/6.97 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int K) L2))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int _let_1) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int K) L2) _let_1))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ tptp.times_times_int B))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ _let_2 C)) (@ (@ tptp.plus_plus_int (@ _let_2 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) B)) C))) (@ _let_1 B))))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) C) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.60/6.97 (assert (forall ((M tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) M) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.modulo_modulo_int M) K)) M))))
% 6.60/6.97 (assert (not (= tptp.zero_z5237406670263579293d_enat tptp.one_on7984719198319812577d_enat)))
% 6.60/6.97 (assert (forall ((M tptp.int) (D tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q3 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q3))))))
% 6.60/6.97 (assert (forall ((M tptp.int) (D tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int M) D) tptp.zero_zero_int) (exists ((Q5 tptp.int)) (= M (@ (@ tptp.times_times_int D) Q5))))))
% 6.60/6.97 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.times_7803423173614009249d_enat M) N) tptp.zero_z5237406670263579293d_enat) (or (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.60/6.97 (assert (forall ((M tptp.extended_enat) (N tptp.extended_enat)) (= (= (@ (@ tptp.plus_p3455044024723400733d_enat M) N) tptp.zero_z5237406670263579293d_enat) (and (= M tptp.zero_z5237406670263579293d_enat) (= N tptp.zero_z5237406670263579293d_enat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 B))) (@ _let_1 A)) (@ (@ tptp.minus_minus_int (@ _let_1 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.plus_plus_int B) tptp.one_one_int)) A))) tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((Z tptp.extended_enat) (Y tptp.extended_enat) (X tptp.extended_enat)) (let ((_let_1 (@ tptp.plus_p3455044024723400733d_enat X))) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Z) Y) (= (@ _let_1 (@ (@ tptp.minus_3235023915231533773d_enat Y) Z)) (@ (@ tptp.minus_3235023915231533773d_enat (@ _let_1 Y)) Z))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ (@ tptp.modulo_modulo_int (@ _let_2 (@ _let_1 B))) (@ _let_1 A)) (@ _let_2 (@ _let_1 (@ (@ tptp.modulo_modulo_int B) A)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ (@ tptp.plus_plus_nat N3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ P N))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high X) N)) (@ _let_1 M)))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ (@ tptp.ord_less_nat X) (@ _let_1 (@ (@ tptp.plus_plus_nat N) M))) (=> (@ _let_2 N) (=> (@ _let_2 M) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_low X) N)) (@ _let_1 N)))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.power_power_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xn) _let_2))) (let ((_let_6 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (= _let_5 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_4 _let_6))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_2) L2) (=> (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_4 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (not (@ tptp.vEBT_VEBT_minNull Newnode)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_3)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real B) A)) _let_1)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real B) A)) _let_1)))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat Mi) X) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ tptp.ord_max_nat X) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low X) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary))))))))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (X tptp.nat) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Mi) _let_2))) (let ((_let_4 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (@ (@ tptp.ord_less_nat X) Mi) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (not (= X Ma)) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) (@ (@ tptp.ord_max_nat Mi) Ma)))) Deg) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_3) (@ (@ tptp.vEBT_vebt_insert _let_4) (@ (@ tptp.vEBT_VEBT_low Mi) _let_2)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_4)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_3)) Summary)))))))))))))
% 6.60/6.97 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int W) (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.60/6.97 (assert (forall ((L2 tptp.num) (R tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5026877609467782581ep_nat L2) (@ (@ tptp.product_Pair_nat_nat Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_nat L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_nat_nat _let_1) R))))))))))
% 6.60/6.97 (assert (forall ((L2 tptp.num) (R tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique5024387138958732305ep_int L2) (@ (@ tptp.product_Pair_int_int Q2) R)))) (let ((_let_3 (@ tptp.numeral_numeral_int L2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.product_Pair_int_int _let_1) R))))))))))
% 6.60/6.97 (assert (forall ((L2 tptp.num) (R tptp.code_integer) (Q2 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q2))) (let ((_let_2 (@ (@ tptp.unique4921790084139445826nteger L2) (@ (@ tptp.produc1086072967326762835nteger Q2) R)))) (let ((_let_3 (@ tptp.numera6620942414471956472nteger L2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_3) R))) (and (=> _let_4 (= _let_2 (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R) _let_3)))) (=> (not _let_4) (= _let_2 (@ (@ tptp.produc1086072967326762835nteger _let_1) R))))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N) (=> (not (= Mi Ma)) (and (@ (@ tptp.ord_less_nat Mi) Ma) (exists ((M4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (= (@ tptp.some_nat M4) (@ tptp.vEBT_vebt_mint Summary)) (@ (@ tptp.ord_less_nat M4) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat N) (@ (@ tptp.divide_divide_nat N) _let_1))))))))))))
% 6.60/6.97 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= (@ tptp.some_nat (@ tptp.the_nat Option)) Option))))
% 6.60/6.97 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option)) Option))))
% 6.60/6.97 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= (@ tptp.some_num (@ tptp.the_num Option)) Option))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull T) (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT)) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (@ tptp.vEBT_VEBT_minNull T))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Maxi tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Maxi)) (@ (@ tptp.vEBT_vebt_member T) Maxi)))))
% 6.60/6.97 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.some_nat X22) (@ tptp.some_nat Y22)) (= X22 Y22))))
% 6.60/6.97 (assert (forall ((X22 tptp.product_prod_nat_nat) (Y22 tptp.product_prod_nat_nat)) (= (= (@ tptp.some_P7363390416028606310at_nat X22) (@ tptp.some_P7363390416028606310at_nat Y22)) (= X22 Y22))))
% 6.60/6.97 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.some_num X22) (@ tptp.some_num Y22)) (= X22 Y22))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (Mini tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat Mini)) (=> (@ (@ tptp.vEBT_vebt_member T) X) (@ (@ tptp.ord_less_eq_nat Mini) X))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X)) (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (@ (@ tptp.vEBT_VEBT_min_in_set (@ tptp.vEBT_VEBT_set_vebt T)) X) (= (@ tptp.vEBT_vebt_mint T) (@ tptp.some_nat X))))))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (=> (and (= X Mi) (= X Ma)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Deg) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.some_nat M) (@ tptp.vEBT_vebt_mint T)) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.60/6.97 (assert (forall ((X tptp.option_nat)) (= (not (= X tptp.none_nat)) (exists ((Y3 tptp.nat)) (= X (@ tptp.some_nat Y3))))))
% 6.60/6.97 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (not (= X tptp.none_P5556105721700978146at_nat)) (exists ((Y3 tptp.product_prod_nat_nat)) (= X (@ tptp.some_P7363390416028606310at_nat Y3))))))
% 6.60/6.97 (assert (forall ((X tptp.option_num)) (= (not (= X tptp.none_num)) (exists ((Y3 tptp.num)) (= X (@ tptp.some_num Y3))))))
% 6.60/6.97 (assert (forall ((X tptp.option_nat)) (= (forall ((Y3 tptp.nat)) (not (= X (@ tptp.some_nat Y3)))) (= X tptp.none_nat))))
% 6.60/6.97 (assert (forall ((X tptp.option4927543243414619207at_nat)) (= (forall ((Y3 tptp.product_prod_nat_nat)) (not (= X (@ tptp.some_P7363390416028606310at_nat Y3)))) (= X tptp.none_P5556105721700978146at_nat))))
% 6.60/6.97 (assert (forall ((X tptp.option_num)) (= (forall ((Y3 tptp.num)) (not (= X (@ tptp.some_num Y3)))) (= X tptp.none_num))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.ord_max_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) A) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.ord_max_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_max_nat A) tptp.zero_zero_nat) A)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) N) N)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_max_nat N) tptp.zero_zero_nat) N)))
% 6.60/6.97 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat U))) (let ((_let_2 (@ tptp.numera1916890842035813515d_enat V))) (let ((_let_3 (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le2932123472753598470d_enat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.60/6.97 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.60/6.97 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.60/6.97 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.60/6.97 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat U))) (let ((_let_2 (@ tptp.numeral_numeral_nat V))) (let ((_let_3 (@ (@ tptp.ord_max_nat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.60/6.97 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.zero_z5237406670263579293d_enat) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.zero_z3403309356797280102nteger) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.zero_zero_real) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.zero_zero_rat) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.zero_zero_nat) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.zero_zero_int) _let_1))))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_real tptp.zero_zero_real) tptp.one_one_real) tptp.one_one_real))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_rat tptp.zero_zero_rat) tptp.one_one_rat) tptp.one_one_rat))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_nat tptp.zero_zero_nat) tptp.one_one_nat) tptp.one_one_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat) tptp.one_on7984719198319812577d_enat))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_int tptp.zero_zero_int) tptp.one_one_int) tptp.one_one_int))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_real tptp.one_one_real) tptp.zero_zero_real) tptp.one_one_real))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) tptp.zero_zero_rat) tptp.one_one_rat))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) tptp.zero_zero_nat) tptp.one_one_nat))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) tptp.zero_z5237406670263579293d_enat) tptp.one_on7984719198319812577d_enat))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_int tptp.one_one_int) tptp.zero_zero_int) tptp.one_one_int))
% 6.60/6.97 (assert (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.one_on7984719198319812577d_enat) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer tptp.one_one_Code_integer) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real tptp.one_one_real) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat tptp.one_one_rat) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat tptp.one_one_nat) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int tptp.one_one_int) _let_1) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera1916890842035813515d_enat X))) (= (@ (@ tptp.ord_ma741700101516333627d_enat _let_1) tptp.one_on7984719198319812577d_enat) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger X))) (= (@ (@ tptp.ord_max_Code_integer _let_1) tptp.one_one_Code_integer) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real X))) (= (@ (@ tptp.ord_max_real _let_1) tptp.one_one_real) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat X))) (= (@ (@ tptp.ord_max_rat _let_1) tptp.one_one_rat) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat X))) (= (@ (@ tptp.ord_max_nat _let_1) tptp.one_one_nat) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int X))) (= (@ (@ tptp.ord_max_int _let_1) tptp.one_one_int) _let_1))))
% 6.60/6.97 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int W) (@ (@ tptp.minus_minus_int Z) tptp.one_one_int)) (@ (@ tptp.ord_less_int W) Z))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.plus_plus_real X) Z)) (@ (@ tptp.plus_plus_real Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.plus_plus_rat X) Z)) (@ (@ tptp.plus_plus_rat Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat X) Z)) (@ (@ tptp.plus_plus_nat Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.plus_plus_int X) Z)) (@ (@ tptp.plus_plus_int Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Z)) (@ (@ tptp.plus_p5714425477246183910nteger Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real X))) (= (@ _let_1 (@ (@ tptp.ord_max_real Y) Z)) (@ (@ tptp.ord_max_real (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.plus_plus_rat X))) (= (@ _let_1 (@ (@ tptp.ord_max_rat Y) Z)) (@ (@ tptp.ord_max_rat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat X))) (= (@ _let_1 (@ (@ tptp.ord_max_nat Y) Z)) (@ (@ tptp.ord_max_nat (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X))) (= (@ _let_1 (@ (@ tptp.ord_max_int Y) Z)) (@ (@ tptp.ord_max_int (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.60/6.97 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.plus_p5714425477246183910nteger X))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer Y) Z)) (@ (@ tptp.ord_max_Code_integer (@ _let_1 Y)) (@ _let_1 Z))))))
% 6.60/6.97 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (@ (@ tptp.ord_max_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) Z)) (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.ord_max_real X) Y)) Z) (@ (@ tptp.ord_max_real (@ (@ tptp.minus_minus_real X) Z)) (@ (@ tptp.minus_minus_real Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (@ (@ tptp.ord_max_rat (@ (@ tptp.minus_minus_rat X) Z)) (@ (@ tptp.minus_minus_rat Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.ord_max_int X) Y)) Z) (@ (@ tptp.ord_max_int (@ (@ tptp.minus_minus_int X) Z)) (@ (@ tptp.minus_minus_int Y) Z)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.plus_plus_nat M) Q2)) (@ (@ tptp.plus_plus_nat N) Q2)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.ord_max_nat M) N)) Q2) (@ (@ tptp.ord_max_nat (@ (@ tptp.times_times_nat M) Q2)) (@ (@ tptp.times_times_nat N) Q2)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ (@ tptp.ord_max_nat N) Q2)) (@ (@ tptp.ord_max_nat (@ _let_1 N)) (@ _let_1 Q2))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat N) M)) M) (@ (@ tptp.ord_max_nat N) M))))
% 6.60/6.97 (assert (forall ((K tptp.int)) (= (@ (@ tptp.minus_minus_int K) tptp.zero_zero_int) K)))
% 6.60/6.97 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int Z1) Z22)) W) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.60/6.97 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.minus_minus_int Z1) Z22)) (@ (@ tptp.minus_minus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.60/6.97 (assert (forall ((X22 tptp.nat)) (not (= tptp.none_nat (@ tptp.some_nat X22)))))
% 6.60/6.97 (assert (forall ((X22 tptp.product_prod_nat_nat)) (not (= tptp.none_P5556105721700978146at_nat (@ tptp.some_P7363390416028606310at_nat X22)))))
% 6.60/6.97 (assert (forall ((X22 tptp.num)) (not (= tptp.none_num (@ tptp.some_num X22)))))
% 6.60/6.97 (assert (forall ((Option tptp.option_nat) (X22 tptp.nat)) (=> (= Option (@ tptp.some_nat X22)) (not (= Option tptp.none_nat)))))
% 6.60/6.97 (assert (forall ((Option tptp.option4927543243414619207at_nat) (X22 tptp.product_prod_nat_nat)) (=> (= Option (@ tptp.some_P7363390416028606310at_nat X22)) (not (= Option tptp.none_P5556105721700978146at_nat)))))
% 6.60/6.97 (assert (forall ((Option tptp.option_num) (X22 tptp.num)) (=> (= Option (@ tptp.some_num X22)) (not (= Option tptp.none_num)))))
% 6.60/6.97 (assert (forall ((Y tptp.option_nat)) (=> (not (= Y tptp.none_nat)) (not (forall ((X23 tptp.nat)) (not (= Y (@ tptp.some_nat X23))))))))
% 6.60/6.97 (assert (forall ((Y tptp.option4927543243414619207at_nat)) (=> (not (= Y tptp.none_P5556105721700978146at_nat)) (not (forall ((X23 tptp.product_prod_nat_nat)) (not (= Y (@ tptp.some_P7363390416028606310at_nat X23))))))))
% 6.60/6.97 (assert (forall ((Y tptp.option_num)) (=> (not (= Y tptp.none_num)) (not (forall ((X23 tptp.num)) (not (= Y (@ tptp.some_num X23))))))))
% 6.60/6.97 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (exists ((X7 tptp.option_nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.option_nat Bool))) (or (@ P4 tptp.none_nat) (exists ((X3 tptp.nat)) (@ P4 (@ tptp.some_nat X3)))))))
% 6.60/6.97 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (exists ((X7 tptp.option4927543243414619207at_nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (or (@ P4 tptp.none_P5556105721700978146at_nat) (exists ((X3 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X3)))))))
% 6.60/6.97 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (exists ((X7 tptp.option_num)) (@ P3 X7))) (lambda ((P4 (-> tptp.option_num Bool))) (or (@ P4 tptp.none_num) (exists ((X3 tptp.num)) (@ P4 (@ tptp.some_num X3)))))))
% 6.60/6.97 (assert (= (lambda ((P3 (-> tptp.option_nat Bool))) (forall ((X7 tptp.option_nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.option_nat Bool))) (and (@ P4 tptp.none_nat) (forall ((X3 tptp.nat)) (@ P4 (@ tptp.some_nat X3)))))))
% 6.60/6.97 (assert (= (lambda ((P3 (-> tptp.option4927543243414619207at_nat Bool))) (forall ((X7 tptp.option4927543243414619207at_nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.option4927543243414619207at_nat Bool))) (and (@ P4 tptp.none_P5556105721700978146at_nat) (forall ((X3 tptp.product_prod_nat_nat)) (@ P4 (@ tptp.some_P7363390416028606310at_nat X3)))))))
% 6.60/6.97 (assert (= (lambda ((P3 (-> tptp.option_num Bool))) (forall ((X7 tptp.option_num)) (@ P3 X7))) (lambda ((P4 (-> tptp.option_num Bool))) (and (@ P4 tptp.none_num) (forall ((X3 tptp.num)) (@ P4 (@ tptp.some_num X3)))))))
% 6.60/6.97 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_nat B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option_nat) (P (-> tptp.option_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.nat) (B5 tptp.num)) (=> (= X (@ tptp.some_nat A5)) (=> (= Y (@ tptp.some_num B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_nat B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option4927543243414619207at_nat) (P (-> tptp.option4927543243414619207at_nat tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.product_prod_nat_nat) (B5 tptp.num)) (=> (= X (@ tptp.some_P7363390416028606310at_nat A5)) (=> (= Y (@ tptp.some_num B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_nat Bool)) (Y tptp.option_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.nat)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_nat B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option4927543243414619207at_nat Bool)) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_P5556105721700978146at_nat) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.product_prod_nat_nat)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_P7363390416028606310at_nat B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (forall ((X tptp.option_num) (P (-> tptp.option_num tptp.option_num Bool)) (Y tptp.option_num)) (let ((_let_1 (@ (@ P X) Y))) (=> (=> (= X tptp.none_num) _let_1) (=> (=> (= Y tptp.none_num) _let_1) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (= X (@ tptp.some_num A5)) (=> (= Y (@ tptp.some_num B5)) (@ (@ P X) Y)))) _let_1))))))
% 6.60/6.97 (assert (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.60/6.97 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((K tptp.int)) (= (@ (@ tptp.times_times_int K) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.times_times_int tptp.zero_zero_int) L2) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((K tptp.int)) (= (@ (@ tptp.plus_plus_int K) tptp.zero_zero_int) K)))
% 6.60/6.97 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.plus_plus_int tptp.zero_zero_int) L2) L2)))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((W tptp.int) (Z1 tptp.int) (Z22 tptp.int)) (let ((_let_1 (@ tptp.times_times_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z1) Z22)) (@ (@ tptp.plus_plus_int (@ _let_1 Z1)) (@ _let_1 Z22))))))
% 6.60/6.97 (assert (forall ((Z1 tptp.int) (Z22 tptp.int) (W tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int Z1) Z22)) W) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Z1) W)) (@ (@ tptp.times_times_int Z22) W)))))
% 6.60/6.97 (assert (forall ((X22 tptp.nat)) (= (@ tptp.the_nat (@ tptp.some_nat X22)) X22)))
% 6.60/6.97 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.the_Pr8591224930841456533at_nat (@ tptp.some_P7363390416028606310at_nat X22)) X22)))
% 6.60/6.97 (assert (forall ((X22 tptp.num)) (= (@ tptp.the_num (@ tptp.some_num X22)) X22)))
% 6.60/6.97 (assert (forall ((Option tptp.option_nat) (Option2 tptp.option_nat)) (let ((_let_1 (= Option2 tptp.none_nat))) (let ((_let_2 (= Option tptp.none_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_nat Option) (@ tptp.the_nat Option2)))) (= Option Option2)))))))
% 6.60/6.97 (assert (forall ((Option tptp.option4927543243414619207at_nat) (Option2 tptp.option4927543243414619207at_nat)) (let ((_let_1 (= Option2 tptp.none_P5556105721700978146at_nat))) (let ((_let_2 (= Option tptp.none_P5556105721700978146at_nat))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_Pr8591224930841456533at_nat Option) (@ tptp.the_Pr8591224930841456533at_nat Option2)))) (= Option Option2)))))))
% 6.60/6.97 (assert (forall ((Option tptp.option_num) (Option2 tptp.option_num)) (let ((_let_1 (= Option2 tptp.none_num))) (let ((_let_2 (= Option tptp.none_num))) (=> (= _let_2 _let_1) (=> (=> (not _let_2) (=> (not _let_1) (= (@ tptp.the_num Option) (@ tptp.the_num Option2)))) (= Option Option2)))))))
% 6.60/6.97 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M N) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.60/6.97 (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)))))))
% 6.60/6.97 (assert (forall ((Z tptp.int)) (not (= (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z) tptp.zero_zero_int))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((W tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int W))) (= (@ _let_1 (@ (@ tptp.plus_plus_int Z) tptp.one_one_int)) (or (@ _let_1 Z) (= W Z))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((Option tptp.option_nat)) (=> (not (= Option tptp.none_nat)) (= Option (@ tptp.some_nat (@ tptp.the_nat Option))))))
% 6.60/6.97 (assert (forall ((Option tptp.option4927543243414619207at_nat)) (=> (not (= Option tptp.none_P5556105721700978146at_nat)) (= Option (@ tptp.some_P7363390416028606310at_nat (@ tptp.the_Pr8591224930841456533at_nat Option))))))
% 6.60/6.97 (assert (forall ((Option tptp.option_num)) (=> (not (= Option tptp.none_num)) (= Option (@ tptp.some_num (@ tptp.the_num Option))))))
% 6.60/6.97 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.60/6.97 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (and (= M tptp.one_one_int) (= N tptp.one_one_int))))))
% 6.60/6.97 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)) Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_int W) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z))))
% 6.60/6.97 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int W) tptp.one_one_int)) Z) (@ (@ tptp.ord_less_int W) Z))))
% 6.60/6.97 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) Z)))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (N tptp.nat) (Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Va) _let_1))) (let ((_let_3 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) N) (=> (= N (@ tptp.suc (@ tptp.suc Va))) (=> (not (@ (@ tptp.ord_less_nat Ma) Mi)) (=> (not (= Ma Mi)) (@ (@ tptp.ord_less_nat (@ (@ tptp.vEBT_VEBT_high (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_3) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.power_power_nat _let_1) _let_2)))) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3))))) (@ tptp.suc _let_2))) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))))))))))
% 6.60/6.97 (assert (let ((_let_1 (= tptp.xa tptp.ma))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (let ((_let_3 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_vebt_delete tptp.summary) _let_2)))) (let ((_let_4 (@ tptp.the_nat _let_3))) (let ((_let_5 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (and (=> _let_1 (= tptp.mi (@ (@ (@ tptp.if_nat (= _let_3 tptp.none_nat)) tptp.mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_5) (@ (@ tptp.divide_divide_nat tptp.deg) _let_5))) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_2) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_2)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na)))) _let_4))))))) (=> (not _let_1) (= tptp.mi tptp.ma)))))))))
% 6.60/6.97 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ (@ tptp.if_int (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int)) tptp.one_one_int) tptp.zero_zero_int))) (@ (@ tptp.divide_divide_int B3) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.vEBT_invar_vebt (@ tptp.vEBT_vebt_buildup N)) N))))
% 6.60/6.97 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ (@ tptp.if_nat (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat)) tptp.one_one_nat) tptp.zero_zero_nat))) (@ (@ tptp.divide_divide_nat B3) N))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.vEBT_VEBT_set_vebt T)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat))))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_mul (@ tptp.vEBT_V4262088993061758097ft_nat tptp.times_times_nat)))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_add (@ tptp.vEBT_V4262088993061758097ft_nat tptp.plus_plus_nat)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.60/6.97 (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)))))))))
% 6.60/6.97 (assert (= tptp.vEBT_VEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_vebt_member T2)))))
% 6.60/6.97 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) (@ tptp.suc (@ tptp.suc N))) (exists ((Info2 tptp.option4927543243414619207at_nat) (TreeList3 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT)) (= Tree (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc (@ tptp.suc N))) TreeList3) S3))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.plus_plus_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_add (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (= (@ (@ tptp.times_times_nat X) Y) Z) (= (@ (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat X)) (@ tptp.some_nat Y)) (@ tptp.some_nat Z)))))
% 6.60/6.97 (assert (forall ((X22 tptp.num) (Y22 tptp.num)) (= (= (@ tptp.bit0 X22) (@ tptp.bit0 Y22)) (= X22 Y22))))
% 6.60/6.97 (assert (forall ((X22 tptp.nat) (Y22 tptp.nat)) (= (= (@ tptp.suc X22) (@ tptp.suc Y22)) (= X22 Y22))))
% 6.60/6.97 (assert (forall ((Nat tptp.nat) (Nat2 tptp.nat)) (= (= (@ tptp.suc Nat) (@ tptp.suc Nat2)) (= Nat Nat2))))
% 6.60/6.97 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat Q2) tptp.zero_z5237406670263579293d_enat) Q2)))
% 6.60/6.97 (assert (forall ((Q2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat tptp.zero_z5237406670263579293d_enat) Q2) Q2)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc N))))
% 6.60/6.97 (assert (forall ((I tptp.set_nat) (L2 tptp.set_nat) (U tptp.set_nat)) (= (@ (@ tptp.member_set_nat I) (@ (@ tptp.set_or4548717258645045905et_nat L2) U)) (and (@ (@ tptp.ord_less_eq_set_nat L2) I) (@ (@ tptp.ord_less_eq_set_nat I) U)))))
% 6.60/6.97 (assert (forall ((I tptp.set_int) (L2 tptp.set_int) (U tptp.set_int)) (= (@ (@ tptp.member_set_int I) (@ (@ tptp.set_or370866239135849197et_int L2) U)) (and (@ (@ tptp.ord_less_eq_set_int L2) I) (@ (@ tptp.ord_less_eq_set_int I) U)))))
% 6.60/6.97 (assert (forall ((I tptp.rat) (L2 tptp.rat) (U tptp.rat)) (= (@ (@ tptp.member_rat I) (@ (@ tptp.set_or633870826150836451st_rat L2) U)) (and (@ (@ tptp.ord_less_eq_rat L2) I) (@ (@ tptp.ord_less_eq_rat I) U)))))
% 6.60/6.97 (assert (forall ((I tptp.num) (L2 tptp.num) (U tptp.num)) (= (@ (@ tptp.member_num I) (@ (@ tptp.set_or7049704709247886629st_num L2) U)) (and (@ (@ tptp.ord_less_eq_num L2) I) (@ (@ tptp.ord_less_eq_num I) U)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.member_nat I) (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (and (@ (@ tptp.ord_less_eq_nat L2) I) (@ (@ tptp.ord_less_eq_nat I) U)))))
% 6.60/6.97 (assert (forall ((I tptp.int) (L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.member_int I) (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (and (@ (@ tptp.ord_less_eq_int L2) I) (@ (@ tptp.ord_less_eq_int I) U)))))
% 6.60/6.97 (assert (forall ((I tptp.real) (L2 tptp.real) (U tptp.real)) (= (@ (@ tptp.member_real I) (@ (@ tptp.set_or1222579329274155063t_real L2) U)) (and (@ (@ tptp.ord_less_eq_real L2) I) (@ (@ tptp.ord_less_eq_real I) U)))))
% 6.60/6.97 (assert (forall ((L2 tptp.set_int) (H2 tptp.set_int) (L3 tptp.set_int) (H3 tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int L2) H2) (@ (@ tptp.set_or370866239135849197et_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_set_int L2) H2)) (not (@ (@ tptp.ord_less_eq_set_int L3) H3)))))))
% 6.60/6.97 (assert (forall ((L2 tptp.rat) (H2 tptp.rat) (L3 tptp.rat) (H3 tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat L2) H2) (@ (@ tptp.set_or633870826150836451st_rat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_rat L2) H2)) (not (@ (@ tptp.ord_less_eq_rat L3) H3)))))))
% 6.60/6.97 (assert (forall ((L2 tptp.num) (H2 tptp.num) (L3 tptp.num) (H3 tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num L2) H2) (@ (@ tptp.set_or7049704709247886629st_num L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_num L2) H2)) (not (@ (@ tptp.ord_less_eq_num L3) H3)))))))
% 6.60/6.97 (assert (forall ((L2 tptp.nat) (H2 tptp.nat) (L3 tptp.nat) (H3 tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat L2) H2) (@ (@ tptp.set_or1269000886237332187st_nat L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_nat L2) H2)) (not (@ (@ tptp.ord_less_eq_nat L3) H3)))))))
% 6.60/6.97 (assert (forall ((L2 tptp.int) (H2 tptp.int) (L3 tptp.int) (H3 tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int L2) H2) (@ (@ tptp.set_or1266510415728281911st_int L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_int L2) H2)) (not (@ (@ tptp.ord_less_eq_int L3) H3)))))))
% 6.60/6.97 (assert (forall ((L2 tptp.real) (H2 tptp.real) (L3 tptp.real) (H3 tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real L2) H2) (@ (@ tptp.set_or1222579329274155063t_real L3) H3)) (or (and (= L2 L3) (= H2 H3)) (and (not (@ (@ tptp.ord_less_eq_real L2) H2)) (not (@ (@ tptp.ord_less_eq_real L3) H3)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.suc M)) (@ (@ tptp.ord_less_eq_nat N) M))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ tptp.suc (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N)) (@ tptp.suc K)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat M) N)) K))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int N) K)) (@ _let_1 K)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se7879613467334960850it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat M) N)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat tptp.zero_zero_rat) (@ tptp.suc N)) tptp.zero_zero_rat)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_nat tptp.zero_zero_nat) (@ tptp.suc N)) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real tptp.zero_zero_real) (@ tptp.suc N)) tptp.zero_zero_real)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int tptp.zero_zero_int) (@ tptp.suc N)) tptp.zero_zero_int)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.zero_zero_complex) (@ tptp.suc N)) tptp.zero_zero_complex)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.suc tptp.zero_zero_nat)) A)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.suc N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc tptp.zero_zero_nat)) (= N tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (= (@ (@ tptp.ord_le4403425263959731960et_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ (@ tptp.ord_less_eq_set_int C) A) (@ (@ tptp.ord_less_eq_set_int B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int B) D))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ (@ tptp.ord_less_eq_real C) A) (@ (@ tptp.ord_less_eq_real B) D))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.times_times_nat M) N)) (and (= M _let_1) (= N _let_1))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.times_times_nat M) N) _let_1) (and (= M _let_1) (= N _let_1))))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.divide_divide_nat M) (@ tptp.suc tptp.zero_zero_nat)) M)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.power_power_nat _let_1) N) _let_1))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.power_power_nat X) M) _let_1) (or (= M tptp.zero_zero_nat) (= X _let_1))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat M) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) tptp.one_one_nat) N)))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (= (@ _let_1 (@ (@ tptp.times_times_nat M) N)) (and (@ _let_1 M) (@ _let_1 N))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (= (@ tptp.suc (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat K) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat M) (@ (@ tptp.times_times_nat N) K)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat K) N)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (K tptp.nat) (M tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N) K)) M))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc N)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ tptp.suc (@ tptp.suc N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat M) _let_1))))))
% 6.60/6.97 (assert (= (@ tptp.suc tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) _let_1) (@ (@ tptp.modulo_modulo_nat M) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) N))))
% 6.60/6.97 (assert (forall ((K tptp.num) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (=> (not (= _let_1 tptp.one_one_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) _let_1) tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (= _let_1 (@ tptp.suc tptp.zero_zero_nat))) (= _let_1 tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2))) (let ((_let_2 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) _let_1))) (let ((_let_3 (@ tptp.nth_VEBT_VEBT _let_2))) (let ((_let_4 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_5 (@ (@ tptp.divide_divide_nat Deg) _let_4))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_4) _let_5))) (let ((_let_7 (@ tptp.if_nat (= X Ma)))) (let ((_let_8 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_5))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_4) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_5) L2) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_1)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 _let_11)))))) Ma)))) Deg) _let_2) _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_8 (@ (@ _let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_3 H2))))) Ma)))) Deg) _let_2) Summary)))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT) (Summary tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high X) _let_4))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_6 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_4) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_5 (@ (@ (@ tptp.if_nat (= X Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_3) _let_4)) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn))))))))))))))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (H2 tptp.nat) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= X Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Mi))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 Ma))) Deg) TreeList2) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (=> (and (@ (@ tptp.ord_less_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_12 H2) (=> (= (@ (@ tptp.vEBT_VEBT_low X) _let_3) L2) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT TreeList2) H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_high _let_7) _let_3))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_8)) (@ (@ tptp.vEBT_VEBT_low _let_7) _let_3)))) (let ((_let_10 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_8) _let_9))) (let ((_let_11 (@ tptp.nth_VEBT_VEBT _let_10))) (let ((_let_12 (@ tptp.if_nat (= _let_7 Ma)))) (let ((_let_13 (@ tptp.product_Pair_nat_nat _let_7))) (let ((_let_14 (@ (@ tptp.vEBT_vebt_delete Summary) _let_8))) (let ((_let_15 (@ tptp.vEBT_vebt_maxt _let_14))) (let ((_let_16 (@ tptp.the_nat _let_15))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_8) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_9)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ (@ tptp.if_nat (= _let_15 tptp.none_nat)) _let_7) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_16)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_16)))))) Ma)))) Deg) _let_10) _let_14)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_13 (@ (@ _let_12 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_11 _let_8))))) Ma)))) Deg) _let_10) Summary))) _let_1)))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT) (Sn tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt Sn))) (let ((_let_2 (@ tptp.the_nat _let_1))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat Deg) _let_3))) (let ((_let_5 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_high Xn) _let_4))) (let ((_let_8 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_3) Deg) (=> (= _let_7 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_8) _let_5)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_8))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_4) L2) (=> (@ (@ tptp.ord_less_nat _let_7) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_6 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (=> (@ tptp.vEBT_VEBT_minNull Newnode) (=> (= Sn (@ (@ tptp.vEBT_vebt_delete Summary) H2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Xn) (@ (@ (@ tptp.if_nat (= Xn Ma)) (@ (@ (@ tptp.if_nat (= _let_1 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_2)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT Newlist) _let_2)))))) Ma)))) Deg) Newlist) Sn)))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat) (Newnode tptp.vEBT_VEBT) (Newlist tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT Newlist))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_5 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_6 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_7 (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X))) (let ((_let_8 (@ tptp.vEBT_VEBT_minNull Newnode))) (let ((_let_9 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ tptp.the_nat _let_10))) (let ((_let_12 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_3))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_12 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_3) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (=> (= Newnode (@ (@ tptp.vEBT_vebt_delete (@ _let_12 H2)) L2)) (=> (= Newlist (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) Newnode)) (and (=> _let_8 (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ (@ tptp.if_nat (= _let_10 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_11)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 _let_11)))))) Ma)))) Deg) Newlist) _let_9))) (=> (not _let_8) (= _let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_6 (@ (@ _let_5 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_4)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_1 H2))))) Ma)))) Deg) Newlist) Summary)))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (Xn tptp.nat) (H2 tptp.nat) (Summary tptp.vEBT_VEBT) (TreeList2 tptp.list_VEBT_VEBT) (L2 tptp.nat)) (let ((_let_1 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete (@ _let_1 H2)) L2))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) H2) _let_2))) (let ((_let_4 (@ tptp.nth_VEBT_VEBT _let_3))) (let ((_let_5 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_6 (@ (@ tptp.divide_divide_nat Deg) _let_5))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_5) _let_6))) (let ((_let_8 (@ tptp.if_nat (= Xn Ma)))) (let ((_let_9 (@ tptp.product_Pair_nat_nat Xn))) (let ((_let_10 (@ (@ tptp.vEBT_vebt_delete Summary) H2))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ tptp.the_nat _let_11))) (let ((_let_13 (@ (@ tptp.vEBT_VEBT_high Xn) _let_6))) (let ((_let_14 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (=> (and (= X Mi) (@ (@ tptp.ord_less_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_5) Deg) (=> (= _let_13 H2) (=> (= Xn (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_14) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_1 _let_14))))) (=> (= (@ (@ tptp.vEBT_VEBT_low Xn) _let_6) L2) (=> (@ (@ tptp.ord_less_nat _let_13) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_2)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ (@ tptp.if_nat (= _let_11 tptp.none_nat)) Xn) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_12)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 _let_12)))))) Ma)))) Deg) _let_3) _let_10)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_9 (@ (@ _let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat H2) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_4 H2))))) Ma)))) Deg) _let_3) Summary))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat Deg) _let_2))) (let ((_let_4 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ (@ tptp.power_power_nat _let_2) _let_3))) (let ((_let_7 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_4) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_5 _let_4)))))) (let ((_let_8 (= X Mi))) (let ((_let_9 (@ tptp.if_nat _let_8))) (let ((_let_10 (@ (@ _let_9 _let_7) X))) (let ((_let_11 (@ (@ tptp.vEBT_VEBT_high _let_10) _let_3))) (let ((_let_12 (@ (@ tptp.vEBT_vebt_delete (@ _let_5 _let_11)) (@ (@ tptp.vEBT_VEBT_low _let_10) _let_3)))) (let ((_let_13 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_11) _let_12))) (let ((_let_14 (@ tptp.nth_VEBT_VEBT _let_13))) (let ((_let_15 (@ tptp.if_nat (and (=> _let_8 (= _let_7 Ma)) (=> (not _let_8) (= X Ma)))))) (let ((_let_16 (@ (@ _let_9 _let_10) Mi))) (let ((_let_17 (@ tptp.product_Pair_nat_nat _let_16))) (let ((_let_18 (@ (@ tptp.vEBT_vebt_delete Summary) _let_11))) (let ((_let_19 (@ tptp.vEBT_vebt_maxt _let_18))) (let ((_let_20 (@ tptp.the_nat _let_19))) (=> (and (@ (@ tptp.ord_less_eq_nat Mi) X) (@ (@ tptp.ord_less_eq_nat X) Ma)) (=> (not (= Mi Ma)) (=> (@ (@ tptp.ord_less_eq_nat _let_2) Deg) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_11) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_12)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ (@ tptp.if_nat (= _let_19 tptp.none_nat)) _let_16) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_6) _let_20)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_20)))))) Ma)))) Deg) _let_13) _let_18)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_17 (@ (@ _let_15 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_11) _let_6)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_14 _let_11))))) Ma)))) Deg) _let_13) Summary))) _let_1)))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Mi tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (X tptp.nat) (Ma tptp.nat) (Mi tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_pred Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_mint _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat X) Ma) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_pred _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_maxt (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (Ma tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4))))))) tptp.none_nat)))))))))))))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (Mi tptp.nat) (X tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Ma tptp.nat) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat Deg) _let_1))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.vEBT_vebt_succ Summary) _let_3))) (let ((_let_5 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_6 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_2))))) (let ((_let_7 (@ (@ tptp.vEBT_VEBT_low X) _let_2))) (let ((_let_8 (@ _let_5 _let_3))) (let ((_let_9 (@ tptp.vEBT_vebt_maxt _let_8))) (=> (@ (@ tptp.ord_less_eq_nat _let_1) Deg) (=> (@ (@ tptp.ord_less_eq_nat Mi) X) (=> (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) X) (@ (@ (@ tptp.if_option_nat (and (not (= _let_9 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_7)) _let_9))) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 (@ tptp.some_nat _let_3))) (@ (@ tptp.vEBT_vebt_succ _let_8) _let_7))) (@ (@ (@ tptp.if_option_nat (= _let_4 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_6 _let_4)) (@ tptp.vEBT_vebt_mint (@ _let_5 (@ tptp.the_nat _let_4)))))))))))))))))))))
% 6.60/6.97 (assert (let ((_let_1 (@ (@ tptp.vEBT_VEBT_high tptp.xa) tptp.na))) (let ((_let_2 (@ (@ tptp.vEBT_vebt_delete tptp.summary) _let_1))) (let ((_let_3 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT tptp.treeList) _let_1) (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.nth_VEBT_VEBT tptp.treeList) _let_1)) (@ (@ tptp.vEBT_VEBT_low tptp.xa) tptp.na))))) (let ((_let_4 (@ tptp.vEBT_vebt_maxt _let_2))) (let ((_let_5 (@ tptp.the_nat _let_4))) (let ((_let_6 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_7 (@ tptp.product_Pair_nat_nat tptp.mi))) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_7 tptp.ma))) tptp.deg) tptp.treeList) tptp.summary)) tptp.xa) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_7 (@ (@ (@ tptp.if_nat (= tptp.xa tptp.ma)) (@ (@ (@ tptp.if_nat (= _let_4 tptp.none_nat)) tptp.mi) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.power_power_nat _let_6) (@ (@ tptp.divide_divide_nat tptp.deg) _let_6))) _let_5)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ (@ tptp.nth_VEBT_VEBT _let_3) _let_5)))))) tptp.ma)))) tptp.deg) _let_3) _let_2))))))))))
% 6.60/6.97 (assert (forall ((C tptp.real)) (= (lambda ((X3 tptp.real)) (@ (@ tptp.times_times_real X3) C)) (@ tptp.times_times_real C))))
% 6.60/6.97 (assert (forall ((C tptp.rat)) (= (lambda ((X3 tptp.rat)) (@ (@ tptp.times_times_rat X3) C)) (@ tptp.times_times_rat C))))
% 6.60/6.97 (assert (forall ((C tptp.nat)) (= (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat X3) C)) (@ tptp.times_times_nat C))))
% 6.60/6.97 (assert (forall ((C tptp.int)) (= (lambda ((X3 tptp.int)) (@ (@ tptp.times_times_int X3) C)) (@ tptp.times_times_int C))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= (@ tptp.suc X) (@ tptp.suc Y)) (= X Y))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (= N (@ tptp.suc N)))))
% 6.60/6.97 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))))
% 6.60/6.97 (assert (= tptp.ord_max_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A3) B2)) B2) A3))))
% 6.60/6.97 (assert (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B2)) B2) A3))))
% 6.60/6.97 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))))
% 6.60/6.97 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))))
% 6.60/6.97 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))))
% 6.60/6.97 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))))
% 6.60/6.97 (assert (= (lambda ((H tptp.complex)) tptp.zero_zero_complex) (@ tptp.times_times_complex tptp.zero_zero_complex)))
% 6.60/6.97 (assert (= (lambda ((H tptp.real)) tptp.zero_zero_real) (@ tptp.times_times_real tptp.zero_zero_real)))
% 6.60/6.97 (assert (= (lambda ((H tptp.rat)) tptp.zero_zero_rat) (@ tptp.times_times_rat tptp.zero_zero_rat)))
% 6.60/6.97 (assert (= (lambda ((H tptp.nat)) tptp.zero_zero_nat) (@ tptp.times_times_nat tptp.zero_zero_nat)))
% 6.60/6.97 (assert (= (lambda ((H tptp.int)) tptp.zero_zero_int) (@ tptp.times_times_int tptp.zero_zero_int)))
% 6.60/6.97 (assert (= (lambda ((X3 tptp.complex)) X3) (@ tptp.times_times_complex tptp.one_one_complex)))
% 6.60/6.97 (assert (= (lambda ((X3 tptp.real)) X3) (@ tptp.times_times_real tptp.one_one_real)))
% 6.60/6.97 (assert (= (lambda ((X3 tptp.rat)) X3) (@ tptp.times_times_rat tptp.one_one_rat)))
% 6.60/6.97 (assert (= (lambda ((X3 tptp.nat)) X3) (@ tptp.times_times_nat tptp.one_one_nat)))
% 6.60/6.97 (assert (= (lambda ((X3 tptp.int)) X3) (@ tptp.times_times_int tptp.one_one_int)))
% 6.60/6.97 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (=> (not (= X (@ tptp.suc tptp.zero_zero_nat))) (not (forall ((Va2 tptp.nat)) (not (= X (@ tptp.suc (@ tptp.suc Va2))))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc M)))))
% 6.60/6.97 (assert (forall ((M tptp.nat)) (not (= (@ tptp.suc M) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ P K) (=> (forall ((N3 tptp.nat)) (=> (@ P (@ tptp.suc N3)) (@ P N3))) (@ P tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((X6 tptp.nat)) (@ (@ P X6) tptp.zero_zero_nat)) (=> (forall ((Y5 tptp.nat)) (@ (@ P tptp.zero_zero_nat) (@ tptp.suc Y5))) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ P X6) Y5) (@ (@ P (@ tptp.suc X6)) (@ tptp.suc Y5)))) (@ (@ P M) N))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc N3)))) (@ P N)))))
% 6.60/6.97 (assert (forall ((Y tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (not (forall ((Nat3 tptp.nat)) (not (= Y (@ tptp.suc Nat3))))))))
% 6.60/6.97 (assert (forall ((Nat tptp.nat) (X22 tptp.nat)) (=> (= Nat (@ tptp.suc X22)) (not (= Nat tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((Nat2 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc Nat2)))))
% 6.60/6.97 (assert (forall ((Nat2 tptp.nat)) (not (= (@ tptp.suc Nat2) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((X22 tptp.nat)) (not (= tptp.zero_zero_nat (@ tptp.suc X22)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (= (@ _let_1 (@ tptp.suc M)) (= N M))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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) (J2 tptp.nat) (K3 tptp.nat)) (let ((_let_1 (@ P I4))) (=> (@ (@ tptp.ord_less_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) K3) (=> (@ _let_1 J2) (=> (@ (@ P J2) K3) (@ _let_1 K3))))))) (@ (@ P I) J))))))
% 6.60/6.97 (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)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat N))) (=> (not (@ _let_1 M)) (=> (@ _let_1 (@ tptp.suc M)) (= M N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) M) (exists ((M6 tptp.nat)) (and (= M (@ tptp.suc M6)) (@ (@ tptp.ord_less_nat N) M6))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N)) (@ P I5))) (and (@ P N) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ P I5)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_nat M) N)) (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (= (@ _let_1 (@ tptp.suc N)) (or (@ _let_1 N) (= M N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N)) (@ P I5))) (or (@ P N) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N) (@ P I5)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat M))) (=> (@ _let_1 (@ tptp.suc N)) (=> (not (@ _let_1 N)) (= M N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (=> (@ (@ tptp.ord_less_nat M) N) (=> (not (= _let_1 N)) (@ (@ tptp.ord_less_nat _let_1) N))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc I)) K) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2)))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) K) (=> (not (= K (@ tptp.suc I))) (not (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) J2) (not (= K (@ tptp.suc J2))))))))))
% 6.60/6.97 (assert (= tptp.vEBT_set_vebt (lambda ((T2 tptp.vEBT_VEBT)) (@ tptp.collect_nat (@ tptp.vEBT_V8194947554948674370ptions T2)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (R4 (-> tptp.nat tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (forall ((X6 tptp.nat)) (@ (@ R4 X6) X6)) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat) (Z5 tptp.nat)) (let ((_let_1 (@ R4 X6))) (=> (@ _let_1 Y5) (=> (@ (@ R4 Y5) Z5) (@ _let_1 Z5))))) (=> (forall ((N3 tptp.nat)) (@ (@ R4 N3) (@ tptp.suc N3))) (@ (@ R4 M) N)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ P M) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (forall ((N3 tptp.nat)) (=> (forall ((M2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M2)) N3) (@ P M2))) (@ P N3))) (@ P N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat M) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (= (@ _let_2 _let_1) (or (@ _let_2 N) (= M _let_1)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M7 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) M7) (exists ((M4 tptp.nat)) (= M7 (@ tptp.suc M4))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_1 N) (@ _let_1 (@ tptp.suc N))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.ord_less_eq_nat M))) (=> (@ _let_2 _let_1) (=> (not (@ _let_2 N)) (= M _let_1)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat M) (@ tptp.suc N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.plus_plus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) N)))))
% 6.60/6.97 (assert (forall ((A2 tptp.nat) (K tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat K))) (=> (= A2 (@ _let_1 A)) (= (@ tptp.suc A2) (@ _let_1 (@ tptp.suc A)))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (= (@ _let_1 M) (@ _let_1 N)) (= M N)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_complex _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_real _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_rat _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_nat _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit0 N)) (@ (@ tptp.plus_plus_int _let_1) _let_1)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) N) (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc M))) N))))
% 6.60/6.97 (assert (forall ((K tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se7879613467334960850it_int N) K))))
% 6.60/6.97 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_complex _let_2) _let_2))))))
% 6.60/6.97 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_real _let_2) _let_2))))))
% 6.60/6.97 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_rat _let_2) _let_2))))))
% 6.60/6.97 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_nat _let_2) _let_2))))))
% 6.60/6.97 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 W))) (@ (@ tptp.times_times_int _let_2) _let_2))))))
% 6.60/6.97 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int) (D tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (= (@ (@ tptp.ord_less_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (@ (@ tptp.set_or370866239135849197et_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_set_int B) D) (or (@ (@ tptp.ord_less_set_int C) A) (@ (@ tptp.ord_less_set_int B) D)))) (@ _let_1 D))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (= (@ (@ tptp.ord_less_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (@ (@ tptp.set_or633870826150836451st_rat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat B) D) (or (@ (@ tptp.ord_less_rat C) A) (@ (@ tptp.ord_less_rat B) D)))) (@ _let_1 D))))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num) (D tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (= (@ (@ tptp.ord_less_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (@ (@ tptp.set_or7049704709247886629st_num C) D)) (and (or (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_num B) D) (or (@ (@ tptp.ord_less_num C) A) (@ (@ tptp.ord_less_num B) D)))) (@ _let_1 D))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (= (@ (@ tptp.ord_less_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1269000886237332187st_nat C) D)) (and (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_nat B) D) (or (@ (@ tptp.ord_less_nat C) A) (@ (@ tptp.ord_less_nat B) D)))) (@ _let_1 D))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (= (@ (@ tptp.ord_less_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (@ (@ tptp.set_or1266510415728281911st_int C) D)) (and (or (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_int B) D) (or (@ (@ tptp.ord_less_int C) A) (@ (@ tptp.ord_less_int B) D)))) (@ _let_1 D))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real C))) (= (@ (@ tptp.ord_less_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C) D)) (and (or (not (@ (@ tptp.ord_less_eq_real A) B)) (and (@ _let_1 A) (@ (@ tptp.ord_less_eq_real B) D) (or (@ (@ tptp.ord_less_real C) A) (@ (@ tptp.ord_less_real B) D)))) (@ _let_1 D))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M3) N) (@ P M3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_real (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_rat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_num (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_nat (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (M tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (= (@ (@ tptp.ord_less_int (@ F N)) (@ F M)) (@ (@ tptp.ord_less_nat N) M)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_real (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_rat (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_num (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_nat (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_nat N) N5) (@ (@ tptp.ord_less_int (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int A) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_complex (@ _let_1 N)) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_real (@ _let_1 N)) A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_rat (@ _let_1 N)) A)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_nat (@ _let_1 N)) A)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.times_times_int (@ _let_1 N)) A)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N5)) (@ F N))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N5)) (@ F N))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N5)) (@ F N))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N5)) (@ F N))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F (@ tptp.suc N3))) (@ F N3))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N5)) (@ F N))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.set_int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_set_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_set_int (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_rat (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.num)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_num (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_num (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.nat)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_nat (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (N5 tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (@ (@ tptp.ord_less_eq_nat N) N5) (@ (@ tptp.ord_less_eq_int (@ F N)) (@ F N5))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (or (= M tptp.zero_zero_nat) (exists ((J3 tptp.nat)) (and (= M (@ tptp.suc J3)) (@ (@ tptp.ord_less_nat J3) N)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M4 tptp.nat)) (= N (@ tptp.suc M4))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N)) (@ P I5))) (and (@ P tptp.zero_zero_nat) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) N) (@ P (@ tptp.suc I5))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (exists ((M3 tptp.nat)) (= N (@ tptp.suc M3))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) (@ tptp.suc N)) (@ P I5))) (or (@ P tptp.zero_zero_nat) (exists ((I5 tptp.nat)) (and (@ (@ tptp.ord_less_nat I5) N) (@ P (@ tptp.suc I5))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (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))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ tptp.ord_less_nat M) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.ord_less_nat N) (@ tptp.suc M)) (= N M)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.60/6.97 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (__flatten_var_0 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N2)) __flatten_var_0))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_nat M) (@ tptp.suc N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= (@ (@ tptp.plus_plus_nat M) N) _let_1) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (= _let_1 (@ (@ tptp.plus_plus_nat M) N)) (or (and (= M _let_1) (= N tptp.zero_zero_nat)) (and (= M tptp.zero_zero_nat) (= N _let_1)))))))
% 6.60/6.97 (assert (forall ((X22 tptp.nat)) (= (@ tptp.size_size_option_nat (@ tptp.some_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((X22 tptp.product_prod_nat_nat)) (= (@ tptp.size_s170228958280169651at_nat (@ tptp.some_P7363390416028606310at_nat X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_option_num (@ tptp.some_num X22)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (not (forall ((Q3 tptp.nat)) (not (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) Q3)))))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) M)))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat I) (@ tptp.suc (@ (@ tptp.plus_plus_nat M) I)))))
% 6.60/6.97 (assert (= tptp.ord_less_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (exists ((K2 tptp.nat)) (= N2 (@ tptp.suc (@ (@ tptp.plus_plus_nat M3) K2)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (exists ((K3 tptp.nat)) (= N (@ tptp.suc (@ (@ tptp.plus_plus_nat M) K3)))))))
% 6.60/6.97 (assert (= (@ tptp.size_size_option_nat tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.60/6.97 (assert (= (@ tptp.size_s170228958280169651at_nat tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat)))
% 6.60/6.97 (assert (= (@ tptp.size_size_option_num tptp.none_num) (@ tptp.suc tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat M) N)) (@ tptp.suc M))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (=> (@ (@ tptp.ord_less_nat N) M) (= (@ tptp.suc (@ _let_1 (@ tptp.suc N))) (@ _let_1 N))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_nat M) N)))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ tptp.suc (@ (@ tptp.minus_minus_nat M) N))))))
% 6.60/6.97 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.suc K)))) (= (@ (@ tptp.ord_less_eq_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N)))))
% 6.60/6.97 (assert (= tptp.one_one_nat (@ tptp.suc tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.suc M)) N))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.times_times_nat (@ tptp.suc M)) N) (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.times_times_nat M) N)))))
% 6.60/6.97 (assert (= tptp.suc (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))
% 6.60/6.97 (assert (= (@ tptp.plus_plus_nat tptp.one_one_nat) tptp.suc))
% 6.60/6.97 (assert (= tptp.suc (@ tptp.plus_plus_nat tptp.one_one_nat)))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ _let_1 tptp.one_one_nat)) N)))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat (@ tptp.suc M)) N))) (let ((_let_3 (= _let_1 N))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat) (P5 tptp.nat) (M tptp.nat)) (=> (@ P N) (=> (@ (@ tptp.ord_less_nat N) P5) (=> (@ (@ tptp.ord_less_nat M) P5) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N3) P5) (=> (@ P N3) (@ P (@ (@ tptp.modulo_modulo_nat (@ tptp.suc N3)) P5))))) (@ P M)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.modulo_modulo_nat M) (@ tptp.suc N))) N)))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_real A) _let_2) (@ (@ tptp.power_power_real B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_rat A) _let_2) (@ (@ tptp.power_power_rat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_nat A) _let_2) (@ (@ tptp.power_power_nat B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.suc N))) (=> (= (@ (@ tptp.power_power_int A) _let_2) (@ (@ tptp.power_power_int B) _let_2)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B))))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat) (B tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) (@ (@ tptp.power_power_rat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (@ (@ tptp.ord_less_eq_rat A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) _let_1)) (@ (@ tptp.power_power_nat B) _let_1)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) B) (@ (@ tptp.ord_less_eq_nat A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) (@ (@ tptp.power_power_int B) _let_1)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int A) B))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc N)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.one_one_rat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc N)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.one_one_nat))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_nat A) (@ tptp.suc N)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc N)))))))
% 6.60/6.97 (assert (= (@ tptp.numeral_numeral_nat tptp.one) (@ tptp.suc tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P N) (=> (not (@ P tptp.zero_zero_nat)) (exists ((K3 tptp.nat)) (and (@ (@ tptp.ord_less_nat K3) N) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I2) K3) (not (@ P I2)))) (@ P (@ tptp.suc K3))))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num)) (or (= A B) (not (@ (@ tptp.ord_less_eq_num A) B)) (not (@ (@ tptp.ord_less_eq_num B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (or (= A B) (not (@ (@ tptp.ord_less_eq_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (or (= A B) (not (@ (@ tptp.ord_less_eq_int A) B)) (not (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.60/6.97 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.60/6.97 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.60/6.97 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.60/6.97 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I))) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat N) M))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat M) N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 N) (=> (@ _let_1 M) (@ _let_1 (@ (@ tptp.times_times_nat M) N)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ P tptp.one_one_nat) (=> (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ P N3) (@ P (@ tptp.suc N3))))) (@ P N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat K) (@ (@ tptp.power_power_nat N) K)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (= (@ (@ tptp.power_power_real R2) (@ tptp.suc N)) A))))))
% 6.60/6.97 (assert (forall ((I tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)))) (=> (@ _let_1 I) (@ _let_1 (@ (@ tptp.power_power_nat I) N))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (X tptp.int)) (or (@ (@ tptp.ord_less_eq_int A) X) (= A X) (@ (@ tptp.ord_less_eq_int X) A))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) A)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) A)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_eq_int A) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_real A) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc N))) tptp.one_one_real)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (=> (@ (@ tptp.ord_less_rat A) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc N))) tptp.one_one_rat)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) A) (=> (@ (@ tptp.ord_less_nat A) tptp.one_one_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat A) (@ tptp.suc N))) tptp.one_one_nat)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (=> (@ (@ tptp.ord_less_int A) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc N))) tptp.one_one_int)))))
% 6.60/6.97 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ _let_1 M) (@ tptp.suc (@ _let_1 N)))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (not (= (@ tptp.suc (@ _let_1 M)) (@ _let_1 N))))))
% 6.60/6.97 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (or (@ (@ tptp.ord_less_nat M3) N2) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M3) N2)) N2))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (@ (@ tptp.ord_less_nat M) N)) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc M)) N) (@ (@ tptp.minus_minus_nat M) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= N (@ tptp.suc (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (Q2 tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q2)) M) (=> (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q2))) (= (@ (@ tptp.divide_divide_nat M) N) Q2))))))
% 6.60/6.97 (assert (= tptp.plus_plus_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N2) (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ (@ tptp.minus_minus_nat M3) tptp.one_one_nat)) N2))))))
% 6.60/6.97 (assert (forall ((V tptp.num) (N tptp.nat)) (= (@ tptp.suc (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat V)) N)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ (@ tptp.plus_plus_num V) tptp.one))) N))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2793503036327961859nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se2793503036327961859nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7879613467334960850it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se7879613467334960850it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se7882103937844011126it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se7882103937844011126it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.60/6.97 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (or (= N tptp.zero_zero_nat) (= N (@ tptp.suc tptp.zero_zero_nat))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat M) N) (@ tptp.suc (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat M) N)) N)))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (= (@ P (@ (@ tptp.divide_divide_nat M) N)) (or (and (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_nat)) (exists ((Q5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat N))) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 Q5)) M) (@ (@ tptp.ord_less_nat M) (@ _let_1 (@ tptp.suc Q5))) (@ P Q5))))))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) M) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ (@ tptp.times_times_nat M) N))) M) tptp.one_one_nat))))
% 6.60/6.97 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_complex A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_complex A) (@ (@ tptp.power_power_complex (@ _let_2 N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_real A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_real A) (@ (@ tptp.power_power_real (@ _let_2 N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_rat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_rat A) (@ (@ tptp.power_power_rat (@ _let_2 N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_nat A) (@ (@ tptp.power_power_nat (@ _let_2 N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int A))) (= (@ _let_2 (@ tptp.suc (@ (@ tptp.times_times_nat _let_1) N))) (@ (@ tptp.times_times_int A) (@ (@ tptp.power_power_int (@ _let_2 N)) _let_1)))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (N tptp.nat)) (=> (@ P tptp.zero_zero_nat) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (@ P (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (=> (forall ((N3 tptp.nat)) (=> (@ P N3) (@ P (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N3))))) (@ P N))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.60/6.97 (assert (forall ((B4 tptp.real) (A4 tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real B4) A4)) (@ (@ tptp.ord_less_real A4) B4))))
% 6.60/6.97 (assert (forall ((B4 tptp.rat) (A4 tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat B4) A4)) (@ (@ tptp.ord_less_rat A4) B4))))
% 6.60/6.97 (assert (forall ((B4 tptp.num) (A4 tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num B4) A4)) (@ (@ tptp.ord_less_num A4) B4))))
% 6.60/6.97 (assert (forall ((B4 tptp.nat) (A4 tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat B4) A4)) (@ (@ tptp.ord_less_nat A4) B4))))
% 6.60/6.97 (assert (forall ((B4 tptp.int) (A4 tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int B4) A4)) (@ (@ tptp.ord_less_int A4) B4))))
% 6.60/6.97 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) tptp.zero_zero_complex) A)))
% 6.60/6.97 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) tptp.zero_zero_real) A)))
% 6.60/6.97 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) tptp.zero_zero_rat) A)))
% 6.60/6.97 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.plus_plus_nat A) tptp.zero_zero_nat) A)))
% 6.60/6.97 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) tptp.zero_zero_int) A)))
% 6.60/6.97 (assert (forall ((X22 tptp.num)) (not (= tptp.one (@ tptp.bit0 X22)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (@ _let_1 (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ _let_1 A)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_real))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_rat))))
% 6.60/6.97 (assert (forall ((A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) tptp.zero_zero_int))))
% 6.60/6.97 (assert (forall ((M tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (= (@ (@ tptp.divide_divide_int (@ _let_1 M)) K) (@ _let_1 (@ (@ tptp.minus_minus_nat M) (@ tptp.suc tptp.zero_zero_nat)))))))))
% 6.60/6.97 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat)) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X_1))) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_1))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary)) Deg))))))))))
% 6.60/6.97 (assert (forall ((A2 tptp.nat) (B3 tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat A2) B3) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ (@ tptp.modulo_modulo_nat A2) N) tptp.zero_zero_nat) (=> (= (@ (@ tptp.modulo_modulo_nat B3) N) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat (@ (@ tptp.divide_divide_nat A2) N)) (@ (@ tptp.divide_divide_nat B3) N))))))))
% 6.60/6.97 (assert (forall ((A2 tptp.nat) (N tptp.nat)) (= A2 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A2) N)) N)) (@ (@ tptp.modulo_modulo_nat A2) N)))))
% 6.60/6.97 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (=> (= (@ (@ tptp.modulo_modulo_int A2) N) tptp.zero_zero_int) (=> (= (@ (@ tptp.modulo_modulo_int B3) N) tptp.zero_zero_int) (@ (@ tptp.ord_less_int (@ (@ tptp.divide_divide_int A2) N)) (@ (@ tptp.divide_divide_int B3) N))))))))
% 6.60/6.97 (assert (forall ((A2 tptp.int) (N tptp.int)) (= A2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A2) N)) N)) (@ (@ tptp.modulo_modulo_int A2) N)))))
% 6.60/6.97 (assert (forall ((TreeList2 tptp.list_VEBT_VEBT) (N tptp.nat) (Summary tptp.vEBT_VEBT) (M tptp.nat) (Deg tptp.nat) (Mi tptp.nat) (Ma tptp.nat)) (let ((_let_1 (= Mi Ma))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_invar_vebt X6) N))) (=> (@ (@ tptp.vEBT_invar_vebt Summary) M) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList2) (@ _let_2 M)) (=> (= M (@ tptp.suc N)) (=> (= Deg (@ (@ tptp.plus_plus_nat N) M)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I4)))) (=> (=> _let_1 (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X_1 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X6) X_1)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi) Ma) (=> (@ (@ tptp.ord_less_nat Ma) (@ _let_2 Deg)) (=> (=> (not _let_1) (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low Ma) N))) (forall ((X6 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X6) N) I4) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I4)) (@ (@ tptp.vEBT_VEBT_low X6) N))) (and (@ (@ tptp.ord_less_nat Mi) X6) (@ (@ tptp.ord_less_eq_nat X6) Ma)))))))) (@ (@ tptp.vEBT_invar_vebt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Deg) TreeList2) Summary)) Deg)))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= X Mi))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) X))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= X Ma))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (@ (@ tptp.vEBT_vebt_delete _let_2) X))) (let ((_let_24 (and _let_9 _let_16))) (let ((_let_25 (or (@ (@ tptp.ord_less_nat X) Mi) (@ (@ tptp.ord_less_nat Ma) X)))) (and (=> _let_25 (= _let_23 _let_2)) (=> (not _let_25) (and (=> _let_24 (= _let_23 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary))) (=> (not _let_24) (= _let_23 (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma)))) _let_1) _let_14) Summary))) _let_2)))))))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((Ma tptp.nat) (X tptp.nat) (Mi tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma) X))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Ma))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi) X)) (@ tptp.some_nat Mi)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high X) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList2))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low X) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_2) TreeList2) Summary)) X))) (let ((_let_12 (@ (@ tptp.ord_less_nat X) Mi))) (and (=> _let_12 (= _let_11 (@ tptp.some_nat Mi))) (=> (not _let_12) (= _let_11 (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList2))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat X) Mi)))) (let ((_let_5 (@ (@ _let_4 Mi) X))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_6))) (= (@ (@ tptp.vEBT_vebt_insert _let_2) X) (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)) (not (or (= X Mi) (= X Ma))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 X) Mi)) (@ (@ tptp.ord_max_nat _let_5) Ma)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList2) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary) _let_6)) Summary))) _let_2)))))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma) X)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat X) Mi)))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Summary)) X) (=> (not (= X Mi)) (=> (not (= X Ma)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))))))))))
% 6.60/6.97 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc V)))) (= (@ (@ tptp.vEBT_vebt_insert (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Summary)) X) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat X) X))) _let_1) TreeList2) Summary)))))
% 6.60/6.97 (assert (forall ((V tptp.product_prod_nat_nat) (Vh tptp.list_VEBT_VEBT) (Vi tptp.vEBT_VEBT) (Vj tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vh) Vi)) Vj) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((V tptp.product_prod_nat_nat) (Vg tptp.list_VEBT_VEBT) (Vh tptp.vEBT_VEBT) (Vi tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vg) Vh)) Vi) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Tr tptp.list_VEBT_VEBT) (Sm tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) (@ tptp.suc tptp.zero_zero_nat)) Tr) Sm))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Uu tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg) TreeList2) Summary))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) Uu) _let_1))))
% 6.60/6.97 (assert (forall ((Uz tptp.product_prod_nat_nat) (Va tptp.nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz)) Va) Vb) Vc)))))
% 6.60/6.97 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) X))))
% 6.60/6.97 (assert (forall ((Uw tptp.nat) (Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT)) (@ tptp.vEBT_VEBT_minNull (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw) Ux) Uy))))
% 6.60/6.97 (assert (= tptp.vEBT_is_pred_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) Xs2) (@ (@ tptp.ord_less_nat Y3) X3) (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) Xs2) (=> (@ (@ tptp.ord_less_nat Z3) X3) (@ (@ tptp.ord_less_eq_nat Z3) Y3))))))))
% 6.60/6.97 (assert (= tptp.vEBT_is_succ_in_set (lambda ((Xs2 tptp.set_nat) (X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.member_nat Y3) Xs2) (@ (@ tptp.ord_less_nat X3) Y3) (forall ((Z3 tptp.nat)) (=> (@ (@ tptp.member_nat Z3) Xs2) (=> (@ (@ tptp.ord_less_nat X3) Z3) (@ (@ tptp.ord_less_eq_nat Y3) Z3))))))))
% 6.60/6.97 (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))))
% 6.60/6.97 (assert (forall ((V tptp.product_prod_nat_nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Uy) Uz)) X))))
% 6.60/6.97 (assert (forall ((Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT) (Va tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux) Uy) Uz)) Va) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((Uy tptp.nat) (Uz tptp.list_VEBT_VEBT) (Va tptp.vEBT_VEBT) (Vb tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy) Uz) Va)) Vb) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((V tptp.product_prod_nat_nat) (Vb tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (not (@ (@ tptp.vEBT_vebt_member (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) (@ tptp.suc tptp.zero_zero_nat)) Vb) Vc)) X))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (TrLst tptp.list_VEBT_VEBT) (Smry tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) TrLst) Smry))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) X) _let_1))))
% 6.60/6.97 (assert (forall ((V tptp.product_prod_nat_nat) (Vc tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (Ve tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vc) Vd)) Ve) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((V tptp.product_prod_nat_nat) (Vd tptp.list_VEBT_VEBT) (Ve tptp.vEBT_VEBT) (Vf tptp.nat)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V)) tptp.zero_zero_nat) Vd) Ve)) Vf) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= Xa2 tptp.zero_zero_nat) _let_1)) (=> (forall ((A5 Bool)) (=> (exists ((Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (=> (exists ((Va2 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc Va2)))) (not (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))))))) (=> (=> (exists ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_mint _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_pred _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_maxt (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat)))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (forall ((Uu2 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uu2) B5)) (=> (= Xa2 tptp.zero_zero_nat) (not (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat))))))) (=> (=> (exists ((Uv2 Bool) (Uw2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2))) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc N3))) _let_1)) (=> (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) _let_1) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_4))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_1) _let_3))))) (let ((_let_8 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) (let ((_let_9 (@ _let_6 _let_4))) (let ((_let_10 (@ tptp.vEBT_vebt_maxt _let_9))) (let ((_let_11 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_2) TreeList3) Summary2)) (not (and (=> _let_11 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_11) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_10 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_8)) _let_10))) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 (@ tptp.some_nat _let_4))) (@ (@ tptp.vEBT_vebt_succ _let_9) _let_8))) (@ (@ (@ tptp.if_option_nat (= _let_5 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_7 _let_5)) (@ tptp.vEBT_vebt_mint (@ _let_6 (@ tptp.the_nat _let_5))))))) tptp.none_nat))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (=> (= Xa2 tptp.zero_zero_nat) (not (= Y (@ (@ tptp.vEBT_Leaf false) B5)))))) (=> (forall ((A5 Bool)) (=> (exists ((B5 Bool)) (= X (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= Xa2 (@ tptp.suc tptp.zero_zero_nat)) (not (= Y (@ (@ tptp.vEBT_Leaf A5) false)))))) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (exists ((N3 tptp.nat)) (= Xa2 (@ tptp.suc (@ tptp.suc N3)))) (not (= Y _let_1)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2))) (=> (= X _let_1) (not (= Y _let_1))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (=> (= X _let_1) (not (= Y _let_1))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (not (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))))))))))))))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X6) (@ P (@ (@ tptp.plus_plus_int X6) D4))))) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ P6 X6) (@ P6 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X2 tptp.int)) (@ P X2)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y3 tptp.int)) (and (@ (@ tptp.member_int Y3) A2) (@ P (@ (@ tptp.minus_minus_int Y3) X3))))))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X6 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) D4))))) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ P6 X6) (@ P6 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D4))))) (= (exists ((X2 tptp.int)) (@ P X2)) (or (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (@ P6 X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (exists ((Y3 tptp.int)) (and (@ (@ tptp.member_int Y3) B3) (@ P (@ (@ tptp.plus_plus_int Y3) X3))))))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D4))))))))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool)) (not (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= N tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5)))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT)) (=> (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A5 Bool) (B5 Bool)) (= T (@ (@ tptp.vEBT_Leaf A5) B5))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT)) (= (@ (@ tptp.vEBT_invar_vebt T) tptp.one_one_nat) (exists ((A3 Bool) (B2 Bool)) (= T (@ (@ tptp.vEBT_Leaf A3) B2))))))
% 6.60/6.97 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.60/6.97 (assert (forall ((Y tptp.vEBT_VEBT)) (=> (forall ((X112 tptp.option4927543243414619207at_nat) (X122 tptp.nat) (X132 tptp.list_VEBT_VEBT) (X142 tptp.vEBT_VEBT)) (not (= Y (@ (@ (@ (@ tptp.vEBT_Node X112) X122) X132) X142)))) (not (forall ((X212 Bool) (X223 Bool)) (not (= Y (@ (@ tptp.vEBT_Leaf X212) X223))))))))
% 6.60/6.97 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT) (X21 Bool) (X222 Bool)) (not (= (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14) (@ (@ tptp.vEBT_Leaf X21) X222)))))
% 6.60/6.97 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool) (D3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) D3)))) (not (forall ((Mima tptp.option4927543243414619207at_nat) (Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Deg3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Mima) Deg2) TreeList3) Summary2)) Deg3))))))))
% 6.60/6.97 (assert (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf false) false)))
% 6.60/6.97 (assert (forall ((Uv Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf true) Uv)))))
% 6.60/6.97 (assert (forall ((Uu Bool)) (not (@ tptp.vEBT_VEBT_minNull (@ (@ tptp.vEBT_Leaf Uu) true)))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A) B))) (= (@ (@ tptp.vEBT_vebt_delete _let_1) (@ tptp.suc (@ tptp.suc N))) _let_1))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool)) (= (@ (@ tptp.vEBT_vebt_delete (@ (@ tptp.vEBT_Leaf A) B)) tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) B))))
% 6.60/6.97 (assert (= (@ tptp.vEBT_vebt_buildup tptp.zero_zero_nat) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.60/6.97 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X6)))) (=> (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) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Uy2) (@ tptp.suc V2)) TreeList3) S3)) X6)))))))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool)) (@ (@ tptp.vEBT_invar_vebt (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc tptp.zero_zero_nat))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (= (@ (@ tptp.vEBT_vebt_delete (@ _let_1 B)) (@ tptp.suc tptp.zero_zero_nat)) (@ _let_1 false)))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2)))))))))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.60/6.97 (assert (= (@ tptp.vEBT_vebt_buildup (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.vEBT_Leaf false) false)))
% 6.60/6.97 (assert (forall ((X tptp.nat) (A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ (@ tptp.vEBT_vebt_insert _let_2) X))) (let ((_let_4 (= X tptp.one_one_nat))) (let ((_let_5 (= X tptp.zero_zero_nat))) (and (=> _let_5 (= _let_3 (@ (@ tptp.vEBT_Leaf true) B))) (=> (not _let_5) (and (=> _let_4 (= _let_3 (@ _let_1 true))) (=> (not _let_4) (= _let_3 _let_2))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (forall ((Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf true) Uv2)))) (=> (forall ((Uu2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) true)))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X6) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (not (@ (@ tptp.ord_less_real X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (not (@ (@ tptp.ord_less_rat X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (not (@ (@ tptp.ord_less_num X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (not (@ (@ tptp.ord_less_nat X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (not (@ (@ tptp.ord_less_int X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (@ (@ tptp.ord_less_real T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (@ (@ tptp.ord_less_rat T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (@ (@ tptp.ord_less_num T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (@ (@ tptp.ord_less_nat T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (@ (@ tptp.ord_less_int T) X4))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (and (@ P X4) (@ Q X4)) (and (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.real Bool)) (P6 (-> tptp.real Bool)) (Q (-> tptp.real Bool)) (Q6 (-> tptp.real Bool))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.real)) (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.rat Bool)) (P6 (-> tptp.rat Bool)) (Q (-> tptp.rat Bool)) (Q6 (-> tptp.rat Bool))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.rat)) (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.num Bool)) (P6 (-> tptp.num Bool)) (Q (-> tptp.num Bool)) (Q6 (-> tptp.num Bool))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.num)) (forall ((X6 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (P6 (-> tptp.nat Bool)) (Q (-> tptp.nat Bool)) (Q6 (-> tptp.nat Bool))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.nat)) (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (P6 (-> tptp.int Bool)) (Q (-> tptp.int Bool)) (Q6 (-> tptp.int Bool))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z4) (= (@ P X6) (@ P6 X6))))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z4) (= (@ Q X6) (@ Q6 X6))))) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (= (or (@ P X4) (@ Q X4)) (or (@ P6 X4) (@ Q6 X4))))))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (not (= X4 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X4))) (=> (@ _let_1 Z5) (@ _let_1 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X4))) (=> (@ _let_1 Z5) (@ _let_1 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X4))) (=> (@ _let_1 Z5) (@ _let_1 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X4))) (=> (@ _let_1 Z5) (@ _let_1 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X4))) (=> (@ _let_1 Z5) (@ _let_1 T)))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (not (@ (@ tptp.ord_less_real T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (not (@ (@ tptp.ord_less_rat T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (not (@ (@ tptp.ord_less_num T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (not (@ (@ tptp.ord_less_nat T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (not (@ (@ tptp.ord_less_int T) X4)))))))
% 6.60/6.97 (assert (forall ((Uv Bool) (Uw Bool) (N tptp.nat)) (= (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uv) Uw)) (@ tptp.suc N)) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((Uu Bool) (Uv Bool)) (= (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf Uu) Uv)) tptp.zero_zero_nat) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT)) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (not (= X (@ (@ tptp.vEBT_Leaf false) false))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2)))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (not Y))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (=> (= X (@ (@ tptp.vEBT_Leaf false) false)) _let_1) (=> (=> (exists ((Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf true) Uv2))) Y) (=> (=> (exists ((Uu2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) true))) Y) (=> (=> (exists ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) _let_1) (not (=> (exists ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) Y))))))))))
% 6.60/6.97 (assert (forall ((A Bool) (Uw Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) Uw)) (@ tptp.suc tptp.zero_zero_nat)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))
% 6.60/6.97 (assert (forall ((B Bool) (Uu Bool)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_succ (@ (@ tptp.vEBT_Leaf Uu) B)) tptp.zero_zero_nat))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))
% 6.60/6.97 (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) (X6 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)) X6)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X6 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)) X6)))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2)) X6)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) Uv2)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (Uw2 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) Uw2)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B5 Bool) (Va2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc (@ tptp.suc Va2)))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT) (Vb2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3)) Vb2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT) (Vf2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2)) Vf2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT) (Vj2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2)) Vj2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X6)))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((Uu2 Bool) (B5 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uu2) B5)) tptp.zero_zero_nat)))) (=> (forall ((Uv2 Bool) (Uw2 Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (@ tptp.suc N3))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (Va3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2)) Va3)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT) (Ve2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2)) Ve2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT) (Vi2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2)) Vi2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X6))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) tptp.zero_zero_nat)))) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc tptp.zero_zero_nat))))) (=> (forall ((A5 Bool) (B5 Bool) (N3 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) (@ tptp.suc (@ tptp.suc N3)))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (Uu2 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) Uu2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT) (X6 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) TrLst2) Smry2)) X6)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2)) X6)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X6)))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X6)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) tptp.zero_zero_nat) Ts2) S3)) X6)))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (S3 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node Info2) (@ tptp.suc tptp.zero_zero_nat)) Ts2) S3)) X6)))) (=> (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc (@ tptp.suc V2))) TreeList3) Summary2)) X6)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X6)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc9072475918466114483BT_nat)) (=> (forall ((A5 Bool) (B5 Bool) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) X6)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)) X6)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)) X6)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)) X6)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT) (X6 tptp.nat)) (not (= X (@ (@ tptp.produc738532404422230701BT_nat (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2)) X6)))))))))))
% 6.60/6.97 (assert (forall ((B Bool) (A Bool) (Va tptp.nat)) (let ((_let_1 (@ (@ tptp.vEBT_vebt_pred (@ (@ tptp.vEBT_Leaf A) B)) (@ tptp.suc (@ tptp.suc Va))))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (not (@ (@ tptp.ord_less_eq_real X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (not (@ (@ tptp.ord_less_eq_rat X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (not (@ (@ tptp.ord_less_eq_num X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (not (@ (@ tptp.ord_less_eq_nat X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (not (@ (@ tptp.ord_less_eq_int X4) T)))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real Z5) X4) (@ (@ tptp.ord_less_eq_real T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z5) X4) (@ (@ tptp.ord_less_eq_rat T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num Z5) X4) (@ (@ tptp.ord_less_eq_num T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Z5) X4) (@ (@ tptp.ord_less_eq_nat T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int Z5) X4) (@ (@ tptp.ord_less_eq_int T) X4))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (@ (@ tptp.ord_less_eq_real X4) T))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (@ (@ tptp.ord_less_eq_rat X4) T))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (@ (@ tptp.ord_less_eq_num X4) T))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (@ (@ tptp.ord_less_eq_nat X4) T))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (@ (@ tptp.ord_less_eq_int X4) T))))))
% 6.60/6.97 (assert (forall ((T tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (=> (@ (@ tptp.ord_less_real X4) Z5) (not (@ (@ tptp.ord_less_eq_real T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X4) Z5) (not (@ (@ tptp.ord_less_eq_rat T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.num)) (exists ((Z5 tptp.num)) (forall ((X4 tptp.num)) (=> (@ (@ tptp.ord_less_num X4) Z5) (not (@ (@ tptp.ord_less_eq_num T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X4) Z5) (not (@ (@ tptp.ord_less_eq_nat T) X4)))))))
% 6.60/6.97 (assert (forall ((T tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (=> (@ (@ tptp.ord_less_int X4) Z5) (not (@ (@ tptp.ord_less_eq_int T) X4)))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X6 tptp.real) (K3 tptp.real)) (= (@ P X6) (@ P (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X6 tptp.real) (K3 tptp.real)) (= (@ Q X6) (@ Q (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X6 tptp.rat) (K3 tptp.rat)) (= (@ P X6) (@ P (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X6 tptp.rat) (K3 tptp.rat)) (= (@ Q X6) (@ Q (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ Q X6) (@ Q (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4)))) (= (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.real Bool)) (D4 tptp.real) (Q (-> tptp.real Bool))) (=> (forall ((X6 tptp.real) (K3 tptp.real)) (= (@ P X6) (@ P (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K3) D4))))) (=> (forall ((X6 tptp.real) (K3 tptp.real)) (= (@ Q X6) (@ Q (@ (@ tptp.minus_minus_real X6) (@ (@ tptp.times_times_real K3) D4))))) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.rat Bool)) (D4 tptp.rat) (Q (-> tptp.rat Bool))) (=> (forall ((X6 tptp.rat) (K3 tptp.rat)) (= (@ P X6) (@ P (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K3) D4))))) (=> (forall ((X6 tptp.rat) (K3 tptp.rat)) (= (@ Q X6) (@ Q (@ (@ tptp.minus_minus_rat X6) (@ (@ tptp.times_times_rat K3) D4))))) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (D4 tptp.int) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D4))))) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ Q X6) (@ Q (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D4))))) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4)))) (= (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1)))))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (X5 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X X5) (=> (=> _let_2 (= P P6)) (= (and (@ _let_1 X) P) (and _let_2 P6))))))))
% 6.60/6.97 (assert (forall ((X tptp.int) (X5 tptp.int) (P Bool) (P6 Bool)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ _let_1 X5))) (=> (= X X5) (=> (=> _let_2 (= P P6)) (= (=> (@ _let_1 X) P) (=> _let_2 P6))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X6 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) D4))))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X6 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X6) (@ Q (@ (@ tptp.minus_minus_int X6) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X6 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) D4))))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) B3) (not (= X6 (@ (@ tptp.plus_plus_int Xb) Xa))))))) (=> (@ Q X6) (@ Q (@ (@ tptp.minus_minus_int X6) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X6) (@ P (@ (@ tptp.plus_plus_int X6) D4))))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X6) (@ Q (@ (@ tptp.plus_plus_int X6) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (and (@ P X4) (@ Q X4)) (and (@ P _let_1) (@ Q _let_1))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ P X6) (@ P (@ (@ tptp.plus_plus_int X6) D4))))) (=> (forall ((X6 tptp.int)) (=> (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb tptp.int)) (=> (@ (@ tptp.member_int Xb) A2) (not (= X6 (@ (@ tptp.minus_minus_int Xb) Xa))))))) (=> (@ Q X6) (@ Q (@ (@ tptp.plus_plus_int X6) D4))))) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int X4) D4))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (or (@ P X4) (@ Q X4)) (or (@ P _let_1) (@ Q _let_1))))))))))
% 6.60/6.97 (assert (forall ((D tptp.int) (P6 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ P6 X6) (@ P6 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int Z4) X6) (= (@ P X6) (@ P6 X6))))) (=> (exists ((X_12 tptp.int)) (@ P6 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.60/6.97 (assert (forall ((D tptp.int) (P1 (-> tptp.int Bool)) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ P1 X6) (@ P1 (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D))))) (=> (exists ((Z4 tptp.int)) (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Z4) (= (@ P X6) (@ P1 X6))))) (=> (exists ((X_12 tptp.int)) (@ P1 X_12)) (exists ((X_1 tptp.int)) (@ P X_1))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_vebt_member X) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_vebt_member X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2)))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_vebt_member X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) Y) (=> (=> (exists ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) Y) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc Va2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_4 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (exists ((Summary2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc (@ tptp.suc Va2))) TreeList3) Summary2))) (= Y (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_5 (=> _let_5 (and _let_4 (=> _let_4 (and (=> _let_3 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X6 tptp.int)) (=> (@ P X6) (@ P (@ (@ tptp.plus_plus_int X6) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.plus_plus_int X4) (@ (@ tptp.times_times_int K) D))))))))))
% 6.60/6.97 (assert (forall ((D tptp.int) (P (-> tptp.int Bool)) (K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X6 tptp.int)) (=> (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) D)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (forall ((X4 tptp.int)) (=> (@ P X4) (@ P (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K) D))))))))))
% 6.60/6.97 (assert (forall ((D tptp.int) (P (-> tptp.int Bool))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (=> (forall ((X6 tptp.int) (K3 tptp.int)) (= (@ P X6) (@ P (@ (@ tptp.minus_minus_int X6) (@ (@ tptp.times_times_int K3) D))))) (= (exists ((X2 tptp.int)) (@ P X2)) (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D)) (@ P X3))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D4)))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.plus_plus_int X4) D4)) T))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.plus_plus_int X4) D4) T)))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.plus_plus_int X4) D4) T))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.minus_minus_int X4) D4))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_int X4) T) (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int T) B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (= X4 T)) (not (= (@ (@ tptp.minus_minus_int X4) D4) T)))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.minus_minus_int T) tptp.one_one_int)) B3) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (= X4 T) (= (@ (@ tptp.minus_minus_int X4) D4) T))))))))
% 6.60/6.97 (assert (= tptp.vEBT_invar_vebt (lambda ((A1 tptp.vEBT_VEBT) (A22 tptp.nat)) (or (and (exists ((A3 Bool) (B2 Bool)) (= A1 (@ (@ tptp.vEBT_Leaf A3) B2))) (= A22 (@ tptp.suc tptp.zero_zero_nat))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) A22) TreeList) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_1) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (= A22 (@ (@ tptp.plus_plus_nat N2) _let_1)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) N2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 N2)) (= A22 (@ (@ tptp.plus_plus_nat N2) N2)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N2) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low X3) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))) (exists ((TreeList tptp.list_VEBT_VEBT) (N2 tptp.nat) (Summary3 tptp.vEBT_VEBT) (Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (= Mi3 Ma3))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.suc N2))) (and (= A1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi3) Ma3))) A22) TreeList) Summary3)) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (@ (@ tptp.vEBT_invar_vebt X3) N2))) (@ (@ tptp.vEBT_invar_vebt Summary3) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList) (@ _let_2 _let_3)) (= A22 (@ (@ tptp.plus_plus_nat N2) _let_3)) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary3) I5)))) (=> _let_1 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ _let_2 A22)) (=> (not _let_1) (forall ((I5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.suc N2))) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma3) N2) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low Ma3) N2))) (forall ((X3 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X3) N2) I5) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList) I5)) (@ (@ tptp.vEBT_VEBT_low X3) N2))) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))))))
% 6.60/6.97 (assert (forall ((A12 tptp.vEBT_VEBT) (A23 tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt A12) A23) (=> (=> (exists ((A5 Bool) (B5 Bool)) (= A12 (@ (@ tptp.vEBT_Leaf A5) B5))) (not (= A23 (@ tptp.suc tptp.zero_zero_nat)))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat)) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X_12))) (not (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12))))))))))))))) (=> (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 N3) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2))))))))))))))))))))))) (not (forall ((TreeList3 tptp.list_VEBT_VEBT) (N3 tptp.nat) (Summary2 tptp.vEBT_VEBT) (M4 tptp.nat) (Deg2 tptp.nat) (Mi2 tptp.nat) (Ma2 tptp.nat)) (let ((_let_1 (= Mi2 Ma2))) (let ((_let_2 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (= A12 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Deg2) TreeList3) Summary2)) (=> (= A23 Deg2) (=> (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_invar_vebt X4) N3))) (=> (@ (@ tptp.vEBT_invar_vebt Summary2) M4) (=> (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ _let_2 M4)) (=> (= M4 (@ tptp.suc N3)) (=> (= Deg2 (@ (@ tptp.plus_plus_nat N3) M4)) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I2)))) (=> (=> _let_1 (forall ((X4 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X4) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X_12 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X4) X_12)))))) (=> (@ (@ tptp.ord_less_eq_nat Mi2) Ma2) (=> (@ (@ tptp.ord_less_nat Ma2) (@ _let_2 Deg2)) (not (=> (not _let_1) (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I2) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) M4)) (and (=> (= (@ (@ tptp.vEBT_VEBT_high Ma2) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low Ma2) N3))) (forall ((X4 tptp.nat)) (=> (and (= (@ (@ tptp.vEBT_VEBT_high X4) N3) I2) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I2)) (@ (@ tptp.vEBT_VEBT_low X4) N3))) (and (@ (@ tptp.ord_less_nat Mi2) X4) (@ (@ tptp.ord_less_eq_nat X4) Ma2)))))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_insert X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (not (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2)))))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (not (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2))))))))))))))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int T))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_1 X4) (@ _let_1 (@ (@ tptp.plus_plus_int X4) D4)))))))))
% 6.60/6.97 (assert (forall ((D4 tptp.int) (T tptp.int) (A2 tptp.set_int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D4) (=> (@ (@ tptp.member_int (@ (@ tptp.plus_plus_int T) tptp.one_one_int)) A2) (forall ((X4 tptp.int)) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ (@ tptp.ord_less_eq_int X4) T) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int X4) D4)) T))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat)) (=> (exists ((Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Mi2)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat)))))))) (=> (=> (exists ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (not (= Y tptp.none_nat))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (not (= Y (@ tptp.some_nat Ma2)))))))))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_mint (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (= _let_1 tptp.none_nat))))))))
% 6.60/6.97 (assert (forall ((B Bool) (A Bool)) (let ((_let_1 (@ tptp.vEBT_vebt_maxt (@ (@ tptp.vEBT_Leaf A) B)))) (and (=> B (= _let_1 (@ tptp.some_nat tptp.one_one_nat))) (=> (not B) (and (=> A (= _let_1 (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A) (= _let_1 tptp.none_nat))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (=> (exists ((Uu2 Bool) (Uv2 Bool)) (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) Y) (=> (=> (exists ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) Y) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (= Y (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (= Y (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf Uu2) Uv2)))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (or (= Xa2 Mi2) (= Xa2 Ma2)))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) Y) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (= Y (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (=> (exists ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (= 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))))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((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))))))))))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.60/6.97 (assert (forall ((N tptp.nat) (X tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ tptp.vEBT_vebt_buildup N)) X))))
% 6.60/6.97 (assert (= tptp.vEBT_V8194947554948674370ptions (lambda ((T2 tptp.vEBT_VEBT) (X3 tptp.nat)) (or (@ (@ tptp.vEBT_V5719532721284313246member T2) X3) (@ (@ tptp.vEBT_VEBT_membermima T2) X3)))))
% 6.60/6.97 (assert (forall ((Tree tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt Tree) N) (=> (@ (@ tptp.vEBT_vebt_member Tree) X) (or (@ (@ tptp.vEBT_V5719532721284313246member Tree) X) (@ (@ tptp.vEBT_VEBT_membermima Tree) X))))))
% 6.60/6.97 (assert (forall ((Uu tptp.option4927543243414619207at_nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT) (Ux tptp.nat)) (not (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ (@ (@ tptp.vEBT_Node Uu) tptp.zero_zero_nat) Uv) Uw)) Ux))))
% 6.60/6.97 (assert (forall ((Ux tptp.list_VEBT_VEBT) (Uy tptp.vEBT_VEBT) (Uz tptp.nat)) (not (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux) Uy)) Uz))))
% 6.60/6.97 (assert (forall ((A Bool) (B Bool) (X tptp.nat)) (let ((_let_1 (= X tptp.one_one_nat))) (let ((_let_2 (= X tptp.zero_zero_nat))) (= (@ (@ tptp.vEBT_V5719532721284313246member (@ (@ tptp.vEBT_Leaf A) B)) X) (and (=> _let_2 A) (=> (not _let_2) (and (=> _let_1 B) _let_1))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Va tptp.list_VEBT_VEBT) (Vb tptp.vEBT_VEBT) (X tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) tptp.zero_zero_nat) Va) Vb)) X) (or (= X Mi) (= X Ma)))))
% 6.60/6.97 (assert (forall ((X tptp.produc8306885398267862888on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat tptp.nat)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat tptp.nat)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat tptp.nat)) (A5 tptp.nat) (B5 tptp.nat)) (not (= X (@ (@ tptp.produc8929957630744042906on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat A5)) (@ tptp.some_nat B5)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc5542196010084753463at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A5 tptp.product_prod_nat_nat) (B5 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc2899441246263362727at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat A5)) (@ tptp.some_P7363390416028606310at_nat B5)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc1193250871479095198on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num tptp.num)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num tptp.num)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num tptp.num)) (A5 tptp.num) (B5 tptp.num)) (not (= X (@ (@ tptp.produc5778274026573060048on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num A5)) (@ tptp.some_num B5)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc2233624965454879586on_nat)) (=> (forall ((Uu2 (-> tptp.nat tptp.nat Bool)) (Uv2 tptp.option_nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uu2) (@ (@ tptp.produc5098337634421038937on_nat tptp.none_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.nat tptp.nat Bool)) (V2 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat Uw2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat V2)) tptp.none_nat))))) (not (forall ((F2 (-> tptp.nat tptp.nat Bool)) (X6 tptp.nat) (Y5 tptp.nat)) (not (= X (@ (@ tptp.produc4035269172776083154on_nat F2) (@ (@ tptp.produc5098337634421038937on_nat (@ tptp.some_nat X6)) (@ tptp.some_nat Y5)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc5491161045314408544at_nat)) (=> (forall ((Uu2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (Uv2 tptp.option4927543243414619207at_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uu2) (@ (@ tptp.produc488173922507101015at_nat tptp.none_P5556105721700978146at_nat) Uv2))))) (=> (forall ((Uw2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (V2 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat Uw2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat V2)) tptp.none_P5556105721700978146at_nat))))) (not (forall ((F2 (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool)) (X6 tptp.product_prod_nat_nat) (Y5 tptp.product_prod_nat_nat)) (not (= X (@ (@ tptp.produc3994169339658061776at_nat F2) (@ (@ tptp.produc488173922507101015at_nat (@ tptp.some_P7363390416028606310at_nat X6)) (@ tptp.some_P7363390416028606310at_nat Y5)))))))))))
% 6.60/6.97 (assert (forall ((X tptp.produc7036089656553540234on_num)) (=> (forall ((Uu2 (-> tptp.num tptp.num Bool)) (Uv2 tptp.option_num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uu2) (@ (@ tptp.produc8585076106096196333on_num tptp.none_num) Uv2))))) (=> (forall ((Uw2 (-> tptp.num tptp.num Bool)) (V2 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num Uw2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num V2)) tptp.none_num))))) (not (forall ((F2 (-> tptp.num tptp.num Bool)) (X6 tptp.num) (Y5 tptp.num)) (not (= X (@ (@ tptp.produc3576312749637752826on_num F2) (@ (@ tptp.produc8585076106096196333on_num (@ tptp.some_num X6)) (@ tptp.some_num Y5)))))))))))
% 6.60/6.97 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.product_prod_nat_nat) (B tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat F) (@ tptp.some_P7363390416028606310at_nat A)) (@ tptp.some_P7363390416028606310at_nat B)) (@ tptp.some_P7363390416028606310at_nat (@ (@ F A) B)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.num tptp.num tptp.num)) (A tptp.num) (B tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num F) (@ tptp.some_num A)) (@ tptp.some_num B)) (@ tptp.some_num (@ (@ F A) B)))))
% 6.60/6.97 (assert (forall ((F (-> tptp.nat tptp.nat tptp.nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat F) (@ tptp.some_nat A)) (@ tptp.some_nat B)) (@ tptp.some_nat (@ (@ F A) B)))))
% 6.60/6.97 (assert (forall ((Uu (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Uv tptp.option4927543243414619207at_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uu) tptp.none_P5556105721700978146at_nat) Uv) tptp.none_P5556105721700978146at_nat)))
% 6.60/6.97 (assert (forall ((Uu (-> tptp.num tptp.num tptp.num)) (Uv tptp.option_num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uu) tptp.none_num) Uv) tptp.none_num)))
% 6.60/6.97 (assert (forall ((Uu (-> tptp.nat tptp.nat tptp.nat)) (Uv tptp.option_nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uu) tptp.none_nat) Uv) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((Uw (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (V tptp.product_prod_nat_nat)) (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat Uw) (@ tptp.some_P7363390416028606310at_nat V)) tptp.none_P5556105721700978146at_nat) tptp.none_P5556105721700978146at_nat)))
% 6.60/6.97 (assert (forall ((Uw (-> tptp.num tptp.num tptp.num)) (V tptp.num)) (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num Uw) (@ tptp.some_num V)) tptp.none_num) tptp.none_num)))
% 6.60/6.97 (assert (forall ((Uw (-> tptp.nat tptp.nat tptp.nat)) (V tptp.nat)) (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat Uw) (@ tptp.some_nat V)) tptp.none_nat) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Xa2 tptp.option4927543243414619207at_nat) (Xb3 tptp.option4927543243414619207at_nat) (Y tptp.option4927543243414619207at_nat)) (let ((_let_1 (not (= Y tptp.none_P5556105721700978146at_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V1502963449132264192at_nat X) Xa2) Xb3) Y) (=> (=> (= Xa2 tptp.none_P5556105721700978146at_nat) _let_1) (=> (=> (exists ((V2 tptp.product_prod_nat_nat)) (= Xa2 (@ tptp.some_P7363390416028606310at_nat V2))) (=> (= Xb3 tptp.none_P5556105721700978146at_nat) _let_1)) (not (forall ((A5 tptp.product_prod_nat_nat)) (=> (= Xa2 (@ tptp.some_P7363390416028606310at_nat A5)) (forall ((B5 tptp.product_prod_nat_nat)) (=> (= Xb3 (@ tptp.some_P7363390416028606310at_nat B5)) (not (= Y (@ tptp.some_P7363390416028606310at_nat (@ (@ X A5) B5)))))))))))))))
% 6.60/6.97 (assert (forall ((X (-> tptp.num tptp.num tptp.num)) (Xa2 tptp.option_num) (Xb3 tptp.option_num) (Y tptp.option_num)) (let ((_let_1 (not (= Y tptp.none_num)))) (=> (= (@ (@ (@ tptp.vEBT_V819420779217536731ft_num X) Xa2) Xb3) Y) (=> (=> (= Xa2 tptp.none_num) _let_1) (=> (=> (exists ((V2 tptp.num)) (= Xa2 (@ tptp.some_num V2))) (=> (= Xb3 tptp.none_num) _let_1)) (not (forall ((A5 tptp.num)) (=> (= Xa2 (@ tptp.some_num A5)) (forall ((B5 tptp.num)) (=> (= Xb3 (@ tptp.some_num B5)) (not (= Y (@ tptp.some_num (@ (@ X A5) B5)))))))))))))))
% 6.60/6.97 (assert (forall ((X (-> tptp.nat tptp.nat tptp.nat)) (Xa2 tptp.option_nat) (Xb3 tptp.option_nat) (Y tptp.option_nat)) (let ((_let_1 (not (= Y tptp.none_nat)))) (=> (= (@ (@ (@ tptp.vEBT_V4262088993061758097ft_nat X) Xa2) Xb3) Y) (=> (=> (= Xa2 tptp.none_nat) _let_1) (=> (=> (exists ((V2 tptp.nat)) (= Xa2 (@ tptp.some_nat V2))) (=> (= Xb3 tptp.none_nat) _let_1)) (not (forall ((A5 tptp.nat)) (=> (= Xa2 (@ tptp.some_nat A5)) (forall ((B5 tptp.nat)) (=> (= Xb3 (@ tptp.some_nat B5)) (not (= Y (@ tptp.some_nat (@ (@ X A5) B5)))))))))))))))
% 6.60/6.97 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((Uu tptp.nat) (Uv tptp.list_VEBT_VEBT) (Uw tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu) Uv) Uw)) tptp.none_nat)))
% 6.60/6.97 (assert (forall ((V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vd tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList2) Vd)) X) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4))))))))
% 6.60/6.97 (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))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (V tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Vc tptp.vEBT_VEBT) (X tptp.nat)) (let ((_let_1 (@ tptp.suc V))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high X) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList2)))) (= (@ (@ tptp.vEBT_VEBT_membermima (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) _let_1) TreeList2) Vc)) X) (or (= X Mi) (= X Ma) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList2) _let_3)) (@ (@ tptp.vEBT_VEBT_low X) _let_2))) _let_4)))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT)) (=> (forall ((A5 Bool) (B5 Bool)) (not (= X (@ (@ tptp.vEBT_Leaf A5) B5)))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2)))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (not (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2)))))))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_maxt (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Ma))))
% 6.60/6.97 (assert (forall ((Mi tptp.nat) (Ma tptp.nat) (Ux tptp.nat) (Uy tptp.list_VEBT_VEBT) (Uz tptp.vEBT_VEBT)) (= (@ tptp.vEBT_vebt_mint (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi) Ma))) Ux) Uy) Uz)) (@ tptp.some_nat Mi))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat)) (=> (exists ((Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vc2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc V2)) TreeList3) Vc2))) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.suc V2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_nat _let_2) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (exists ((Vd2 tptp.vEBT_VEBT)) (= X (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) (@ tptp.suc V2)) TreeList3) Vd2))) (not (and (=> _let_3 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_2)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_1))) _let_3)))))))))))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_V5719532721284313246member X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))) (=> (forall ((Uu2 tptp.option4927543243414619207at_nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (not (= 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))))))))))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_succ T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y3 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat X) Y3)))) tptp.bot_bot_set_nat)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (= (= (@ (@ tptp.vEBT_vebt_pred T) X) tptp.none_nat) (= (@ tptp.collect_nat (lambda ((Y3 tptp.nat)) (and (@ (@ tptp.vEBT_vebt_member T) Y3) (@ (@ tptp.ord_less_nat Y3) X)))) tptp.bot_bot_set_nat)))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_succ X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) B5))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((Uv2 Bool) (Uw2 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc N3))) (=> (= Xa2 _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf Uv2) Uw2)) _let_1))))))))) (=> (forall ((Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vc2 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vc2) Vd2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vg2 tptp.list_VEBT_VEBT) (Vh2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vg2) Vh2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_succ Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_maxt _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Xa2) Mi2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Mi2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_less (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_succ _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) tptp.none_nat) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_mint (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_succ_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (not (= A2 B3)) (@ (@ tptp.ord_less_set_int A2) B3)))))
% 6.60/6.97 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.option_nat)) (=> (= (@ (@ tptp.vEBT_vebt_pred X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (Uw2 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) Uw2))) (=> (= X _let_2) (=> (= Xa2 _let_1) (=> (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1))))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (=> (= Xa2 _let_1) (=> (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.vEBT_Leaf A5) B5)) _let_1))))))))) (=> (forall ((Uy2 tptp.nat) (Uz2 tptp.list_VEBT_VEBT) (Va3 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uy2) Uz2) Va3))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vd2 tptp.list_VEBT_VEBT) (Ve2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Vd2) Ve2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vh2 tptp.list_VEBT_VEBT) (Vi2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vh2) Vi2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_4))) (let ((_let_6 (@ (@ tptp.vEBT_vebt_pred Summary2) _let_5))) (let ((_let_7 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_8 (@ tptp.vEBT_VEBT_mul (@ tptp.some_nat (@ (@ tptp.power_power_nat _let_3) _let_4))))) (let ((_let_9 (@ (@ tptp.vEBT_VEBT_low Xa2) _let_4))) (let ((_let_10 (@ _let_7 _let_5))) (let ((_let_11 (@ tptp.vEBT_vebt_mint _let_10))) (let ((_let_12 (@ (@ tptp.ord_less_nat Ma2) Xa2))) (=> (= X _let_2) (=> (and (=> _let_12 (= Y (@ tptp.some_nat Ma2))) (=> (not _let_12) (= Y (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat _let_5) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_option_nat (and (not (= _let_11 tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_greater (@ tptp.some_nat _let_9)) _let_11))) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 (@ tptp.some_nat _let_5))) (@ (@ tptp.vEBT_vebt_pred _let_10) _let_9))) (@ (@ (@ tptp.if_option_nat (= _let_6 tptp.none_nat)) (@ (@ (@ tptp.if_option_nat (@ (@ tptp.ord_less_nat Mi2) Xa2)) (@ tptp.some_nat Mi2)) tptp.none_nat)) (@ (@ tptp.vEBT_VEBT_add (@ _let_8 _let_6)) (@ tptp.vEBT_vebt_maxt (@ _let_7 (@ tptp.the_nat _let_6))))))) tptp.none_nat)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_pred_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))
% 6.60/6.97 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.ord_max_real A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.60/6.97 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (= (@ (@ tptp.ord_max_real A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.60/6.97 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat) (Z tptp.extended_enat)) (= (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) Z) (and (@ (@ tptp.ord_le72135733267957522d_enat X) Z) (@ (@ tptp.ord_le72135733267957522d_enat Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer X) Y)) Z) (and (@ (@ tptp.ord_le6747313008572928689nteger X) Z) (@ (@ tptp.ord_le6747313008572928689nteger Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real X) Y)) Z) (and (@ (@ tptp.ord_less_real X) Z) (@ (@ tptp.ord_less_real Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat X) Y)) Z) (and (@ (@ tptp.ord_less_rat X) Z) (@ (@ tptp.ord_less_rat Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (= (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num X) Y)) Z) (and (@ (@ tptp.ord_less_num X) Z) (@ (@ tptp.ord_less_num Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat X) Y)) Z) (and (@ (@ tptp.ord_less_nat X) Z) (@ (@ tptp.ord_less_nat Y) Z)))))
% 6.60/6.97 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int X) Y)) Z) (and (@ (@ tptp.ord_less_int X) Z) (@ (@ tptp.ord_less_int Y) Z)))))
% 6.60/6.97 (assert (forall ((N tptp.nat)) (= (@ tptp.vEBT_VEBT_set_vebt (@ tptp.vEBT_vebt_buildup N)) tptp.bot_bot_set_nat)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) tptp.bot_bot_set_int) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) tptp.bot_bot_set_real) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) tptp.bot_bot_set_nat) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int tptp.bot_bot_set_int) A2) tptp.bot_bot_set_int)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real tptp.bot_bot_set_real) A2) tptp.bot_bot_set_real)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat tptp.bot_bot_set_nat) A2) tptp.bot_bot_set_nat)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.minus_minus_set_int A2) A2) tptp.bot_bot_set_int)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.minus_minus_set_real A2) A2) tptp.bot_bot_set_real)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.minus_minus_set_nat A2) A2) tptp.bot_bot_set_nat)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= A2 B3)))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (forall ((X6 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X6))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le211207098394363844omplex A2) B3))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (forall ((X6 tptp.real)) (let ((_let_1 (@ tptp.member_real X6))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_real A2) B3))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (forall ((X6 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X6))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (forall ((X6 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X6))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (forall ((X6 tptp.int)) (let ((_let_1 (@ tptp.member_int X6))) (=> (@ _let_1 A2) (@ _let_1 B3)))) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_maxt T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.60/6.97 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (=> (= (@ tptp.vEBT_vebt_mint T) tptp.none_nat) (= (@ tptp.vEBT_VEBT_set_vebt T) tptp.bot_bot_set_nat)))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real A2) B3) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real A2) B3))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat A2) B3) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat A2) B3))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int A2) B3) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) tptp.bot_bot_set_nat) (= A2 tptp.bot_bot_set_nat))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) tptp.bot_bot_set_real) (= A2 tptp.bot_bot_set_real))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) tptp.bot_bot_set_int) (= A2 tptp.bot_bot_set_int))))
% 6.60/6.97 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (and (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (and (@ (@ tptp.ord_le3102999989581377725nteger B) A) (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (and (@ (@ tptp.ord_less_eq_rat B) A) (@ (@ tptp.ord_less_eq_rat C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (and (@ (@ tptp.ord_less_eq_num B) A) (@ (@ tptp.ord_less_eq_num C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (and (@ (@ tptp.ord_less_eq_nat B) A) (@ (@ tptp.ord_less_eq_nat C) A)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (and (@ (@ tptp.ord_less_eq_int B) A) (@ (@ tptp.ord_less_eq_int C) A)))))
% 6.60/6.97 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) B) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (= (@ (@ tptp.ord_max_Code_integer A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= (@ (@ tptp.ord_max_rat A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (= (@ (@ tptp.ord_max_num A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= (@ (@ tptp.ord_max_nat A) B) B))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (= (@ (@ tptp.ord_max_int A) B) B))))
% 6.60/6.97 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= (@ (@ tptp.ord_ma741700101516333627d_enat A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= (@ (@ tptp.ord_max_Code_integer A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= (@ (@ tptp.ord_max_rat A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= (@ (@ tptp.ord_max_num A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= (@ (@ tptp.ord_max_nat A) B) A))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= (@ (@ tptp.ord_max_int A) B) A))))
% 6.60/6.97 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= tptp.bot_bot_set_set_int (@ (@ tptp.set_or370866239135849197et_int A) B)) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= tptp.bot_bot_set_rat (@ (@ tptp.set_or633870826150836451st_rat A) B)) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num)) (= (= tptp.bot_bot_set_num (@ (@ tptp.set_or7049704709247886629st_num A) B)) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.bot_bot_set_nat (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (= tptp.bot_bot_set_int (@ (@ tptp.set_or1266510415728281911st_int A) B)) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= tptp.bot_bot_set_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (= (@ (@ tptp.set_or370866239135849197et_int A) B) tptp.bot_bot_set_set_int) (not (@ (@ tptp.ord_less_eq_set_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat) (not (@ (@ tptp.ord_less_eq_rat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num)) (= (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num) (not (@ (@ tptp.ord_less_eq_num A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat) (not (@ (@ tptp.ord_less_eq_nat A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int) (not (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real) (not (@ (@ tptp.ord_less_eq_real A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (= (@ (@ tptp.set_or633870826150836451st_rat A) B) tptp.bot_bot_set_rat))))
% 6.60/6.97 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (= (@ (@ tptp.set_or7049704709247886629st_num A) B) tptp.bot_bot_set_num))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) tptp.bot_bot_set_nat))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) tptp.bot_bot_set_int))))
% 6.60/6.97 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) tptp.bot_bot_set_real))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C4 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C4) (= (@ (@ tptp.minus_minus_set_nat B3) (@ (@ tptp.minus_minus_set_nat C4) A2)) A2)))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (= (@ (@ tptp.minus_minus_set_int B3) (@ (@ tptp.minus_minus_set_int C4) A2)) A2)))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (C4 tptp.set_nat) (D4 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat D4) B3) (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_set_nat C4) D4))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (C4 tptp.set_int) (D4 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) C4) (=> (@ (@ tptp.ord_less_eq_set_int D4) B3) (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_set_int C4) D4))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (= (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)) (forall ((X3 tptp.product_prod_int_int)) (=> (@ P X3) (@ Q X3))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)) (forall ((X3 tptp.complex)) (=> (@ P X3) (@ Q X3))))))
% 6.60/6.97 (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 ((X3 tptp.set_nat)) (=> (@ P X3) (@ Q X3))))))
% 6.60/6.97 (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 ((X3 tptp.nat)) (=> (@ P X3) (@ Q X3))))))
% 6.60/6.97 (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 ((X3 tptp.int)) (=> (@ P X3) (@ Q X3))))))
% 6.60/6.97 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (@ (@ tptp.ord_less_eq_set_int B6) A6)))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (@ _let_1 C4))))))
% 6.60/6.97 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (Q (-> tptp.product_prod_int_int Bool))) (=> (forall ((X6 tptp.product_prod_int_int)) (=> (@ P X6) (@ Q X6))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int P)) (@ tptp.collec213857154873943460nt_int Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.complex Bool)) (Q (-> tptp.complex Bool))) (=> (forall ((X6 tptp.complex)) (=> (@ P X6) (@ Q X6))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex P)) (@ tptp.collect_complex Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.set_nat Bool)) (Q (-> tptp.set_nat Bool))) (=> (forall ((X6 tptp.set_nat)) (=> (@ P X6) (@ Q X6))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat P)) (@ tptp.collect_set_nat Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.nat Bool)) (Q (-> tptp.nat Bool))) (=> (forall ((X6 tptp.nat)) (=> (@ P X6) (@ Q X6))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat P)) (@ tptp.collect_nat Q)))))
% 6.60/6.97 (assert (forall ((P (-> tptp.int Bool)) (Q (-> tptp.int Bool))) (=> (forall ((X6 tptp.int)) (=> (@ P X6) (@ Q X6))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int P)) (@ tptp.collect_int Q)))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A2) A2)))
% 6.60/6.97 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((T2 tptp.complex)) (let ((_let_1 (@ tptp.member_complex T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((T2 tptp.real)) (let ((_let_1 (@ tptp.member_real T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((T2 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((T2 tptp.nat)) (let ((_let_1 (@ tptp.member_nat T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((T2 tptp.int)) (let ((_let_1 (@ tptp.member_int T2))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.60/6.97 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (forall ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (forall ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (forall ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (forall ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (=> (@ _let_1 A6) (@ _let_1 B6)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (= A2 B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (not (@ (@ tptp.ord_less_eq_set_int B3) A2)))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (C tptp.complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (C tptp.real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (C tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (C tptp.nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C tptp.int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X tptp.complex)) (let ((_let_1 (@ tptp.member_complex X))) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ tptp.member_real X))) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (X tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X))) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ tptp.member_nat X))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ tptp.member_int X))) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ _let_1 A2) (@ _let_1 B3))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex A2) B3) (exists ((B5 tptp.complex)) (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real A2) B3) (exists ((B5 tptp.real)) (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (=> (@ (@ tptp.ord_less_set_set_nat A2) B3) (exists ((B5 tptp.set_nat)) (@ (@ tptp.member_set_nat B5) (@ (@ tptp.minus_2163939370556025621et_nat B3) A2))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (exists ((B5 tptp.int)) (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int B3) A2))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat A2) B3) (exists ((B5 tptp.nat)) (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B3) A2))))))
% 6.60/6.97 (assert (forall ((A2 tptp.set_real) (P (-> tptp.real Bool))) (@ (@ tptp.ord_less_eq_set_real (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ P X3))))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_Pr958786334691620121nt_int) (P (-> tptp.product_prod_int_int Bool))) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (and (@ (@ tptp.member5262025264175285858nt_int X3) A2) (@ P X3))))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.complex Bool))) (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_nat Bool))) (@ (@ tptp.ord_le6893508408891458716et_nat (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X3) A2) (@ P X3))))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.nat Bool))) (@ (@ tptp.ord_less_eq_set_nat (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) A2)))
% 6.60/6.97 (assert (forall ((A2 tptp.set_int) (P (-> tptp.int Bool))) (@ (@ tptp.ord_less_eq_set_int (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) A2)))
% 6.60/6.97 (assert (= tptp.ord_le211207098394363844omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ (@ tptp.ord_le4573692005234683329plex_o (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A6))) (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) B6))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ (@ tptp.ord_less_eq_real_o (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A6))) (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) B6))))))
% 6.60/6.97 (assert (= tptp.ord_le6893508408891458716et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ (@ tptp.ord_le3964352015994296041_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) B6))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B6))))))
% 6.60/6.97 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B6))))))
% 6.60/6.97 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (D tptp.extended_enat) (B tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat D) B) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat C) D)) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger D) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer C) D)) (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.rat) (A tptp.rat) (D tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat C) A) (=> (@ (@ tptp.ord_less_eq_rat D) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat C) D)) (@ (@ tptp.ord_max_rat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.num) (A tptp.num) (D tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num C) A) (=> (@ (@ tptp.ord_less_eq_num D) B) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num C) D)) (@ (@ tptp.ord_max_num A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.nat) (A tptp.nat) (D tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) A) (=> (@ (@ tptp.ord_less_eq_nat D) B) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat C) D)) (@ (@ tptp.ord_max_nat A) B))))))
% 6.60/6.97 (assert (forall ((C tptp.int) (A tptp.int) (D tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int C) A) (=> (@ (@ tptp.ord_less_eq_int D) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int C) D)) (@ (@ tptp.ord_max_int A) B))))))
% 6.60/6.97 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (= A (@ (@ tptp.ord_max_Code_integer A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A (@ (@ tptp.ord_max_rat A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A (@ (@ tptp.ord_max_num A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A (@ (@ tptp.ord_max_nat A) B)))))
% 6.60/6.97 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A (@ (@ tptp.ord_max_int A) B)))))
% 6.60/6.97 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (=> (= A (@ (@ tptp.ord_ma741700101516333627d_enat A) B)) (@ (@ tptp.ord_le2932123472753598470d_enat B) A))))
% 6.60/6.97 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= A (@ (@ tptp.ord_max_Code_integer A) B)) (@ (@ tptp.ord_le3102999989581377725nteger B) A))))
% 6.60/6.97 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= A (@ (@ tptp.ord_max_rat A) B)) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.60/6.97 (assert (forall ((A tptp.num) (B tptp.num)) (=> (= A (@ (@ tptp.ord_max_num A) B)) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.60/6.97 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A (@ (@ tptp.ord_max_nat A) B)) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.60/6.97 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A (@ (@ tptp.ord_max_int A) B)) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.60/6.97 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (not (@ (@ tptp.ord_le2932123472753598470d_enat C) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (not (@ (@ tptp.ord_le3102999989581377725nteger C) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_rat B) A) (not (@ (@ tptp.ord_less_eq_rat C) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_num B) A) (not (@ (@ tptp.ord_less_eq_num C) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_nat B) A) (not (@ (@ tptp.ord_less_eq_nat C) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_eq_int B) A) (not (@ (@ tptp.ord_less_eq_int C) A)))))))
% 6.60/6.97 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat) (C tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat B) A) (=> (@ (@ tptp.ord_le2932123472753598470d_enat C) A) (@ (@ tptp.ord_le2932123472753598470d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A)))))
% 6.60/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger B) A) (=> (@ (@ tptp.ord_le3102999989581377725nteger C) A) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.ord_max_Code_integer B) C)) A)))))
% 6.60/6.98 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.ord_max_rat B) C)) A)))))
% 6.60/6.98 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) A) (@ (@ tptp.ord_less_eq_num (@ (@ tptp.ord_max_num B) C)) A)))))
% 6.60/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) A) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.ord_max_nat B) C)) A)))))
% 6.60/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.ord_max_int B) C)) A)))))
% 6.60/6.98 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)))))
% 6.60/6.98 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (= A3 (@ (@ tptp.ord_max_Code_integer A3) B2)))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= A3 (@ (@ tptp.ord_max_rat A3) B2)))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= A3 (@ (@ tptp.ord_max_num A3) B2)))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= A3 (@ (@ tptp.ord_max_nat A3) B2)))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= A3 (@ (@ tptp.ord_max_int A3) B2)))))
% 6.60/6.98 (assert (forall ((A tptp.extended_enat) (B tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat A) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.60/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ (@ tptp.ord_max_Code_integer A) B))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.ord_max_rat A) B))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (@ (@ tptp.ord_less_eq_num A) (@ (@ tptp.ord_max_num A) B))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ (@ tptp.ord_max_nat A) B))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.ord_max_int A) B))))
% 6.60/6.98 (assert (forall ((B tptp.extended_enat) (A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat B) (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))
% 6.60/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ (@ tptp.ord_max_Code_integer A) B))))
% 6.60/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.ord_max_rat A) B))))
% 6.60/6.98 (assert (forall ((B tptp.num) (A tptp.num)) (@ (@ tptp.ord_less_eq_num B) (@ (@ tptp.ord_max_num A) B))))
% 6.60/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ (@ tptp.ord_max_nat A) B))))
% 6.60/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.ord_less_eq_int B) (@ (@ tptp.ord_max_int A) B))))
% 6.60/6.98 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) A3))))
% 6.60/6.98 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A3) B2) A3))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) A3))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) A3))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) A3))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) A3))))
% 6.60/6.98 (assert (= tptp.ord_le2932123472753598470d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (= (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2) B2))))
% 6.60/6.98 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.ord_max_Code_integer A3) B2) B2))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (= (@ (@ tptp.ord_max_rat A3) B2) B2))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (= (@ (@ tptp.ord_max_num A3) B2) B2))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.ord_max_nat A3) B2) B2))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.ord_max_int A3) B2) B2))))
% 6.60/6.98 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le2932123472753598470d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.60/6.98 (assert (forall ((Z tptp.extended_enat) (X tptp.extended_enat) (Y tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat Z))) (= (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.code_integer) (X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger Z))) (= (@ _let_1 (@ (@ tptp.ord_max_Code_integer X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Z))) (= (@ _let_1 (@ (@ tptp.ord_max_real X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_rat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.num) (X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.ord_less_num Z))) (= (@ _let_1 (@ (@ tptp.ord_max_num X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat Z))) (= (@ _let_1 (@ (@ tptp.ord_max_nat X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_int Z))) (= (@ _let_1 (@ (@ tptp.ord_max_int X) Y)) (or (@ _let_1 X) (@ _let_1 Y))))))
% 6.60/6.98 (assert (forall ((B tptp.extended_enat) (C tptp.extended_enat) (A tptp.extended_enat)) (=> (@ (@ tptp.ord_le72135733267957522d_enat (@ (@ tptp.ord_ma741700101516333627d_enat B) C)) A) (not (=> (@ (@ tptp.ord_le72135733267957522d_enat B) A) (not (@ (@ tptp.ord_le72135733267957522d_enat C) A)))))))
% 6.60/6.98 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.ord_max_Code_integer B) C)) A) (not (=> (@ (@ tptp.ord_le6747313008572928689nteger B) A) (not (@ (@ tptp.ord_le6747313008572928689nteger C) A)))))))
% 6.60/6.98 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.ord_max_real B) C)) A) (not (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real C) A)))))))
% 6.60/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.ord_max_rat B) C)) A) (not (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat C) A)))))))
% 6.60/6.98 (assert (forall ((B tptp.num) (C tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num (@ (@ tptp.ord_max_num B) C)) A) (not (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num C) A)))))))
% 6.60/6.98 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.ord_max_nat B) C)) A) (not (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat C) A)))))))
% 6.60/6.98 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int (@ (@ tptp.ord_max_int B) C)) A) (not (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int C) A)))))))
% 6.60/6.98 (assert (= tptp.ord_le72135733267957522d_enat (lambda ((B2 tptp.extended_enat) (A3 tptp.extended_enat)) (and (= A3 (@ (@ tptp.ord_ma741700101516333627d_enat A3) B2)) (not (= A3 B2))))))
% 6.60/6.98 (assert (= tptp.ord_le6747313008572928689nteger (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (and (= A3 (@ (@ tptp.ord_max_Code_integer A3) B2)) (not (= A3 B2))))))
% 6.60/6.98 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (= A3 (@ (@ tptp.ord_max_real A3) B2)) (not (= A3 B2))))))
% 6.60/6.98 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (= A3 (@ (@ tptp.ord_max_rat A3) B2)) (not (= A3 B2))))))
% 6.60/6.98 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (= A3 (@ (@ tptp.ord_max_num A3) B2)) (not (= A3 B2))))))
% 6.60/6.98 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (= A3 (@ (@ tptp.ord_max_nat A3) B2)) (not (= A3 B2))))))
% 6.60/6.98 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (= A3 (@ (@ tptp.ord_max_int A3) B2)) (not (= A3 B2))))))
% 6.60/6.98 (assert (forall ((C tptp.extended_enat) (A tptp.extended_enat) (B tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.num) (A tptp.num) (B tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 A) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.extended_enat) (B tptp.extended_enat) (A tptp.extended_enat)) (let ((_let_1 (@ tptp.ord_le72135733267957522d_enat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_ma741700101516333627d_enat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_Code_integer A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_real A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_rat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.num) (B tptp.num) (A tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_num A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_nat A) B))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.ord_max_int A) B))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (not (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int B3) A2))))))
% 6.60/6.98 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (= A6 B6))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A2))) (=> (@ _let_1 B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) C4) (@ _let_1 C4))))))
% 6.60/6.98 (assert (= tptp.ord_less_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A6) B6) (not (@ (@ tptp.ord_less_eq_set_int B6) A6))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (C4 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ (@ tptp.ord_less_set_int B3) C4) (@ (@ tptp.ord_less_set_int A2) C4)))))
% 6.60/6.98 (assert (= tptp.ord_less_eq_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A6) B6) (= A6 B6)))))
% 6.60/6.98 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y tptp.vEBT_VEBT)) (=> (= (@ (@ tptp.vEBT_vebt_delete X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (= Xa2 tptp.zero_zero_nat) (=> (= Y (@ (@ tptp.vEBT_Leaf false) B5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) tptp.zero_zero_nat)))))))) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.vEBT_Leaf A5))) (let ((_let_3 (@ _let_2 B5))) (=> (= X _let_3) (=> (= Xa2 _let_1) (=> (= Y (@ _let_2 false)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) _let_1)))))))))) (=> (forall ((A5 Bool) (B5 Bool)) (=> (= X (@ (@ tptp.vEBT_Leaf A5) B5)) (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc N3)))) (let ((_let_2 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= Xa2 _let_1) (=> (= Y _let_2) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) _let_1)))))))))) (=> (forall ((Deg2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Deg2) TreeList3) Summary2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (TrLst2 tptp.list_VEBT_VEBT) (Smry2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) TrLst2) Smry2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Tr2 tptp.list_VEBT_VEBT) (Sm2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) (@ tptp.suc tptp.zero_zero_nat)) Tr2) Sm2))) (=> (= X _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_4 (@ (@ tptp.divide_divide_nat _let_1) _let_3))) (let ((_let_5 (@ tptp.the_nat (@ tptp.vEBT_vebt_mint Summary2)))) (let ((_let_6 (@ tptp.nth_VEBT_VEBT TreeList3))) (let ((_let_7 (@ (@ tptp.power_power_nat _let_3) _let_4))) (let ((_let_8 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_5) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_mint (@ _let_6 _let_5)))))) (let ((_let_9 (= Xa2 Mi2))) (let ((_let_10 (@ tptp.if_nat _let_9))) (let ((_let_11 (@ (@ _let_10 _let_8) Xa2))) (let ((_let_12 (@ (@ tptp.vEBT_VEBT_high _let_11) _let_4))) (let ((_let_13 (@ (@ tptp.vEBT_vebt_delete (@ _let_6 _let_12)) (@ (@ tptp.vEBT_VEBT_low _let_11) _let_4)))) (let ((_let_14 (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_12) _let_13))) (let ((_let_15 (@ tptp.nth_VEBT_VEBT _let_14))) (let ((_let_16 (= Xa2 Ma2))) (let ((_let_17 (@ tptp.if_nat (and (=> _let_9 (= _let_8 Ma2)) (=> (not _let_9) _let_16))))) (let ((_let_18 (@ (@ _let_10 _let_11) Mi2))) (let ((_let_19 (@ tptp.product_Pair_nat_nat _let_18))) (let ((_let_20 (@ (@ tptp.vEBT_vebt_delete Summary2) _let_12))) (let ((_let_21 (@ tptp.vEBT_vebt_maxt _let_20))) (let ((_let_22 (@ tptp.the_nat _let_21))) (let ((_let_23 (and _let_9 _let_16))) (let ((_let_24 (or (@ (@ tptp.ord_less_nat Xa2) Mi2) (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (=> (= X _let_2) (=> (and (=> _let_24 (= Y _let_2)) (=> (not _let_24) (and (=> _let_23 (= Y (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Summary2))) (=> (not _let_23) (= Y (@ (@ (@ tptp.if_VEBT_VEBT (@ (@ tptp.ord_less_nat _let_12) (@ tptp.size_s6755466524823107622T_VEBT TreeList3))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_13)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ (@ tptp.if_nat (= _let_21 tptp.none_nat)) _let_18) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_7) _let_22)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_22)))))) Ma2)))) _let_1) _let_14) _let_20)) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ _let_19 (@ (@ _let_17 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_12) _let_7)) (@ tptp.the_nat (@ tptp.vEBT_vebt_maxt (@ _let_15 _let_12))))) Ma2)))) _let_1) _let_14) Summary2))) _let_2)))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_delete_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))))))))))))))))))))))))))))))))))
% 6.60/6.98 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ tptp.vEBT_Leaf A5))) (let ((_let_2 (@ _let_1 B5))) (let ((_let_3 (= Xa2 tptp.one_one_nat))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_2) (=> (and (=> _let_4 (= Y (@ (@ tptp.vEBT_Leaf true) B5))) (=> (not _let_4) (and (=> _let_3 (= Y (@ _let_1 true))) (=> (not _let_3) (= Y _let_2))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2)))))))))) (=> (forall ((Info2 tptp.option4927543243414619207at_nat) (Ts2 tptp.list_VEBT_VEBT) (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) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ tptp.if_nat (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_5 (@ (@ _let_4 Mi2) Xa2))) (let ((_let_6 (@ (@ tptp.vEBT_VEBT_high _let_5) _let_3))) (let ((_let_7 (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_6))) (=> (= X _let_2) (=> (= Y (@ (@ (@ tptp.if_VEBT_VEBT (and (@ (@ tptp.ord_less_nat _let_6) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))) (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat (@ (@ _let_4 Xa2) Mi2)) (@ (@ tptp.ord_max_nat _let_5) Ma2)))) _let_1) (@ (@ (@ tptp.list_u1324408373059187874T_VEBT TreeList3) _let_6) (@ (@ tptp.vEBT_vebt_insert _let_7) (@ (@ tptp.vEBT_VEBT_low _let_5) _let_3)))) (@ (@ (@ tptp.if_VEBT_VEBT (@ tptp.vEBT_VEBT_minNull _let_7)) (@ (@ tptp.vEBT_vebt_insert Summary2) _let_6)) Summary2))) _let_2)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_insert_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.60/6.98 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))))
% 6.60/6.98 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) tptp.zero_zero_nat) Uy2) Uz2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((V2 tptp.product_prod_nat_nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat V2)) (@ tptp.suc tptp.zero_zero_nat)) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_7 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (=> (= X _let_2) (=> (= Y (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_7 (=> _let_7 (and _let_6 (=> _let_6 (and (=> _let_5 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)))))))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))))
% 6.60/6.98 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1))))))))) (=> (forall ((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))))))))))))))))
% 6.60/6.98 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Uy2 tptp.option4927543243414619207at_nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (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))))))))))))))))
% 6.60/6.98 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (let ((_let_2 (= Xa2 tptp.one_one_nat))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= X _let_1) (=> (= Y (and (=> _let_3 A5) (=> (not _let_3) (and (=> _let_2 B5) _let_2)))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V5765760719290551771er_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))))) (=> (forall ((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))))))))))))))))))
% 6.60/6.98 (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 ((A5 Bool) (B5 Bool)) (let ((_let_1 (= Xa2 tptp.one_one_nat))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (let ((_let_3 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_3) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_3) Xa2)) (not (and (=> _let_2 A5) (=> (not _let_2) (and (=> _let_1 B5) _let_1)))))))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Summary2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (not (@ (@ tptp.ord_less_nat Ma2) Xa2)))) (let ((_let_6 (not (@ (@ tptp.ord_less_nat Xa2) Mi2)))) (let ((_let_7 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Summary2))) (=> (= X _let_7) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_vebt_member_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_7) Xa2)) (not (=> (not (= Xa2 Mi2)) (=> (not (= Xa2 Ma2)) (and _let_6 (=> _let_6 (and _let_5 (=> _let_5 (and (=> _let_4 (@ (@ tptp.vEBT_vebt_member (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))))))))
% 6.60/6.98 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 A2) (=> (not (@ _let_1 B3)) (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (= (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (and (@ _let_1 A2) (not (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (= (@ (@ tptp.minus_minus_set_nat _let_1) B3) _let_1))))
% 6.60/6.98 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (not (=> (@ _let_1 A2) (@ _let_1 B3)))))))
% 6.60/6.98 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ _let_1 A2)))))
% 6.60/6.98 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (@ _let_1 A2)))))
% 6.60/6.98 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (@ _let_1 A2)))))
% 6.60/6.98 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ _let_1 A2)))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ _let_1 A2)))))
% 6.60/6.98 (assert (forall ((C tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex C))) (=> (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (not (@ _let_1 B3))))))
% 6.60/6.98 (assert (forall ((C tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.member_real C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) B3)) (not (@ _let_1 B3))))))
% 6.60/6.98 (assert (forall ((C tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)) (not (@ _let_1 B3))))))
% 6.60/6.98 (assert (forall ((C tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.member_int C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (not (@ _let_1 B3))))))
% 6.60/6.98 (assert (forall ((C tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat C))) (=> (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (not (@ _let_1 B3))))))
% 6.60/6.98 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (@ (@ tptp.minus_minus_real_o (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) A6))) (lambda ((X3 tptp.real)) (@ (@ tptp.member_real X3) B6)))))))
% 6.60/6.98 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (@ (@ tptp.minus_711738161318947805_int_o (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X3) A6))) (lambda ((X3 tptp.product_prod_int_int)) (@ (@ tptp.member5262025264175285858nt_int X3) B6)))))))
% 6.60/6.98 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ tptp.collect_complex (@ (@ tptp.minus_8727706125548526216plex_o (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) A6))) (lambda ((X3 tptp.complex)) (@ (@ tptp.member_complex X3) B6)))))))
% 6.60/6.98 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (@ (@ tptp.minus_6910147592129066416_nat_o (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) A6))) (lambda ((X3 tptp.set_nat)) (@ (@ tptp.member_set_nat X3) B6)))))))
% 6.60/6.98 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (@ (@ tptp.minus_minus_int_o (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) A6))) (lambda ((X3 tptp.int)) (@ (@ tptp.member_int X3) B6)))))))
% 6.60/6.98 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (@ (@ tptp.minus_minus_nat_o (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) A6))) (lambda ((X3 tptp.nat)) (@ (@ tptp.member_nat X3) B6)))))))
% 6.60/6.98 (assert (= tptp.minus_minus_set_real (lambda ((A6 tptp.set_real) (B6 tptp.set_real)) (@ tptp.collect_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.member_real X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.60/6.98 (assert (= tptp.minus_1052850069191792384nt_int (lambda ((A6 tptp.set_Pr958786334691620121nt_int) (B6 tptp.set_Pr958786334691620121nt_int)) (@ tptp.collec213857154873943460nt_int (lambda ((X3 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member5262025264175285858nt_int X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.60/6.98 (assert (= tptp.minus_811609699411566653omplex (lambda ((A6 tptp.set_complex) (B6 tptp.set_complex)) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ tptp.member_complex X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.60/6.98 (assert (= tptp.minus_2163939370556025621et_nat (lambda ((A6 tptp.set_set_nat) (B6 tptp.set_set_nat)) (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (let ((_let_1 (@ tptp.member_set_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.60/6.98 (assert (= tptp.minus_minus_set_int (lambda ((A6 tptp.set_int) (B6 tptp.set_int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (let ((_let_1 (@ tptp.member_int X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.60/6.98 (assert (= tptp.minus_minus_set_nat (lambda ((A6 tptp.set_nat) (B6 tptp.set_nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (let ((_let_1 (@ tptp.member_nat X3))) (and (@ _let_1 A6) (not (@ _let_1 B6)))))))))
% 6.60/6.98 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat) (Y Bool)) (=> (= (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) Y) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_4 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_3))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_4) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (=> (= X _let_2) (=> (= Y (and (=> _let_5 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_4)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_3))) _let_5)) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_2) Xa2))))))))))))))))))))
% 6.60/6.98 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (not (@ (@ tptp.vEBT_VEBT_membermima X) Xa2)) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Uu2 Bool) (Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) tptp.zero_zero_nat) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2)))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))))))))))
% 6.60/6.98 (assert (forall ((X tptp.vEBT_VEBT) (Xa2 tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_membermima X) Xa2) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat X) Xa2)) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Va3 tptp.list_VEBT_VEBT) (Vb2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) tptp.zero_zero_nat) Va3) Vb2))) (=> (= X _let_1) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2))))))) (=> (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) _let_1) TreeList3) Vc2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (or (= Xa2 Mi2) (= Xa2 Ma2) (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4))))))))))) (not (forall ((V2 tptp.nat) (TreeList3 tptp.list_VEBT_VEBT) (Vd2 tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc V2))) (let ((_let_2 (@ (@ tptp.divide_divide_nat _let_1) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ (@ tptp.vEBT_VEBT_high Xa2) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_3) (@ tptp.size_s6755466524823107622T_VEBT TreeList3)))) (let ((_let_5 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1) TreeList3) Vd2))) (=> (= X _let_5) (=> (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_V4351362008482014158ma_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_5) Xa2)) (not (and (=> _let_4 (@ (@ tptp.vEBT_VEBT_membermima (@ (@ tptp.nth_VEBT_VEBT TreeList3) _let_3)) (@ (@ tptp.vEBT_VEBT_low Xa2) _let_2))) _let_4)))))))))))))))))
% 6.60/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int tptp.zero_zero_nat) A) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.60/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat tptp.zero_zero_nat) A) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se8260200283734997820nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se8260200283734997820nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4203085406695923979it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se4203085406695923979it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se4205575877204974255it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se4205575877204974255it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_se1345352211410354436nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se2159334234014336723it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se2161824704523386999it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real) (P (-> tptp.real tptp.real Bool))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((A5 tptp.real) (B5 tptp.real) (C2 tptp.real)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (=> (@ (@ P B5) C2) (=> (@ (@ tptp.ord_less_eq_real A5) B5) (=> (@ (@ tptp.ord_less_eq_real B5) C2) (@ _let_1 C2))))))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X6) (=> (@ (@ tptp.ord_less_eq_real X6) B) (exists ((D5 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D5) (forall ((A5 tptp.real) (B5 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A5) X6) (@ (@ tptp.ord_less_eq_real X6) B5) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real B5) A5)) D5)) (@ (@ P A5) B5)))))))) (@ (@ P A) B))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int N) K)) (@ _let_1 K)))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int N) K)) (@ _let_1 K)))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2159334234014336723it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se4203085406695923979it_int N) K)) K)))
% 6.60/6.98 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_eq_real X) Y)))))
% 6.60/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_eq_rat X) Y)))))
% 6.60/6.98 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_eq_int X) Y)))))
% 6.60/6.98 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real Z))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat Z))) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_eq_rat (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))))
% 6.60/6.98 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.times_times_int Z))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_eq_int (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_int X) Y))))))
% 6.60/6.98 (assert (forall ((Q2 tptp.nat) (R tptp.nat)) (= (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.product_Pair_nat_nat Q2) R)) (= R tptp.zero_zero_nat))))
% 6.60/6.98 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.product_Pair_int_int Q2) R)) (= R tptp.zero_zero_int))))
% 6.60/6.98 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int) (=> (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) B) (@ _let_2 R)) (@ (@ (@ tptp.eucl_rel_int (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ _let_1 A))) (@ _let_1 B)) (@ _let_2 (@ (@ tptp.minus_minus_int (@ _let_1 R)) tptp.one_one_int)))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4953567300277697838T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) N) (@ (@ tptp.produc537772716801021591T_VEBT (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr4606735188037164562VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) N) (@ (@ tptp.produc8721562602347293563VEBT_o (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1791586995822124652BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) N) (@ (@ tptp.produc738532404422230701BT_nat (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6837108013167703752BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) N) (@ (@ tptp.produc736041933913180425BT_int (@ (@ tptp.nth_VEBT_VEBT Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr6777367263587873994T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) N) (@ (@ tptp.produc2982872950893828659T_VEBT (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Product_prod_o_o (@ (@ tptp.product_o_o Xs) Ys)) N) (@ (@ tptp.product_Pair_o_o (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_nat)) (let ((_let_1 (@ tptp.size_size_list_nat Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr5826913651314560976_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) N) (@ (@ tptp.product_Pair_o_nat (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_nat Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_o) (Ys tptp.list_int)) (let ((_let_1 (@ tptp.size_size_list_int Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) _let_1)) (= (@ (@ tptp.nth_Pr1649062631805364268_o_int (@ (@ tptp.product_o_int Xs) Ys)) N) (@ (@ tptp.product_Pair_o_int (@ (@ tptp.nth_o Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_int Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (let ((_let_1 (@ tptp.size_s6755466524823107622T_VEBT Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr744662078594809490T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) N) (@ (@ tptp.produc599794634098209291T_VEBT (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_VEBT_VEBT Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (Xs tptp.list_nat) (Ys tptp.list_o)) (let ((_let_1 (@ tptp.size_size_list_o Ys))) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) _let_1)) (= (@ (@ tptp.nth_Pr112076138515278198_nat_o (@ (@ tptp.product_nat_o Xs) Ys)) N) (@ (@ tptp.product_Pair_nat_o (@ (@ tptp.nth_nat Xs) (@ (@ tptp.divide_divide_nat N) _let_1))) (@ (@ tptp.nth_o Ys) (@ (@ tptp.modulo_modulo_nat N) _let_1))))))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Z tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat X) Z) (=> (@ (@ tptp.vEBT_VEBT_max_in_set A2) Z) (=> (@ tptp.finite_finite_nat B3) (=> (= A2 B3) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set A2) X) X_1))))))))
% 6.60/6.98 (assert (forall ((Z tptp.nat) (X tptp.nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.ord_less_nat Z) X) (=> (@ (@ tptp.vEBT_VEBT_min_in_set A2) Z) (=> (@ tptp.finite_finite_nat A2) (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set A2) X) X_1)))))))
% 6.60/6.98 (assert (forall ((T tptp.vEBT_VEBT) (N tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) N) (@ tptp.finite_finite_nat (@ tptp.vEBT_VEBT_set_vebt T)))))
% 6.60/6.98 (assert (forall ((Xs tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_pred_in_set Xs) A) X_1))) (=> (@ tptp.finite_finite_nat Xs) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (@ (@ tptp.ord_less_nat X4) A))))))))
% 6.60/6.98 (assert (forall ((Xs tptp.set_nat) (A tptp.nat)) (=> (not (exists ((X_1 tptp.nat)) (@ (@ (@ tptp.vEBT_is_succ_in_set Xs) A) X_1))) (=> (@ tptp.finite_finite_nat Xs) (not (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) Xs) (@ (@ tptp.ord_less_nat A) X4))))))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_VEBT_VEBT)) (@ tptp.finite5795047828879050333T_VEBT (@ tptp.set_VEBT_VEBT2 Xs))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_nat)) (@ tptp.finite_finite_nat (@ tptp.set_nat2 Xs))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_int)) (@ tptp.finite_finite_int (@ tptp.set_int2 Xs))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_complex)) (@ tptp.finite3207457112153483333omplex (@ tptp.set_complex2 Xs))))
% 6.60/6.98 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))) (@ (@ tptp.ord_less_rat A) B))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))) (@ (@ tptp.ord_less_real A) B))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s7466405169056248089T_VEBT (@ (@ tptp.produc4743750530478302277T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_o)) (= (@ tptp.size_s9168528473962070013VEBT_o (@ (@ tptp.product_VEBT_VEBT_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_nat)) (= (@ tptp.size_s6152045936467909847BT_nat (@ (@ tptp.produc7295137177222721919BT_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_nat Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_VEBT_VEBT) (Ys tptp.list_int)) (= (@ tptp.size_s3661962791536183091BT_int (@ (@ tptp.produc7292646706713671643BT_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_s6755466524823107622T_VEBT Xs)) (@ tptp.size_size_list_int Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4313452262239582901T_VEBT (@ (@ tptp.product_o_VEBT_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_o)) (= (@ tptp.size_s1515746228057227161od_o_o (@ (@ tptp.product_o_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_nat)) (= (@ tptp.size_s5443766701097040955_o_nat (@ (@ tptp.product_o_nat Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_nat Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_o) (Ys tptp.list_int)) (= (@ tptp.size_s2953683556165314199_o_int (@ (@ tptp.product_o_int Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_o Xs)) (@ tptp.size_size_list_int Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_VEBT_VEBT)) (= (@ tptp.size_s4762443039079500285T_VEBT (@ (@ tptp.produc7156399406898700509T_VEBT Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_s6755466524823107622T_VEBT Ys)))))
% 6.60/6.98 (assert (forall ((Xs tptp.list_nat) (Ys tptp.list_o)) (= (@ tptp.size_s6491369823275344609_nat_o (@ (@ tptp.product_nat_o Xs) Ys)) (@ (@ tptp.times_times_nat (@ tptp.size_size_list_nat Xs)) (@ tptp.size_size_list_o Ys)))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q4 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R3)) (= R R3))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int) (Q4 tptp.int) (R3 tptp.int)) (let ((_let_1 (@ (@ tptp.eucl_rel_int A) B))) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (@ _let_1 (@ (@ tptp.product_Pair_int_int Q4) R3)) (= Q2 Q4))))))
% 6.60/6.98 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) N4) (@ (@ tptp.ord_less_nat X6) N))) (@ tptp.finite_finite_nat N4))))
% 6.60/6.98 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N6) (@ (@ tptp.ord_less_nat X3) M3)))))))
% 6.60/6.98 (assert (= tptp.finite_finite_nat (lambda ((N6 tptp.set_nat)) (exists ((M3 tptp.nat)) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) N6) (@ (@ tptp.ord_less_eq_nat X3) M3)))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_VEBT_VEBT)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (exists ((Xs3 tptp.list_VEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 Xs3) A2)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (exists ((Xs3 tptp.list_nat)) (= (@ tptp.set_nat2 Xs3) A2)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (exists ((Xs3 tptp.list_int)) (= (@ tptp.set_int2 Xs3) A2)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (exists ((Xs3 tptp.list_complex)) (= (@ tptp.set_complex2 Xs3) A2)))))
% 6.60/6.98 (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)))))))
% 6.60/6.98 (assert (forall ((F (-> tptp.nat tptp.nat)) (U tptp.nat)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N3) (@ F N3))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ F N2)) U)))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (= (@ tptp.size_s3451745648224563538omplex Xs2) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (= (@ tptp.size_s6755466524823107622T_VEBT Xs2) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs2 tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs2)) A2) (= (@ tptp.size_size_list_o Xs2) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (= (@ tptp.size_size_list_nat Xs2) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (= (@ tptp.size_size_list_int Xs2) N))))))))
% 6.60/6.98 (assert (forall ((K tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) tptp.zero_zero_int) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K))))
% 6.60/6.98 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.divide_divide_int K) L2) Q2))))
% 6.60/6.98 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R tptp.int)) (=> (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)) (= (@ (@ tptp.modulo_modulo_int K) L2) R))))
% 6.60/6.98 (assert (forall ((S2 tptp.set_real)) (=> (@ tptp.finite_finite_real S2) (=> (not (= S2 tptp.bot_bot_set_real)) (exists ((X6 tptp.real)) (and (@ (@ tptp.member_real X6) S2) (not (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) S2) (@ (@ tptp.ord_less_real Xa) X6))))))))))
% 6.60/6.98 (assert (forall ((S2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat S2) (=> (not (= S2 tptp.bot_bot_set_rat)) (exists ((X6 tptp.rat)) (and (@ (@ tptp.member_rat X6) S2) (not (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) S2) (@ (@ tptp.ord_less_rat Xa) X6))))))))))
% 6.60/6.98 (assert (forall ((S2 tptp.set_num)) (=> (@ tptp.finite_finite_num S2) (=> (not (= S2 tptp.bot_bot_set_num)) (exists ((X6 tptp.num)) (and (@ (@ tptp.member_num X6) S2) (not (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) S2) (@ (@ tptp.ord_less_num Xa) X6))))))))))
% 6.60/6.98 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (=> (not (= S2 tptp.bot_bot_set_nat)) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) S2) (not (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) S2) (@ (@ tptp.ord_less_nat Xa) X6))))))))))
% 6.60/6.98 (assert (forall ((S2 tptp.set_int)) (=> (@ tptp.finite_finite_int S2) (=> (not (= S2 tptp.bot_bot_set_int)) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) S2) (not (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) S2) (@ (@ tptp.ord_less_int Xa) X6))))))))))
% 6.60/6.98 (assert (forall ((X8 tptp.set_real)) (=> (not (= X8 tptp.bot_bot_set_real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) X8) (exists ((Xa tptp.real)) (and (@ (@ tptp.member_real Xa) X8) (@ (@ tptp.ord_less_real X6) Xa))))) (not (@ tptp.finite_finite_real X8))))))
% 6.60/6.98 (assert (forall ((X8 tptp.set_rat)) (=> (not (= X8 tptp.bot_bot_set_rat)) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.member_rat X6) X8) (exists ((Xa tptp.rat)) (and (@ (@ tptp.member_rat Xa) X8) (@ (@ tptp.ord_less_rat X6) Xa))))) (not (@ tptp.finite_finite_rat X8))))))
% 6.60/6.98 (assert (forall ((X8 tptp.set_num)) (=> (not (= X8 tptp.bot_bot_set_num)) (=> (forall ((X6 tptp.num)) (=> (@ (@ tptp.member_num X6) X8) (exists ((Xa tptp.num)) (and (@ (@ tptp.member_num Xa) X8) (@ (@ tptp.ord_less_num X6) Xa))))) (not (@ tptp.finite_finite_num X8))))))
% 6.60/6.98 (assert (forall ((X8 tptp.set_nat)) (=> (not (= X8 tptp.bot_bot_set_nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) X8) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) X8) (@ (@ tptp.ord_less_nat X6) Xa))))) (not (@ tptp.finite_finite_nat X8))))))
% 6.60/6.98 (assert (forall ((X8 tptp.set_int)) (=> (not (= X8 tptp.bot_bot_set_int)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) X8) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) X8) (@ (@ tptp.ord_less_int X6) Xa))))) (not (@ tptp.finite_finite_int X8))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ tptp.finite_finite_rat (@ (@ tptp.set_or633870826150836451st_rat A) B))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ tptp.finite_finite_real (@ (@ tptp.set_or1222579329274155063t_real A) B))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_complex) (N tptp.nat)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite8712137658972009173omplex (@ tptp.collect_list_complex (lambda ((Xs2 tptp.list_complex)) (and (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.set_complex2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s3451745648224563538omplex Xs2)) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_VEBT_VEBT) (N tptp.nat)) (=> (@ tptp.finite5795047828879050333T_VEBT A2) (@ tptp.finite3004134309566078307T_VEBT (@ tptp.collec5608196760682091941T_VEBT (lambda ((Xs2 tptp.list_VEBT_VEBT)) (and (@ (@ tptp.ord_le4337996190870823476T_VEBT (@ tptp.set_VEBT_VEBT2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_s6755466524823107622T_VEBT Xs2)) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_o) (N tptp.nat)) (=> (@ tptp.finite_finite_o A2) (@ tptp.finite_finite_list_o (@ tptp.collect_list_o (lambda ((Xs2 tptp.list_o)) (and (@ (@ tptp.ord_less_eq_set_o (@ tptp.set_o2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_o Xs2)) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite8100373058378681591st_nat (@ tptp.collect_list_nat (lambda ((Xs2 tptp.list_nat)) (and (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_nat2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_nat Xs2)) N))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (N tptp.nat)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite3922522038869484883st_int (@ tptp.collect_list_int (lambda ((Xs2 tptp.list_int)) (and (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_int2 Xs2)) A2) (@ (@ tptp.ord_less_eq_nat (@ tptp.size_size_list_int Xs2)) N))))))))
% 6.60/6.98 (assert (forall ((L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (= K (@ (@ tptp.times_times_int Q2) L2)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) tptp.zero_zero_int))))))
% 6.60/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int K) L2)) (@ (@ tptp.modulo_modulo_int K) L2)))))
% 6.60/6.98 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N4))))
% 6.60/6.98 (assert (forall ((K tptp.int) (L2 tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.ord_less_int L2))) (let ((_let_2 (@ _let_1 tptp.zero_zero_int))) (let ((_let_3 (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))) (= (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)) (and (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int L2) Q2)) R)) (=> _let_3 (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) R) (@ (@ tptp.ord_less_int R) L2))) (=> (not _let_3) (and (=> _let_2 (and (@ _let_1 R) (@ (@ tptp.ord_less_eq_int R) tptp.zero_zero_int))) (=> (not _let_2) (= Q2 tptp.zero_zero_int)))))))))))
% 6.60/6.98 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (= (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real X) Z)) (@ (@ tptp.times_times_real Y) Z)) (@ (@ tptp.ord_less_real X) Y)))))
% 6.60/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Z) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat X) Z)) (@ (@ tptp.times_times_rat Y) Z)) (@ (@ tptp.ord_less_rat X) Y)))))
% 6.60/6.98 (assert (forall ((Z tptp.int) (X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int X) Z)) (@ (@ tptp.times_times_int Y) Z)) (@ (@ tptp.ord_less_int X) Y)))))
% 6.60/6.98 (assert (forall ((B tptp.int) (A tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.plus_plus_int tptp.one_one_int))) (let ((_let_3 (@ tptp.product_Pair_int_int Q2))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ _let_3 R)) (@ (@ (@ tptp.eucl_rel_int (@ _let_2 (@ _let_1 A))) (@ _let_1 B)) (@ _let_3 (@ _let_2 (@ _let_1 R)))))))))))
% 6.60/6.98 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat N2) K))))))
% 6.60/6.98 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.ord_less_nat N2) K))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite1152437895449049373et_nat (@ tptp.collect_set_nat (lambda ((B6 tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat B6) A2)))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite6551019134538273531omplex (@ tptp.collect_set_complex (lambda ((B6 tptp.set_complex)) (@ (@ tptp.ord_le211207098394363844omplex B6) A2)))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite6197958912794628473et_int (@ tptp.collect_set_int (lambda ((B6 tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int B6) A2)))))))
% 6.60/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((Z3 tptp.real)) (= (@ (@ tptp.power_power_real Z3) N) tptp.one_one_real)))))))
% 6.60/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) tptp.one_one_complex)))))))
% 6.60/6.98 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (= (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B3)) (@ tptp.finite_finite_int A2)))))
% 6.60/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B3) (= (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.60/6.98 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (= (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ tptp.finite_finite_nat A2)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (@ tptp.finite_finite_int (@ (@ tptp.minus_minus_set_int A2) B3)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A2) (@ tptp.finite3207457112153483333omplex (@ (@ tptp.minus_811609699411566653omplex A2) B3)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (@ tptp.finite_finite_nat (@ (@ tptp.minus_minus_set_nat A2) B3)))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_one_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_one_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_times_complex (@ X I5)) (@ Y I5)) tptp.one_one_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.one_one_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.one_one_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.times_times_real (@ X I5)) (@ Y I5)) tptp.one_one_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.one_one_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.times_times_rat (@ X I5)) (@ Y I5)) tptp.one_one_rat))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.one_one_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.one_one_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.times_times_rat (@ X I5)) (@ Y I5)) tptp.one_one_rat))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.complex)) (Y (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.complex)) (Y (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.complex)) (Y (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.complex)) (Y (-> tptp.complex tptp.complex))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_zero_complex)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_zero_complex)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_plus_complex (@ X I5)) (@ Y I5)) tptp.zero_zero_complex))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (Y (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.real)) (Y (-> tptp.nat tptp.real))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (Y (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.member_int I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (Y (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ X I5) tptp.zero_zero_real)))))) (=> (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ Y I5) tptp.zero_zero_real)))))) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((I5 tptp.complex)) (and (@ (@ tptp.member_complex I5) I6) (not (= (@ (@ tptp.plus_plus_real (@ X I5)) (@ Y I5)) tptp.zero_zero_real))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.rat)) (Y (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ X I5) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ Y I5) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_real (@ tptp.collect_real (lambda ((I5 tptp.real)) (and (@ (@ tptp.member_real I5) I6) (not (= (@ (@ tptp.plus_plus_rat (@ X I5)) (@ Y I5)) tptp.zero_zero_rat))))))))))
% 6.60/6.98 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (Y (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ X I5) tptp.zero_zero_rat)))))) (=> (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ Y I5) tptp.zero_zero_rat)))))) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (and (@ (@ tptp.member_nat I5) I6) (not (= (@ (@ tptp.plus_plus_rat (@ X I5)) (@ Y I5)) tptp.zero_zero_rat))))))))))
% 6.60/6.98 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I5) (@ (@ tptp.ord_less_eq_int I5) B)))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_int A) I5) (@ (@ tptp.ord_less_eq_int I5) B)))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((I5 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A) I5) (@ (@ tptp.ord_less_int I5) B)))))))
% 6.60/6.98 (assert (forall ((M5 tptp.set_list_VEBT_VEBT)) (=> (@ tptp.finite3004134309566078307T_VEBT M5) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_VEBT_VEBT)) (=> (@ (@ tptp.member2936631157270082147T_VEBT X4) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_s6755466524823107622T_VEBT X4)) N3)))))))
% 6.60/6.98 (assert (forall ((M5 tptp.set_list_o)) (=> (@ tptp.finite_finite_list_o M5) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_o)) (=> (@ (@ tptp.member_list_o X4) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_o X4)) N3)))))))
% 6.60/6.98 (assert (forall ((M5 tptp.set_list_nat)) (=> (@ tptp.finite8100373058378681591st_nat M5) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_nat)) (=> (@ (@ tptp.member_list_nat X4) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_nat X4)) N3)))))))
% 6.60/6.98 (assert (forall ((M5 tptp.set_list_int)) (=> (@ tptp.finite3922522038869484883st_int M5) (exists ((N3 tptp.nat)) (forall ((X4 tptp.list_int)) (=> (@ (@ tptp.member_list_int X4) M5) (@ (@ tptp.ord_less_nat (@ tptp.size_size_list_int X4)) N3)))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X6 tptp.real)) (and (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_real A) X6) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X6) A2) (@ (@ tptp.ord_less_eq_set_nat A) X6) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X6 tptp.set_int)) (and (@ (@ tptp.member_set_int X6) A2) (@ (@ tptp.ord_less_eq_set_int A) X6) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X6 tptp.rat)) (and (@ (@ tptp.member_rat X6) A2) (@ (@ tptp.ord_less_eq_rat A) X6) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X6 tptp.num)) (and (@ (@ tptp.member_num X6) A2) (@ (@ tptp.ord_less_eq_num A) X6) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_nat A) X6) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_int A) X6) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_real) (A tptp.real)) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real A) A2) (exists ((X6 tptp.real)) (and (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_real X6) A) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_set_nat) (A tptp.set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ (@ tptp.member_set_nat A) A2) (exists ((X6 tptp.set_nat)) (and (@ (@ tptp.member_set_nat X6) A2) (@ (@ tptp.ord_less_eq_set_nat X6) A) (forall ((Xa tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_nat Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_set_int) (A tptp.set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (@ (@ tptp.member_set_int A) A2) (exists ((X6 tptp.set_int)) (and (@ (@ tptp.member_set_int X6) A2) (@ (@ tptp.ord_less_eq_set_int X6) A) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_rat) (A tptp.rat)) (=> (@ tptp.finite_finite_rat A2) (=> (@ (@ tptp.member_rat A) A2) (exists ((X6 tptp.rat)) (and (@ (@ tptp.member_rat X6) A2) (@ (@ tptp.ord_less_eq_rat X6) A) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_num) (A tptp.num)) (=> (@ tptp.finite_finite_num A2) (=> (@ (@ tptp.member_num A) A2) (exists ((X6 tptp.num)) (and (@ (@ tptp.member_num X6) A2) (@ (@ tptp.ord_less_eq_num X6) A) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat) (A tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.member_nat A) A2) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_nat X6) A) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (A tptp.int)) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int A) A2) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_int X6) A) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ tptp.finite_finite_nat B3) (@ tptp.finite_finite_nat A2)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ tptp.finite3207457112153483333omplex B3) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (=> (@ tptp.finite_finite_int B3) (@ tptp.finite_finite_int A2)))))
% 6.60/6.98 (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))))))
% 6.60/6.98 (assert (forall ((S2 tptp.set_complex) (T3 tptp.set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (not (@ tptp.finite3207457112153483333omplex S2)) (not (@ tptp.finite3207457112153483333omplex T3))))))
% 6.60/6.98 (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))))))
% 6.60/6.98 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (@ tptp.finite_finite_nat A2)))))
% 6.60/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (@ tptp.finite3207457112153483333omplex A2)))))
% 6.60/6.98 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ tptp.finite_finite_int A2)))))
% 6.60/6.98 (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)))))))
% 6.60/6.98 (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)))))))
% 6.60/6.98 (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)))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X6 tptp.real)) (and (@ (@ tptp.member_real X6) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X6 tptp.set_int)) (and (@ (@ tptp.member_set_int X6) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X6 tptp.rat)) (and (@ (@ tptp.member_rat X6) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X6 tptp.num)) (and (@ (@ tptp.member_num X6) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int Xa) X6) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_real)) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (exists ((X6 tptp.real)) (and (@ (@ tptp.member_real X6) A2) (forall ((Xa tptp.real)) (=> (@ (@ tptp.member_real Xa) A2) (=> (@ (@ tptp.ord_less_eq_real X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_set_int)) (=> (@ tptp.finite6197958912794628473et_int A2) (=> (not (= A2 tptp.bot_bot_set_set_int)) (exists ((X6 tptp.set_int)) (and (@ (@ tptp.member_set_int X6) A2) (forall ((Xa tptp.set_int)) (=> (@ (@ tptp.member_set_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_set_int X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A2) (=> (not (= A2 tptp.bot_bot_set_rat)) (exists ((X6 tptp.rat)) (and (@ (@ tptp.member_rat X6) A2) (forall ((Xa tptp.rat)) (=> (@ (@ tptp.member_rat Xa) A2) (=> (@ (@ tptp.ord_less_eq_rat X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_num)) (=> (@ tptp.finite_finite_num A2) (=> (not (= A2 tptp.bot_bot_set_num)) (exists ((X6 tptp.num)) (and (@ (@ tptp.member_num X6) A2) (forall ((Xa tptp.num)) (=> (@ (@ tptp.member_num Xa) A2) (=> (@ (@ tptp.ord_less_eq_num X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A2) (forall ((Xa tptp.nat)) (=> (@ (@ tptp.member_nat Xa) A2) (=> (@ (@ tptp.ord_less_eq_nat X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (forall ((A2 tptp.set_int)) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (exists ((X6 tptp.int)) (and (@ (@ tptp.member_int X6) A2) (forall ((Xa tptp.int)) (=> (@ (@ tptp.member_int Xa) A2) (=> (@ (@ tptp.ord_less_eq_int X6) Xa) (= X6 Xa))))))))))
% 6.60/6.98 (assert (= (@ tptp.arcosh_real tptp.one_one_real) tptp.zero_zero_real))
% 6.60/6.98 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.finite3207457112153483333omplex (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) C)))))))
% 6.60/6.98 (assert (= (@ tptp.artanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.60/6.98 (assert (= (@ tptp.arsinh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.60/6.98 (assert (forall ((X1 tptp.int) (X22 tptp.int) (Y1 tptp.int) (Y22 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int X1) X22) (@ (@ tptp.product_Pair_int_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.60/6.98 (assert (forall ((X1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger X1) X22) (@ (@ tptp.produc6137756002093451184nteger Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.60/6.98 (assert (forall ((X1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (X22 tptp.produc8923325533196201883nteger) (Y1 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y22 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger X1) X22) (@ (@ tptp.produc8603105652947943368nteger Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.60/6.98 (assert (forall ((X1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int X1) X22) (@ (@ tptp.produc5700946648718959541nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.60/6.98 (assert (forall ((X1 (-> tptp.int tptp.option6357759511663192854e_term)) (X22 tptp.product_prod_int_int) (Y1 (-> tptp.int tptp.option6357759511663192854e_term)) (Y22 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int X1) X22) (@ (@ tptp.produc4305682042979456191nt_int Y1) Y22)) (and (= X1 Y1) (= X22 Y22)))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int) (B4 tptp.int)) (= (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A4) B4)) (and (= A A4) (= B B4)))))
% 6.60/6.98 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A4 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A4) B4)) (and (= A A4) (= B B4)))))
% 6.60/6.98 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (= (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A4) B4)) (and (= A A4) (= B B4)))))
% 6.60/6.98 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A4) B4)) (and (= A A4) (= B B4)))))
% 6.60/6.98 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (= (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) (and (= A A4) (= B B4)))))
% 6.60/6.98 (assert (forall ((Y tptp.product_prod_int_int)) (not (forall ((A5 tptp.int) (B5 tptp.int)) (not (= Y (@ (@ tptp.product_Pair_int_int A5) B5)))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc8763457246119570046nteger)) (not (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (not (= Y (@ (@ tptp.produc6137756002093451184nteger A5) B5)))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc1908205239877642774nteger)) (not (forall ((A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (not (= Y (@ (@ tptp.produc8603105652947943368nteger A5) B5)))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A5) B5)))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A5) B5)))))))
% 6.60/6.98 (assert (forall ((P5 tptp.product_prod_int_int)) (exists ((X6 tptp.int) (Y5 tptp.int)) (= P5 (@ (@ tptp.product_Pair_int_int X6) Y5)))))
% 6.60/6.98 (assert (forall ((P5 tptp.produc8763457246119570046nteger)) (exists ((X6 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (= P5 (@ (@ tptp.produc6137756002093451184nteger X6) Y5)))))
% 6.60/6.98 (assert (forall ((P5 tptp.produc1908205239877642774nteger)) (exists ((X6 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (= P5 (@ (@ tptp.produc8603105652947943368nteger X6) Y5)))))
% 6.60/6.98 (assert (forall ((P5 tptp.produc2285326912895808259nt_int)) (exists ((X6 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int)) (= P5 (@ (@ tptp.produc5700946648718959541nt_int X6) Y5)))))
% 6.60/6.98 (assert (forall ((P5 tptp.produc7773217078559923341nt_int)) (exists ((X6 (-> tptp.int tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int)) (= P5 (@ (@ tptp.produc4305682042979456191nt_int X6) Y5)))))
% 6.60/6.98 (assert (forall ((P (-> tptp.product_prod_int_int Bool)) (P5 tptp.product_prod_int_int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (@ P (@ (@ tptp.product_Pair_int_int A5) B5))) (@ P P5))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (P5 tptp.produc8763457246119570046nteger)) (=> (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc6137756002093451184nteger A5) B5))) (@ P P5))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (P5 tptp.produc1908205239877642774nteger)) (=> (forall ((A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (@ P (@ (@ tptp.produc8603105652947943368nteger A5) B5))) (@ P P5))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (P5 tptp.produc2285326912895808259nt_int)) (=> (forall ((A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A5) B5))) (@ P P5))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (P5 tptp.produc7773217078559923341nt_int)) (=> (forall ((A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A5) B5))) (@ P P5))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int) (B4 tptp.int)) (=> (= (@ (@ tptp.product_Pair_int_int A) B) (@ (@ tptp.product_Pair_int_int A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.60/6.98 (assert (forall ((A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A4 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc6137756002093451184nteger A) B) (@ (@ tptp.produc6137756002093451184nteger A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.60/6.98 (assert (forall ((A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger) (A4 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B4 tptp.produc8923325533196201883nteger)) (=> (= (@ (@ tptp.produc8603105652947943368nteger A) B) (@ (@ tptp.produc8603105652947943368nteger A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.60/6.98 (assert (forall ((A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A4 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc5700946648718959541nt_int A) B) (@ (@ tptp.produc5700946648718959541nt_int A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.60/6.98 (assert (forall ((A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int) (A4 (-> tptp.int tptp.option6357759511663192854e_term)) (B4 tptp.product_prod_int_int)) (=> (= (@ (@ tptp.produc4305682042979456191nt_int A) B) (@ (@ tptp.produc4305682042979456191nt_int A4) B4)) (not (=> (= A A4) (not (= B B4)))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc8763457246119570046nteger)) (not (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.code_integer) (C2 tptp.code_integer)) (not (= Y (@ (@ tptp.produc6137756002093451184nteger A5) (@ (@ tptp.produc1086072967326762835nteger B5) C2))))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc1908205239877642774nteger)) (not (forall ((A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.code_integer) (C2 tptp.code_integer)) (not (= Y (@ (@ tptp.produc8603105652947943368nteger A5) (@ (@ tptp.produc1086072967326762835nteger B5) C2))))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc2285326912895808259nt_int)) (not (forall ((A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.int) (C2 tptp.int)) (not (= Y (@ (@ tptp.produc5700946648718959541nt_int A5) (@ (@ tptp.product_Pair_int_int B5) C2))))))))
% 6.60/6.98 (assert (forall ((Y tptp.produc7773217078559923341nt_int)) (not (forall ((A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.int) (C2 tptp.int)) (not (= Y (@ (@ tptp.produc4305682042979456191nt_int A5) (@ (@ tptp.product_Pair_int_int B5) C2))))))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc8763457246119570046nteger Bool)) (X tptp.produc8763457246119570046nteger)) (=> (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.code_integer) (C2 tptp.code_integer)) (@ P (@ (@ tptp.produc6137756002093451184nteger A5) (@ (@ tptp.produc1086072967326762835nteger B5) C2)))) (@ P X))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc1908205239877642774nteger Bool)) (X tptp.produc1908205239877642774nteger)) (=> (forall ((A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.code_integer) (C2 tptp.code_integer)) (@ P (@ (@ tptp.produc8603105652947943368nteger A5) (@ (@ tptp.produc1086072967326762835nteger B5) C2)))) (@ P X))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc2285326912895808259nt_int Bool)) (X tptp.produc2285326912895808259nt_int)) (=> (forall ((A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.int) (C2 tptp.int)) (@ P (@ (@ tptp.produc5700946648718959541nt_int A5) (@ (@ tptp.product_Pair_int_int B5) C2)))) (@ P X))))
% 6.60/6.98 (assert (forall ((P (-> tptp.produc7773217078559923341nt_int Bool)) (X tptp.produc7773217078559923341nt_int)) (=> (forall ((A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.int) (C2 tptp.int)) (@ P (@ (@ tptp.produc4305682042979456191nt_int A5) (@ (@ tptp.product_Pair_int_int B5) C2)))) (@ P X))))
% 6.60/6.98 (assert (= tptp.artanh_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X3)) (@ (@ tptp.minus_minus_real tptp.one_one_real) X3)))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.60/6.98 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (M tptp.nat) (N tptp.nat)) (=> (forall ((M4 tptp.nat)) (@ (@ P M4) tptp.zero_zero_nat)) (=> (forall ((M4 tptp.nat) (N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (=> (@ (@ P N3) (@ (@ tptp.modulo_modulo_nat M4) N3)) (@ (@ P M4) N3)))) (@ (@ P M) N)))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ (@ tptp.bit_concat_bit (@ tptp.suc N)) K) L2) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int K) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ (@ tptp.bit_concat_bit N) (@ (@ tptp.divide_divide_int K) _let_1)) L2)))))))
% 6.60/6.98 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int A) A)))
% 6.60/6.98 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) A)))
% 6.60/6.98 (assert (forall ((A tptp.num)) (@ (@ tptp.ord_less_eq_num A) A)))
% 6.60/6.98 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) A)))
% 6.60/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) A)))
% 6.60/6.98 (assert (forall ((X tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int X) X)))
% 6.60/6.98 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat X) X)))
% 6.60/6.98 (assert (forall ((X tptp.num)) (@ (@ tptp.ord_less_eq_num X) X)))
% 6.60/6.98 (assert (forall ((X tptp.nat)) (@ (@ tptp.ord_less_eq_nat X) X)))
% 6.60/6.98 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_eq_int X) X)))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (= (@ tptp.ln_ln_real X) (@ tptp.ln_ln_real Y)) (= X Y)))))))
% 6.60/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit tptp.zero_zero_nat) K) L2) L2)))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (= (@ _let_1 (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (= (@ tptp.ln_ln_real X) tptp.zero_zero_real) (= X tptp.one_one_real)))))
% 6.60/6.98 (assert (= (@ tptp.ln_ln_real tptp.one_one_real) tptp.zero_zero_real))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit N) K) L2)) (@ _let_1 L2)))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ (@ tptp.bit_concat_bit N) K) L2)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.60/6.98 (assert (forall ((N tptp.nat) (K tptp.int) (M tptp.nat) (L2 tptp.int) (R tptp.int)) (let ((_let_1 (@ (@ tptp.bit_concat_bit N) K))) (= (@ _let_1 (@ (@ (@ tptp.bit_concat_bit M) L2) R)) (@ (@ (@ tptp.bit_concat_bit (@ (@ tptp.plus_plus_nat M) N)) (@ _let_1 L2)) R)))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) X))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) X))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 (@ tptp.ln_ln_real X)) (=> (@ _let_1 X) (@ (@ tptp.ord_less_real tptp.one_one_real) X))))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real X)) tptp.zero_zero_real)))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.60/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)))))
% 6.60/6.98 (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)))))
% 6.60/6.98 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.60/6.98 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.60/6.98 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.60/6.98 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num A) (@ F C)))))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (= X Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (= X Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (= X Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_nat (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_nat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_int (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_int (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_num (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_eq_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (F (-> tptp.nat tptp.num)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (F (-> tptp.int tptp.num)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_int B) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (@ (@ tptp.ord_less_eq_set_int B2) A3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (@ (@ tptp.ord_less_eq_rat B2) A3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (@ (@ tptp.ord_less_eq_num B2) A3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (@ (@ tptp.ord_less_eq_nat B2) A3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (@ (@ tptp.ord_less_eq_int B2) A3)))))
% 6.60/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (= A B)))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat B) A) (= A B)))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_eq_num B) A) (= A B)))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_eq_nat B) A) (= A B)))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int B) A) (= A B)))))
% 6.60/6.98 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.60/6.98 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.60/6.98 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.60/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.60/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.60/6.98 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (= A B)))))
% 6.60/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat A) B) (= A B)))))
% 6.60/6.98 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ (@ tptp.ord_less_eq_num A) B) (= A B)))))
% 6.60/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat A) B) (= A B)))))
% 6.60/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ (@ tptp.ord_less_eq_int A) B) (= A B)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (@ (@ tptp.ord_less_eq_set_int A3) B2)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (@ (@ tptp.ord_less_eq_rat A3) B2)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (@ (@ tptp.ord_less_eq_num A3) B2)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (@ (@ tptp.ord_less_eq_nat A3) B2)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (@ (@ tptp.ord_less_eq_int A3) B2)))))
% 6.60/6.98 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.60/6.98 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.60/6.98 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.60/6.98 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B)))))
% 6.60/6.98 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.60/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.60/6.98 (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)))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= X Y)))))
% 6.60/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.60/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ (@ tptp.ord_less_eq_set_int A) C)))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ (@ tptp.ord_less_eq_rat A) C)))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ (@ tptp.ord_less_eq_num A) C)))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ (@ tptp.ord_less_eq_nat A) C)))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ (@ tptp.ord_less_eq_int A) C)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.set_int) (Z2 tptp.set_int)) (= Y4 Z2)) (lambda ((X3 tptp.set_int) (Y3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y3) (@ (@ tptp.ord_less_eq_set_int Y3) X3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.rat) (Z2 tptp.rat)) (= Y4 Z2)) (lambda ((X3 tptp.rat) (Y3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y3) (@ (@ tptp.ord_less_eq_rat Y3) X3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.num) (Z2 tptp.num)) (= Y4 Z2)) (lambda ((X3 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y3) (@ (@ tptp.ord_less_eq_num Y3) X3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y3) (@ (@ tptp.ord_less_eq_nat Y3) X3)))))
% 6.60/6.98 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((X3 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y3) (@ (@ tptp.ord_less_eq_int Y3) X3)))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_rat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_rat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_num X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_num Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_num Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_nat Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_nat Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int X))) (let ((_let_2 (@ _let_1 Y))) (let ((_let_3 (@ tptp.ord_less_eq_int Z))) (let ((_let_4 (@ _let_3 X))) (let ((_let_5 (@ tptp.ord_less_eq_int Y))) (let ((_let_6 (@ _let_5 Z))) (let ((_let_7 (@ _let_5 X))) (let ((_let_8 (@ _let_3 Y))) (let ((_let_9 (@ _let_1 Z))) (=> (=> _let_2 (not _let_6)) (=> (=> _let_7 (not _let_9)) (=> (=> _let_9 (not _let_8)) (=> (=> _let_8 (not _let_7)) (=> (=> _let_6 (not _let_4)) (not (=> _let_4 (not _let_2)))))))))))))))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat A) B)) (and (@ (@ tptp.ord_less_eq_rat B) A) (not (= B A))))))
% 6.60/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num A) B)) (and (@ (@ tptp.ord_less_eq_num B) A) (not (= B A))))))
% 6.60/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat A) B)) (and (@ (@ tptp.ord_less_eq_nat B) A) (not (= B A))))))
% 6.60/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int A) B)) (and (@ (@ tptp.ord_less_eq_int B) A) (not (= B A))))))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= Y X)))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= Y X)))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= Y X)))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= Y X)))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= Y X)))))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_real X) Y) (= X Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_num X) Y) (= X Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_int X) Y) (= X Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (P Bool)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_real Y) X) P))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (P Bool)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) X) P))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num) (P Bool)) (=> (@ (@ tptp.ord_less_num X) Y) (=> (@ (@ tptp.ord_less_num Y) X) P))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (P Bool)) (=> (@ (@ tptp.ord_less_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) X) P))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (P Bool)) (=> (@ (@ tptp.ord_less_int X) Y) (=> (@ (@ tptp.ord_less_int Y) X) P))))
% 6.60/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.60/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.60/6.98 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real X) X))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (not (@ (@ tptp.ord_less_rat X) X))))
% 6.68/6.98 (assert (forall ((X tptp.num)) (not (@ (@ tptp.ord_less_num X) X))))
% 6.68/6.98 (assert (forall ((X tptp.nat)) (not (@ (@ tptp.ord_less_nat X) X))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (not (@ (@ tptp.ord_less_int X) X))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (= (@ F B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (F (-> tptp.real tptp.num)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.real tptp.nat)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (F (-> tptp.real tptp.int)) (B tptp.real) (C tptp.real)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (=> (= A (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_num Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (= X Y)) (or (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_int Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (@ (@ tptp.ord_less_real Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (@ (@ tptp.ord_less_rat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (@ (@ tptp.ord_less_num Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (@ (@ tptp.ord_less_nat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (@ (@ tptp.ord_less_int Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (= X Y)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (= A B)))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (= A B)))))
% 6.68/6.98 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (= A B)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (= A B)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (= A B)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (or (@ (@ tptp.ord_less_real Y) X) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (or (@ (@ tptp.ord_less_rat Y) X) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (or (@ (@ tptp.ord_less_num Y) X) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (or (@ (@ tptp.ord_less_nat Y) X) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (or (@ (@ tptp.ord_less_int Y) X) (= X Y)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_real B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_rat B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_num B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_nat B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_int B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.real tptp.real Bool)) (A tptp.real) (B tptp.real)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ tptp.ord_less_real A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.real)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.real) (B5 tptp.real)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (A tptp.rat) (B tptp.rat)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.rat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.rat) (B5 tptp.rat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.num tptp.num Bool)) (A tptp.num) (B tptp.num)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ tptp.ord_less_num A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.num)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.num) (B5 tptp.num)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int A5) B5) (@ (@ P A5) B5))) (=> (forall ((A5 tptp.int)) (@ (@ P A5) A5)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ P B5) A5) (@ (@ P A5) B5))) (@ (@ P A) B))))))
% 6.68/6.98 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((N2 tptp.nat)) (and (@ P4 N2) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N2) (not (@ P4 M3)))))))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real A) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat A) A))))
% 6.68/6.98 (assert (forall ((A tptp.num)) (not (@ (@ tptp.ord_less_num A) A))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int A) A))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (not (@ (@ tptp.ord_less_real A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (not (@ (@ tptp.ord_less_rat A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (not (@ (@ tptp.ord_less_num A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (not (@ (@ tptp.ord_less_nat A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (not (@ (@ tptp.ord_less_int A) B)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_real Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_rat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_num Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_nat Y) X)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (=> (not (= X Y)) (@ (@ tptp.ord_less_int Y) X)))))
% 6.68/6.98 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_real Y) X)) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat Y) X)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_num Y) X)) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat Y) X)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_int Y) X)) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat Y2) X6) (@ P Y2))) (@ P X6))) (@ P A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (= B C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (= A B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (= A B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (= A B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (= A B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (= A B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (not (@ (@ tptp.ord_less_real B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (not (@ (@ tptp.ord_less_rat B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (not (@ (@ tptp.ord_less_num B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (not (@ (@ tptp.ord_less_nat B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (not (@ (@ tptp.ord_less_int B) A)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (not (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (not (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (not (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (not (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (not (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real X) Z5) (@ (@ tptp.ord_less_real Z5) Y))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (exists ((Z5 tptp.rat)) (and (@ (@ tptp.ord_less_rat X) Z5) (@ (@ tptp.ord_less_rat Z5) Y))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (exists ((X_1 tptp.real)) (@ (@ tptp.ord_less_real X) X_1))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (exists ((X_1 tptp.rat)) (@ (@ tptp.ord_less_rat X) X_1))))
% 6.68/6.98 (assert (forall ((X tptp.nat)) (exists ((X_1 tptp.nat)) (@ (@ tptp.ord_less_nat X) X_1))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (exists ((X_1 tptp.int)) (@ (@ tptp.ord_less_int X) X_1))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (@ (@ tptp.ord_less_real Y5) X))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (exists ((Y5 tptp.rat)) (@ (@ tptp.ord_less_rat Y5) X))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (exists ((Y5 tptp.int)) (@ (@ tptp.ord_less_int Y5) X))))
% 6.68/6.98 (assert (forall ((X tptp.product_prod_int_int)) (not (forall ((D3 tptp.int) (I4 tptp.int)) (not (= X (@ (@ tptp.product_Pair_int_int D3) I4)))))))
% 6.68/6.98 (assert (forall ((X tptp.produc7773217078559923341nt_int)) (not (forall ((F2 (-> tptp.int tptp.option6357759511663192854e_term)) (D3 tptp.int) (I4 tptp.int)) (not (= X (@ (@ tptp.produc4305682042979456191nt_int F2) (@ (@ tptp.product_Pair_int_int D3) I4))))))))
% 6.68/6.98 (assert (forall ((X tptp.produc2285326912895808259nt_int)) (not (forall ((F2 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (D3 tptp.int) (I4 tptp.int)) (not (= X (@ (@ tptp.produc5700946648718959541nt_int F2) (@ (@ tptp.product_Pair_int_int D3) I4))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ln_ln_real X)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (= (@ tptp.ln_ln_real X) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (= X tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.ln_ln_real (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real X)) (@ tptp.ln_ln_real Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) Y)) Y)))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (or (@ (@ tptp.ord_less_real X) Y) (= X Y)))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (or (@ (@ tptp.ord_less_rat X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (or (@ (@ tptp.ord_less_num X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (or (@ (@ tptp.ord_less_nat X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (or (@ (@ tptp.ord_less_int X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (or (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_real Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (or (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_rat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (or (@ (@ tptp.ord_less_eq_num X) Y) (@ (@ tptp.ord_less_num Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (or (@ (@ tptp.ord_less_eq_nat X) Y) (@ (@ tptp.ord_less_nat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (or (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_int Y) X))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_real (@ F B)) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_num A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (F (-> tptp.nat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_nat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (F (-> tptp.int tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_int A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ F B)) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (F (-> tptp.rat tptp.num)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.rat tptp.nat)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (F (-> tptp.rat tptp.int)) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (F (-> tptp.num tptp.num)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (F (-> tptp.num tptp.nat)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (F (-> tptp.num tptp.int)) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 (@ F B)) (=> (@ (@ tptp.ord_less_eq_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ _let_1 (@ F C))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (F (-> tptp.rat tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.real)) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_real (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.rat)) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_rat (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.num)) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_num (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_num (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.nat)) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_nat (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_nat (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (F (-> tptp.num tptp.int)) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_int (@ F B)) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X6) Y5) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_int (@ F A)) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.real tptp.real)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.rat tptp.real)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.num tptp.real)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.nat tptp.real)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (F (-> tptp.int tptp.real)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_real A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Y5) (@ (@ tptp.ord_less_real (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_real A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.real tptp.rat)) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_real B) C) (=> (forall ((X6 tptp.real) (Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.rat tptp.rat)) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_rat B) C) (=> (forall ((X6 tptp.rat) (Y5 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.num tptp.rat)) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_num B) C) (=> (forall ((X6 tptp.num) (Y5 tptp.num)) (=> (@ (@ tptp.ord_less_num X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.nat tptp.rat)) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_nat B) C) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (@ (@ tptp.ord_less_nat X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (F (-> tptp.int tptp.rat)) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_rat A) (@ F B)) (=> (@ (@ tptp.ord_less_int B) C) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (@ (@ tptp.ord_less_int X6) Y5) (@ (@ tptp.ord_less_rat (@ F X6)) (@ F Y5)))) (@ (@ tptp.ord_less_rat A) (@ F C)))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_set_int Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_rat Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (let ((_let_1 (@ tptp.ord_less_num X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_num Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_nat Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int X))) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ _let_1 Z))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) Z) (@ (@ tptp.ord_less_real X) Z)))))
% 6.68/6.98 (assert (forall ((X tptp.set_int) (Y tptp.set_int) (Z tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int X) Y) (=> (@ (@ tptp.ord_less_set_int Y) Z) (@ (@ tptp.ord_less_set_int X) Z)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (=> (@ (@ tptp.ord_less_rat Y) Z) (@ (@ tptp.ord_less_rat X) Z)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num) (Z tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (=> (@ (@ tptp.ord_less_num Y) Z) (@ (@ tptp.ord_less_num X) Z)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (Z tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (=> (@ (@ tptp.ord_less_nat Y) Z) (@ (@ tptp.ord_less_nat X) Z)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int X) Z)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_real A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_rat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_num A) B) (@ (@ tptp.ord_less_num A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (@ (@ tptp.ord_less_nat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A B)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_real A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_set_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_rat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_num A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_nat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (not (= A B)) (@ (@ tptp.ord_less_int A) B)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_num X) Y) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_nat X) Y) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_int X) Y) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (not (@ (@ tptp.ord_less_eq_real X) Y)) (@ (@ tptp.ord_less_real Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (not (@ (@ tptp.ord_less_eq_rat X) Y)) (@ (@ tptp.ord_less_rat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (= (not (@ (@ tptp.ord_less_eq_num X) Y)) (@ (@ tptp.ord_less_num Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (not (@ (@ tptp.ord_less_eq_nat X) Y)) (@ (@ tptp.ord_less_nat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (= (not (@ (@ tptp.ord_less_eq_int X) Y)) (@ (@ tptp.ord_less_int Y) X))))
% 6.68/6.98 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y3) (not (= X3 Y3))))))
% 6.68/6.98 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y3) (not (= X3 Y3))))))
% 6.68/6.98 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y3) (not (= X3 Y3))))))
% 6.68/6.98 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y3) (not (= X3 Y3))))))
% 6.68/6.98 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y3) (not (= X3 Y3))))))
% 6.68/6.98 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y3) (not (= X3 Y3))))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_real (lambda ((X3 tptp.real) (Y3 tptp.real)) (or (@ (@ tptp.ord_less_real X3) Y3) (= X3 Y3)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_set_int (lambda ((X3 tptp.set_int) (Y3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int X3) Y3) (= X3 Y3)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y3) (= X3 Y3)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_num (lambda ((X3 tptp.num) (Y3 tptp.num)) (or (@ (@ tptp.ord_less_num X3) Y3) (= X3 Y3)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (or (@ (@ tptp.ord_less_nat X3) Y3) (= X3 Y3)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Y3 tptp.int)) (or (@ (@ tptp.ord_less_int X3) Y3) (= X3 Y3)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (@ (@ tptp.ord_less_eq_real B) A))))
% 6.68/6.98 (assert (forall ((B tptp.set_int) (A tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (@ (@ tptp.ord_less_eq_set_int B) A))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (@ (@ tptp.ord_less_eq_rat B) A))))
% 6.68/6.98 (assert (forall ((B tptp.num) (A tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (@ (@ tptp.ord_less_eq_num B) A))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (@ (@ tptp.ord_less_eq_nat B) A))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (@ (@ tptp.ord_less_eq_int B) A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.68/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int A) B) (@ (@ tptp.ord_less_eq_set_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (=> (@ (@ tptp.ord_less_num A) B) (@ (@ tptp.ord_less_eq_num A) B))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat A) B) (@ (@ tptp.ord_less_eq_nat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.68/6.98 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (@ (@ tptp.ord_less_eq_real A3) B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (@ (@ tptp.ord_less_eq_set_int A3) B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (@ (@ tptp.ord_less_eq_rat A3) B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (@ (@ tptp.ord_less_eq_num A3) B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (@ (@ tptp.ord_less_eq_nat A3) B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (@ (@ tptp.ord_less_eq_int A3) B2))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_real B) A) (=> (@ (@ tptp.ord_less_eq_real C) B) (@ (@ tptp.ord_less_real C) A)))))
% 6.68/6.98 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int B) A) (=> (@ (@ tptp.ord_less_eq_set_int C) B) (@ (@ tptp.ord_less_set_int C) A)))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_rat B) A) (=> (@ (@ tptp.ord_less_eq_rat C) B) (@ (@ tptp.ord_less_rat C) A)))))
% 6.68/6.98 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_num B) A) (=> (@ (@ tptp.ord_less_eq_num C) B) (@ (@ tptp.ord_less_num C) A)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_nat B) A) (=> (@ (@ tptp.ord_less_eq_nat C) B) (@ (@ tptp.ord_less_nat C) A)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_int B) A) (=> (@ (@ tptp.ord_less_eq_int C) B) (@ (@ tptp.ord_less_int C) A)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real C))) (=> (@ (@ tptp.ord_less_eq_real B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.set_int) (A tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int C))) (=> (@ (@ tptp.ord_less_eq_set_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat C))) (=> (@ (@ tptp.ord_less_eq_rat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.num) (A tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num C))) (=> (@ (@ tptp.ord_less_eq_num B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat C))) (=> (@ (@ tptp.ord_less_eq_nat B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int C))) (=> (@ (@ tptp.ord_less_eq_int B) A) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (= tptp.ord_less_real (lambda ((B2 tptp.real) (A3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real B2) A3) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int B2) A3) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat B2) A3) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_num (lambda ((B2 tptp.num) (A3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num B2) A3) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat B2) A3) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_int (lambda ((B2 tptp.int) (A3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int B2) A3) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_real (lambda ((B2 tptp.real) (A3 tptp.real)) (or (@ (@ tptp.ord_less_real B2) A3) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_set_int (lambda ((B2 tptp.set_int) (A3 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int B2) A3) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (or (@ (@ tptp.ord_less_rat B2) A3) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_num (lambda ((B2 tptp.num) (A3 tptp.num)) (or (@ (@ tptp.ord_less_num B2) A3) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (or (@ (@ tptp.ord_less_nat B2) A3) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_int (lambda ((B2 tptp.int) (A3 tptp.int)) (or (@ (@ tptp.ord_less_int B2) A3) (= A3 B2)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real X) W2) (=> (@ (@ tptp.ord_less_real W2) Y) (@ (@ tptp.ord_less_eq_real W2) Z)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) Y) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X) W2) (=> (@ (@ tptp.ord_less_rat W2) Y) (@ (@ tptp.ord_less_eq_rat W2) Z)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X) (=> (forall ((W2 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) W2) (=> (@ (@ tptp.ord_less_real W2) X) (@ (@ tptp.ord_less_eq_real Y) W2)))) (@ (@ tptp.ord_less_eq_real Y) Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X) (=> (forall ((W2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) W2) (=> (@ (@ tptp.ord_less_rat W2) X) (@ (@ tptp.ord_less_eq_rat Y) W2)))) (@ (@ tptp.ord_less_eq_rat Y) Z)))))
% 6.68/6.98 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (@ (@ tptp.ord_less_eq_real B2) A3))))))
% 6.68/6.98 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (@ (@ tptp.ord_less_eq_set_int B2) A3))))))
% 6.68/6.98 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (@ (@ tptp.ord_less_eq_rat B2) A3))))))
% 6.68/6.98 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (@ (@ tptp.ord_less_eq_num B2) A3))))))
% 6.68/6.98 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (@ (@ tptp.ord_less_eq_nat B2) A3))))))
% 6.68/6.98 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (@ (@ tptp.ord_less_eq_int B2) A3))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_real B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (let ((_let_1 (@ tptp.ord_less_set_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_set_int B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_rat B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (let ((_let_1 (@ tptp.ord_less_num A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_num B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_nat B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.ord_less_eq_int B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_real B) C) (@ (@ tptp.ord_less_real A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int) (C tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) B) (=> (@ (@ tptp.ord_less_set_int B) C) (@ (@ tptp.ord_less_set_int A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_rat B) C) (@ (@ tptp.ord_less_rat A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num) (C tptp.num)) (=> (@ (@ tptp.ord_less_eq_num A) B) (=> (@ (@ tptp.ord_less_num B) C) (@ (@ tptp.ord_less_num A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) B) (=> (@ (@ tptp.ord_less_nat B) C) (@ (@ tptp.ord_less_nat A) C)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_int B) C) (@ (@ tptp.ord_less_int A) C)))))
% 6.68/6.98 (assert (= tptp.ord_less_real (lambda ((A3 tptp.real) (B2 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A3) B2) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int A3) B2) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat A3) B2) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_num (lambda ((A3 tptp.num) (B2 tptp.num)) (and (@ (@ tptp.ord_less_eq_num A3) B2) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat A3) B2) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_int (lambda ((A3 tptp.int) (B2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int A3) B2) (not (= A3 B2))))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_real (lambda ((A3 tptp.real) (B2 tptp.real)) (or (@ (@ tptp.ord_less_real A3) B2) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (or (@ (@ tptp.ord_less_set_int A3) B2) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (or (@ (@ tptp.ord_less_rat A3) B2) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_num (lambda ((A3 tptp.num) (B2 tptp.num)) (or (@ (@ tptp.ord_less_num A3) B2) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (or (@ (@ tptp.ord_less_nat A3) B2) (= A3 B2)))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_int (lambda ((A3 tptp.int) (B2 tptp.int)) (or (@ (@ tptp.ord_less_int A3) B2) (= A3 B2)))))
% 6.68/6.98 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.ord_less_eq_real Y) X)) (@ (@ tptp.ord_less_real X) Y))))
% 6.68/6.98 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (not (@ (@ tptp.ord_less_eq_rat Y) X)) (@ (@ tptp.ord_less_rat X) Y))))
% 6.68/6.98 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (not (@ (@ tptp.ord_less_eq_num Y) X)) (@ (@ tptp.ord_less_num X) Y))))
% 6.68/6.98 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (@ (@ tptp.ord_less_eq_nat Y) X)) (@ (@ tptp.ord_less_nat X) Y))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (not (@ (@ tptp.ord_less_eq_int Y) X)) (@ (@ tptp.ord_less_int X) Y))))
% 6.68/6.98 (assert (= tptp.ord_less_real (lambda ((X3 tptp.real) (Y3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real X3) Y3) (not (@ (@ tptp.ord_less_eq_real Y3) X3))))))
% 6.68/6.98 (assert (= tptp.ord_less_set_int (lambda ((X3 tptp.set_int) (Y3 tptp.set_int)) (and (@ (@ tptp.ord_less_eq_set_int X3) Y3) (not (@ (@ tptp.ord_less_eq_set_int Y3) X3))))))
% 6.68/6.98 (assert (= tptp.ord_less_rat (lambda ((X3 tptp.rat) (Y3 tptp.rat)) (and (@ (@ tptp.ord_less_eq_rat X3) Y3) (not (@ (@ tptp.ord_less_eq_rat Y3) X3))))))
% 6.68/6.98 (assert (= tptp.ord_less_num (lambda ((X3 tptp.num) (Y3 tptp.num)) (and (@ (@ tptp.ord_less_eq_num X3) Y3) (not (@ (@ tptp.ord_less_eq_num Y3) X3))))))
% 6.68/6.98 (assert (= tptp.ord_less_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat X3) Y3) (not (@ (@ tptp.ord_less_eq_nat Y3) X3))))))
% 6.68/6.98 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Y3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int X3) Y3) (not (@ (@ tptp.ord_less_eq_int Y3) X3))))))
% 6.68/6.98 (assert (forall ((Y tptp.real) (Z tptp.real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real X6) Y) (@ (@ tptp.ord_less_eq_real X6) Z))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.68/6.98 (assert (forall ((Y tptp.rat) (Z tptp.rat)) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat X6) Y) (@ (@ tptp.ord_less_eq_rat X6) Z))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (Y tptp.real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real Z) X6) (@ (@ tptp.ord_less_eq_real Y) X6))) (@ (@ tptp.ord_less_eq_real Y) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (Y tptp.rat)) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat Z) X6) (@ (@ tptp.ord_less_eq_rat Y) X6))) (@ (@ tptp.ord_less_eq_rat Y) Z))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (= (not (@ (@ tptp.ord_less_real X) Y)) (= X Y)))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (not (@ (@ tptp.ord_less_rat X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (not (@ (@ tptp.ord_less_num X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (not (@ (@ tptp.ord_less_nat X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (not (@ (@ tptp.ord_less_int X) Y)) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (= (@ (@ tptp.ord_less_eq_real X) Y) (= X Y)))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (= (@ (@ tptp.ord_less_eq_rat X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (= (@ (@ tptp.ord_less_eq_num X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (= (@ (@ tptp.ord_less_eq_nat X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (= (@ (@ tptp.ord_less_eq_int X) Y) (= X Y)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (not (@ (@ tptp.ord_less_real A) B)) (or (not (@ (@ tptp.ord_less_eq_real A) B)) (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.set_int) (B tptp.set_int)) (= (not (@ (@ tptp.ord_less_set_int A) B)) (or (not (@ (@ tptp.ord_less_eq_set_int A) B)) (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (not (@ (@ tptp.ord_less_rat A) B)) (or (not (@ (@ tptp.ord_less_eq_rat A) B)) (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.num) (B tptp.num)) (= (not (@ (@ tptp.ord_less_num A) B)) (or (not (@ (@ tptp.ord_less_eq_num A) B)) (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (not (@ (@ tptp.ord_less_nat A) B)) (or (not (@ (@ tptp.ord_less_eq_nat A) B)) (= A B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (not (@ (@ tptp.ord_less_int A) B)) (or (not (@ (@ tptp.ord_less_eq_int A) B)) (= A B)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (@ (@ tptp.ord_less_real X) Y)) (@ (@ tptp.ord_less_eq_real Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (not (@ (@ tptp.ord_less_rat X) Y)) (@ (@ tptp.ord_less_eq_rat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (not (@ (@ tptp.ord_less_num X) Y)) (@ (@ tptp.ord_less_eq_num Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (not (@ (@ tptp.ord_less_nat X) Y)) (@ (@ tptp.ord_less_eq_nat Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (not (@ (@ tptp.ord_less_int X) Y)) (@ (@ tptp.ord_less_eq_int Y) X))))
% 6.68/6.98 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real Y) X) (not (@ (@ tptp.ord_less_real X) Y)))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (not (@ (@ tptp.ord_less_rat X) Y)))))
% 6.68/6.98 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (not (@ (@ tptp.ord_less_num X) Y)))))
% 6.68/6.98 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (not (@ (@ tptp.ord_less_nat X) Y)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (not (@ (@ tptp.ord_less_int X) Y)))))
% 6.68/6.98 (assert (forall ((A tptp.set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.68/6.98 (assert (forall ((A tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.68/6.98 (assert (forall ((A tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.68/6.98 (assert (forall ((A tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.68/6.98 (assert (forall ((A tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A) tptp.bot_bot_set_nat) (= A tptp.bot_bot_set_nat))))
% 6.68/6.98 (assert (forall ((A tptp.extended_enat)) (= (@ (@ tptp.ord_le2932123472753598470d_enat A) tptp.bot_bo4199563552545308370d_enat) (= A tptp.bot_bo4199563552545308370d_enat))))
% 6.68/6.98 (assert (forall ((A tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A) tptp.bot_bot_set_real) (= A tptp.bot_bot_set_real))))
% 6.68/6.98 (assert (forall ((A tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A) tptp.bot_bot_set_int) (= A tptp.bot_bot_set_int))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat A) tptp.bot_bot_nat) (= A tptp.bot_bot_nat))))
% 6.68/6.98 (assert (forall ((A tptp.set_nat)) (@ (@ tptp.ord_less_eq_set_nat tptp.bot_bot_set_nat) A)))
% 6.68/6.98 (assert (forall ((A tptp.extended_enat)) (@ (@ tptp.ord_le2932123472753598470d_enat tptp.bot_bo4199563552545308370d_enat) A)))
% 6.68/6.98 (assert (forall ((A tptp.set_real)) (@ (@ tptp.ord_less_eq_set_real tptp.bot_bot_set_real) A)))
% 6.68/6.98 (assert (forall ((A tptp.set_int)) (@ (@ tptp.ord_less_eq_set_int tptp.bot_bot_set_int) A)))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.bot_bot_nat) A)))
% 6.68/6.98 (assert (forall ((A tptp.set_nat)) (= (not (= A tptp.bot_bot_set_nat)) (@ (@ tptp.ord_less_set_nat tptp.bot_bot_set_nat) A))))
% 6.68/6.98 (assert (forall ((A tptp.extended_enat)) (= (not (= A tptp.bot_bo4199563552545308370d_enat)) (@ (@ tptp.ord_le72135733267957522d_enat tptp.bot_bo4199563552545308370d_enat) A))))
% 6.68/6.98 (assert (forall ((A tptp.set_int)) (= (not (= A tptp.bot_bot_set_int)) (@ (@ tptp.ord_less_set_int tptp.bot_bot_set_int) A))))
% 6.68/6.98 (assert (forall ((A tptp.set_real)) (= (not (= A tptp.bot_bot_set_real)) (@ (@ tptp.ord_less_set_real tptp.bot_bot_set_real) A))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (= (not (= A tptp.bot_bot_nat)) (@ (@ tptp.ord_less_nat tptp.bot_bot_nat) A))))
% 6.68/6.98 (assert (forall ((A tptp.set_nat)) (not (@ (@ tptp.ord_less_set_nat A) tptp.bot_bot_set_nat))))
% 6.68/6.98 (assert (forall ((A tptp.extended_enat)) (not (@ (@ tptp.ord_le72135733267957522d_enat A) tptp.bot_bo4199563552545308370d_enat))))
% 6.68/6.98 (assert (forall ((A tptp.set_int)) (not (@ (@ tptp.ord_less_set_int A) tptp.bot_bot_set_int))))
% 6.68/6.98 (assert (forall ((A tptp.set_real)) (not (@ (@ tptp.ord_less_set_real A) tptp.bot_bot_set_real))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (not (@ (@ tptp.ord_less_nat A) tptp.bot_bot_nat))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat tptp.nat Bool)) (A tptp.nat) (B tptp.nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (= (@ (@ P A5) B5) (@ (@ P B5) A5))) (=> (forall ((A5 tptp.nat)) (@ (@ P A5) tptp.zero_zero_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (let ((_let_1 (@ P A5))) (=> (@ _let_1 B5) (@ _let_1 (@ (@ tptp.plus_plus_nat A5) B5))))) (@ (@ P A) B))))))
% 6.68/6.98 (assert (= tptp.ord_ma741700101516333627d_enat (lambda ((A3 tptp.extended_enat) (B2 tptp.extended_enat)) (@ (@ (@ tptp.if_Extended_enat (@ (@ tptp.ord_le2932123472753598470d_enat A3) B2)) B2) A3))))
% 6.68/6.98 (assert (= tptp.ord_max_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le3102999989581377725nteger A3) B2)) B2) A3))))
% 6.68/6.98 (assert (= tptp.ord_max_set_int (lambda ((A3 tptp.set_int) (B2 tptp.set_int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_eq_set_int A3) B2)) B2) A3))))
% 6.68/6.98 (assert (= tptp.ord_max_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_eq_rat A3) B2)) B2) A3))))
% 6.68/6.98 (assert (= tptp.ord_max_num (lambda ((A3 tptp.num) (B2 tptp.num)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_less_eq_num A3) B2)) B2) A3))))
% 6.68/6.98 (assert (= tptp.ord_max_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_eq_nat A3) B2)) B2) A3))))
% 6.68/6.98 (assert (= tptp.ord_max_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_eq_int A3) B2)) B2) A3))))
% 6.68/6.98 (assert (forall ((Y tptp.extended_enat) (X tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat Y) X) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) X))))
% 6.68/6.98 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger Y) X) (= (@ (@ tptp.ord_max_Code_integer X) Y) X))))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat Y) X) (= (@ (@ tptp.ord_max_rat X) Y) X))))
% 6.68/6.98 (assert (forall ((Y tptp.num) (X tptp.num)) (=> (@ (@ tptp.ord_less_eq_num Y) X) (= (@ (@ tptp.ord_max_num X) Y) X))))
% 6.68/6.98 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat Y) X) (= (@ (@ tptp.ord_max_nat X) Y) X))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Y) X) (= (@ (@ tptp.ord_max_int X) Y) X))))
% 6.68/6.98 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (=> (@ (@ tptp.ord_le2932123472753598470d_enat X) Y) (= (@ (@ tptp.ord_ma741700101516333627d_enat X) Y) Y))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) Y) (= (@ (@ tptp.ord_max_Code_integer X) Y) Y))))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (= (@ (@ tptp.ord_max_rat X) Y) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (Y tptp.num)) (=> (@ (@ tptp.ord_less_eq_num X) Y) (= (@ (@ tptp.ord_max_num X) Y) Y))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat X) Y) (= (@ (@ tptp.ord_max_nat X) Y) Y))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (= (@ (@ tptp.ord_max_int X) Y) Y))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)))))))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_real (@ tptp.ln_ln_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.tanh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))) (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_nat (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_nat A) _let_2))))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ tptp.plus_plus_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo_modulo_int (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo_modulo_int A) _let_2))))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_3 A)) _let_2) (@ _let_3 (@ (@ tptp.modulo364778990260209775nteger A) _let_2))))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_2) (@ (@ tptp.divide6298287555418463151nteger A) _let_2))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_nat _let_1) N))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_2) (@ (@ tptp.divide_divide_nat A) _let_2))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_2) (@ (@ tptp.divide_divide_int A) _let_2))))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) (@ tptp.uminus_uminus_real B)) (= A B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) (@ tptp.uminus_uminus_int B)) (= A B))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) (@ tptp.uminus1482373934393186551omplex B)) (= A B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) (@ tptp.uminus1351360451143612070nteger B)) (= A B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) (@ tptp.uminus_uminus_rat B)) (= A B))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ tptp.uminus_uminus_real (@ tptp.uminus_uminus_real A)) A)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ tptp.uminus_uminus_int (@ tptp.uminus_uminus_int A)) A)))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ tptp.uminus1482373934393186551omplex A)) A)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ tptp.uminus1351360451143612070nteger A)) A)))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ tptp.uminus_uminus_rat A)) A)))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat M) tptp.one_one_nat) (= M tptp.one_one_nat))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) A) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) A) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) A) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= A (@ tptp.uminus_uminus_real A)) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= A (@ tptp.uminus_uminus_int A)) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat A)) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= (@ tptp.uminus_uminus_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= (@ tptp.uminus_uminus_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.uminus_uminus_real A)) (= tptp.zero_zero_real A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.uminus_uminus_int A)) (= tptp.zero_zero_int A))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex A)) (= tptp.zero_zero_complex A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger A)) (= tptp.zero_z3403309356797280102nteger A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat A)) (= tptp.zero_zero_rat A))))
% 6.68/6.98 (assert (= (@ tptp.uminus_uminus_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.98 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.68/6.98 (assert (= (@ tptp.uminus1482373934393186551omplex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.68/6.98 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (= (@ tptp.uminus_uminus_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) B))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) B))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) B))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) B))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= M N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= M N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= M N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= M N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= M N))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.times_times_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.times_3573771949741848930nteger A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.times_times_rat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.times_times_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.times_times_complex A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex A))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex A) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real A) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.plus_plus_real A) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ (@ tptp.plus_plus_int A) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.plus_plus_complex A) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.plus_p5714425477246183910nteger A) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.plus_plus_rat A) B)) B)))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)) (@ (@ tptp.minus_minus_real B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)) (@ (@ tptp.minus_minus_int B) A))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)) (@ (@ tptp.minus_minus_complex B) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)) (@ (@ tptp.minus_minus_rat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger A) B))))
% 6.68/6.98 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.dvd_dvd_nat M) _let_1) (= M _let_1)))))
% 6.68/6.98 (assert (forall ((K tptp.nat)) (@ (@ tptp.dvd_dvd_nat (@ tptp.suc tptp.zero_zero_nat)) K)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real A) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat A) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) A)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) A)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) A)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) A)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) A)) (@ _let_1 B)))))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_Code_integer tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_rat tptp.zero_zero_rat) tptp.zero_zero_rat))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= tptp.zero_z3403309356797280102nteger (@ tptp.abs_abs_Code_integer A)) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= tptp.zero_zero_real (@ tptp.abs_abs_real A)) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= tptp.zero_zero_rat (@ tptp.abs_abs_rat A)) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= tptp.zero_zero_int (@ tptp.abs_abs_int A)) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat B) A)) (@ (@ tptp.divide_divide_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int B) A)) (@ (@ tptp.divide_divide_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.uminus_uminus_real X)) Y) (@ (@ tptp.dvd_dvd_real X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.uminus_uminus_int X)) Y) (@ (@ tptp.dvd_dvd_int X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ tptp.uminus1482373934393186551omplex X)) Y) (@ (@ tptp.dvd_dvd_complex X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.uminus1351360451143612070nteger X)) Y) (@ (@ tptp.dvd_dvd_Code_integer X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.uminus_uminus_rat X)) Y) (@ (@ tptp.dvd_dvd_rat X) Y))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex X))) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex Y)) (@ _let_1 Y)))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger Y)) (@ _let_1 Y)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (= (@ _let_1 (@ tptp.uminus_uminus_rat Y)) (@ _let_1 Y)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer A))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.times_3573771949741848930nteger A) A)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.times_times_real A) A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat A))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.times_times_rat A) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int A))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.times_times_int A) A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_complex tptp.one_one_complex) tptp.one_one_complex))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.abs_abs_complex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.abs_abs_complex A)) (@ tptp.abs_abs_complex B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ tptp.abs_abs_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.abs_abs_complex A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (= K tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.real) (K tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real M))) (= (@ _let_1 (@ tptp.abs_abs_real K)) (@ _let_1 K)))))
% 6.68/6.98 (assert (forall ((M tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int M))) (= (@ _let_1 (@ tptp.abs_abs_int K)) (@ _let_1 K)))))
% 6.68/6.98 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer M))) (= (@ _let_1 (@ tptp.abs_abs_Code_integer K)) (@ _let_1 K)))))
% 6.68/6.98 (assert (forall ((M tptp.rat) (K tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat M))) (= (@ _let_1 (@ tptp.abs_abs_rat K)) (@ _let_1 K)))))
% 6.68/6.98 (assert (forall ((M tptp.real) (K tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ tptp.abs_abs_real M)) K) (@ (@ tptp.dvd_dvd_real M) K))))
% 6.68/6.98 (assert (forall ((M tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.abs_abs_int M)) K) (@ (@ tptp.dvd_dvd_int M) K))))
% 6.68/6.98 (assert (forall ((M tptp.code_integer) (K tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.abs_abs_Code_integer M)) K) (@ (@ tptp.dvd_dvd_Code_integer M) K))))
% 6.68/6.98 (assert (forall ((M tptp.rat) (K tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ tptp.abs_abs_rat M)) K) (@ (@ tptp.dvd_dvd_rat M) K))))
% 6.68/6.98 (assert (= (@ tptp.tanh_complex tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.68/6.98 (assert (= (@ tptp.tanh_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (= (@ tptp.tanh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) (@ tptp.tanh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (= (@ _let_1 (@ tptp.uminus_uminus_real A)) (@ _let_1 tptp.zero_zero_real)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int A))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le6747313008572928689nteger A))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (= (@ _let_1 (@ tptp.uminus_uminus_rat A)) (@ _let_1 tptp.zero_zero_rat)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) A) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) A) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) A) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) A) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real A)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int A)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger A)) (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real tptp.zero_zero_real) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.zero_zero_int) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real A) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int A) (@ tptp.uminus_uminus_int A)) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex A) (@ tptp.uminus1482373934393186551omplex A)) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) (@ tptp.uminus1351360451143612070nteger A)) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat A) (@ tptp.uminus_uminus_rat A)) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) A) (@ tptp.uminus_uminus_real A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) A) (@ tptp.uminus_uminus_int A))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) A) (@ tptp.uminus1482373934393186551omplex A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) A) (@ tptp.uminus1351360451143612070nteger A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) A) (@ tptp.uminus_uminus_rat A))))
% 6.68/6.98 (assert (forall ((B tptp.real)) (= (@ (@ tptp.minus_minus_real tptp.zero_zero_real) B) (@ tptp.uminus_uminus_real B))))
% 6.68/6.98 (assert (forall ((B tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) B) (@ tptp.uminus_uminus_int B))))
% 6.68/6.98 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.minus_minus_complex tptp.zero_zero_complex) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.68/6.98 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.minus_minus_rat tptp.zero_zero_rat) B) (@ tptp.uminus_uminus_rat B))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (let ((_let_2 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real _let_2)) (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int _let_2) _let_1)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (let ((_let_2 (@ tptp.numera6690914467698888265omplex M))) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex _let_2)) (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M))) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger _let_2)) (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_2) _let_1)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (let ((_let_2 (@ tptp.numeral_numeral_rat M))) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat _let_2)) (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat _let_2) _let_1)))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.times_3573771949741848930nteger C) A)) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.times_times_nat C) A)) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.times_times_int C) A)) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_Code_integer B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (not (= A tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_nat B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (not (= A tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 B)) (@ _let_1 C)) (@ (@ tptp.dvd_dvd_int B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) C)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (= (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.times_times_complex A) C)) (@ (@ tptp.times_times_complex B) C)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (= (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) C)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (= (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) C)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) C)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger C))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer A) B))))))
% 6.68/6.98 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex C))) (= (@ (@ tptp.dvd_dvd_complex (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_complex) (@ (@ tptp.dvd_dvd_complex A) B))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real C))) (= (@ (@ tptp.dvd_dvd_real (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_real) (@ (@ tptp.dvd_dvd_real A) B))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat C))) (= (@ (@ tptp.dvd_dvd_rat (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_rat) (@ (@ tptp.dvd_dvd_rat A) B))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 A)) (@ _let_1 B)) (or (= C tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int A) B))))))
% 6.68/6.98 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real Z) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int Z) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int Z))))
% 6.68/6.98 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex Z) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.68/6.98 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger Z) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.68/6.98 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat Z) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat Z))))
% 6.68/6.98 (assert (forall ((Z tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Z) (@ tptp.uminus_uminus_real Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int tptp.one_one_int)) Z) (@ tptp.uminus_uminus_int Z))))
% 6.68/6.98 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) Z) (@ tptp.uminus1482373934393186551omplex Z))))
% 6.68/6.98 (assert (forall ((Z tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) Z) (@ tptp.uminus1351360451143612070nteger Z))))
% 6.68/6.98 (assert (forall ((Z tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) Z) (@ tptp.uminus_uminus_rat Z))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) A) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) A) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) A) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) A) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A)) (not (= A tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.abs_abs_real A)) (not (= A tptp.zero_zero_real)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A)) (not (= A tptp.zero_zero_rat)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.abs_abs_int A)) (not (= A tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.minus_minus_real B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.minus_minus_int B) A))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.minus_minus_complex B) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.minus_8373710615458151222nteger B) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.minus_minus_rat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.plus_plus_real A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.plus_plus_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex A) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.plus_plus_complex A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.plus_p5714425477246183910nteger A) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.plus_plus_rat A) B))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (@ (@ tptp.divide_divide_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real X))))
% 6.68/6.98 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex X))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.divide_divide_rat X) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat X))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) (@ (@ tptp.times_3573771949741848930nteger C) A))) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) (@ (@ tptp.times_times_real C) A))) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) (@ (@ tptp.times_times_rat C) A))) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) (@ (@ tptp.times_times_nat C) A))) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) (@ (@ tptp.times_times_int C) A))) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger C) A)) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (= (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real C) A)) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.times_times_rat C) A)) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat C) A)) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int C) A)) B)) (@ _let_1 B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.times_3573771949741848930nteger A) (@ (@ tptp.divide6298287555418463151nteger B) A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.times_times_nat A) (@ (@ tptp.divide_divide_nat B) A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.times_times_int A) (@ (@ tptp.divide_divide_int B) A)) B))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) tptp.one_one_nat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ _let_1 (@ _let_1 A)) A)))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)) C) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int A) B)) C) (@ (@ tptp.minus_minus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int _let_1)) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N))) (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger _let_1)) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat _let_1)) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (@ (@ tptp.modulo_modulo_nat B) A) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (@ (@ tptp.modulo_modulo_int B) A) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (@ (@ tptp.modulo364778990260209775nteger B) A) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int B) A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.minus_8373710615458151222nteger B) A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N)) (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N)) (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N)) (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (A tptp.real)) (= (= (@ (@ tptp.plus_plus_real X) (@ tptp.uminus_uminus_real A)) tptp.zero_zero_real) (= X A))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tanh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.tanh_real X)) (@ _let_1 X)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_numeral_dbl_real _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_numeral_dbl_int _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu7009210354673126013omplex _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu8804712462038260780nteger _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_numeral_dbl_rat _let_1))))))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.zero_zero_complex))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) tptp.zero_zero_real))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) tptp.zero_zero_int))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) tptp.zero_zero_complex))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) tptp.zero_zero_rat))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.minus_minus_real _let_1) _let_1) tptp.zero_zero_real)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.minus_minus_int _let_1) _let_1) tptp.zero_zero_int)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.minus_minus_complex _let_1) _let_1) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.minus_8373710615458151222nteger _let_1) _let_1) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.minus_minus_rat _let_1) _let_1) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (= N tptp.one))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) (or (@ _let_1 A) (= B tptp.zero_zero_real))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (= (@ _let_1 (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) (or (@ _let_1 A) (= B tptp.zero_zero_rat))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real A) (@ tptp.abs_abs_real B))) tptp.zero_zero_real) (or (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat A) (@ tptp.abs_abs_rat B))) tptp.zero_zero_rat) (or (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= B tptp.zero_zero_rat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) tptp.one_one_real))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) tptp.one_one_complex))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)))) (= (@ _let_1 (@ _let_1 A)) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc N)) (not (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc N))) (@ _let_1 N)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) A)) (@ (@ tptp.divide6298287555418463151nteger B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat B) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) A)) (@ (@ tptp.divide_divide_nat B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int B) (@ (@ tptp.divide_divide_int tptp.one_one_int) A)) (@ (@ tptp.divide_divide_int B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) A)) A) B))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) A)) A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) A)) A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real U))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger U))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat U))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int U))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.numeral_numeral_real V))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger V))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.numeral_numeral_rat V))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.numeral_numeral_int V))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real U)))) (let ((_let_2 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V)))) (let ((_let_3 (@ (@ tptp.ord_max_real _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_real _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger U)))) (let ((_let_2 (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V)))) (let ((_let_3 (@ (@ tptp.ord_max_Code_integer _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_le3102999989581377725nteger _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat U)))) (let ((_let_2 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V)))) (let ((_let_3 (@ (@ tptp.ord_max_rat _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_rat _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((U tptp.num) (V tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int U)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V)))) (let ((_let_3 (@ (@ tptp.ord_max_int _let_1) _let_2))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_1) _let_2))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 _let_1)))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N)) (@ (@ tptp.dvd_dvd_nat A) B)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N)) (@ (@ tptp.dvd_dvd_int A) B)))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) N)))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real V)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int V)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex V)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger V)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger W))) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat V)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W))) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real V))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) Y)) (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int V))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int W)) Y)) (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex V))) (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) Y)) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger V))) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger W)) Y)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num) (Y tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat V))) (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat W)) Y)) (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num V) W)))) Y))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.times_times_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.times_times_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.times_times_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.times_times_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.times_times_num M) N)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.artanh_real (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.artanh_real X))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_eq_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.ord_less_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ tptp.ord_less_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ (@ tptp.ord_less_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ (@ tptp.ord_less_num N) M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)))) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)))) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)))) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (not (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_eq_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_eq_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real A) _let_1))) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (W tptp.num) (A tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex A) _let_1))) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) _let_1) A) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat A) _let_1))) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_real))) (= (= A (@ (@ tptp.divide_divide_real B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_complex))) (= (= A (@ (@ tptp.divide1717551699836669952omplex B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_complex))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= _let_1 tptp.zero_zero_rat))) (= (= A (@ (@ tptp.divide_divide_rat B) _let_1)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat A) _let_1) B)) (=> _let_2 (= A tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (not (= M tptp.one)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) _let_1)) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) _let_1)) B)))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) _let_1)) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) _let_1)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (= (@ (@ tptp.ord_less_real A) (@ (@ tptp.divide_divide_real B) _let_1)) (@ (@ tptp.ord_less_real B) (@ (@ tptp.times_times_real A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (= (@ (@ tptp.ord_less_rat A) (@ (@ tptp.divide_divide_rat B) _let_1)) (@ (@ tptp.ord_less_rat B) (@ (@ tptp.times_times_rat A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.times_times_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int A) B))) (not (= (not (@ _let_1 A)) (not (@ _let_1 B))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) B)) (= (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real A) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int A) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex A) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger A) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat A) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.power_power_complex A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N)) (or (not (= A tptp.zero_z3403309356797280102nteger)) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) (or (not (= A tptp.zero_zero_real)) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N)) (or (not (= A tptp.zero_zero_rat)) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N)) (or (not (= A tptp.zero_zero_int)) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1)) (@ _let_2 A))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (= (@ _let_2 (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ _let_2 A))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (= (@ _let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ _let_2 A))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ tptp.suc (@ (@ tptp.divide_divide_nat N) _let_1)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc N)) _let_1) (@ (@ tptp.divide_divide_nat N) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or _let_3 (and (not _let_3) (@ _let_1 A)))))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_real A) tptp.zero_zero_real))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1)) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int))))))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.plus_plus_real _let_1) _let_1) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.plus_plus_int _let_1) _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.plus_plus_complex _let_1) _let_1) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.plus_plus_rat _let_1) _let_1) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.divide6298287555418463151nteger _let_1) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) (not (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) (not (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) (not (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int A) B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real _let_1) N) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_int _let_1) N) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_complex _let_1) N) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) N) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_rat _let_1) N) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N) tptp.one_one_real))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N) tptp.one_one_complex))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N) tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N) tptp.one_one_rat))))
% 6.68/6.98 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.68/6.98 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int))
% 6.68/6.98 (assert (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ tptp.suc (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) N))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) _let_1) (@ (@ tptp.power_power_real A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) _let_1) (@ (@ tptp.power_power_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) _let_1) (@ (@ tptp.power_power_complex A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) _let_1) (@ (@ tptp.power_power_rat A) _let_1)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (or (@ (@ tptp.ord_less_nat M) N) (@ _let_1 (@ (@ tptp.plus_plus_nat M) N)))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num tptp.one) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) tptp.one_one_complex) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ (@ tptp.plus_plus_num M) tptp.one))))))
% 6.68/6.98 (assert (= (@ tptp.neg_numeral_dbl_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_numeral_dbl_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu7009210354673126013omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu8804712462038260780nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_numeral_dbl_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_real A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_real))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_rat))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ tptp.numeral_numeral_nat W))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_2))) (= (@ _let_1 (@ (@ tptp.power_power_int A) _let_2)) (or (= _let_2 tptp.zero_zero_nat) (and _let_3 (not (= A tptp.zero_zero_int))) (and (not _let_3) (@ _let_1 A)))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) A)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat tptp.one_one_nat) A)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int tptp.one_one_int) A)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) tptp.one_one_Code_integer))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) _let_1)) tptp.one_one_nat))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) _let_1)) tptp.one_one_int))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) tptp.one_one_Code_integer)) _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) tptp.one_one_nat)) _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) tptp.one_one_int)) _let_1) (@ (@ tptp.divide_divide_int A) _let_1))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_8256067586552552935nteger A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_nat A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (and (@ _let_1 A) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_real)))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int)))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_complex)))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_rat)))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat N) _let_1)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) tptp.one_one_Code_integer) A)))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1))) tptp.one_one_nat) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1))) tptp.one_one_int) A)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) _let_1)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_2 (= A tptp.zero_zero_real)))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) _let_1)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_2 (= A tptp.zero_zero_rat)))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat W))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) _let_1))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) _let_1)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) _let_1) (or (and (not _let_2) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_2 (= A tptp.zero_zero_int)))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer)) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat)) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int)) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ _let_1 (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ _let_1 (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.divide6298287555418463151nteger A) B))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))))))
% 6.68/6.98 (assert (forall ((L2 tptp.real) (K tptp.real)) (=> (= (@ tptp.abs_abs_real L2) (@ tptp.abs_abs_real K)) (@ (@ tptp.dvd_dvd_real L2) K))))
% 6.68/6.98 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (= (@ tptp.abs_abs_int L2) (@ tptp.abs_abs_int K)) (@ (@ tptp.dvd_dvd_int L2) K))))
% 6.68/6.98 (assert (forall ((L2 tptp.code_integer) (K tptp.code_integer)) (=> (= (@ tptp.abs_abs_Code_integer L2) (@ tptp.abs_abs_Code_integer K)) (@ (@ tptp.dvd_dvd_Code_integer L2) K))))
% 6.68/6.98 (assert (forall ((L2 tptp.rat) (K tptp.rat)) (=> (= (@ tptp.abs_abs_rat L2) (@ tptp.abs_abs_rat K)) (@ (@ tptp.dvd_dvd_rat L2) K))))
% 6.68/6.98 (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))))))
% 6.68/6.98 (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))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer X) (@ tptp.abs_abs_Code_integer Y)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (= (@ tptp.abs_abs_rat X) (@ tptp.abs_abs_rat Y)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) A)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int A) A)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) A)))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ tptp.uminus_uminus_real B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ tptp.uminus_uminus_int B) A))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ tptp.uminus1482373934393186551omplex B) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ tptp.uminus1351360451143612070nteger B) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ tptp.uminus_uminus_rat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= B (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= B (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (and (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (and (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (and (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (and (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) (@ tptp.abs_abs_real A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.abs_abs_Code_integer A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.abs_abs_rat A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) (@ tptp.abs_abs_int A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.abs_abs_real A))) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.abs_abs_Code_integer A))) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.abs_abs_rat A))) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.abs_abs_int A))) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.abs_abs_real B)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (or (= B A) (= B (@ tptp.uminus_uminus_real A)))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.abs_abs_Code_integer B)) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) A) (or (= B A) (= B (@ tptp.uminus1351360451143612070nteger A)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.abs_abs_rat B)) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A) (or (= B A) (= B (@ tptp.uminus_uminus_rat A)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.abs_abs_int B)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A) (or (= B A) (= B (@ tptp.uminus_uminus_int A)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.abs_abs_real A) B) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) B) (or (= A B) (= A (@ tptp.uminus_uminus_real B)))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) B) (and (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) B) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.abs_abs_rat A) B) (and (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) B) (or (= A B) (= A (@ tptp.uminus_uminus_rat B)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.abs_abs_int A) B) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (or (= A B) (= A (@ tptp.uminus_uminus_int B)))))))
% 6.68/6.98 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.68/6.98 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.68/6.98 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.68/6.98 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (= (@ tptp.abs_abs_real A) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int A) tptp.zero_zero_int) (= (@ tptp.abs_abs_int A) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) tptp.zero_z3403309356797280102nteger) (= (@ tptp.abs_abs_Code_integer A) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) tptp.zero_zero_rat) (= (@ tptp.abs_abs_rat A) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.68/6.98 (assert (= tptp.abs_abs_int (lambda ((A3 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int A3) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int A3)) A3))))
% 6.68/6.98 (assert (= tptp.abs_abs_Code_integer (lambda ((A3 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger A3) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger A3)) A3))))
% 6.68/6.98 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.68/6.98 (assert (= tptp.abs_abs_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real A3) tptp.zero_zero_real)) (@ tptp.uminus_uminus_real A3)) A3))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) B) (@ (@ tptp.ord_less_eq_real A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) B) (@ (@ tptp.ord_le3102999989581377725nteger A) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) B) (@ (@ tptp.ord_less_eq_rat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) B) (@ (@ tptp.ord_less_eq_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real A) (@ tptp.abs_abs_real A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.abs_abs_Code_integer A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat A) (@ tptp.abs_abs_rat A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int A) (@ tptp.abs_abs_int A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= (@ tptp.abs_abs_Code_integer A) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (= (@ tptp.abs_abs_complex A) tptp.zero_zero_complex) (= A tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= (@ tptp.abs_abs_real A) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= (@ tptp.abs_abs_rat A) tptp.zero_zero_rat) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= (@ tptp.abs_abs_int A) tptp.zero_zero_int) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_Code_integer tptp.one_one_Code_integer) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_real tptp.one_one_real) tptp.one_one_real))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.68/6.98 (assert (= (@ tptp.abs_abs_int tptp.one_one_int) tptp.one_one_int))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.tanh_real X))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ tptp.abs_abs_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ tptp.abs_abs_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.68/6.98 (assert (= tptp.bot_bot_nat tptp.zero_zero_nat))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) A) (= A tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex tptp.zero_zero_complex) A) (= A tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real tptp.zero_zero_real) A) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat tptp.zero_zero_rat) A) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) A) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (=> (= A3 tptp.zero_zero_complex) (= B2 tptp.zero_zero_complex)))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_real (lambda ((A3 tptp.real) (B2 tptp.real)) (=> (= A3 tptp.zero_zero_real) (= B2 tptp.zero_zero_real)))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (=> (= A3 tptp.zero_zero_rat) (= B2 tptp.zero_zero_rat)))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (not (forall ((K3 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger B) K3))))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (not (forall ((K3 tptp.real)) (not (= A (@ (@ tptp.times_times_real B) K3))))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (not (forall ((K3 tptp.rat)) (not (= A (@ (@ tptp.times_times_rat B) K3))))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (not (forall ((K3 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat B) K3))))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (not (forall ((K3 tptp.int)) (not (= A (@ (@ tptp.times_times_int B) K3))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (K tptp.code_integer)) (=> (= A (@ (@ tptp.times_3573771949741848930nteger B) K)) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (K tptp.real)) (=> (= A (@ (@ tptp.times_times_real B) K)) (@ (@ tptp.dvd_dvd_real B) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (K tptp.rat)) (=> (= A (@ (@ tptp.times_times_rat B) K)) (@ (@ tptp.dvd_dvd_rat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (K tptp.nat)) (=> (= A (@ (@ tptp.times_times_nat B) K)) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (K tptp.int)) (=> (= A (@ (@ tptp.times_times_int B) K)) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_Code_integer (lambda ((B2 tptp.code_integer) (A3 tptp.code_integer)) (exists ((K2 tptp.code_integer)) (= A3 (@ (@ tptp.times_3573771949741848930nteger B2) K2))))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_real (lambda ((B2 tptp.real) (A3 tptp.real)) (exists ((K2 tptp.real)) (= A3 (@ (@ tptp.times_times_real B2) K2))))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_rat (lambda ((B2 tptp.rat) (A3 tptp.rat)) (exists ((K2 tptp.rat)) (= A3 (@ (@ tptp.times_times_rat B2) K2))))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_nat (lambda ((B2 tptp.nat) (A3 tptp.nat)) (exists ((K2 tptp.nat)) (= A3 (@ (@ tptp.times_times_nat B2) K2))))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_int (lambda ((B2 tptp.int) (A3 tptp.int)) (exists ((K2 tptp.int)) (= A3 (@ (@ tptp.times_times_int B2) K2))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_real B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_rat B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_nat B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (@ _let_1 (@ (@ tptp.times_times_int B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real A) C))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat A) C))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger A) B))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real A) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (=> (@ (@ tptp.dvd_dvd_real A) B) (=> (@ (@ tptp.dvd_dvd_real C) D) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) C)) (@ (@ tptp.times_times_real B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat A) B) (=> (@ (@ tptp.dvd_dvd_rat C) D) (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) C)) (@ (@ tptp.times_times_rat B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.dvd_dvd_real (@ (@ tptp.times_times_real A) B)) C) (@ (@ tptp.dvd_dvd_real B) C))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat (@ (@ tptp.times_times_rat A) B)) C) (@ (@ tptp.dvd_dvd_rat B) C))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger B) A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.dvd_dvd_real A) (@ (@ tptp.times_times_real B) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.dvd_dvd_rat A) (@ (@ tptp.times_times_rat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) A))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat B) C)) (exists ((B7 tptp.nat) (C5 tptp.nat)) (and (= A (@ (@ tptp.times_times_nat B7) C5)) (@ (@ tptp.dvd_dvd_nat B7) B) (@ (@ tptp.dvd_dvd_nat C5) C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int B) C)) (exists ((B7 tptp.int) (C5 tptp.int)) (and (= A (@ (@ tptp.times_times_int B7) C5)) (@ (@ tptp.dvd_dvd_int B7) B) (@ (@ tptp.dvd_dvd_int C5) C))))))
% 6.68/6.98 (assert (forall ((P5 tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat P5) (@ (@ tptp.times_times_nat A) B)) (not (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.times_times_nat X6) Y5)) (=> (@ (@ tptp.dvd_dvd_nat X6) A) (not (@ (@ tptp.dvd_dvd_nat Y5) B)))))))))
% 6.68/6.98 (assert (forall ((P5 tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int P5) (@ (@ tptp.times_times_int A) B)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.times_times_int X6) Y5)) (=> (@ (@ tptp.dvd_dvd_int X6) A) (not (@ (@ tptp.dvd_dvd_int Y5) B)))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_real B) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ _let_1 C) (@ _let_1 (@ (@ tptp.plus_plus_int B) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 C) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_real B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_rat B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_nat B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.plus_plus_int B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer tptp.one_one_Code_integer) A)))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (@ (@ tptp.dvd_dvd_complex tptp.one_one_complex) A)))
% 6.68/6.98 (assert (forall ((A tptp.real)) (@ (@ tptp.dvd_dvd_real tptp.one_one_real) A)))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (@ (@ tptp.dvd_dvd_rat tptp.one_one_rat) A)))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat tptp.one_one_nat) A)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.dvd_dvd_int tptp.one_one_int) A)))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer B))) (=> (@ _let_1 tptp.one_one_Code_integer) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat B))) (=> (@ _let_1 tptp.one_one_nat) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int B))) (=> (@ _let_1 tptp.one_one_int) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (@ _let_1 tptp.one_one_Code_integer))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (@ _let_1 tptp.one_one_nat))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ _let_1 B) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (@ _let_1 tptp.one_one_int))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_eq_real B) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le3102999989581377725nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_eq_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_eq_int B) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger A) B) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (= (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger C) B)) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (= (@ _let_1 (@ (@ tptp.minus_minus_int C) B)) (@ _let_1 (@ (@ tptp.minus_minus_int B) C))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (Z tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_8373710615458151222nteger Y) Z)))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_real Y) Z)))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_rat Y) Z)))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int X))) (=> (@ _let_1 Y) (=> (@ _let_1 Z) (@ _let_1 (@ (@ tptp.minus_minus_int Y) Z)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.ord_less_real B) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.ord_less_int B) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.ord_le6747313008572928689nteger B) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.ord_less_rat B) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) A))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int A) B) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger A) B) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat A) B) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (= A B)))))))
% 6.68/6.98 (assert (forall ((C tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (= A B)))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (= A B)))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (= A B)))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (= A B)))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 A) (=> (@ _let_1 B) (= (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (= A B)))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) C) (@ (@ tptp.divide6298287555418463151nteger B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (C tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.dvd_dvd_complex C))) (=> (= (@ (@ tptp.divide1717551699836669952omplex A) C) (@ (@ tptp.divide1717551699836669952omplex B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real C))) (=> (= (@ (@ tptp.divide_divide_real A) C) (@ (@ tptp.divide_divide_real B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat C))) (=> (= (@ (@ tptp.divide_divide_rat A) C) (@ (@ tptp.divide_divide_rat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (= (@ (@ tptp.divide_divide_nat A) C) (@ (@ tptp.divide_divide_nat B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (= (@ (@ tptp.divide_divide_int A) C) (@ (@ tptp.divide_divide_int B) C)) (=> (@ _let_1 A) (=> (@ _let_1 B) (= A B)))))))
% 6.68/6.98 (assert (forall ((D tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer D) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 D)) (@ (@ tptp.divide6298287555418463151nteger B) D)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((D tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat D) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.divide_divide_nat (@ _let_1 D)) (@ (@ tptp.divide_divide_nat B) D)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int D) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.divide_divide_int (@ _let_1 D)) (@ (@ tptp.divide_divide_int B) D)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M)) (@ tptp.numeral_numeral_real N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.numera6690914467698888265omplex N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.numeral_numeral_rat N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_real M) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_int M) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex M) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger M) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.numeral_numeral_rat M) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) N)))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) N)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) N)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) N)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.times_times_real A) A) (@ (@ tptp.times_times_real B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_real B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.times_times_int A) A) (@ (@ tptp.times_times_int B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_int B))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.times_times_complex A) A) (@ (@ tptp.times_times_complex B) B)) (or (= A B) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger A) A) (@ (@ tptp.times_3573771949741848930nteger B) B)) (or (= A B) (= A (@ tptp.uminus1351360451143612070nteger B))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.times_times_rat A) A) (@ (@ tptp.times_times_rat B) B)) (or (= A B) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real A)) B) (@ (@ tptp.times_times_real A) (@ tptp.uminus_uminus_real B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.times_times_int A) (@ tptp.uminus_uminus_int B)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex A)) B) (@ (@ tptp.times_times_complex A) (@ tptp.uminus1482373934393186551omplex B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.times_3573771949741848930nteger A) (@ tptp.uminus1351360451143612070nteger B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat A)) B) (@ (@ tptp.times_times_rat A) (@ tptp.uminus_uminus_rat B)))))
% 6.68/6.98 (assert (forall ((A2 tptp.real) (K tptp.real) (A tptp.real)) (=> (= A2 (@ (@ tptp.plus_plus_real K) A)) (= (@ tptp.uminus_uminus_real A2) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ tptp.uminus_uminus_real A))))))
% 6.68/6.98 (assert (forall ((A2 tptp.int) (K tptp.int) (A tptp.int)) (=> (= A2 (@ (@ tptp.plus_plus_int K) A)) (= (@ tptp.uminus_uminus_int A2) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ tptp.uminus_uminus_int A))))))
% 6.68/6.98 (assert (forall ((A2 tptp.complex) (K tptp.complex) (A tptp.complex)) (=> (= A2 (@ (@ tptp.plus_plus_complex K) A)) (= (@ tptp.uminus1482373934393186551omplex A2) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.68/6.98 (assert (forall ((A2 tptp.code_integer) (K tptp.code_integer) (A tptp.code_integer)) (=> (= A2 (@ (@ tptp.plus_p5714425477246183910nteger K) A)) (= (@ tptp.uminus1351360451143612070nteger A2) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ tptp.uminus1351360451143612070nteger A))))))
% 6.68/6.98 (assert (forall ((A2 tptp.rat) (K tptp.rat) (A tptp.rat)) (=> (= A2 (@ (@ tptp.plus_plus_rat K) A)) (= (@ tptp.uminus_uminus_rat A2) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ tptp.uminus_uminus_rat A))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.uminus_uminus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (not (= tptp.one_one_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.68/6.98 (assert (not (= tptp.one_one_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.68/6.98 (assert (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.68/6.98 (assert (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ tptp.uminus_uminus_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ tptp.uminus_uminus_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real B)) A) (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) B))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int B)) A) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int A)) B))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex B)) A) (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger B)) A) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat B)) A) (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.divide_divide_int A) (@ tptp.uminus_uminus_int B)) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ (@ tptp.divide6298287555418463151nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (@ (@ tptp.dvd_dvd_nat A) tptp.zero_zero_nat)))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (not (and (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (not (= tptp.zero_zero_nat A))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) A) (= A tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.modulo_modulo_nat (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.modulo_modulo_int (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.modulo364778990260209775nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.modulo364778990260209775nteger (@ _let_1 B)) C) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_nat M) N)))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo_modulo_int M) N)))))))
% 6.68/6.98 (assert (forall ((K tptp.code_integer) (M tptp.code_integer) (N tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger M) N)))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (=> (@ _let_1 B) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_nat A) B)) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int A) B)) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer C))) (=> (@ _let_1 B) (= (@ _let_1 (@ (@ tptp.modulo364778990260209775nteger A) B)) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int A) (@ tptp.uminus_uminus_int B)) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.uminus1351360451143612070nteger B)) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (A4 tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) (@ (@ tptp.modulo_modulo_int A4) B)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A4)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (A4 tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) (@ (@ tptp.modulo364778990260209775nteger A4) B)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A4)) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) B))) B) (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) B))) B) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.uminus1351360451143612070nteger A)) B))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 M) (=> (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_int M) N)) (=> (@ _let_1 N) (@ _let_1 M))))))
% 6.68/6.98 (assert (= tptp.bot_bo4199563552545308370d_enat tptp.zero_z5237406670263579293d_enat))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus_uminus_int A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.uminus1351360451143612070nteger A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) A)))) (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) B)))) (@ (@ tptp.dvd_dvd_complex A) B))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B 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) B)))) (@ (@ tptp.dvd_dvd_nat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le7084787975880047091nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (@ (@ tptp.dvd_dvd_Code_integer A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B 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) B)))) (@ (@ tptp.dvd_dvd_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_set_complex (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) A)))) (@ tptp.collect_complex (lambda ((C3 tptp.complex)) (@ (@ tptp.dvd_dvd_complex C3) B)))) (and (@ (@ tptp.dvd_dvd_complex A) B) (not (@ (@ tptp.dvd_dvd_complex B) A))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B 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) B)))) (and (@ (@ tptp.dvd_dvd_nat A) B) (not (@ (@ tptp.dvd_dvd_nat B) A))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B 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) B)))) (and (@ (@ tptp.dvd_dvd_int A) B) (not (@ (@ tptp.dvd_dvd_int B) A))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.ord_le1307284697595431911nteger (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) A)))) (@ tptp.collect_Code_integer (lambda ((C3 tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer C3) B)))) (and (@ (@ tptp.dvd_dvd_Code_integer A) B) (not (@ (@ tptp.dvd_dvd_Code_integer B) A))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N) (@ (@ tptp.power_power_rat A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N) (@ (@ tptp.power_power_real A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (= (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N) (@ (@ tptp.power_power_int A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.abs_abs_real A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.abs_abs_rat A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.abs_abs_int A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) A) (= (@ tptp.abs_abs_Code_integer A) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ tptp.abs_abs_real A) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A) (= (@ tptp.abs_abs_rat A) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (= (@ tptp.abs_abs_int A) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer A)) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real A)) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (not (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat A)) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (not (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int A)) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ (@ tptp.power_power_real A) N))) (let ((_let_2 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int A) N))) (let ((_let_2 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_int _let_1)))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ (@ tptp.power_power_complex A) N))) (let ((_let_2 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1482373934393186551omplex _let_1)))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger A) N))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus1351360451143612070nteger _let_1)))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.power_power_rat A) N))) (let ((_let_2 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ tptp.uminus_uminus_rat _let_1)))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.plus_p5714425477246183910nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.plus_plus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer B))) (let ((_let_2 (@ tptp.abs_abs_Code_integer A))) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_2) C) (=> (@ (@ tptp.ord_le6747313008572928689nteger _let_1) D) (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.times_3573771949741848930nteger _let_2) _let_1)) (@ (@ tptp.times_3573771949741848930nteger C) D))))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real B))) (let ((_let_2 (@ tptp.abs_abs_real A))) (=> (@ (@ tptp.ord_less_real _let_2) C) (=> (@ (@ tptp.ord_less_real _let_1) D) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real _let_2) _let_1)) (@ (@ tptp.times_times_real C) D))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (C tptp.rat) (B tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.abs_abs_rat B))) (let ((_let_2 (@ tptp.abs_abs_rat A))) (=> (@ (@ tptp.ord_less_rat _let_2) C) (=> (@ (@ tptp.ord_less_rat _let_1) D) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat _let_2) _let_1)) (@ (@ tptp.times_times_rat C) D))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int B))) (let ((_let_2 (@ tptp.abs_abs_int A))) (=> (@ (@ tptp.ord_less_int _let_2) C) (=> (@ (@ tptp.ord_less_int _let_1) D) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.times_times_int C) D))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat A) B)) (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B))))))
% 6.68/6.98 (assert (not (@ (@ tptp.dvd_dvd_Code_integer tptp.zero_z3403309356797280102nteger) tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (not (@ (@ tptp.dvd_dvd_nat tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.68/6.98 (assert (not (@ (@ tptp.dvd_dvd_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.68/6.98 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z5 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S)))) (=> (@ (@ tptp.ord_less_real Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S)))) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S)))) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S)))) (=> (@ (@ tptp.ord_less_int Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z5 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S))))) (=> (@ (@ tptp.ord_less_real Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S))))) (=> (@ (@ tptp.ord_less_rat Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S))))) (=> (@ (@ tptp.ord_less_nat Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S))))) (=> (@ (@ tptp.ord_less_int Z5) X4) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z5 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S)))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S)))) (=> (@ (@ tptp.ord_less_real X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S)))) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S)))) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S)))) (=> (@ (@ tptp.ord_less_int X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.code_integer) (S tptp.code_integer)) (exists ((Z5 tptp.code_integer)) (forall ((X4 tptp.code_integer)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_Code_integer D) (@ (@ tptp.plus_p5714425477246183910nteger X4) S))))) (=> (@ (@ tptp.ord_le6747313008572928689nteger X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.real) (S tptp.real)) (exists ((Z5 tptp.real)) (forall ((X4 tptp.real)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_real D) (@ (@ tptp.plus_plus_real X4) S))))) (=> (@ (@ tptp.ord_less_real X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.rat) (S tptp.rat)) (exists ((Z5 tptp.rat)) (forall ((X4 tptp.rat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_rat D) (@ (@ tptp.plus_plus_rat X4) S))))) (=> (@ (@ tptp.ord_less_rat X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.nat) (S tptp.nat)) (exists ((Z5 tptp.nat)) (forall ((X4 tptp.nat)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_nat D) (@ (@ tptp.plus_plus_nat X4) S))))) (=> (@ (@ tptp.ord_less_nat X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (S tptp.int)) (exists ((Z5 tptp.int)) (forall ((X4 tptp.int)) (let ((_let_1 (not (@ (@ tptp.dvd_dvd_int D) (@ (@ tptp.plus_plus_int X4) S))))) (=> (@ (@ tptp.ord_less_int X4) Z5) (= _let_1 _let_1)))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (@ (@ tptp.dvd_dvd_complex B) A) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) tptp.zero_zero_complex) (= A tptp.zero_zero_complex)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_real B) A) (= (= (@ (@ tptp.divide_divide_real A) B) tptp.zero_zero_real) (= A tptp.zero_zero_real)))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat B) A) (= (= (@ (@ tptp.divide_divide_rat A) B) tptp.zero_zero_rat) (= A tptp.zero_zero_rat)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) tptp.one_one_Code_integer) (and (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) tptp.one_one_nat) (and (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) tptp.one_one_int) (and (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger C) B)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat C) B)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int C) B)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) B)) C) (@ (@ tptp.dvd_dvd_int B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ _let_1 B) (@ _let_1 C)) (= B C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.times_3573771949741848930nteger B) A) (@ (@ tptp.times_3573771949741848930nteger C) A)) (= B C)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.times_times_nat B) A) (@ (@ tptp.times_times_nat C) A)) (= B C)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.times_times_int B) A) (@ (@ tptp.times_times_int C) A)) (= B C)))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger B) C)) A) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger B) A)) C)))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat B) C)) A) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat B) A)) C)))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int B) C)) A) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int B) A)) C)))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.times_3573771949741848930nteger (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) B) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.times_times_nat (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) B) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.times_times_int (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (let ((_let_2 (@ (@ tptp.times_3573771949741848930nteger B) C))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (let ((_let_2 (@ (@ tptp.times_times_nat B) C))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ (@ tptp.times_times_int B) C))) (=> (@ (@ tptp.dvd_dvd_int _let_2) A) (= (@ _let_1 _let_2) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (D tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (=> (@ (@ tptp.dvd_dvd_Code_integer D) C) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger C) D)) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) (@ (@ tptp.times_3573771949741848930nteger B) D)))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (D tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (=> (@ (@ tptp.dvd_dvd_nat D) C) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_nat C) D)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) (@ (@ tptp.times_times_nat B) D)))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (D tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (=> (@ (@ tptp.dvd_dvd_int D) C) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) (@ (@ tptp.divide_divide_int C) D)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) A) (= (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) C) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.divide6298287555418463151nteger A) C)) (@ (@ tptp.divide6298287555418463151nteger B) C))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat C) A) (= (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat A) B)) C) (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat A) C)) (@ (@ tptp.divide_divide_nat B) C))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int C) A) (= (@ (@ tptp.divide_divide_int (@ (@ tptp.plus_plus_int A) B)) C) (@ (@ tptp.plus_plus_int (@ (@ tptp.divide_divide_int A) C)) (@ (@ tptp.divide_divide_int B) C))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger C) A)) (= B C)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat C) A)) (= B C)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int C) A)) (= B C)))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) C)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) C)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) C)))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger C) B)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat C) B)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int C) B)) (@ _let_1 C))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.numeral_numeral_real N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.numera6620942414471956472nteger N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.numeral_numeral_rat N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.68/6.98 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ tptp.uminus_uminus_real A) B) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ tptp.uminus_uminus_int A) B) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.uminus1482373934393186551omplex A) B) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ tptp.uminus1351360451143612070nteger A) B) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ tptp.uminus_uminus_rat A) B) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= A (@ tptp.uminus_uminus_real B)) (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= A (@ tptp.uminus_uminus_int B)) (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= A (@ tptp.uminus1482373934393186551omplex B)) (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= A (@ tptp.uminus1351360451143612070nteger B)) (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= A (@ tptp.uminus_uminus_rat B)) (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= (@ tptp.uminus_uminus_real A) B))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= (@ tptp.uminus_uminus_int A) B))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (=> (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= (@ tptp.uminus1482373934393186551omplex A) B))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= (@ tptp.uminus1351360451143612070nteger A) B))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (=> (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= (@ tptp.uminus_uminus_rat A) B))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) A) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int A)) A) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) A) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger A)) A) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) A) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.plus_plus_real A) B) tptp.zero_zero_real) (= B (@ tptp.uminus_uminus_real A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.plus_plus_int A) B) tptp.zero_zero_int) (= B (@ tptp.uminus_uminus_int A)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.plus_plus_complex A) B) tptp.zero_zero_complex) (= B (@ tptp.uminus1482373934393186551omplex A)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.plus_p5714425477246183910nteger A) B) tptp.zero_z3403309356797280102nteger) (= B (@ tptp.uminus1351360451143612070nteger A)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.plus_plus_rat A) B) tptp.zero_zero_rat) (= B (@ tptp.uminus_uminus_rat A)))))
% 6.68/6.98 (assert (not (= tptp.zero_zero_real (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.68/6.98 (assert (not (= tptp.zero_zero_int (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.68/6.98 (assert (not (= tptp.zero_zero_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))
% 6.68/6.98 (assert (not (= tptp.zero_z3403309356797280102nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (not (= tptp.zero_zero_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int))
% 6.68/6.98 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.one_one_rat))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((W tptp.num) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ (@ tptp.times_times_real _let_1) (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real X) (@ tptp.uminus_uminus_real _let_1))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int W))) (= (@ (@ tptp.times_times_int _let_1) (@ tptp.uminus_uminus_int X)) (@ (@ tptp.times_times_int X) (@ tptp.uminus_uminus_int _let_1))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (X tptp.complex)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ (@ tptp.times_times_complex _let_1) (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex X) (@ tptp.uminus1482373934393186551omplex _let_1))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger W))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ tptp.uminus1351360451143612070nteger X)) (@ (@ tptp.times_3573771949741848930nteger X) (@ tptp.uminus1351360451143612070nteger _let_1))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_rat W))) (= (@ (@ tptp.times_times_rat _let_1) (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat X) (@ tptp.uminus_uminus_rat _let_1))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.power_8256067586552552935nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) N) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.power_power_nat (@ (@ tptp.divide_divide_nat A) B)) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.power_power_nat A) N)) (@ (@ tptp.power_power_nat B) N))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.power_power_int (@ (@ tptp.divide_divide_int A) B)) N) (@ (@ tptp.divide_divide_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real A)) (@ tptp.uminus_uminus_real B)) (@ (@ tptp.divide_divide_real A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex A)) (@ tptp.uminus1482373934393186551omplex B)) (@ (@ tptp.divide1717551699836669952omplex A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (@ (@ tptp.divide_divide_rat (@ tptp.uminus_uminus_rat A)) (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.divide_divide_rat A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.divide_divide_real A))) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.uminus_uminus_real (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_real B)))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.divide1717551699836669952omplex A))) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.uminus1482373934393186551omplex (@ _let_1 B)) (@ _let_1 (@ tptp.uminus1482373934393186551omplex B)))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.divide_divide_rat A))) (=> (not (= B tptp.zero_zero_rat)) (= (@ tptp.uminus_uminus_rat (@ _let_1 B)) (@ _let_1 (@ tptp.uminus_uminus_rat B)))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.one_one_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.one_one_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.one_one_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.one_one_Code_integer (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.one_one_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_real N) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6690914467698888265omplex N) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= (@ tptp.numera6620942414471956472nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= (@ tptp.numeral_numeral_rat N) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.times_times_real X) X) tptp.one_one_real) (or (= X tptp.one_one_real) (= X (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.times_times_int X) X) tptp.one_one_int) (or (= X tptp.one_one_int) (= X (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.68/6.98 (assert (forall ((X tptp.complex)) (= (= (@ (@ tptp.times_times_complex X) X) tptp.one_one_complex) (or (= X tptp.one_one_complex) (= X (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.times_3573771949741848930nteger X) X) tptp.one_one_Code_integer) (or (= X tptp.one_one_Code_integer) (= X (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.times_times_rat X) X) tptp.one_one_rat) (or (= X tptp.one_one_rat) (= X (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat B2) A3) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (= (@ (@ tptp.modulo_modulo_int B2) A3) tptp.zero_zero_int))))
% 6.68/6.98 (assert (= tptp.dvd_dvd_Code_integer (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (= (@ (@ tptp.modulo364778990260209775nteger B2) A3) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat B) A))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int B) A))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer B) A))))
% 6.68/6.98 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.68/6.98 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.68/6.98 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.68/6.98 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.68/6.98 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.68/6.98 (assert (= tptp.minus_minus_real (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_real A3) (@ tptp.uminus_uminus_real B2)))))
% 6.68/6.98 (assert (= tptp.minus_minus_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.plus_plus_int A3) (@ tptp.uminus_uminus_int B2)))))
% 6.68/6.98 (assert (= tptp.minus_minus_complex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.plus_plus_complex A3) (@ tptp.uminus1482373934393186551omplex B2)))))
% 6.68/6.98 (assert (= tptp.minus_8373710615458151222nteger (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (@ (@ tptp.plus_p5714425477246183910nteger A3) (@ tptp.uminus1351360451143612070nteger B2)))))
% 6.68/6.98 (assert (= tptp.minus_minus_rat (lambda ((A3 tptp.rat) (B2 tptp.rat)) (@ (@ tptp.plus_plus_rat A3) (@ tptp.uminus_uminus_rat B2)))))
% 6.68/6.98 (assert (forall ((B3 tptp.real) (K tptp.real) (B tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real A))) (=> (= B3 (@ (@ tptp.plus_plus_real K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real K)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B3 tptp.int) (K tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int A))) (=> (= B3 (@ (@ tptp.plus_plus_int K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int K)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B3 tptp.complex) (K tptp.complex) (B tptp.complex) (A tptp.complex)) (let ((_let_1 (@ tptp.minus_minus_complex A))) (=> (= B3 (@ (@ tptp.plus_plus_complex K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex K)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B3 tptp.code_integer) (K tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.minus_8373710615458151222nteger A))) (=> (= B3 (@ (@ tptp.plus_p5714425477246183910nteger K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger K)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((B3 tptp.rat) (K tptp.rat) (B tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.minus_minus_rat A))) (=> (= B3 (@ (@ tptp.plus_plus_rat K) B)) (= (@ _let_1 B3) (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat K)) (@ _let_1 B)))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat) (B tptp.code_integer) (M tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) B))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (N tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat A))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) B))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat) (B tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_real A))) (=> (@ (@ tptp.dvd_dvd_real (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_real (@ _let_1 M)) B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_int A))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) B))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (N tptp.nat) (B tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex A))) (=> (@ (@ tptp.dvd_dvd_complex (@ _let_1 N)) B) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_complex (@ _let_1 M)) B))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_Code_integer X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger X) N)) (@ (@ tptp.power_8256067586552552935nteger Y) M))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat X) N)) (@ (@ tptp.power_power_nat Y) M))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_real X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) M))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_int X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) M))))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (Y tptp.complex) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.dvd_dvd_complex X) Y) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ (@ tptp.dvd_dvd_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) M))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int)) (= (= (@ (@ tptp.modulo_modulo_int A) C) (@ (@ tptp.modulo_modulo_int B) C)) (@ (@ tptp.dvd_dvd_int C) (@ (@ tptp.minus_minus_int A) B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer)) (= (= (@ (@ tptp.modulo364778990260209775nteger A) C) (@ (@ tptp.modulo364778990260209775nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer C) (@ (@ tptp.minus_8373710615458151222nteger A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.dvd_dvd_nat B) (@ (@ tptp.minus_minus_nat A) (@ (@ tptp.modulo_modulo_nat A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (@ (@ tptp.dvd_dvd_int B) (@ (@ tptp.minus_minus_int A) (@ (@ tptp.modulo_modulo_int A) B)))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (@ (@ tptp.dvd_dvd_Code_integer B) (@ (@ tptp.minus_8373710615458151222nteger A) (@ (@ tptp.modulo364778990260209775nteger A) B)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (not (@ (@ tptp.dvd_dvd_nat N) M))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_nat M) N) (@ _let_1 M))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (U tptp.real) (V tptp.real)) (=> (= X Y) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real U)) V) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X) U)) Y))) V)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)) (or (@ (@ tptp.ord_less_nat N) M) (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 M) (=> (@ _let_1 N) (=> (@ (@ tptp.dvd_dvd_int M) N) (=> (@ (@ tptp.dvd_dvd_int N) M) (= M N))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 N) (@ _let_1 (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 M) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 N)))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat K))) (=> (@ _let_1 (@ (@ tptp.minus_minus_nat M) N)) (=> (@ _let_1 N) (=> (@ (@ tptp.ord_less_eq_nat N) M) (@ _let_1 M)))))))
% 6.68/6.98 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) M) (=> (@ (@ tptp.ord_less_int M) N) (not (@ (@ tptp.dvd_dvd_int N) M))))))
% 6.68/6.98 (assert (forall ((D tptp.nat) (A tptp.nat) (B tptp.nat) (X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D))) (=> (@ _let_3 A) (=> (@ _let_3 B) (=> (or (= (@ _let_1 X) (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) D)) (= (@ _let_2 X) (@ (@ tptp.plus_plus_nat (@ _let_1 Y)) D))) (exists ((X6 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ (@ tptp.plus_plus_nat A) B))) (let ((_let_3 (@ tptp.times_times_nat _let_2))) (let ((_let_4 (@ tptp.dvd_dvd_nat D))) (and (@ _let_4 A) (@ _let_4 _let_2) (or (= (@ _let_1 X6) (@ (@ tptp.plus_plus_nat (@ _let_3 Y5)) D)) (= (@ _let_3 X6) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D)))))))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X6 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ _let_1 X6) (@ (@ tptp.plus_plus_nat (@ _let_2 Y5)) D3)) (= (@ _let_2 X6) (@ (@ tptp.plus_plus_nat (@ _let_1 Y5)) D3))))))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (=> (not (= K tptp.zero_zero_int)) (@ (@ tptp.dvd_dvd_int M) N))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (M tptp.int) (T tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (=> (not (= K tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int M) T) (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 T)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (exists ((D3 tptp.nat) (X6 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (let ((_let_2 (@ tptp.times_times_nat B))) (let ((_let_3 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_3 A) (@ _let_3 B) (or (= (@ (@ tptp.minus_minus_nat (@ _let_1 X6)) (@ _let_2 Y5)) D3) (= (@ (@ tptp.minus_minus_nat (@ _let_2 X6)) (@ _let_1 Y5)) D3)))))))))
% 6.68/6.98 (assert (forall ((U tptp.real) (X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real U) U))) (@ (@ tptp.times_times_real X) X))))
% 6.68/6.98 (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))))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (N tptp.int) (M tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int K))) (= (@ _let_1 (@ (@ tptp.plus_plus_int N) (@ (@ tptp.times_times_int K) M))) (@ _let_1 N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger A) N)) (@ (@ tptp.power_8256067586552552935nteger B) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.68/6.98 (assert (= tptp.minus_minus_real (lambda ((X3 tptp.real) (Y3 tptp.real)) (@ (@ tptp.plus_plus_real X3) (@ tptp.uminus_uminus_real Y3)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (let ((_let_2 (@ (@ tptp.power_power_real _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_real)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (let ((_let_2 (@ (@ tptp.power_power_int _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_int)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (let ((_let_2 (@ (@ tptp.power_power_complex _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_complex)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (let ((_let_2 (@ (@ tptp.power_8256067586552552935nteger _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_Code_integer)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (let ((_let_2 (@ (@ tptp.power_power_rat _let_1) N))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (and (=> _let_3 (= _let_2 tptp.one_one_rat)) (=> (not _let_3) (= _let_2 _let_1))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.tanh_real X)) tptp.one_one_real)))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) E2))) (= X tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (=> (forall ((E2 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E2) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) E2))) (= X tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_le3102999989581377725nteger A) tptp.zero_z3403309356797280102nteger)) (or (@ _let_1 B) (@ (@ tptp.ord_le3102999989581377725nteger B) tptp.zero_z3403309356797280102nteger))) (= (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_real B) tptp.zero_zero_real))) (= (@ tptp.abs_abs_real (@ (@ tptp.times_times_real A) B)) (@ (@ tptp.times_times_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_rat B) tptp.zero_zero_rat))) (= (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat A) B)) (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (and (or (@ _let_1 A) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (or (@ _let_1 B) (@ (@ tptp.ord_less_eq_int B) tptp.zero_zero_int))) (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.times_times_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.abs_abs_Code_integer Y)) X) (@ tptp.abs_abs_Code_integer (@ (@ tptp.times_3573771949741848930nteger Y) X))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real (@ tptp.abs_abs_real Y)) X) (@ tptp.abs_abs_real (@ (@ tptp.times_times_real Y) X))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X) (= (@ (@ tptp.times_times_rat (@ tptp.abs_abs_rat Y)) X) (@ tptp.abs_abs_rat (@ (@ tptp.times_times_rat Y) X))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int Y)) X) (@ tptp.abs_abs_int (@ (@ tptp.times_times_int Y) X))))))
% 6.68/6.98 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (= (@ (@ tptp.divide_divide_real (@ tptp.abs_abs_real X)) Y) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) Y))))))
% 6.68/6.98 (assert (forall ((Y tptp.rat) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.divide_divide_rat (@ tptp.abs_abs_rat X)) Y) (@ tptp.abs_abs_rat (@ (@ tptp.divide_divide_rat X) Y))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.abs_abs_Code_integer A)) N))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.abs_abs_rat A)) N))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.abs_abs_int A)) N))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) B))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer A)) (@ tptp.abs_abs_Code_integer B)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real A)) (@ tptp.abs_abs_real B)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) B))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat A)) (@ tptp.abs_abs_rat B)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) B))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int A)) (@ tptp.abs_abs_int B)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer) (D tptp.code_integer)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.plus_p5714425477246183910nteger A) B)) (@ (@ tptp.plus_p5714425477246183910nteger C) D)))) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger A) C))) (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat A) B)) (@ (@ tptp.plus_plus_rat C) D)))) (@ (@ tptp.plus_plus_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat A) C))) (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat B) D))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int A) B)) (@ (@ tptp.plus_plus_int C) D)))) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int A) C))) (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int B) D))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R) (and (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X) (@ (@ tptp.ord_le3102999989581377725nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R) (and (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real A) R)) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.plus_plus_real A) R))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R) (and (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat A) R)) X) (@ (@ tptp.ord_less_eq_rat X) (@ (@ tptp.plus_plus_rat A) R))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R) (and (@ (@ tptp.ord_less_eq_int (@ (@ tptp.minus_minus_int A) R)) X) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.plus_plus_int A) R))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (A tptp.code_integer) (R tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger X) A))) R) (and (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.minus_8373710615458151222nteger A) R)) X) (@ (@ tptp.ord_le6747313008572928689nteger X) (@ (@ tptp.plus_p5714425477246183910nteger A) R))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (A tptp.real) (R tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) A))) R) (and (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real A) R)) X) (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real A) R))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (A tptp.rat) (R tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) A))) R) (and (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat A) R)) X) (@ (@ tptp.ord_less_rat X) (@ (@ tptp.plus_plus_rat A) R))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (A tptp.int) (R tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) A))) R) (and (@ (@ tptp.ord_less_int (@ (@ tptp.minus_minus_int A) R)) X) (@ (@ tptp.ord_less_int X) (@ (@ tptp.plus_plus_int A) R))))))
% 6.68/6.98 (assert (forall ((I tptp.int)) (=> (not (= I tptp.zero_zero_int)) (@ tptp.finite_finite_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (@ (@ tptp.dvd_dvd_int D2) I)))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (=> (= (@ (@ tptp.divide_divide_nat X) _let_1) (@ (@ tptp.divide_divide_nat Y) _let_1)) (=> (= (@ _let_2 X) (@ _let_2 Y)) (= X Y)))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.code_integer Bool)) (L2 tptp.code_integer)) (= (exists ((X3 tptp.code_integer)) (@ P (@ (@ tptp.times_3573771949741848930nteger L2) X3))) (exists ((X3 tptp.code_integer)) (and (@ (@ tptp.dvd_dvd_Code_integer L2) (@ (@ tptp.plus_p5714425477246183910nteger X3) tptp.zero_z3403309356797280102nteger)) (@ P X3))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.complex Bool)) (L2 tptp.complex)) (= (exists ((X3 tptp.complex)) (@ P (@ (@ tptp.times_times_complex L2) X3))) (exists ((X3 tptp.complex)) (and (@ (@ tptp.dvd_dvd_complex L2) (@ (@ tptp.plus_plus_complex X3) tptp.zero_zero_complex)) (@ P X3))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.real Bool)) (L2 tptp.real)) (= (exists ((X3 tptp.real)) (@ P (@ (@ tptp.times_times_real L2) X3))) (exists ((X3 tptp.real)) (and (@ (@ tptp.dvd_dvd_real L2) (@ (@ tptp.plus_plus_real X3) tptp.zero_zero_real)) (@ P X3))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.rat Bool)) (L2 tptp.rat)) (= (exists ((X3 tptp.rat)) (@ P (@ (@ tptp.times_times_rat L2) X3))) (exists ((X3 tptp.rat)) (and (@ (@ tptp.dvd_dvd_rat L2) (@ (@ tptp.plus_plus_rat X3) tptp.zero_zero_rat)) (@ P X3))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat Bool)) (L2 tptp.nat)) (= (exists ((X3 tptp.nat)) (@ P (@ (@ tptp.times_times_nat L2) X3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat L2) (@ (@ tptp.plus_plus_nat X3) tptp.zero_zero_nat)) (@ P X3))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.int Bool)) (L2 tptp.int)) (= (exists ((X3 tptp.int)) (@ P (@ (@ tptp.times_times_int L2) X3))) (exists ((X3 tptp.int)) (and (@ (@ tptp.dvd_dvd_int L2) (@ (@ tptp.plus_plus_int X3) tptp.zero_zero_int)) (@ P X3))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((C2 tptp.code_integer)) (not (= B (@ (@ tptp.times_3573771949741848930nteger A) C2)))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((C2 tptp.nat)) (not (= B (@ (@ tptp.times_times_nat A) C2)))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((C2 tptp.int)) (not (= B (@ (@ tptp.times_times_int A) C2)))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer) (C tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) C) (= B (@ (@ tptp.times_3573771949741848930nteger C) A)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (= (= (@ (@ tptp.divide_divide_nat B) A) C) (= B (@ (@ tptp.times_times_nat C) A)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (= (= (@ (@ tptp.divide_divide_int B) A) C) (= B (@ (@ tptp.times_times_int C) A)))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (not (= B tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.times_3573771949741848930nteger C) B)))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.times_times_nat C) B)))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.times_times_int C) B)))))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer C) B) (= (@ (@ tptp.dvd_dvd_Code_integer A) (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.times_3573771949741848930nteger A) C)) B))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat C) B) (= (@ (@ tptp.dvd_dvd_nat A) (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat A) C)) B))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int C) B) (= (@ (@ tptp.dvd_dvd_int A) (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int A) C)) B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer) (B tptp.code_integer) (D tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (not (= C tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) B) (=> (@ (@ tptp.dvd_dvd_Code_integer C) D) (= (= (@ (@ tptp.divide6298287555418463151nteger B) A) (@ (@ tptp.divide6298287555418463151nteger D) C)) (= (@ (@ tptp.times_3573771949741848930nteger B) C) (@ (@ tptp.times_3573771949741848930nteger A) D)))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (C tptp.nat) (B tptp.nat) (D tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (not (= C tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat A) B) (=> (@ (@ tptp.dvd_dvd_nat C) D) (= (= (@ (@ tptp.divide_divide_nat B) A) (@ (@ tptp.divide_divide_nat D) C)) (= (@ (@ tptp.times_times_nat B) C) (@ (@ tptp.times_times_nat A) D)))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int) (B tptp.int) (D tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (not (= C tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int A) B) (=> (@ (@ tptp.dvd_dvd_int C) D) (= (= (@ (@ tptp.divide_divide_int B) A) (@ (@ tptp.divide_divide_int D) C)) (= (@ (@ tptp.times_times_int B) C) (@ (@ tptp.times_times_int A) D)))))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) tptp.zero_z3403309356797280102nteger) (= A tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) tptp.zero_zero_nat) (= A tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) tptp.zero_zero_int) (= A tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))))
% 6.68/6.98 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X4 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T))))))))
% 6.68/6.98 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (@ _let_1 (@ (@ tptp.plus_plus_real X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4))) T))))))))
% 6.68/6.98 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4))) T))))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (@ _let_1 (@ (@ tptp.plus_plus_int X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4))) T))))))))
% 6.68/6.98 (assert (forall ((D tptp.code_integer) (D4 tptp.code_integer) (T tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer D) D4) (forall ((X4 tptp.code_integer) (K4 tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer D))) (= (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger X4) T))) (not (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.minus_8373710615458151222nteger X4) (@ (@ tptp.times_3573771949741848930nteger K4) D4))) T)))))))))
% 6.68/6.98 (assert (forall ((D tptp.real) (D4 tptp.real) (T tptp.real)) (=> (@ (@ tptp.dvd_dvd_real D) D4) (forall ((X4 tptp.real) (K4 tptp.real)) (let ((_let_1 (@ tptp.dvd_dvd_real D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_real X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_real (@ (@ tptp.minus_minus_real X4) (@ (@ tptp.times_times_real K4) D4))) T)))))))))
% 6.68/6.98 (assert (forall ((D tptp.rat) (D4 tptp.rat) (T tptp.rat)) (=> (@ (@ tptp.dvd_dvd_rat D) D4) (forall ((X4 tptp.rat) (K4 tptp.rat)) (let ((_let_1 (@ tptp.dvd_dvd_rat D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_rat X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_rat (@ (@ tptp.minus_minus_rat X4) (@ (@ tptp.times_times_rat K4) D4))) T)))))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (D4 tptp.int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X4 tptp.int) (K4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) (@ (@ tptp.times_times_int K4) D4))) T)))))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= (@ (@ tptp.divide6298287555418463151nteger A) B) C) (= A (@ (@ tptp.times_3573771949741848930nteger C) B))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= (@ (@ tptp.divide_divide_nat A) B) C) (= A (@ (@ tptp.times_times_nat C) B))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= (@ (@ tptp.divide_divide_int A) B) C) (= A (@ (@ tptp.times_times_int C) B))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (= A (@ (@ tptp.divide6298287555418463151nteger C) B)) (= (@ (@ tptp.times_3573771949741848930nteger A) B) C)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (= A (@ (@ tptp.divide_divide_nat C) B)) (= (@ (@ tptp.times_times_nat A) B) C)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (= A (@ (@ tptp.divide_divide_int C) B)) (= (@ (@ tptp.times_times_int A) B) C)))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (B tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer B) A) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (B tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat B) A) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int B) A) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.divide6298287555418463151nteger A) B)) C) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) C)) B)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.times_times_nat (@ (@ tptp.divide_divide_nat A) B)) C) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) C)) B)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.times_times_int (@ (@ tptp.divide_divide_int A) B)) C) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) C)) B)))))
% 6.68/6.98 (assert (forall ((C tptp.code_integer) (A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.times_3573771949741848930nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.divide6298287555418463151nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C))))))
% 6.68/6.98 (assert (forall ((C tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat A))) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.divide_divide_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C))))))
% 6.68/6.98 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int A))) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.divide_divide_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C))))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (C tptp.code_integer) (A tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger A))) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (=> (@ (@ tptp.dvd_dvd_Code_integer C) tptp.one_one_Code_integer) (= (@ _let_1 (@ (@ tptp.times_3573771949741848930nteger B) C)) (@ (@ tptp.divide6298287555418463151nteger (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (C tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat A))) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (=> (@ (@ tptp.dvd_dvd_nat C) tptp.one_one_nat) (= (@ _let_1 (@ (@ tptp.times_times_nat B) C)) (@ (@ tptp.divide_divide_nat (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (C tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (=> (@ (@ tptp.dvd_dvd_int C) tptp.one_one_int) (= (@ _let_1 (@ (@ tptp.times_times_int B) C)) (@ (@ tptp.divide_divide_int (@ _let_1 B)) C)))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))))))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.68/6.98 (assert (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (not (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.zero_zero_real))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.68/6.98 (assert (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) tptp.zero_zero_rat))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) tptp.one_one_real)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) tptp.one_one_int)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) tptp.one_one_rat)))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger A) N)) tptp.one_one_Code_integer) (or (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat A) N)) tptp.one_one_nat) (or (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int A) N)) tptp.one_one_int) (or (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.modulo_modulo_nat A) B) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer) (A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.modulo364778990260209775nteger A) B) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= A (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_real A) C) (@ tptp.uminus_uminus_real B))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= A (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_complex A) C) (@ tptp.uminus1482373934393186551omplex B))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= A (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> (not _let_1) (= (@ (@ tptp.times_times_rat A) C) (@ tptp.uminus_uminus_rat B))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (= C tptp.zero_zero_real))) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_real B) (@ (@ tptp.times_times_real A) C))) (=> _let_1 (= A tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (let ((_let_1 (= C tptp.zero_zero_complex))) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus1482373934393186551omplex B) (@ (@ tptp.times_times_complex A) C))) (=> _let_1 (= A tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (= C tptp.zero_zero_rat))) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C)) A) (and (=> (not _let_1) (= (@ tptp.uminus_uminus_rat B) (@ (@ tptp.times_times_rat A) C))) (=> _let_1 (= A tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real) (C tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B)) C) (= (@ tptp.uminus_uminus_real A) (@ (@ tptp.times_times_real C) B))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex) (C tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) C) (= (@ tptp.uminus1482373934393186551omplex A) (@ (@ tptp.times_times_complex C) B))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat) (C tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B)) C) (= (@ tptp.uminus_uminus_rat A) (@ (@ tptp.times_times_rat C) B))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (= C (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) B))) (= (@ (@ tptp.times_times_real C) B) (@ tptp.uminus_uminus_real A))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (C tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (= C (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) B))) (= (@ (@ tptp.times_times_complex C) B) (@ tptp.uminus1482373934393186551omplex A))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (=> (not (= B tptp.zero_zero_rat)) (= (= C (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) B))) (= (@ (@ tptp.times_times_rat C) B) (@ tptp.uminus_uminus_rat A))))))
% 6.68/6.98 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real B) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) (@ tptp.uminus_uminus_real B))))
% 6.68/6.98 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int B) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) (@ tptp.uminus_uminus_int B))))
% 6.68/6.98 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) (@ tptp.uminus1482373934393186551omplex B))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger B) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) (@ tptp.uminus1351360451143612070nteger B))))
% 6.68/6.98 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat B) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) (@ tptp.uminus_uminus_rat B))))
% 6.68/6.98 (assert (forall ((B tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one))) B) (@ tptp.uminus_uminus_real B))))
% 6.68/6.98 (assert (forall ((B tptp.int)) (= (@ (@ tptp.times_times_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one))) B) (@ tptp.uminus_uminus_int B))))
% 6.68/6.98 (assert (forall ((B tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one))) B) (@ tptp.uminus1482373934393186551omplex B))))
% 6.68/6.98 (assert (forall ((B tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one))) B) (@ tptp.uminus1351360451143612070nteger B))))
% 6.68/6.98 (assert (forall ((B tptp.rat)) (= (@ (@ tptp.times_times_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one))) B) (@ tptp.uminus_uminus_rat B))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.divide_divide_real A) B) (@ tptp.uminus_uminus_real tptp.one_one_real)) (and (not (= B tptp.zero_zero_real)) (= A (@ tptp.uminus_uminus_real B))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ (@ tptp.divide1717551699836669952omplex A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (not (= B tptp.zero_zero_complex)) (= A (@ tptp.uminus1482373934393186551omplex B))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat)) (= (= (@ (@ tptp.divide_divide_rat A) B) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (and (not (= B tptp.zero_zero_rat)) (= A (@ tptp.uminus_uminus_rat B))))))
% 6.68/6.98 (assert (= (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real tptp.one)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.68/6.98 (assert (= (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int tptp.one)) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.68/6.98 (assert (= (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex tptp.one)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.68/6.98 (assert (= (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger tptp.one)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat tptp.one)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)) (@ (@ tptp.power_power_real A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)) N)) (@ (@ tptp.power_power_int A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N)) (@ (@ tptp.power_power_complex A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N) (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) N)) (@ (@ tptp.power_8256067586552552935nteger A) N)))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) N)) (@ (@ tptp.power_power_rat A) N)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ (@ tptp.power_power_int X) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ (@ tptp.power_power_complex X) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ (@ tptp.power_8256067586552552935nteger X) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ (@ tptp.power_power_rat X) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y2))) D3) (and (@ (@ tptp.ord_less_real A) Y2) (@ (@ tptp.ord_less_real Y2) B))))))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat K) N) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_nat K) N)))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.dvd_dvd_nat M) N))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((D3 tptp.nat) (X6 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D3))) (and (@ _let_1 A) (@ _let_1 B) (= (@ (@ tptp.times_times_nat A) X6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y5)) D3))))))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Z) N) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) N) (@ (@ tptp.ord_less_eq_int Z) N)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.modulo_modulo_nat M) N)) (not (@ (@ tptp.dvd_dvd_nat N) M)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real X) Y)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.uminus_uminus_real X)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) Y))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (M tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (= (@ (@ tptp.modulo_modulo_nat M) Q2) (@ (@ tptp.modulo_modulo_nat N) Q2)) (@ (@ tptp.dvd_dvd_nat Q2) (@ (@ tptp.minus_minus_nat M) N))))))
% 6.68/6.98 (assert (forall ((X tptp.product_prod_nat_nat)) (not (forall ((K3 tptp.nat) (M4 tptp.nat)) (not (= X (@ (@ tptp.product_Pair_nat_nat K3) M4)))))))
% 6.68/6.98 (assert (forall ((M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ tptp.finite_finite_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M)))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer)) (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger tptp.one_one_Code_integer) (@ tptp.abs_abs_Code_integer X)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.abs_abs_real X)))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.abs_abs_rat X)))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.abs_abs_int X)))))
% 6.68/6.98 (assert (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat))
% 6.68/6.98 (assert (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (C tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer A) tptp.one_one_Code_integer) (not (=> (not (= A tptp.zero_z3403309356797280102nteger)) (forall ((B5 tptp.code_integer)) (let ((_let_1 (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer))) (=> (not (= B5 tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B5) tptp.one_one_Code_integer) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_3573771949741848930nteger A) B5) tptp.one_one_Code_integer) (not (= (@ (@ tptp.divide6298287555418463151nteger C) A) (@ (@ tptp.times_3573771949741848930nteger C) B5)))))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (C tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat A) tptp.one_one_nat) (not (=> (not (= A tptp.zero_zero_nat)) (forall ((B5 tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat tptp.one_one_nat))) (=> (not (= B5 tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B5) tptp.one_one_nat) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_nat A) B5) tptp.one_one_nat) (not (= (@ (@ tptp.divide_divide_nat C) A) (@ (@ tptp.times_times_nat C) B5)))))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (C tptp.int)) (=> (@ (@ tptp.dvd_dvd_int A) tptp.one_one_int) (not (=> (not (= A tptp.zero_zero_int)) (forall ((B5 tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int tptp.one_one_int))) (=> (not (= B5 tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B5) tptp.one_one_int) (=> (= (@ _let_1 A) B5) (=> (= (@ _let_1 B5) A) (=> (= (@ (@ tptp.times_times_int A) B5) tptp.one_one_int) (not (= (@ (@ tptp.divide_divide_int C) A) (@ (@ tptp.times_times_int C) B5)))))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger A) B)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int A) B)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (=> (not (= A tptp.zero_z3403309356797280102nteger)) (=> (@ (@ tptp.dvd_dvd_Code_integer B) tptp.one_one_Code_integer) (= (@ (@ tptp.divide6298287555418463151nteger A) (@ (@ tptp.times_3573771949741848930nteger B) A)) (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) B))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (=> (@ (@ tptp.dvd_dvd_nat B) tptp.one_one_nat) (= (@ (@ tptp.divide_divide_nat A) (@ (@ tptp.times_times_nat B) A)) (@ (@ tptp.divide_divide_nat tptp.one_one_nat) B))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (=> (not (= A tptp.zero_zero_int)) (=> (@ (@ tptp.dvd_dvd_int B) tptp.one_one_int) (= (@ (@ tptp.divide_divide_int A) (@ (@ tptp.times_times_int B) A)) (@ (@ tptp.divide_divide_int tptp.one_one_int) B))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5))))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_p5714425477246183910nteger A) B)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B)))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (not (@ _let_1 A)) (=> (not (@ _let_1 B)) (@ _let_1 (@ (@ tptp.plus_plus_int A) B)))))))
% 6.68/6.98 (assert (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_nat)))
% 6.68/6.98 (assert (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.one_one_int)))
% 6.68/6.98 (assert (= (lambda ((Y4 tptp.code_integer) (Z2 tptp.code_integer)) (= Y4 Z2)) (lambda ((A3 tptp.code_integer) (B2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_Code_integer _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide6298287555418463151nteger A3) _let_1) (@ (@ tptp.divide6298287555418463151nteger B2) _let_1))))))))
% 6.68/6.98 (assert (= (lambda ((Y4 tptp.nat) (Z2 tptp.nat)) (= Y4 Z2)) (lambda ((A3 tptp.nat) (B2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_nat A3) _let_1) (@ (@ tptp.divide_divide_nat B2) _let_1))))))))
% 6.68/6.98 (assert (= (lambda ((Y4 tptp.int) (Z2 tptp.int)) (= Y4 Z2)) (lambda ((A3 tptp.int) (B2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (and (= (@ _let_2 A3) (@ _let_2 B2)) (= (@ (@ tptp.divide_divide_int A3) _let_1) (@ (@ tptp.divide_divide_int B2) _let_1))))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger X))) (=> (not (= X tptp.zero_z3403309356797280102nteger)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_Code_integer X) tptp.one_one_Code_integer) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat X))) (=> (not (= X tptp.zero_zero_nat)) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_nat X) tptp.one_one_nat) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (not (= X tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ _let_1 M)) (@ _let_1 N)) (or (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_nat M) N)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ tptp.uminus_uminus_real B))) (let ((_let_4 (@ (@ tptp.times_times_real A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ tptp.uminus_uminus_rat B))) (let ((_let_4 (@ (@ tptp.times_times_rat A) C))) (let ((_let_5 (@ _let_1 C))) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 A)))))))))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= (@ (@ tptp.divide_divide_real B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_real _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (C tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= (@ (@ tptp.divide1717551699836669952omplex B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_complex _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= (@ (@ tptp.divide_divide_rat B) C) _let_1) (and (=> (not _let_2) (= B (@ (@ tptp.times_times_rat _let_1) C))) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (= C tptp.zero_zero_real))) (= (= _let_1 (@ (@ tptp.divide_divide_real B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_real _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (B tptp.complex) (C tptp.complex)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (let ((_let_2 (= C tptp.zero_zero_complex))) (= (= _let_1 (@ (@ tptp.divide1717551699836669952omplex B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_complex _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_complex))))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (= C tptp.zero_zero_rat))) (= (= _let_1 (@ (@ tptp.divide_divide_rat B) C)) (and (=> (not _let_2) (= (@ (@ tptp.times_times_rat _let_1) C) B)) (=> _let_2 (= _let_1 tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 B)) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.code_integer)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_Code_integer)) (@ (@ tptp.dvd_dvd_Code_integer X) (@ (@ tptp.power_8256067586552552935nteger X) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.rat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_rat)) (@ (@ tptp.dvd_dvd_rat X) (@ (@ tptp.power_power_rat X) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_nat)) (@ (@ tptp.dvd_dvd_nat X) (@ (@ tptp.power_power_nat X) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_real)) (@ (@ tptp.dvd_dvd_real X) (@ (@ tptp.power_power_real X) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_int)) (@ (@ tptp.dvd_dvd_int X) (@ (@ tptp.power_power_int X) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= X tptp.one_one_complex)) (@ (@ tptp.dvd_dvd_complex X) (@ (@ tptp.power_power_complex X) N)))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real A)) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex A)) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat A) Z))) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat A)) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_real B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real A) (@ (@ tptp.times_times_real B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.complex) (A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_complex))) (and (=> _let_2 (= _let_1 (@ tptp.uminus1482373934393186551omplex B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex A) (@ (@ tptp.times_times_complex B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (A tptp.rat) (B tptp.rat)) (let ((_let_1 (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat A) Z)) B))) (let ((_let_2 (= Z tptp.zero_zero_rat))) (and (=> _let_2 (= _let_1 (@ tptp.uminus_uminus_rat B))) (=> (not _let_2) (= _let_1 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat A) (@ (@ tptp.times_times_rat B) Z))) Z))))))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (X tptp.real) (Y tptp.real)) (=> (not (= Z tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real X) Z))) Y) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) (@ (@ tptp.times_times_real Y) Z))) Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.complex) (X tptp.complex) (Y tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.divide1717551699836669952omplex X) Z))) Y) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex Y) Z))) Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (X tptp.rat) (Y tptp.rat)) (=> (not (= Z tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat X) Z))) Y) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat X)) (@ (@ tptp.times_times_rat Y) Z))) Z)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_real X) _let_1) (@ (@ tptp.power_power_real Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_real Y)))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_int X) _let_1) (@ (@ tptp.power_power_int Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_int Y)))))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_complex X) _let_1) (@ (@ tptp.power_power_complex Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1482373934393186551omplex Y)))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_8256067586552552935nteger X) _let_1) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus1351360451143612070nteger Y)))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= (@ (@ tptp.power_power_rat X) _let_1) (@ (@ tptp.power_power_rat Y) _let_1)) (or (= X Y) (= X (@ tptp.uminus_uminus_rat Y)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((Y2 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y2))) D3) (and (@ (@ tptp.ord_less_eq_real A) Y2) (@ (@ tptp.ord_less_eq_real Y2) B))))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)))) (= (@ _let_2 N) (@ _let_2 (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1)))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat M) N)) M) (= N tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (= (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.times_times_nat N) M)) M) (= N tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((Q2 tptp.nat) (N tptp.nat) (R tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat R) M))) (let ((_let_2 (@ tptp.dvd_dvd_nat M))) (let ((_let_3 (@ tptp.ord_less_eq_nat Q2))) (=> (@ _let_3 N) (=> (@ _let_3 _let_1) (= (@ _let_2 (@ (@ tptp.minus_minus_nat N) Q2)) (@ _let_2 (@ (@ tptp.plus_plus_nat N) (@ (@ tptp.minus_minus_nat _let_1) Q2)))))))))))
% 6.68/6.98 (assert (forall ((I tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat I))) (=> (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) I) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.68/6.98 (assert (forall ((R tptp.nat) (N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat R) N) (=> (@ (@ tptp.ord_less_eq_nat R) M) (=> (@ (@ tptp.dvd_dvd_nat N) (@ (@ tptp.minus_minus_nat M) R)) (= (@ (@ tptp.modulo_modulo_nat M) N) R))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))))
% 6.68/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.modulo_modulo_int K) L2)) (or (@ (@ tptp.dvd_dvd_int L2) K) (and (= L2 tptp.zero_zero_int) (@ _let_1 K)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) L2))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (not (@ _let_2 (@ _let_1 T))) (not (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T)))))))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (D4 tptp.int) (A2 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int X4))) (let ((_let_2 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) A2) (not (= X4 (@ (@ tptp.minus_minus_int Xb2) Xa3))))))) (=> (@ _let_2 (@ _let_1 T)) (@ _let_2 (@ (@ tptp.plus_plus_int (@ _let_1 D4)) T))))))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (not (@ _let_1 (@ (@ tptp.plus_plus_int X4) T))) (not (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D4)) T))))))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (D4 tptp.int) (B3 tptp.set_int) (T tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) D4) (forall ((X4 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (=> (forall ((Xa3 tptp.int)) (=> (@ (@ tptp.member_int Xa3) (@ (@ tptp.set_or1266510415728281911st_int tptp.one_one_int) D4)) (forall ((Xb2 tptp.int)) (=> (@ (@ tptp.member_int Xb2) B3) (not (= X4 (@ (@ tptp.plus_plus_int Xb2) Xa3))))))) (=> (@ _let_1 (@ (@ tptp.plus_plus_int X4) T)) (@ _let_1 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int X4) D4)) T)))))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) (@ tptp.abs_abs_Code_integer Y)) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) (@ tptp.abs_abs_rat Y)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (= (@ tptp.abs_abs_Code_integer X) tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (= (= (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (= (@ tptp.abs_abs_rat X) tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.abs_abs_real X) tptp.one_one_real))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (= (= (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) A)))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)) A)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)) A)))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_nat _let_1) A) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_int _let_1) A) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) A) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ tptp.uminus_uminus_real B))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_real)))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat A))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ tptp.uminus_uminus_rat B))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_1 (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_3) _let_4)) (=> (not _let_5) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_4) _let_3)) (=> (not _let_2) (@ _let_1 tptp.zero_zero_rat)))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (C tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_2 (@ tptp.uminus_uminus_real B))) (let ((_let_3 (@ (@ tptp.times_times_real A) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_real _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (A tptp.rat)) (let ((_let_1 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_2 (@ tptp.uminus_uminus_rat B))) (let ((_let_3 (@ (@ tptp.times_times_rat A) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat _let_2) _let_3)) (=> (not _let_4) (and (=> _let_1 (@ (@ tptp.ord_less_eq_rat _let_3) _let_2)) (=> (not _let_1) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) A))))))))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real C) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real A) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real A) C)) (@ tptp.uminus_uminus_real B))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (A tptp.rat) (B tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat A) (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.times_times_rat A) C)) (@ tptp.uminus_uminus_rat B))))))
% 6.68/6.98 (assert (forall ((C tptp.real) (B tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (= (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real B) C))) A) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real B)) (@ (@ tptp.times_times_real A) C))))))
% 6.68/6.98 (assert (forall ((C tptp.rat) (B tptp.rat) (A tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat (@ (@ tptp.divide_divide_rat B) C))) A) (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat B)) (@ (@ tptp.times_times_rat A) C))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_nat _let_1) A)) (= (@ (@ tptp.modulo_modulo_nat A) _let_1) tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_int _let_1) A)) (= (@ (@ tptp.modulo_modulo_int A) _let_1) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A)) (= (@ (@ tptp.modulo364778990260209775nteger A) _let_1) tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_real B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_real _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ _let_2 C))) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_5 (@ (@ tptp.ord_less_rat B) _let_4)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_rat _let_4) B)) (=> (not _let_3) (@ _let_2 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) (@ (@ tptp.power_power_real B) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat) (B tptp.rat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_rat A) B) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) (@ (@ tptp.power_power_rat B) N))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (@ (@ tptp.ord_less_eq_int A) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) (@ (@ tptp.power_power_int B) N))))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (or (= A tptp.one_one_real) (= A (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_int) (or (= A tptp.one_one_int) (= A (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (or (= A tptp.one_one_complex) (= A (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (= (@ (@ tptp.power_8256067586552552935nteger A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_Code_integer) (or (= A tptp.one_one_Code_integer) (= A (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_rat) (or (= A tptp.one_one_rat) (= A (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat K))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K) (= (@ (@ tptp.dvd_dvd_nat (@ _let_1 M)) (@ _let_1 N)) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.uminus_uminus_int tptp.one_one_int)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 (@ (@ tptp.plus_plus_nat N) K)) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se8260200283734997820nteger M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4203085406695923979it_int M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se4205575877204974255it_nat M) A)) (or (@ _let_1 A) (= M tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2793503036327961859nteger M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7879613467334960850it_int M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se7882103937844011126it_nat M) A)) (and (@ _let_1 A) (not (= M tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((U tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real U) _let_1))) (@ (@ tptp.power_power_real X) _let_1)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1345352211410354436nteger M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2159334234014336723it_int M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2161824704523386999it_nat M) A)) (not (= (@ _let_1 A) (= M tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X))) (@ tptp.uminus_uminus_real X))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.code_integer tptp.code_integer Bool)) (X tptp.code_integer)) (=> (forall ((X6 tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) X6) (@ (@ P X6) (@ (@ tptp.power_8256067586552552935nteger X6) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_Code_integer X)) (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.real tptp.real Bool)) (X tptp.real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X6) (@ (@ P X6) (@ (@ tptp.power_power_real X6) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_real X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.rat tptp.rat Bool)) (X tptp.rat)) (=> (forall ((X6 tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) X6) (@ (@ P X6) (@ (@ tptp.power_power_rat X6) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_rat X)) (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.int tptp.int Bool)) (X tptp.int)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X6) (@ (@ P X6) (@ (@ tptp.power_power_int X6) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ P (@ tptp.abs_abs_int X)) (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (forall ((Y tptp.code_integer) (X tptp.code_integer)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) Y) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1)) (@ (@ tptp.power_8256067586552552935nteger Y) _let_1)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) Y))))))
% 6.68/6.98 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) Y))))))
% 6.68/6.98 (assert (forall ((Y tptp.rat) (X tptp.rat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) Y) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) Y))))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) _let_1)) (@ (@ tptp.power_power_int Y) _let_1)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) Y))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer) (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer X)) tptp.one_one_Code_integer))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat) (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat X)) tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int X)) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (=> (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.code_integer)) (not (= A (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_Code_integer))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.nat)) (not (= A (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_nat))))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (=> (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A)) (not (forall ((B5 tptp.int)) (not (= A (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) B5)) tptp.one_one_int))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 tptp.one_one_nat))))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 tptp.one_one_int))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 tptp.one_one_Code_integer))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_nat))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_nat))))))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_zero_int))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_int))))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A) _let_1))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (=> _let_3 (not (= _let_2 tptp.zero_z3403309356797280102nteger))) (not (=> (not _let_3) (not (= _let_2 tptp.one_one_Code_integer))))))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ tptp.ord_less_eq_real _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_real B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_real _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_real B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_real)))))))))))))
% 6.68/6.98 (assert (forall ((W tptp.num) (B tptp.rat) (C tptp.rat)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ tptp.ord_less_eq_rat _let_1))) (let ((_let_3 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_4 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_5 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ _let_2 (@ (@ tptp.divide_divide_rat B) C)) (and (=> _let_5 (@ (@ tptp.ord_less_eq_rat _let_4) B)) (=> (not _let_5) (and (=> _let_3 (@ (@ tptp.ord_less_eq_rat B) _let_4)) (=> (not _let_3) (@ _let_2 tptp.zero_zero_rat)))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.real) (C tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W)))) (let ((_let_2 (@ (@ tptp.ord_less_real C) tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.times_times_real _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_real tptp.zero_zero_real) C))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_real B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_real _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1))))))))))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (C tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))) (let ((_let_2 (@ (@ tptp.ord_less_rat C) tptp.zero_zero_rat))) (let ((_let_3 (@ (@ tptp.times_times_rat _let_1) C))) (let ((_let_4 (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) C))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.divide_divide_rat B) C)) _let_1) (and (=> _let_4 (@ (@ tptp.ord_less_eq_rat B) _let_3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_eq_rat _let_3) B)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) _let_1))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or _let_2 (and (not _let_2) (@ _let_1 A))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat)) (let ((_let_1 (@ tptp.ord_less_eq_rat tptp.zero_zero_rat))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (@ _let_1 A))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.real)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.power_power_real A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.rat)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat A) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.power_power_int A) N)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2))) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.times_times_real _let_2) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X) (=> (@ (@ tptp.ord_le3102999989581377725nteger X) tptp.one_one_Code_integer) (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_Code_integer)))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) X) (=> (@ (@ tptp.ord_less_eq_rat X) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_rat)))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int tptp.one_one_int)) X) (=> (@ (@ tptp.ord_less_eq_int X) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real A)) N))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ (@ tptp.power_power_real A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int A)) N))) (= (@ (@ tptp.times_times_int _let_1) _let_1) (@ (@ tptp.power_power_int A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.98 (assert (forall ((A tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex A)) N))) (= (@ (@ tptp.times_times_complex _let_1) _let_1) (@ (@ tptp.power_power_complex A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger A)) N))) (= (@ (@ tptp.times_3573771949741848930nteger _let_1) _let_1) (@ (@ tptp.power_8256067586552552935nteger A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat A)) N))) (= (@ (@ tptp.times_times_rat _let_1) _let_1) (@ (@ tptp.power_power_rat A) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.98 (assert (forall ((X tptp.nat)) (=> (not (= X tptp.zero_zero_nat)) (not (forall ((N3 tptp.nat)) (not (= X (@ tptp.suc N3))))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_real A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_real))) (and (not _let_2) (@ _let_1 A))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_rat A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_rat))) (and (not _let_2) (@ _let_1 A))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (let ((_let_2 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ _let_1 (@ (@ tptp.power_power_int A) N)) (or (= N tptp.zero_zero_nat) (and _let_2 (not (= A tptp.zero_zero_int))) (and (not _let_2) (@ _let_1 A))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ (@ tptp.power_power_real _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.power_power_int _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ (@ tptp.power_power_complex _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.power_8256067586552552935nteger _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ (@ tptp.power_power_rat _let_1) (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) _let_1))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real) (Z tptp.real)) (= (= X (@ (@ tptp.minus_minus_real Y) Z)) (= Y (@ (@ tptp.plus_plus_real X) Z)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) (@ _let_2 N))) (@ (@ tptp.ord_less_eq_nat M) N))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real A) N)) tptp.zero_zero_real) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real)) (and _let_1 (= A tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat A) N)) tptp.zero_zero_rat) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_rat A) tptp.zero_zero_rat)) (and _let_1 (= A tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int A) N)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (or (and (not _let_1) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)) (and _let_1 (= A tptp.zero_zero_int))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.suc tptp.zero_zero_nat))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) _let_3) (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) _let_3)) _let_2))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_Code_integer _let_1) (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.minus_8373710615458151222nteger (@ _let_2 M)) tptp.one_one_Code_integer)) _let_3)) (or (= _let_3 tptp.zero_z3403309356797280102nteger) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ _let_2 M)) tptp.one_one_nat)) _let_3)) (or (= _let_3 tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ _let_2 N))) (= (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ _let_2 M)) tptp.one_one_int)) _let_3)) (or (= _let_3 tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_nat M) N))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X))) X))) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_8256067586552552935nteger _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_Code_integer _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger (@ (@ tptp.times_3573771949741848930nteger A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_z3403309356797280102nteger) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide6298287555418463151nteger A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_nat _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_nat _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_nat) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_nat A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.power_power_int _let_1))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_4 (@ _let_2 N))) (= (@ _let_3 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int A) (@ _let_2 M))) _let_4)) (or (@ (@ tptp.ord_less_nat N) M) (= _let_4 tptp.zero_zero_int) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ _let_3 (@ (@ tptp.divide_divide_int A) (@ _let_2 (@ (@ tptp.minus_minus_nat N) M)))))))))))))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (= tptp.bit_ri6519982836138164636nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo364778990260209775nteger A3) _let_1))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) (@ tptp.uminus1351360451143612070nteger _let_2)) (@ (@ tptp.plus_p5714425477246183910nteger _let_2) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))))))))))
% 6.68/6.98 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int A3) _let_1))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) (@ tptp.uminus_uminus_int _let_2)) (@ (@ tptp.plus_plus_int _let_2) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))))))))))
% 6.68/6.98 (assert (= tptp.nat_triangle (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N2) (@ tptp.suc N2))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ _let_2 (@ tptp.arctan X)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ _let_2 X)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (not (= Y (@ (@ tptp.vEBT_Leaf false) false))))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (=> (= X tptp.zero_zero_nat) _let_1) (=> (=> (= X (@ tptp.suc tptp.zero_zero_nat)) _let_1) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (=> (= X _let_2) (not (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4)))))))))))))))))))))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1345352211410354436nteger tptp.zero_zero_nat) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.divide6298287555418463151nteger A) _let_1)))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2159334234014336723it_int tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.divide_divide_int A) _let_1)))))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2161824704523386999it_nat tptp.zero_zero_nat) A) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.divide_divide_nat A) _let_1)))))))
% 6.68/6.98 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.nat Bool)) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I))))))
% 6.68/6.98 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.int Bool)) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I))))))
% 6.68/6.98 (assert (forall ((I tptp.nat) (N tptp.nat) (P (-> tptp.vEBT_VEBT Bool)) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (=> (@ P X) (@ P (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A2) B3) (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int B3)) (@ tptp.uminus1532241313380277803et_int A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.uminus1532241313380277803et_int A2)) (@ tptp.uminus1532241313380277803et_int B3)) (@ (@ tptp.ord_less_eq_set_int B3) A2))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (=> P Q))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (=> P Q))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (=> P Q))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (=> P Q))))
% 6.68/6.98 (assert (= (@ tptp.zero_n1201886186963655149omplex false) tptp.zero_zero_complex))
% 6.68/6.98 (assert (= (@ tptp.zero_n3304061248610475627l_real false) tptp.zero_zero_real))
% 6.68/6.98 (assert (= (@ tptp.zero_n2052037380579107095ol_rat false) tptp.zero_zero_rat))
% 6.68/6.98 (assert (= (@ tptp.zero_n2687167440665602831ol_nat false) tptp.zero_zero_nat))
% 6.68/6.98 (assert (= (@ tptp.zero_n2684676970156552555ol_int false) tptp.zero_zero_int))
% 6.68/6.98 (assert (= (@ tptp.zero_n356916108424825756nteger false) tptp.zero_z3403309356797280102nteger))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.zero_zero_complex) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.zero_zero_real) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.zero_zero_rat) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.zero_zero_nat) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.zero_zero_int) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.zero_z3403309356797280102nteger) (not P))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)) (and (not P) Q))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)) (and (not P) Q))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)) (and (not P) Q))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)) (and (not P) Q))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)) (and (not P) Q))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n1201886186963655149omplex P) tptp.one_one_complex) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n3304061248610475627l_real P) tptp.one_one_real) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2052037380579107095ol_rat P) tptp.one_one_rat) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P) tptp.one_one_nat) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P) tptp.one_one_int) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P) tptp.one_one_Code_integer) P)))
% 6.68/6.98 (assert (= (@ tptp.zero_n1201886186963655149omplex true) tptp.one_one_complex))
% 6.68/6.98 (assert (= (@ tptp.zero_n3304061248610475627l_real true) tptp.one_one_real))
% 6.68/6.98 (assert (= (@ tptp.zero_n2052037380579107095ol_rat true) tptp.one_one_rat))
% 6.68/6.98 (assert (= (@ tptp.zero_n2687167440665602831ol_nat true) tptp.one_one_nat))
% 6.68/6.98 (assert (= (@ tptp.zero_n2684676970156552555ol_int true) tptp.one_one_int))
% 6.68/6.98 (assert (= (@ tptp.zero_n356916108424825756nteger true) tptp.one_one_Code_integer))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((M tptp.nat) (X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (= (@ (@ tptp.replicate_VEBT_VEBT M) X) (@ (@ tptp.replicate_VEBT_VEBT N) Y)) (and (= M N) (=> (not (= M tptp.zero_zero_nat)) (= X Y))))))
% 6.68/6.98 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n3304061248610475627l_real P))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2052037380579107095ol_rat P))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2684676970156552555ol_int P))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n356916108424825756nteger P))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((X tptp.int)) (= (@ (@ tptp.dvd_dvd_int X) tptp.one_one_int) (= (@ tptp.abs_abs_int X) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.size_s6755466524823107622T_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) N)))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X Bool)) (= (@ tptp.size_size_list_o (@ (@ tptp.replicate_o N) X)) N)))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.replicate_nat N) X)) N)))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.size_size_list_int (@ (@ tptp.replicate_int N) X)) N)))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (= (@ tptp.arctan X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.68/6.98 (assert (= (@ tptp.arctan tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (or P Q)) (@ (@ tptp.ord_max_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (or P Q)) (@ (@ tptp.ord_max_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (or P Q)) (@ (@ tptp.ord_max_Code_integer (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.68/6.98 (assert (= (@ tptp.nat_triangle tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P)) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P)) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P)) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P)) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P)) P)))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_less_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer) (not P))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ tptp.zero_n1201886186963655149omplex (not P)) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) (@ tptp.zero_n1201886186963655149omplex P)))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ tptp.zero_n3304061248610475627l_real (not P)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ tptp.zero_n3304061248610475627l_real P)))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (not P)) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) (@ tptp.zero_n2052037380579107095ol_rat P)))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (not P)) (@ (@ tptp.minus_minus_int tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int P)))))
% 6.68/6.98 (assert (forall ((P Bool)) (= (@ tptp.zero_n356916108424825756nteger (not P)) (@ (@ tptp.minus_8373710615458151222nteger tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger P)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.modulo_modulo_nat _let_1) N) (@ tptp.zero_n2687167440665602831ol_nat (not (= N _let_1)))))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int Z)) tptp.one_one_int) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ (@ tptp.bit_ri6519982836138164636nteger N) _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_ri631733984087533419it_int N) _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat K)) tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X3))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X3))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X3))) (or (@ P A) (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int) (P (-> tptp.int Bool))) (= (exists ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) A))) (@ P X3))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) A))) (@ P X3))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.vEBT_VEBT) (P (-> tptp.vEBT_VEBT Bool))) (= (exists ((X3 tptp.vEBT_VEBT)) (and (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) A))) (@ P X3))) (and (@ P A) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.member_complex X) (@ tptp.set_complex2 (@ (@ tptp.replicate_complex N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.member_real X) (@ tptp.set_real2 (@ (@ tptp.replicate_real N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((X tptp.set_nat) (N tptp.nat) (Y tptp.set_nat)) (= (@ (@ tptp.member_set_nat X) (@ tptp.set_set_nat2 (@ (@ tptp.replicate_set_nat N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.member_int X) (@ tptp.set_int2 (@ (@ tptp.replicate_int N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (N tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.member_nat X) (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((X tptp.vEBT_VEBT) (N tptp.nat) (Y tptp.vEBT_VEBT)) (= (@ (@ tptp.member_VEBT_VEBT X) (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) Y))) (and (= X Y) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.nat)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_nat (@ (@ tptp.replicate_nat N) X)) I) X))))
% 6.68/6.98 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.int)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_int (@ (@ tptp.replicate_int N) X)) I) X))))
% 6.68/6.98 (assert (forall ((I tptp.nat) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (@ (@ tptp.ord_less_nat I) N) (= (@ (@ tptp.nth_VEBT_VEBT (@ (@ tptp.replicate_VEBT_VEBT N) X)) I) X))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.arctan X)) (@ _let_1 X)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ tptp.nat_triangle _let_1) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle N)) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2687167440665602831ol_nat P5))) P5)))
% 6.68/6.98 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.zero_n2684676970156552555ol_int P5))) P5)))
% 6.68/6.98 (assert (forall ((P5 Bool)) (= (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.zero_n356916108424825756nteger P5))) P5)))
% 6.68/6.98 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_nat (@ tptp.zero_n2687167440665602831ol_nat B)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.zero_zero_nat)))
% 6.68/6.98 (assert (forall ((B Bool)) (= (@ (@ tptp.divide_divide_int (@ tptp.zero_n2684676970156552555ol_int B)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((B Bool)) (= (@ (@ tptp.divide6298287555418463151nteger (@ tptp.zero_n356916108424825756nteger B)) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_ri6519982836138164636nteger tptp.zero_zero_nat) A) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_ri631733984087533419it_int tptp.zero_zero_nat) A) (@ tptp.uminus_uminus_int (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide6298287555418463151nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (= N tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat tptp.one_one_nat) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.modulo364778990260209775nteger tptp.one_one_Code_integer) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat M) N) (=> (@ (@ tptp.dvd_dvd_nat N) M) (= M N)))))
% 6.68/6.98 (assert (forall ((P5 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2687167440665602831ol_nat P5) (@ tptp.zero_n2687167440665602831ol_nat Q2)) (= P5 Q2))))
% 6.68/6.98 (assert (forall ((P5 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n2684676970156552555ol_int P5) (@ tptp.zero_n2684676970156552555ol_int Q2)) (= P5 Q2))))
% 6.68/6.98 (assert (forall ((P5 Bool) (Q2 Bool)) (= (= (@ tptp.zero_n356916108424825756nteger P5) (@ tptp.zero_n356916108424825756nteger Q2)) (= P5 Q2))))
% 6.68/6.98 (assert (= tptp.abs_abs_int (lambda ((I5 tptp.int)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int I5) tptp.zero_zero_int)) (@ tptp.uminus_uminus_int I5)) I5))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n3304061248610475627l_real (and P Q)) (@ (@ tptp.times_times_real (@ tptp.zero_n3304061248610475627l_real P)) (@ tptp.zero_n3304061248610475627l_real Q)))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2052037380579107095ol_rat (and P Q)) (@ (@ tptp.times_times_rat (@ tptp.zero_n2052037380579107095ol_rat P)) (@ tptp.zero_n2052037380579107095ol_rat Q)))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2687167440665602831ol_nat (and P Q)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2687167440665602831ol_nat Q)))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n2684676970156552555ol_int (and P Q)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int P)) (@ tptp.zero_n2684676970156552555ol_int Q)))))
% 6.68/6.98 (assert (forall ((P Bool) (Q Bool)) (= (@ tptp.zero_n356916108424825756nteger (and P Q)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger P)) (@ tptp.zero_n356916108424825756nteger Q)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.68/6.98 (assert (= (@ tptp.uminus_uminus_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.dvd_dvd_int Y) X) (= (@ tptp.abs_abs_int (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int X)) (@ tptp.abs_abs_int Y))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.zero_n2687167440665602831ol_nat P))))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ tptp.zero_n356916108424825756nteger P))))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_real (@ tptp.zero_n3304061248610475627l_real P)) tptp.one_one_real)))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_rat (@ tptp.zero_n2052037380579107095ol_rat P)) tptp.one_one_rat)))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_nat (@ tptp.zero_n2687167440665602831ol_nat P)) tptp.one_one_nat)))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_less_eq_int (@ tptp.zero_n2684676970156552555ol_int P)) tptp.one_one_int)))
% 6.68/6.98 (assert (forall ((P Bool)) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.zero_n356916108424825756nteger P)) tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (= tptp.zero_n1201886186963655149omplex (lambda ((P2 Bool)) (@ (@ (@ tptp.if_complex P2) tptp.one_one_complex) tptp.zero_zero_complex))))
% 6.68/6.98 (assert (= tptp.zero_n3304061248610475627l_real (lambda ((P2 Bool)) (@ (@ (@ tptp.if_real P2) tptp.one_one_real) tptp.zero_zero_real))))
% 6.68/6.98 (assert (= tptp.zero_n2052037380579107095ol_rat (lambda ((P2 Bool)) (@ (@ (@ tptp.if_rat P2) tptp.one_one_rat) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (= tptp.zero_n2687167440665602831ol_nat (lambda ((P2 Bool)) (@ (@ (@ tptp.if_nat P2) tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (= tptp.zero_n2684676970156552555ol_int (lambda ((P2 Bool)) (@ (@ (@ tptp.if_int P2) tptp.one_one_int) tptp.zero_zero_int))))
% 6.68/6.98 (assert (= tptp.zero_n356916108424825756nteger (lambda ((P2 Bool)) (@ (@ (@ tptp.if_Code_integer P2) tptp.one_one_Code_integer) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (and (=> P5 (@ P tptp.one_one_complex)) (=> (not P5) (@ P tptp.zero_zero_complex))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (and (=> P5 (@ P tptp.one_one_real)) (=> (not P5) (@ P tptp.zero_zero_real))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.rat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P5)) (and (=> P5 (@ P tptp.one_one_rat)) (=> (not P5) (@ P tptp.zero_zero_rat))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (and (=> P5 (@ P tptp.one_one_nat)) (=> (not P5) (@ P tptp.zero_zero_nat))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (and (=> P5 (@ P tptp.one_one_int)) (=> (not P5) (@ P tptp.zero_zero_int))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (and (=> P5 (@ P tptp.one_one_Code_integer)) (=> (not P5) (@ P tptp.zero_z3403309356797280102nteger))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.complex Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n1201886186963655149omplex P5)) (not (or (and P5 (not (@ P tptp.one_one_complex))) (and (not P5) (not (@ P tptp.zero_zero_complex))))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.real Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n3304061248610475627l_real P5)) (not (or (and P5 (not (@ P tptp.one_one_real))) (and (not P5) (not (@ P tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.rat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2052037380579107095ol_rat P5)) (not (or (and P5 (not (@ P tptp.one_one_rat))) (and (not P5) (not (@ P tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2687167440665602831ol_nat P5)) (not (or (and P5 (not (@ P tptp.one_one_nat))) (and (not P5) (not (@ P tptp.zero_zero_nat))))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.int Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n2684676970156552555ol_int P5)) (not (or (and P5 (not (@ P tptp.one_one_int))) (and (not P5) (not (@ P tptp.zero_zero_int))))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.code_integer Bool)) (P5 Bool)) (= (@ P (@ tptp.zero_n356916108424825756nteger P5)) (not (or (and P5 (not (@ P tptp.one_one_Code_integer))) (and (not P5) (not (@ P tptp.zero_z3403309356797280102nteger))))))))
% 6.68/6.98 (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))))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_VEBT_VEBT) (X tptp.vEBT_VEBT)) (=> (forall ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 Xs)) (= X6 X))) (= (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.size_s6755466524823107622T_VEBT Xs)) X) Xs))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_o) (X Bool)) (=> (forall ((X6 Bool)) (=> (@ (@ tptp.member_o X6) (@ tptp.set_o2 Xs)) (= X6 X))) (= (@ (@ tptp.replicate_o (@ tptp.size_size_list_o Xs)) X) Xs))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_nat) (X tptp.nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ tptp.set_nat2 Xs)) (= X6 X))) (= (@ (@ tptp.replicate_nat (@ tptp.size_size_list_nat Xs)) X) Xs))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_int) (X tptp.int)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ tptp.set_int2 Xs)) (= X6 X))) (= (@ (@ tptp.replicate_int (@ tptp.size_size_list_int Xs)) X) Xs))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_complex) (N tptp.nat) (X tptp.complex)) (=> (= (@ tptp.size_s3451745648224563538omplex Xs) N) (=> (forall ((Y5 tptp.complex)) (=> (@ (@ tptp.member_complex Y5) (@ tptp.set_complex2 Xs)) (= Y5 X))) (= Xs (@ (@ tptp.replicate_complex N) X))))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_real) (N tptp.nat) (X tptp.real)) (=> (= (@ tptp.size_size_list_real Xs) N) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.member_real Y5) (@ tptp.set_real2 Xs)) (= Y5 X))) (= Xs (@ (@ tptp.replicate_real N) X))))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_set_nat) (N tptp.nat) (X tptp.set_nat)) (=> (= (@ tptp.size_s3254054031482475050et_nat Xs) N) (=> (forall ((Y5 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat Y5) (@ tptp.set_set_nat2 Xs)) (= Y5 X))) (= Xs (@ (@ tptp.replicate_set_nat N) X))))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_VEBT_VEBT) (N tptp.nat) (X tptp.vEBT_VEBT)) (=> (= (@ tptp.size_s6755466524823107622T_VEBT Xs) N) (=> (forall ((Y5 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT Y5) (@ tptp.set_VEBT_VEBT2 Xs)) (= Y5 X))) (= Xs (@ (@ tptp.replicate_VEBT_VEBT N) X))))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_o) (N tptp.nat) (X Bool)) (=> (= (@ tptp.size_size_list_o Xs) N) (=> (forall ((Y5 Bool)) (=> (@ (@ tptp.member_o Y5) (@ tptp.set_o2 Xs)) (= Y5 X))) (= Xs (@ (@ tptp.replicate_o N) X))))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_nat) (N tptp.nat) (X tptp.nat)) (=> (= (@ tptp.size_size_list_nat Xs) N) (=> (forall ((Y5 tptp.nat)) (=> (@ (@ tptp.member_nat Y5) (@ tptp.set_nat2 Xs)) (= Y5 X))) (= Xs (@ (@ tptp.replicate_nat N) X))))))
% 6.68/6.98 (assert (forall ((Xs tptp.list_int) (N tptp.nat) (X tptp.int)) (=> (= (@ tptp.size_size_list_int Xs) N) (=> (forall ((Y5 tptp.int)) (=> (@ (@ tptp.member_int Y5) (@ tptp.set_int2 Xs)) (= Y5 X))) (= Xs (@ (@ tptp.replicate_int N) X))))))
% 6.68/6.98 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ tptp.abs_abs_int (@ (@ tptp.times_times_int M) N)) tptp.one_one_int) (= (@ tptp.abs_abs_int M) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat A2)) (= A2 tptp.bot_bot_set_nat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real A2)) (= A2 tptp.bot_bot_set_real))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int A2)) (= A2 tptp.bot_bot_set_int))))
% 6.68/6.98 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (and (= M tptp.one_one_int) (= N tptp.one_one_int)) (and (= M _let_1) (= N _let_1)))))))
% 6.68/6.98 (assert (forall ((M tptp.int) (N tptp.int)) (=> (= (@ (@ tptp.times_times_int M) N) tptp.one_one_int) (or (= M tptp.one_one_int) (= M (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.68/6.98 (assert (forall ((L2 tptp.int)) (= (@ (@ tptp.minus_minus_int tptp.zero_zero_int) L2) (@ tptp.uminus_uminus_int L2))))
% 6.68/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) tptp.zero_zero_int)) (not (= (@ (@ tptp.modulo_modulo_int K) L2) tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int K))) (=> (not (= (@ _let_1 (@ tptp.uminus_uminus_int L2)) tptp.zero_zero_int)) (not (= (@ _let_1 L2) tptp.zero_zero_int))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) K))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))
% 6.68/6.98 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ _let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (=> (@ (@ tptp.ord_less_int K) _let_1) (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (= (@ (@ tptp.bit_ri631733984087533419it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int _let_1)) K) (@ (@ tptp.ord_less_int K) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.int) (N tptp.int)) (=> (not (= M tptp.zero_zero_int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int M) N)) M) (= (@ tptp.abs_abs_int N) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ (@ tptp.modulo_modulo_int K) L2))) (@ tptp.abs_abs_int L2)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.modulo_modulo_int A) B))) (let ((_let_2 (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= _let_1 tptp.zero_zero_int))) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int B) _let_1)))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.modulo_modulo_int A))) (let ((_let_2 (@ _let_1 B))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= _let_2 tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) B))))))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int K)) L2)) (@ _let_1 (@ (@ tptp.plus_plus_int K) L2))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.plus_plus_int K))) (let ((_let_2 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ _let_1 (@ tptp.abs_abs_int L2))) (@ _let_2 (@ _let_1 L2)))))))
% 6.68/6.98 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_int K) (@ tptp.uminus_uminus_int (@ _let_1 N))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.bit_ri631733984087533419it_int N) K))))))
% 6.68/6.98 (assert (forall ((A2 tptp.int) (B3 tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int A2) B3) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int N)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.divide_divide_int B3) N)) (@ (@ tptp.divide_divide_int A2) N))))))
% 6.68/6.98 (assert (forall ((B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.divide_divide_int _let_1) B) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat _let_1) A))) (@ (@ tptp.modulo_modulo_nat A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int _let_1) A))) (@ (@ tptp.modulo_modulo_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.zero_n356916108424825756nteger (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (@ (@ tptp.modulo364778990260209775nteger A) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri6519982836138164636nteger M) A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int M) A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int K)) L2) (@ (@ tptp.minus_minus_int (@ (@ tptp.minus_minus_int L2) tptp.one_one_int)) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) L2))))))
% 6.68/6.98 (assert (forall ((B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) B) (@ (@ tptp.minus_minus_int B) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int A) B)))) (let ((_let_2 (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int A)) B))) (let ((_let_3 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_3 (= _let_2 _let_1)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.divide_divide_int A))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ _let_1 B)))) (let ((_let_3 (@ _let_1 (@ tptp.uminus_uminus_int B)))) (let ((_let_4 (= (@ (@ tptp.modulo_modulo_int A) B) tptp.zero_zero_int))) (=> (not (= B tptp.zero_zero_int)) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (Q2 tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.if_int (= R tptp.zero_zero_int)))) (let ((_let_2 (@ tptp.uminus_uminus_int Q2))) (=> (@ (@ (@ tptp.eucl_rel_int A) B) (@ (@ tptp.product_Pair_int_int Q2) R)) (=> (not (= B tptp.zero_zero_int)) (@ (@ (@ tptp.eucl_rel_int (@ tptp.uminus_uminus_int A)) B) (@ (@ tptp.product_Pair_int_int (@ (@ _let_1 _let_2) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int))) (@ (@ _let_1 tptp.zero_zero_int) (@ (@ tptp.minus_minus_int B) R))))))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat Bool)) (A tptp.nat)) (=> (forall ((A5 tptp.nat)) (=> (= (@ (@ tptp.divide_divide_nat A5) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.nat) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat B5)) (@ (@ tptp.times_times_nat _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_nat _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.68/6.98 (assert (forall ((P (-> tptp.int Bool)) (A tptp.int)) (=> (forall ((A5 tptp.int)) (=> (= (@ (@ tptp.divide_divide_int A5) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.int) (B5 Bool)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int B5)) (@ (@ tptp.times_times_int _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide_divide_int _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.68/6.98 (assert (forall ((P (-> tptp.code_integer Bool)) (A tptp.code_integer)) (=> (forall ((A5 tptp.code_integer)) (=> (= (@ (@ tptp.divide6298287555418463151nteger A5) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) A5) (@ P A5))) (=> (forall ((A5 tptp.code_integer) (B5 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.zero_n356916108424825756nteger B5)) (@ (@ tptp.times_3573771949741848930nteger _let_1) A5)))) (=> (@ P A5) (=> (= (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1) A5) (@ P _let_2)))))) (@ P A)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_nat I4) N)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (=> (@ (@ tptp.ord_less_eq_int (@ F M)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M) I4) (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K)))))))))
% 6.68/6.98 (assert (forall ((D tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.minus_minus_int X))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int (@ _let_1 (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ _let_1 Z))) tptp.one_one_int)) D))) Z)))))
% 6.68/6.98 (assert (forall ((D tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) D) (@ (@ tptp.ord_less_int Z) (@ (@ tptp.plus_plus_int X) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int X) Z))) tptp.one_one_int)) D))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.68/6.98 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.divide_divide_int _let_1) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) _let_1))))
% 6.68/6.98 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) L2)) tptp.zero_zero_int) (= (@ (@ tptp.divide_divide_int K) L2) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (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)))))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo_modulo_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.modulo364778990260209775nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat M) N))) _let_2))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I4))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_int (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (@ (@ tptp.minus_minus_int K) (@ _let_1 (@ tptp.suc N))))))))
% 6.68/6.98 (assert (forall ((P (-> tptp.int Bool)) (K tptp.int)) (=> (@ P tptp.zero_zero_int) (=> (@ P (@ tptp.uminus_uminus_int tptp.one_one_int)) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 tptp.zero_zero_int)) (@ P (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))) (=> (forall ((K3 tptp.int)) (=> (@ P K3) (=> (not (= K3 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ P (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int K3) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))) (@ P K)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K tptp.int)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat I4) N) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ F (@ (@ tptp.plus_plus_nat I4) tptp.one_one_nat))) (@ F I4)))) tptp.one_one_int))) (=> (@ (@ tptp.ord_less_eq_int (@ F tptp.zero_zero_nat)) K) (=> (@ (@ tptp.ord_less_eq_int K) (@ F N)) (exists ((I4 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat I4) N) (= (@ F I4) K))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_nat _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (= _let_2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide_divide_int _let_2) (@ _let_1 N)) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (and (not (= _let_2 tptp.zero_zero_int)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ _let_1 M))) (= (@ (@ tptp.divide6298287555418463151nteger _let_2) (@ _let_1 N)) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (and (not (= _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.ord_less_eq_nat N) M)))) (@ _let_1 (@ (@ tptp.minus_minus_nat M) N))))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.plus_plus_real (@ tptp.arctan X)) (@ tptp.arctan Y)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y)))))))))
% 6.68/6.98 (assert (forall ((Va tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.suc (@ tptp.suc Va)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_2) _let_1))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_1))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_2))) (let ((_let_8 (@ tptp.vEBT_vebt_buildup _let_2))) (let ((_let_9 (@ (@ tptp.dvd_dvd_nat _let_1) _let_2))) (and (=> _let_9 (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_9) (= _let_8 (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))))))))))))))
% 6.68/6.98 (assert (forall ((X tptp.set_real) (Y tptp.set_real)) (= (= (@ (@ tptp.minus_minus_set_real X) Y) tptp.bot_bot_set_real) (@ (@ tptp.ord_less_eq_set_real X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.set_nat) (Y tptp.set_nat)) (= (= (@ (@ tptp.minus_minus_set_nat X) Y) tptp.bot_bot_set_nat) (@ (@ tptp.ord_less_eq_set_nat X) Y))))
% 6.68/6.98 (assert (forall ((X tptp.set_int) (Y tptp.set_int)) (= (= (@ (@ tptp.minus_minus_set_int X) Y) tptp.bot_bot_set_int) (@ (@ tptp.ord_less_eq_set_int X) Y))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri6519982836138164636nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.modulo364778990260209775nteger A) _let_1)) (@ (@ tptp.times_3573771949741848930nteger _let_1) (@ (@ tptp.bit_ri6519982836138164636nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.modulo_modulo_int A) _let_1)) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.divide_divide_int A) _let_1))))))))
% 6.68/6.98 (assert (forall ((Q2 tptp.int) (R tptp.int)) (= (@ tptp.adjust_div (@ (@ tptp.product_Pair_int_int Q2) R)) (@ (@ tptp.plus_plus_int Q2) (@ tptp.zero_n2684676970156552555ol_int (not (= R tptp.zero_zero_int)))))))
% 6.68/6.98 (assert (forall ((X tptp.nat) (Y tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel))) (let ((_let_3 (= Y (@ (@ tptp.vEBT_Leaf false) false)))) (=> (= (@ tptp.vEBT_vebt_buildup X) Y) (=> (@ _let_2 X) (=> (=> (= X tptp.zero_zero_nat) (=> _let_3 (not (@ _let_2 tptp.zero_zero_nat)))) (=> (=> (= X _let_1) (=> _let_3 (not (@ _let_2 _let_1)))) (not (forall ((Va2 tptp.nat)) (let ((_let_1 (@ tptp.suc (@ tptp.suc Va2)))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ (@ tptp.divide_divide_nat _let_1) _let_2))) (let ((_let_4 (@ tptp.suc _let_3))) (let ((_let_5 (@ tptp.vEBT_vebt_buildup _let_3))) (let ((_let_6 (@ tptp.power_power_nat _let_2))) (let ((_let_7 (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) _let_1))) (let ((_let_8 (@ (@ tptp.dvd_dvd_nat _let_2) _let_1))) (=> (= X _let_1) (=> (and (=> _let_8 (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_3)) _let_5)) _let_5))) (=> (not _let_8) (= Y (@ (@ _let_7 (@ (@ tptp.replicate_VEBT_VEBT (@ _let_6 _let_4)) _let_5)) (@ tptp.vEBT_vebt_buildup _let_4))))) (not (@ (@ tptp.accp_nat tptp.vEBT_v4011308405150292612up_rel) _let_1)))))))))))))))))))))))
% 6.68/6.98 (assert (forall ((X (-> tptp.nat tptp.nat)) (X22 tptp.nat)) (= (@ (@ tptp.size_option_nat X) (@ tptp.some_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat)) (X22 tptp.product_prod_nat_nat)) (= (@ (@ tptp.size_o8335143837870341156at_nat X) (@ tptp.some_P7363390416028606310at_nat X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((X (-> tptp.num tptp.nat)) (X22 tptp.num)) (= (@ (@ tptp.size_option_num X) (@ tptp.some_num X22)) (@ (@ tptp.plus_plus_nat (@ X X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ tptp.nat_set_decode X)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.member_nat (@ tptp.suc N)) (@ tptp.nat_set_decode X)) (@ (@ tptp.member_nat N) (@ tptp.nat_set_decode (@ (@ tptp.divide_divide_nat X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.98 (assert (forall ((R tptp.complex) (A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex R))) (=> (not (= R tptp.zero_zero_complex)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_complex A) (@ _let_1 C)) (@ (@ tptp.plus_plus_complex B) (@ _let_1 D)))))))))
% 6.68/6.98 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (=> (not (= R tptp.zero_zero_real)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real A) (@ _let_1 C)) (@ (@ tptp.plus_plus_real B) (@ _let_1 D)))))))))
% 6.68/6.98 (assert (forall ((R tptp.rat) (A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat R))) (=> (not (= R tptp.zero_zero_rat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_rat B) (@ _let_1 D)))))))))
% 6.68/6.98 (assert (forall ((R tptp.nat) (A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat R))) (=> (not (= R tptp.zero_zero_nat)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat A) (@ _let_1 C)) (@ (@ tptp.plus_plus_nat B) (@ _let_1 D)))))))))
% 6.68/6.98 (assert (forall ((R tptp.int) (A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int R))) (=> (not (= R tptp.zero_zero_int)) (=> (and (= A B) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int A) (@ _let_1 C)) (@ (@ tptp.plus_plus_int B) (@ _let_1 D)))))))))
% 6.68/6.98 (assert (= (@ tptp.nat_set_decode tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat (@ tptp.nat_set_decode M)) (@ tptp.nat_set_decode N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.68/6.98 (assert (forall ((B tptp.complex) (A tptp.complex)) (= (= B (@ (@ tptp.plus_plus_complex B) A)) (= A tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((B tptp.real) (A tptp.real)) (= (= B (@ (@ tptp.plus_plus_real B) A)) (= A tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((B tptp.rat) (A tptp.rat)) (= (= B (@ (@ tptp.plus_plus_rat B) A)) (= A tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((B tptp.nat) (A tptp.nat)) (= (= B (@ (@ tptp.plus_plus_nat B) A)) (= A tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((B tptp.int) (A tptp.int)) (= (= B (@ (@ tptp.plus_plus_int B) A)) (= A tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((W tptp.real) (Y tptp.real) (X tptp.real) (Z tptp.real)) (let ((_let_1 (@ tptp.times_times_real X))) (let ((_let_2 (@ tptp.times_times_real W))) (= (= (@ (@ tptp.plus_plus_real (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_real (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.68/6.98 (assert (forall ((W tptp.rat) (Y tptp.rat) (X tptp.rat) (Z tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat X))) (let ((_let_2 (@ tptp.times_times_rat W))) (= (= (@ (@ tptp.plus_plus_rat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_rat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.68/6.98 (assert (forall ((W tptp.nat) (Y tptp.nat) (X tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat X))) (let ((_let_2 (@ tptp.times_times_nat W))) (= (= (@ (@ tptp.plus_plus_nat (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_nat (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Y tptp.int) (X tptp.int) (Z tptp.int)) (let ((_let_1 (@ tptp.times_times_int X))) (let ((_let_2 (@ tptp.times_times_int W))) (= (= (@ (@ tptp.plus_plus_int (@ _let_2 Y)) (@ _let_1 Z)) (@ (@ tptp.plus_plus_int (@ _let_2 Z)) (@ _let_1 Y))) (or (= W X) (= Y Z)))))))
% 6.68/6.98 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_real (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.68/6.98 (assert (forall ((A tptp.rat) (B tptp.rat) (C tptp.rat) (D tptp.rat)) (let ((_let_1 (@ tptp.times_times_rat B))) (let ((_let_2 (@ tptp.times_times_rat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_rat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_rat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.68/6.98 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat B))) (let ((_let_2 (@ tptp.times_times_nat A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_nat (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_nat (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.times_times_int B))) (let ((_let_2 (@ tptp.times_times_int A))) (= (and (not (= A B)) (not (= C D))) (not (= (@ (@ tptp.plus_plus_int (@ _let_2 C)) (@ _let_1 D)) (@ (@ tptp.plus_plus_int (@ _let_2 D)) (@ _let_1 C)))))))))
% 6.68/6.98 (assert (forall ((X (-> tptp.nat tptp.nat))) (= (@ (@ tptp.size_option_nat X) tptp.none_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((X (-> tptp.product_prod_nat_nat tptp.nat))) (= (@ (@ tptp.size_o8335143837870341156at_nat X) tptp.none_P5556105721700978146at_nat) (@ tptp.suc tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((X (-> tptp.num tptp.nat))) (= (@ (@ tptp.size_option_num X) tptp.none_num) (@ tptp.suc tptp.zero_zero_nat))))
% 6.68/6.98 (assert (= tptp.nat_set_decode (lambda ((X3 tptp.nat)) (@ tptp.collect_nat (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat X3) (@ (@ tptp.power_power_nat _let_1) N2))))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_int)) (= (not (@ tptp.finite_finite_int S2)) (forall ((M3 tptp.int)) (exists ((N2 tptp.int)) (and (@ (@ tptp.ord_less_eq_int M3) (@ tptp.abs_abs_int N2)) (@ (@ tptp.member_int N2) S2)))))))
% 6.68/6.98 (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))))))))))
% 6.68/6.98 (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)))))))))
% 6.68/6.98 (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))))))))))
% 6.68/6.98 (assert (= tptp.ring_18347121197199848620nteger (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.68/6.98 (assert (= tptp.ring_1_of_int_rat (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat _let_1)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_rat (= K2 tptp.zero_zero_int)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus_uminus_rat (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_rat (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_plus_rat _let_3) tptp.one_one_rat))))))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ tptp.bit1 M) (@ tptp.bit1 N)) (= M N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit0 M) (@ tptp.bit1 N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (not (= (@ tptp.bit1 M) (@ tptp.bit0 N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (= tptp.one (@ tptp.bit1 N)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (= (@ tptp.bit1 M) tptp.one))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.zero_zero_int) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.zero_zero_real) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.zero_zero_rat) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_int (@ tptp.ring_1_of_int_int Z)) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_real (@ tptp.ring_1_of_int_real Z)) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_complex (@ tptp.ring_17405671764205052669omplex Z)) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= tptp.zero_zero_rat (@ tptp.ring_1_of_int_rat Z)) (= Z tptp.zero_zero_int))))
% 6.68/6.98 (assert (= (@ tptp.ring_1_of_int_int tptp.zero_zero_int) tptp.zero_zero_int))
% 6.68/6.98 (assert (= (@ tptp.ring_1_of_int_real tptp.zero_zero_int) tptp.zero_zero_real))
% 6.68/6.98 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.zero_zero_int) tptp.zero_zero_complex))
% 6.68/6.98 (assert (= (@ tptp.ring_1_of_int_rat tptp.zero_zero_int) tptp.zero_zero_rat))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_17405671764205052669omplex Z) (@ tptp.numera6690914467698888265omplex N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_real Z) (@ tptp.numeral_numeral_real N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (= (= (@ tptp.ring_1_of_int_rat Z) (@ tptp.numeral_numeral_rat N)) (= Z (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (= (@ tptp.ring_1_of_int_int Z) _let_1) (= Z _let_1)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.numeral_numeral_int K)) (@ tptp.numera6690914467698888265omplex K))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_real K))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_rat K))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_eq_int W) Z))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)) (@ (@ tptp.ord_less_int W) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_int Z) tptp.one_one_int) (= Z tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_real Z) tptp.one_one_real) (= Z tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_17405671764205052669omplex Z) tptp.one_one_complex) (= Z tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (= (@ tptp.ring_1_of_int_rat Z) tptp.one_one_rat) (= Z tptp.one_one_int))))
% 6.68/6.98 (assert (= (@ tptp.ring_1_of_int_int tptp.one_one_int) tptp.one_one_int))
% 6.68/6.98 (assert (= (@ tptp.ring_1_of_int_real tptp.one_one_int) tptp.one_one_real))
% 6.68/6.98 (assert (= (@ tptp.ring_17405671764205052669omplex tptp.one_one_int) tptp.one_one_complex))
% 6.68/6.98 (assert (= (@ tptp.ring_1_of_int_rat tptp.one_one_int) tptp.one_one_rat))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.times_times_int W) Z)) (@ (@ tptp.times_times_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int W) Z)) (@ (@ tptp.plus_plus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_complex (@ tptp.ring_17405671764205052669omplex W)) (@ tptp.ring_17405671764205052669omplex Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real W)) (@ tptp.ring_1_of_int_real Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat W)) (@ tptp.ring_1_of_int_rat Z)))))
% 6.68/6.98 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.minus_minus_int W) Z)) (@ (@ tptp.minus_minus_int (@ tptp.ring_1_of_int_int W)) (@ tptp.ring_1_of_int_int Z)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num M) N)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat X) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_real X) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_1_of_int_int X) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex X) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W)) (= X (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W) (@ tptp.ring_1_of_int_rat X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W) (@ tptp.ring_1_of_int_real X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W) (@ tptp.ring_1_of_int_int X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex B)) W) (@ tptp.ring_17405671764205052669omplex X)) (= (@ (@ tptp.power_power_int B) W) X))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_rat (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat Z)) N))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real Z)) N))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int Z)) N))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.nat)) (= (@ tptp.ring_17405671764205052669omplex (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_complex (@ tptp.ring_17405671764205052669omplex Z)) N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.times_times_num (@ tptp.bit1 M)))) (= (@ _let_1 (@ tptp.bit0 N)) (@ tptp.bit0 (@ _let_1 N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (= (@ (@ tptp.times_times_num (@ tptp.bit0 M)) _let_1) (@ tptp.bit0 (@ (@ tptp.times_times_num M) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (@ (@ tptp.ord_less_num tptp.one) (@ tptp.bit1 N))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (not (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) tptp.one))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit0 N)) (@ tptp.bit1 N))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num N) tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit0 M)) tptp.one) (@ tptp.bit1 M))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) tptp.one) (@ tptp.bit0 (@ (@ tptp.plus_plus_num M) tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.times_times_num (@ tptp.bit1 M)) (@ tptp.bit1 N)) (@ tptp.bit1 (@ (@ tptp.plus_plus_num (@ (@ tptp.plus_plus_num M) N)) (@ tptp.bit0 (@ (@ tptp.times_times_num M) N)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_num (@ tptp.bit0 M)) (@ tptp.bit1 N)) (@ (@ tptp.ord_less_eq_num M) N))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.ord_less_num M) N))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.zero_zero_real) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int Z) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_eq_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_eq_int Z) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real N)) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)) Z))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.numeral_numeral_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) (@ tptp.numeral_numeral_rat N)) (@ (@ tptp.ord_less_int Z) (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) _let_1) (@ (@ tptp.ord_less_int Z) _let_1)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_eq_int Z) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z)) tptp.one_one_real) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z)) tptp.one_one_rat) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int Z)) tptp.one_one_int) (@ (@ tptp.ord_less_int Z) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.ring_1_of_int_real Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ tptp.ring_1_of_int_rat Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.one_one_int))) (= (@ _let_1 (@ tptp.ring_1_of_int_int Z)) (@ _let_1 Z)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int N)) (@ tptp.unique6319869463603278526ux_int (@ (@ tptp.unique5052692396658037445od_int N) M)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat N)) (@ tptp.unique6322359934112328802ux_nat (@ (@ tptp.unique5055182867167087721od_nat N) M)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.unique5706413561485394159nteger (@ (@ tptp.unique3479559517661332726nteger N) M)))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int M) tptp.one) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int M)) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat M) tptp.one) (@ (@ tptp.product_Pair_nat_nat (@ tptp.numeral_numeral_nat M)) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger M) tptp.one) (@ (@ tptp.produc1086072967326762835nteger (@ tptp.numera6620942414471956472nteger M)) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_eq_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (B tptp.int) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ (@ tptp.ord_less_int X) (@ (@ tptp.power_power_int B) W)))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.ring_1_of_int_real B)) W)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.ring_1_of_int_rat B)) W)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.68/6.98 (assert (forall ((B tptp.int) (W tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.ring_1_of_int_int B)) W)) (@ tptp.ring_1_of_int_int X)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int B) W)) X))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit0 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.modulo_modulo_nat M))) (= (@ _let_1 (@ tptp.suc (@ tptp.suc (@ tptp.suc N)))) (@ _let_1 (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (V tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat V))) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) _let_1)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int tptp.one)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat tptp.one)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger tptp.one) (@ tptp.bit1 N)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger tptp.one)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.adjust_div (@ (@ tptp.unique5052692396658037445od_int M) N))))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_real Y) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= (@ tptp.ring_1_of_int_int Y) _let_1) (= Y _let_1)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_17405671764205052669omplex Y) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_18347121197199848620nteger Y) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.ring_1_of_int_rat Y) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N) (@ tptp.ring_1_of_int_real Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (= _let_1 (@ tptp.ring_1_of_int_int Y)) (= _let_1 Y)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex X))) N) (@ tptp.ring_17405671764205052669omplex Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N) (@ tptp.ring_18347121197199848620nteger Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N) (@ tptp.ring_1_of_int_rat Y)) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N) Y))))
% 6.68/6.98 (assert (forall ((V tptp.num) (W tptp.num)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 V))) (@ tptp.numeral_numeral_int (@ tptp.bit0 W))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int W)))) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit1 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5055182867167087721od_nat _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5026877609467782581ep_nat _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique5052692396658037445od_int _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique5024387138958732305ep_int _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.bit1 N))) (let ((_let_2 (@ tptp.bit0 M))) (let ((_let_3 (@ tptp.unique3479559517661332726nteger _let_2))) (let ((_let_4 (@ _let_3 _let_1))) (let ((_let_5 (@ (@ tptp.ord_less_eq_num M) N))) (and (=> _let_5 (= _let_4 (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger _let_2)))) (=> (not _let_5) (= _let_4 (@ (@ tptp.unique4921790084139445826nteger _let_1) (@ _let_3 (@ tptp.bit0 _let_1)))))))))))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_eq_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_eq_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N))) (= (@ (@ tptp.ord_less_int (@ tptp.ring_1_of_int_int A)) _let_1) (@ (@ tptp.ord_less_int A) _let_1)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real X))) N)) (@ tptp.ring_1_of_int_real A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int A)) (@ _let_1 A)))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_le6747313008572928689nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger X))) N)) (@ tptp.ring_18347121197199848620nteger A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.68/6.98 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat X))) N)) (@ tptp.ring_1_of_int_rat A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int X))) N)) A))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.complex)) (let ((_let_1 (@ tptp.ring_17405671764205052669omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.rat)) (let ((_let_1 (@ tptp.ring_1_of_int_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.68/6.98 (assert (forall ((X22 tptp.num) (X32 tptp.num)) (not (= (@ tptp.bit0 X22) (@ tptp.bit1 X32)))))
% 6.68/6.98 (assert (forall ((X32 tptp.num)) (not (= tptp.one (@ tptp.bit1 X32)))))
% 6.68/6.98 (assert (forall ((Y tptp.num)) (=> (not (= Y tptp.one)) (=> (forall ((X23 tptp.num)) (not (= Y (@ tptp.bit0 X23)))) (not (forall ((X33 tptp.num)) (not (= Y (@ tptp.bit1 X33)))))))))
% 6.68/6.98 (assert (forall ((X tptp.product_prod_num_num)) (=> (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one))) (=> (forall ((N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit0 N3))))) (=> (forall ((N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num tptp.one) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit0 N3))))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 M4)) (@ tptp.bit1 N3))))) (=> (forall ((M4 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) tptp.one)))) (=> (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit0 N3))))) (not (forall ((M4 tptp.num) (N3 tptp.num)) (not (= X (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 M4)) (@ tptp.bit1 N3))))))))))))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 N))) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 N))) _let_1))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat Q2))) (let ((_let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) _let_1)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int Q2))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) _let_1)))))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger Q2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_2) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_2)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) _let_1)))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real X)) _let_1) (@ tptp.uminus_uminus_real (@ (@ tptp.power_power_real X) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.int) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_int (@ tptp.uminus_uminus_int X)) _let_1) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int X) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.complex) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex X)) _let_1) (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.power_power_complex X) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.code_integer) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_8256067586552552935nteger (@ tptp.uminus1351360451143612070nteger X)) _let_1) (@ tptp.uminus1351360451143612070nteger (@ (@ tptp.power_8256067586552552935nteger X) _let_1))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 K)))) (= (@ (@ tptp.power_power_rat (@ tptp.uminus_uminus_rat X)) _let_1) (@ tptp.uminus_uminus_rat (@ (@ tptp.power_power_rat X) _let_1))))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X)))))
% 6.68/6.98 (assert (forall ((D tptp.int) (N tptp.int)) (=> (@ (@ tptp.dvd_dvd_int D) N) (= (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) D)) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real D))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex _let_1) _let_1)) tptp.one_one_complex)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real N))) (= (@ tptp.numeral_numeral_real (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real _let_1) _let_1)) tptp.one_one_real)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat N))) (= (@ tptp.numeral_numeral_rat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat _let_1) _let_1)) tptp.one_one_rat)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat _let_1) _let_1)) tptp.one_one_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ tptp.numeral_numeral_int (@ tptp.bit1 N)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int _let_1) _let_1)) tptp.one_one_int)))))
% 6.68/6.98 (assert (forall ((Z tptp.complex) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_complex Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex Z) _let_2)) _let_2))))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_real Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real Z) _let_2)) _let_2))))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_rat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat Z) _let_2)) _let_2))))))
% 6.68/6.98 (assert (forall ((Z tptp.nat) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_nat Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat Z) _let_2)) _let_2))))))
% 6.68/6.98 (assert (forall ((Z tptp.int) (W tptp.num)) (let ((_let_1 (@ tptp.power_power_int Z))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat W)))) (= (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 W))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int Z) _let_2)) _let_2))))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le3102999989581377725nteger tptp.one_one_Code_integer) X)))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X)))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) X)))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.one_one_int) X)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.ring_1_of_int_real Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.ring_1_of_int_rat Z)))))
% 6.68/6.98 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (@ _let_1 (@ tptp.ring_1_of_int_int Z))))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.code_integer)) (=> (@ (@ tptp.ord_le6747313008572928689nteger (@ tptp.abs_abs_Code_integer (@ tptp.ring_18347121197199848620nteger N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_le6747313008572928689nteger tptp.one_one_Code_integer) X)))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.ring_1_of_int_real N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_real tptp.one_one_real) X)))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.rat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ tptp.ring_1_of_int_rat N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_rat tptp.one_one_rat) X)))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int (@ tptp.ring_1_of_int_int N))) X) (or (= N tptp.zero_zero_int) (@ (@ tptp.ord_less_int tptp.one_one_int) X)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_real (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.ring_17405671764205052669omplex (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.ring_18347121197199848620nteger (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.ring_1_of_int_rat (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat N))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int N))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2))) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2))) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((N tptp.num) (Q2 tptp.num)) (not (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2))) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.98 (assert (forall ((A tptp.complex)) (= (@ (@ tptp.power_power_complex A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex A) A)) A))))
% 6.68/6.98 (assert (forall ((A tptp.real)) (= (@ (@ tptp.power_power_real A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real A) A)) A))))
% 6.68/6.98 (assert (forall ((A tptp.rat)) (= (@ (@ tptp.power_power_rat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_rat (@ (@ tptp.times_times_rat A) A)) A))))
% 6.68/6.98 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.power_power_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat A) A)) A))))
% 6.68/6.98 (assert (forall ((A tptp.int)) (= (@ (@ tptp.power_power_int A) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) A)) A))))
% 6.68/6.98 (assert (= (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one)) (@ tptp.suc (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.suc (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) N))))
% 6.68/6.98 (assert (= tptp.ord_less_eq_int (lambda ((N2 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real M3)) tptp.one_one_real)))))
% 6.68/6.98 (assert (= tptp.ord_less_int (lambda ((N2 tptp.int) (M3 tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real N2)) tptp.one_one_real)) (@ tptp.ring_1_of_int_real M3)))))
% 6.68/6.98 (assert (forall ((X tptp.int) (D tptp.int)) (let ((_let_1 (@ tptp.ring_1_of_int_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int X) D))) (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real (@ (@ tptp.modulo_modulo_int X) D))) _let_1))))))
% 6.68/6.98 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int N)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((Q2 tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 N))) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger N)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.numeral_numeral_nat M)) (@ tptp.numeral_numeral_nat Q2)) tptp.zero_zero_nat)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int tptp.one)) _let_1)) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.numeral_numeral_int Q2)) tptp.zero_zero_int)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (Q2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 Q2)))) (= (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 M))) _let_1) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger tptp.one)) _let_1)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.numera6620942414471956472nteger Q2)) tptp.zero_z3403309356797280102nteger)))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.divide_divide_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X))))))
% 6.68/6.98 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc (@ tptp.suc (@ tptp.suc M)))) N) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) M)) N))))
% 6.68/6.98 (assert (forall ((N tptp.int) (X tptp.int)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.ring_1_of_int_real N)) (@ tptp.ring_1_of_int_real X))) (@ tptp.ring_1_of_int_real (@ (@ tptp.divide_divide_int N) X)))) tptp.one_one_real)))
% 6.68/6.98 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.68/6.98 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N2))) (let ((_let_2 (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.divide_divide_int _let_2) _let_1)) (@ (@ tptp.modulo_modulo_int _let_2) _let_1)))))))
% 6.68/6.98 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.68/6.98 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.68/6.98 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.ring_18347121197199848620nteger K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K)))))
% 6.68/6.98 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ _let_1 K)))))
% 6.68/6.98 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ (@ tptp.modulo_modulo_nat M) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))))) (or (= _let_2 tptp.zero_zero_nat) (= _let_2 tptp.one_one_nat) (= _let_2 (@ tptp.numeral_numeral_nat _let_1)) (= _let_2 (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M3 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N2) (@ (@ tptp.member_nat N2) S2)))))))
% 6.68/6.98 (assert (forall ((K tptp.nat) (S2 tptp.set_nat)) (=> (forall ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K) M4) (exists ((N7 tptp.nat)) (and (@ (@ tptp.ord_less_nat M4) N7) (@ (@ tptp.member_nat N7) S2))))) (not (@ tptp.finite_finite_nat S2)))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_nat)) (= (not (@ tptp.finite_finite_nat S2)) (forall ((M3 tptp.nat)) (exists ((N2 tptp.nat)) (and (@ (@ tptp.ord_less_eq_nat M3) N2) (@ (@ tptp.member_nat N2) S2)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (=> (= (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 tptp.one))) (not (@ (@ tptp.dvd_dvd_nat _let_2) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) _let_2))))))))
% 6.68/6.98 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_num M3) N2)) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.unique5026877609467782581ep_nat N2) (@ (@ tptp.unique5055182867167087721od_nat M3) (@ tptp.bit0 N2)))))))
% 6.68/6.98 (assert (= tptp.unique5052692396658037445od_int (lambda ((M3 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_num M3) N2)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) (@ tptp.numeral_numeral_int M3))) (@ (@ tptp.unique5024387138958732305ep_int N2) (@ (@ tptp.unique5052692396658037445od_int M3) (@ tptp.bit0 N2)))))))
% 6.68/6.98 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N2 tptp.num)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_less_num M3) N2)) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.unique4921790084139445826nteger N2) (@ (@ tptp.unique3479559517661332726nteger M3) (@ tptp.bit0 N2)))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (exists ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z5)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (exists ((Z5 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z5)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z5) tptp.one_one_int)))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (exists ((X6 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real X6)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int X6) tptp.one_one_int))) (forall ((Y2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Y2)) X) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Y2) tptp.one_one_int)))) (= Y2 X6)))))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (exists ((X6 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat X6)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int X6) tptp.one_one_int))) (forall ((Y2 tptp.int)) (=> (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Y2)) X) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Y2) tptp.one_one_int)))) (= Y2 X6)))))))
% 6.68/6.98 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit1 tptp.one)))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one)))))
% 6.68/6.98 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.one_one_complex) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 tptp.one))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit1 tptp.one))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 tptp.one))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.one_one_complex) tptp.one_one_complex))
% 6.68/6.98 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.one_one_real) tptp.one_one_real))
% 6.68/6.98 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.one_one_rat) tptp.one_one_rat))
% 6.68/6.98 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.one_one_int) tptp.one_one_int))
% 6.68/6.98 (assert (= (@ tptp.pred_numeral tptp.one) tptp.zero_zero_nat))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (= (@ tptp.suc N) (@ tptp.numeral_numeral_nat K)) (= N (@ tptp.pred_numeral K)))))
% 6.68/6.98 (assert (forall ((K tptp.num) (N tptp.nat)) (= (= (@ tptp.numeral_numeral_nat K) (@ tptp.suc N)) (= (@ tptp.pred_numeral K) N))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu8557863876264182079omplex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.68/6.98 (assert (= (@ tptp.neg_nu8295874005876285629c_real tptp.zero_zero_real) tptp.one_one_real))
% 6.68/6.98 (assert (= (@ tptp.neg_nu5219082963157363817nc_rat tptp.zero_zero_rat) tptp.one_one_rat))
% 6.68/6.98 (assert (= (@ tptp.neg_nu5851722552734809277nc_int tptp.zero_zero_int) tptp.one_one_int))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (= (@ tptp.neg_nu8295874005876285629c_real _let_1) _let_1)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ tptp.neg_nu5851722552734809277nc_int _let_1) _let_1)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex))) (= (@ tptp.neg_nu8557863876264182079omplex _let_1) _let_1)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (@ tptp.neg_nu5831290666863070958nteger _let_1) _let_1)))
% 6.68/6.98 (assert (let ((_let_1 (@ tptp.uminus_uminus_rat tptp.one_one_rat))) (= (@ tptp.neg_nu5219082963157363817nc_rat _let_1) _let_1)))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit1 K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bit1 K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bit1 K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_nat N) (@ tptp.pred_numeral K)))))
% 6.68/6.98 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_nat (@ tptp.pred_numeral K)) N))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit1 K)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K)))))
% 6.68/6.98 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.pred_numeral K)) N))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.pred_numeral K)))))
% 6.68/6.98 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ (@ tptp.minus_minus_nat (@ tptp.pred_numeral K)) N))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.minus_minus_nat N) (@ tptp.pred_numeral K)))))
% 6.68/6.98 (assert (forall ((K tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_max_nat (@ tptp.numeral_numeral_nat K)) (@ tptp.suc N)) (@ tptp.suc (@ (@ tptp.ord_max_nat (@ tptp.pred_numeral K)) N)))))
% 6.68/6.98 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.ord_max_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat K)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) (@ tptp.pred_numeral K))))))
% 6.68/6.98 (assert (= (@ tptp.neg_nu6075765906172075777c_real tptp.zero_zero_real) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.68/6.98 (assert (= (@ tptp.neg_nu3811975205180677377ec_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int tptp.one_one_int)))
% 6.68/6.98 (assert (= (@ tptp.neg_nu6511756317524482435omplex tptp.zero_zero_complex) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.68/6.98 (assert (= (@ tptp.neg_nu7757733837767384882nteger tptp.zero_z3403309356797280102nteger) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)))
% 6.68/6.98 (assert (= (@ tptp.neg_nu3179335615603231917ec_rat tptp.zero_zero_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu8295874005876285629c_real _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu5851722552734809277nc_int _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu8557863876264182079omplex _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu7757733837767384882nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu5831290666863070958nteger _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu5219082963157363817nc_rat _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real K))) (= (@ tptp.neg_nu8295874005876285629c_real (@ tptp.uminus_uminus_real _let_1)) (@ tptp.uminus_uminus_real (@ tptp.neg_nu6075765906172075777c_real _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int K))) (= (@ tptp.neg_nu5851722552734809277nc_int (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.neg_nu3811975205180677377ec_int _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex K))) (= (@ tptp.neg_nu8557863876264182079omplex (@ tptp.uminus1482373934393186551omplex _let_1)) (@ tptp.uminus1482373934393186551omplex (@ tptp.neg_nu6511756317524482435omplex _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger K))) (= (@ tptp.neg_nu5831290666863070958nteger (@ tptp.uminus1351360451143612070nteger _let_1)) (@ tptp.uminus1351360451143612070nteger (@ tptp.neg_nu7757733837767384882nteger _let_1))))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_rat K))) (= (@ tptp.neg_nu5219082963157363817nc_rat (@ tptp.uminus_uminus_rat _let_1)) (@ tptp.uminus_uminus_rat (@ tptp.neg_nu3179335615603231917ec_rat _let_1))))))
% 6.68/6.98 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_ri631733984087533419it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (= tptp.numeral_numeral_nat (lambda ((K2 tptp.num)) (@ tptp.suc (@ tptp.pred_numeral K2)))))
% 6.68/6.98 (assert (= tptp.pred_numeral (lambda ((K2 tptp.num)) (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat K2)) tptp.one_one_nat))))
% 6.68/6.98 (assert (= tptp.neg_nu8557863876264182079omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 6.68/6.98 (assert (= tptp.neg_nu8295874005876285629c_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 6.68/6.98 (assert (= tptp.neg_nu5219082963157363817nc_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.plus_plus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 6.68/6.98 (assert (= tptp.neg_nu5851722552734809277nc_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 6.68/6.98 (assert (= tptp.unique5055182867167087721od_nat (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N2))) (let ((_let_2 (@ tptp.numeral_numeral_nat M3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat _let_2) _let_1)) (@ (@ tptp.modulo_modulo_nat _let_2) _let_1)))))))
% 6.68/6.98 (assert (= tptp.neg_nu6511756317524482435omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex X3) X3)) tptp.one_one_complex))))
% 6.68/6.98 (assert (= tptp.neg_nu6075765906172075777c_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real X3) X3)) tptp.one_one_real))))
% 6.68/6.98 (assert (= tptp.neg_nu3179335615603231917ec_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.plus_plus_rat X3) X3)) tptp.one_one_rat))))
% 6.68/6.98 (assert (= tptp.neg_nu3811975205180677377ec_int (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.plus_plus_int X3) X3)) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((P (-> tptp.nat Bool))) (=> (not (@ P tptp.zero_zero_nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (exists ((N3 tptp.nat)) (and (not (@ P N3)) (@ P (@ tptp.suc N3))))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (exists ((Z5 tptp.int)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.ring_1_of_int_real Z5)))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (exists ((Z5 tptp.int)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.ring_1_of_int_rat Z5)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (exists ((Z5 tptp.int)) (@ (@ tptp.ord_less_real (@ tptp.ring_1_of_int_real Z5)) X))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (exists ((Z5 tptp.int)) (@ (@ tptp.ord_less_rat (@ tptp.ring_1_of_int_rat Z5)) X))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (exists ((Z5 tptp.int)) (@ (@ tptp.ord_less_real X) (@ tptp.ring_1_of_int_real Z5)))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (exists ((Z5 tptp.int)) (@ (@ tptp.ord_less_rat X) (@ tptp.ring_1_of_int_rat Z5)))))
% 6.68/6.98 (assert (forall ((X tptp.real) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_real Y))) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_real _let_2) (@ (@ tptp.plus_plus_real X) _let_1)) (= (@ tptp.archim8280529875227126926d_real X) Y)))))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ring_1_of_int_rat Y))) (=> (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) _let_1)) _let_2) (=> (@ (@ tptp.ord_less_eq_rat _let_2) (@ (@ tptp.plus_plus_rat X) _let_1)) (= (@ tptp.archim7778729529865785530nd_rat X) Y)))))))
% 6.68/6.98 (assert (forall ((X tptp.real) (N tptp.int)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) (@ tptp.ring_1_of_int_real N)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim8280529875227126926d_real X) N))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (N tptp.int)) (=> (@ (@ tptp.ord_less_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat X) (@ tptp.ring_1_of_int_rat N)))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))) (= (@ tptp.archim7778729529865785530nd_rat X) N))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) X))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) X))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X)))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.minus_minus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X)))))
% 6.68/6.98 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real X))) (@ (@ tptp.plus_plus_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (forall ((X tptp.rat)) (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat X))) (@ (@ tptp.plus_plus_rat X) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (= (@ tptp.archim8280529875227126926d_real tptp.zero_zero_real) tptp.zero_zero_int))
% 6.68/6.98 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.zero_zero_rat) tptp.zero_zero_int))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.numeral_numeral_real N)) (@ tptp.numeral_numeral_int N))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.numeral_numeral_rat N)) (@ tptp.numeral_numeral_int N))))
% 6.68/6.98 (assert (= (@ tptp.archim8280529875227126926d_real tptp.one_one_real) tptp.one_one_int))
% 6.68/6.98 (assert (= (@ tptp.archim7778729529865785530nd_rat tptp.one_one_rat) tptp.one_one_int))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.archim8280529875227126926d_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.archim7778729529865785530nd_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))))
% 6.68/6.98 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_eq_rat X) Y) (@ (@ tptp.ord_less_eq_int (@ tptp.archim7778729529865785530nd_rat X)) (@ tptp.archim7778729529865785530nd_rat Y)))))
% 6.68/6.98 (assert (forall ((Z tptp.real) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_real Z))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real (@ tptp.archim8280529875227126926d_real Z))))) (@ tptp.abs_abs_real (@ _let_1 (@ tptp.ring_1_of_int_real M)))))))
% 6.68/6.98 (assert (forall ((Z tptp.rat) (M tptp.int)) (let ((_let_1 (@ tptp.minus_minus_rat Z))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat (@ tptp.archim7778729529865785530nd_rat Z))))) (@ tptp.abs_abs_rat (@ _let_1 (@ tptp.ring_1_of_int_rat M)))))))
% 6.68/6.98 (assert (forall ((M tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bitM M)) (@ tptp.bit0 tptp.one)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) tptp.one_one_int)) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_int)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_nat)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q5) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)) tptp.one_one_Code_integer)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.int) (N tptp.int)) (=> (@ (@ tptp.ord_less_eq_int M) N) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int M) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int N) (@ (@ tptp.plus_plus_int N) tptp.one_one_int))) (@ (@ tptp.times_times_int M) (@ (@ tptp.minus_minus_int M) tptp.one_one_int)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.68/6.98 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.68/6.98 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.68/6.98 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.nat_set_encode A2)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) A2))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.pred_numeral N)))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ tptp.pred_numeral N)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.bit_se2002935070580805687sk_nat N)) (@ _let_1 N)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((Uu3 tptp.int)) tptp.zero_zero_int)) A2) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((Uu3 tptp.complex)) tptp.zero_zero_complex)) A2) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((Uu3 tptp.nat)) tptp.zero_zero_nat)) A2) tptp.zero_zero_nat)))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((Uu3 tptp.nat)) tptp.zero_zero_real)) A2) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat A) B)) (@ (@ F A) B))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (A tptp.int) (B tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.68/6.98 (assert (forall ((G (-> tptp.nat tptp.complex))) (= (@ (@ tptp.groups2073611262835488442omplex G) tptp.bot_bot_set_nat) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((G (-> tptp.nat tptp.rat))) (= (@ (@ tptp.groups2906978787729119204at_rat G) tptp.bot_bot_set_nat) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((G (-> tptp.nat tptp.int))) (= (@ (@ tptp.groups3539618377306564664at_int G) tptp.bot_bot_set_nat) tptp.zero_zero_int)))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.complex))) (= (@ (@ tptp.groups3049146728041665814omplex G) tptp.bot_bot_set_int) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.real))) (= (@ (@ tptp.groups8778361861064173332t_real G) tptp.bot_bot_set_int) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.rat))) (= (@ (@ tptp.groups3906332499630173760nt_rat G) tptp.bot_bot_set_int) tptp.zero_zero_rat)))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.nat))) (= (@ (@ tptp.groups4541462559716669496nt_nat G) tptp.bot_bot_set_int) tptp.zero_zero_nat)))
% 6.68/6.98 (assert (forall ((G (-> tptp.real tptp.complex))) (= (@ (@ tptp.groups5754745047067104278omplex G) tptp.bot_bot_set_real) tptp.zero_zero_complex)))
% 6.68/6.98 (assert (forall ((G (-> tptp.real tptp.real))) (= (@ (@ tptp.groups8097168146408367636l_real G) tptp.bot_bot_set_real) tptp.zero_zero_real)))
% 6.68/6.98 (assert (forall ((G (-> tptp.real tptp.rat))) (= (@ (@ tptp.groups1300246762558778688al_rat G) tptp.bot_bot_set_real) tptp.zero_zero_rat)))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups3049146728041665814omplex G) A2) tptp.zero_zero_complex))))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5808333547571424918x_real G) A2) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ (@ tptp.groups2906978787729119204at_rat G) A2) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (=> (not (@ tptp.finite_finite_int A2)) (= (@ (@ tptp.groups3906332499630173760nt_rat G) A2) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5058264527183730370ex_rat G) A2) tptp.zero_zero_rat))))
% 6.68/6.98 (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))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (=> (not (@ tptp.finite3207457112153483333omplex A2)) (= (@ (@ tptp.groups5693394587270226106ex_nat G) A2) tptp.zero_zero_nat))))
% 6.68/6.98 (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))))
% 6.68/6.98 (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 ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) F3) (= (@ F X3) tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((F3 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex F3) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) F3) tptp.zero_zero_nat) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) F3) (= (@ F X3) tptp.zero_zero_nat)))))))
% 6.68/6.98 (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 ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) F3) (= (@ F X3) tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2002935070580805687sk_nat N) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (= (@ tptp.bit_se2000444600071755411sk_int N) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.68/6.98 (assert (= (@ tptp.bit_se2002935070580805687sk_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.68/6.98 (assert (= (@ tptp.bit_se2000444600071755411sk_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.68/6.98 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S2) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S2) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= A K2)) (@ B K2)) tptp.zero_zero_complex))) S2) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> 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)) (@ B K2)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> 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)) (@ B K2)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> 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)) (@ B K2)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= A K2)) (@ B K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= A K2)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.complex))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5754745047067104278omplex (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S2) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S2) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.complex))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3049146728041665814omplex (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_complex (= K2 A)) (@ B K2)) tptp.zero_zero_complex))) S2) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> 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)) (@ B K2)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> 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)) (@ B K2)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> 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)) (@ B K2)) tptp.zero_zero_real))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) tptp.zero_zero_real))) S2) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.member_real A) S2))) (=> (@ tptp.finite_finite_real S2) (and (=> _let_1 (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_nat) (A tptp.nat) (B (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.member_nat A) S2))) (=> (@ tptp.finite_finite_nat S2) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.member_int A) S2))) (=> (@ tptp.finite_finite_int S2) (and (=> _let_1 (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.member_complex A) S2))) (=> (@ tptp.finite3207457112153483333omplex S2) (and (=> _let_1 (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) (@ B A))) (=> (not _let_1) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) tptp.zero_zero_rat))) S2) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int (@ tptp.abs_abs_int (@ (@ tptp.groups4538972089207619220nt_int F) A2))) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))))
% 6.68/6.98 (assert (= (@ tptp.nat_set_encode tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6511756317524482435omplex (@ tptp.numera6690914467698888265omplex K)) (@ tptp.numera6690914467698888265omplex (@ tptp.bitM K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu6075765906172075777c_real (@ tptp.numeral_numeral_real K)) (@ tptp.numeral_numeral_real (@ tptp.bitM K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3179335615603231917ec_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat (@ tptp.bitM K)))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.neg_nu3811975205180677377ec_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int (@ tptp.bitM K)))))
% 6.68/6.98 (assert (= (@ tptp.bit_se2002935070580805687sk_nat (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat))
% 6.68/6.98 (assert (= (@ tptp.bit_se2000444600071755411sk_int (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_int))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ tptp.abs_abs_int (@ F I5)))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.abs_abs_real (@ F I5)))) A2))))
% 6.68/6.98 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.bit0 K)) (@ tptp.numeral_numeral_nat (@ tptp.bitM K)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5052692396658037445od_int (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.product_Pair_int_int Q5) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5052692396658037445od_int M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique5055182867167087721od_nat (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Q5) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique5055182867167087721od_nat M) N)))))
% 6.68/6.98 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.unique3479559517661332726nteger (@ tptp.bit0 M)) (@ tptp.bit0 N)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger Q5) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) R5)))) (@ (@ tptp.unique3479559517661332726nteger M) N)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.int))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (= (@ G X6) tptp.zero_zero_int))) (= (@ (@ tptp.groups4538972089207619220nt_int G) A2) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.complex))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (= (@ G X6) tptp.zero_zero_complex))) (= (@ (@ tptp.groups7754918857620584856omplex G) A2) tptp.zero_zero_complex))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (= (@ G X6) tptp.zero_zero_nat))) (= (@ (@ tptp.groups3542108847815614940at_nat G) A2) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.real))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (= (@ G X6) tptp.zero_zero_real))) (= (@ (@ tptp.groups6591440286371151544t_real G) A2) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((G (-> tptp.real tptp.complex)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups5754745047067104278omplex G) A2) tptp.zero_zero_complex)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2073611262835488442omplex G) A2) tptp.zero_zero_complex)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.complex)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3049146728041665814omplex G) A2) tptp.zero_zero_complex)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.zero_zero_complex)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.complex tptp.real)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5808333547571424918x_real G) A2) tptp.zero_zero_real)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.real tptp.real)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups8097168146408367636l_real G) A2) tptp.zero_zero_real)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.real)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups8778361861064173332t_real G) A2) tptp.zero_zero_real)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.zero_zero_real)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.complex tptp.rat)) (A2 tptp.set_complex)) (=> (not (= (@ (@ tptp.groups5058264527183730370ex_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) A2) (= (@ G A5) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.real tptp.rat)) (A2 tptp.set_real)) (=> (not (= (@ (@ tptp.groups1300246762558778688al_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) A2) (= (@ G A5) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.nat tptp.rat)) (A2 tptp.set_nat)) (=> (not (= (@ (@ tptp.groups2906978787729119204at_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) A2) (= (@ G A5) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.rat)) (A2 tptp.set_int)) (=> (not (= (@ (@ tptp.groups3906332499630173760nt_rat G) A2) tptp.zero_zero_rat)) (not (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) A2) (= (@ G A5) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2000444600071755411sk_int N))) (= (@ tptp.ring_1_of_int_int _let_1) _let_1))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc27273713700761075at_nat F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X1 tptp.nat) (X22 tptp.nat)) (= (@ (@ tptp.produc8739625826339149834_nat_o F) (@ (@ tptp.product_Pair_nat_nat X1) X22)) (@ (@ F X1) X22))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4245557441103728435nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int Bool)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (X1 tptp.int) (X22 tptp.int)) (= (@ (@ tptp.produc8211389475949308722nt_int F) (@ (@ tptp.product_Pair_int_int X1) X22)) (@ (@ F X1) X22))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.68/6.98 (assert (= (@ tptp.bitM tptp.one) tptp.one))
% 6.68/6.98 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) K5)) (@ (@ tptp.groups5058264527183730370ex_rat G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) K5)) (@ (@ tptp.groups1300246762558778688al_rat G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) K5)) (@ (@ tptp.groups2906978787729119204at_rat G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) K5)) (@ (@ tptp.groups3906332499630173760nt_rat G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) K5)) (@ (@ tptp.groups5693394587270226106ex_nat G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.nat)) (G (-> tptp.real tptp.nat))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) K5)) (@ (@ tptp.groups1935376822645274424al_nat G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) K5) (@ (@ tptp.ord_less_eq_nat (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) K5)) (@ (@ tptp.groups4541462559716669496nt_nat G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups5690904116761175830ex_int F) K5)) (@ (@ tptp.groups5690904116761175830ex_int G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_real) (F (-> tptp.real tptp.int)) (G (-> tptp.real tptp.int))) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups1932886352136224148al_int F) K5)) (@ (@ tptp.groups1932886352136224148al_int G) K5)))))
% 6.68/6.98 (assert (forall ((K5 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) K5) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) K5)) (@ (@ tptp.groups3539618377306564664at_int G) K5)))))
% 6.68/6.98 (assert (forall ((R tptp.int) (F (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.times_times_int R) (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int R) (@ F N2)))) A2))))
% 6.68/6.98 (assert (forall ((R tptp.complex) (F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.times_times_complex R) (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex R) (@ F N2)))) A2))))
% 6.68/6.98 (assert (forall ((R tptp.nat) (F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_nat R) (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat R) (@ F N2)))) A2))))
% 6.68/6.98 (assert (forall ((R tptp.real) (F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.times_times_real R) (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R) (@ F N2)))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (R tptp.int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) R) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((N2 tptp.int)) (@ (@ tptp.times_times_int (@ F N2)) R))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.times_times_complex (@ F N2)) R))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (R tptp.nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) R) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_nat (@ F N2)) R))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) R))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int)) (A2 tptp.set_int) (G (-> tptp.int tptp.int)) (B3 tptp.set_int)) (= (@ (@ tptp.times_times_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) B3)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.groups4538972089207619220nt_int (lambda ((J3 tptp.int)) (@ (@ tptp.times_times_int (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (G (-> tptp.complex tptp.complex)) (B3 tptp.set_complex)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) B3)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((I5 tptp.complex)) (@ (@ tptp.groups7754918857620584856omplex (lambda ((J3 tptp.complex)) (@ (@ tptp.times_times_complex (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) B3)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (G (-> tptp.nat tptp.real)) (B3 tptp.set_nat)) (= (@ (@ tptp.times_times_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) B3)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ G J3)))) B3))) A2))))
% 6.68/6.98 (assert (forall ((G (-> tptp.int tptp.int)) (H2 (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int (@ G X3)) (@ H2 X3)))) A2) (@ (@ tptp.plus_plus_int (@ (@ tptp.groups4538972089207619220nt_int G) A2)) (@ (@ tptp.groups4538972089207619220nt_int H2) A2)))))
% 6.68/6.98 (assert (forall ((G (-> tptp.complex tptp.complex)) (H2 (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.plus_plus_complex (@ G X3)) (@ H2 X3)))) A2) (@ (@ tptp.plus_plus_complex (@ (@ tptp.groups7754918857620584856omplex G) A2)) (@ (@ tptp.groups7754918857620584856omplex H2) A2)))))
% 6.68/6.98 (assert (forall ((G (-> tptp.nat tptp.nat)) (H2 (-> tptp.nat tptp.nat)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ G X3)) (@ H2 X3)))) A2) (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) A2)) (@ (@ tptp.groups3542108847815614940at_nat H2) A2)))))
% 6.68/6.98 (assert (forall ((G (-> tptp.nat tptp.real)) (H2 (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X3 tptp.nat)) (@ (@ tptp.plus_plus_real (@ G X3)) (@ H2 X3)))) A2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) A2)) (@ (@ tptp.groups6591440286371151544t_real H2) A2)))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int)) (A2 tptp.set_int)) (= (@ (@ tptp.groups4538972089207619220nt_int (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_int (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))
% 6.68/6.98 (assert (forall ((F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) (@ (@ tptp.minus_minus_complex (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups7754918857620584856omplex F) A2)) (@ (@ tptp.groups7754918857620584856omplex G) A2)))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((X3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) (@ (@ tptp.groups6591440286371151544t_real G) A2)))))
% 6.68/6.98 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex) (R tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.groups7754918857620584856omplex F) A2)) R) (@ (@ tptp.groups7754918857620584856omplex (lambda ((N2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ F N2)) R))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat) (R tptp.real)) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.groups6591440286371151544t_real F) A2)) R) (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real (@ F N2)) R))) A2))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int)) (A tptp.int) (A2 tptp.set_int)) (= (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int (lambda ((I5 tptp.int)) (@ (@ tptp.modulo_modulo_int (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) A))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat)) (A tptp.nat) (A2 tptp.set_nat)) (= (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.modulo_modulo_nat (@ F I5)) A))) A2)) A) (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) A))))
% 6.68/6.98 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc27273713700761075at_nat P) Z)) (not (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X6) Y5)) (not (@ Q (@ (@ P X6) Y5)))))))))
% 6.68/6.98 (assert (forall ((Q (-> (-> tptp.product_prod_nat_nat Bool) Bool)) (P (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (Z tptp.product_prod_nat_nat)) (=> (@ Q (@ (@ tptp.produc8739625826339149834_nat_o P) Z)) (not (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (= Z (@ (@ tptp.product_Pair_nat_nat X6) Y5)) (not (@ Q (@ (@ P X6) Y5)))))))))
% 6.68/6.98 (assert (forall ((Q (-> tptp.product_prod_int_int Bool)) (P (-> tptp.int tptp.int tptp.product_prod_int_int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4245557441103728435nt_int P) Z)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ Q (@ (@ P X6) Y5)))))))))
% 6.68/6.98 (assert (forall ((Q (-> Bool Bool)) (P (-> tptp.int tptp.int Bool)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc4947309494688390418_int_o P) Z)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ Q (@ (@ P X6) Y5)))))))))
% 6.68/6.98 (assert (forall ((Q (-> tptp.int Bool)) (P (-> tptp.int tptp.int tptp.int)) (Z tptp.product_prod_int_int)) (=> (@ Q (@ (@ tptp.produc8211389475949308722nt_int P) Z)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= Z (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ Q (@ (@ P X6) Y5)))))))))
% 6.68/6.98 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (= (@ tptp.produc27273713700761075at_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X3) Y3)) __flatten_var_0))) F)))
% 6.68/6.98 (assert (forall ((F (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (= (@ tptp.produc8739625826339149834_nat_o (lambda ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ F (@ (@ tptp.product_Pair_nat_nat X3) Y3)) __flatten_var_0))) F)))
% 6.68/6.98 (assert (forall ((F (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (= (@ tptp.produc4245557441103728435nt_int (lambda ((X3 tptp.int) (Y3 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X3) Y3)))) F)))
% 6.68/6.98 (assert (forall ((F (-> tptp.product_prod_int_int Bool))) (= (@ tptp.produc4947309494688390418_int_o (lambda ((X3 tptp.int) (Y3 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X3) Y3)))) F)))
% 6.68/6.98 (assert (forall ((F (-> tptp.product_prod_int_int tptp.int))) (= (@ tptp.produc8211389475949308722nt_int (lambda ((X3 tptp.int) (Y3 tptp.int)) (@ F (@ (@ tptp.product_Pair_int_int X3) Y3)))) F)))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat tptp.product_prod_nat_nat))) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X6) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X6) Y5)))) (= (@ tptp.produc27273713700761075at_nat F) G))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (G (-> tptp.product_prod_nat_nat tptp.product_prod_nat_nat Bool))) (=> (forall ((X6 tptp.nat) (Y5 tptp.nat)) (= (@ (@ F X6) Y5) (@ G (@ (@ tptp.product_Pair_nat_nat X6) Y5)))) (= (@ tptp.produc8739625826339149834_nat_o F) G))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int tptp.product_prod_int_int)) (G (-> tptp.product_prod_int_int tptp.product_prod_int_int))) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (= (@ (@ F X6) Y5) (@ G (@ (@ tptp.product_Pair_int_int X6) Y5)))) (= (@ tptp.produc4245557441103728435nt_int F) G))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int Bool)) (G (-> tptp.product_prod_int_int Bool))) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (= (@ (@ F X6) Y5) (@ G (@ (@ tptp.product_Pair_int_int X6) Y5)))) (= (@ tptp.produc4947309494688390418_int_o F) G))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.int tptp.int)) (G (-> tptp.product_prod_int_int tptp.int))) (=> (forall ((X6 tptp.int) (Y5 tptp.int)) (= (@ (@ F X6) Y5) (@ G (@ (@ tptp.product_Pair_int_int X6) Y5)))) (= (@ tptp.produc8211389475949308722nt_int F) G))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_real (@ F X6)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_real (@ F X6)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_real (@ F X6)) tptp.zero_zero_real))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) tptp.zero_zero_real))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_rat (@ F X6)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_rat (@ F X6)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_rat (@ F X6)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_rat (@ F X6)) tptp.zero_zero_rat))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) tptp.zero_zero_rat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_nat (@ F X6)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_nat (@ F X6)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_nat (@ F X6)) tptp.zero_zero_nat))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))
% 6.68/6.98 (assert (forall ((F (-> tptp.real tptp.rat)) (I6 tptp.set_real) (G (-> tptp.real tptp.rat)) (I tptp.real)) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) I6) (@ (@ tptp.groups1300246762558778688al_rat G) I6)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_real I) I6) (=> (@ tptp.finite_finite_real I6) (= (@ F I) (@ G I))))))))
% 6.68/6.98 (assert (forall ((F (-> tptp.nat tptp.rat)) (I6 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) I6) (@ (@ tptp.groups2906978787729119204at_rat G) I6)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_nat I) I6) (=> (@ tptp.finite_finite_nat I6) (= (@ F I) (@ G I))))))))
% 6.68/6.98 (assert (forall ((F (-> tptp.int tptp.rat)) (I6 tptp.set_int) (G (-> tptp.int tptp.rat)) (I tptp.int)) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) I6) (@ (@ tptp.groups3906332499630173760nt_rat G) I6)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_int I) I6) (=> (@ tptp.finite_finite_int I6) (= (@ F I) (@ G I))))))))
% 6.68/6.98 (assert (forall ((F (-> tptp.complex tptp.rat)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) I6) (@ (@ tptp.groups5058264527183730370ex_rat G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_rat (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I) (@ G I))))))))
% 6.68/6.98 (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))))))))
% 6.68/6.98 (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))))))))
% 6.68/6.98 (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))))))))
% 6.68/6.98 (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))))))))
% 6.68/6.98 (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))))))))
% 6.68/6.98 (assert (forall ((F (-> tptp.complex tptp.int)) (I6 tptp.set_complex) (G (-> tptp.complex tptp.int)) (I tptp.complex)) (=> (= (@ (@ tptp.groups5690904116761175830ex_int F) I6) (@ (@ tptp.groups5690904116761175830ex_int G) I6)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_int (@ F I4)) (@ G I4)))) (=> (@ (@ tptp.member_complex I) I6) (=> (@ tptp.finite3207457112153483333omplex I6) (= (@ F I) (@ G I))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.complex)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups5754745047067104278omplex G) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ P X3))))) (@ (@ tptp.groups5754745047067104278omplex (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups2073611262835488442omplex G) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) (@ (@ tptp.groups2073611262835488442omplex (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups3049146728041665814omplex G) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) (@ (@ tptp.groups3049146728041665814omplex (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_complex (@ P X3)) (@ G X3)) tptp.zero_zero_complex))) A2)))))
% 6.68/6.98 (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 ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ P X3))))) (@ (@ tptp.groups8097168146408367636l_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A2)))))
% 6.68/6.98 (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 ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) (@ (@ tptp.groups8778361861064173332t_real (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A2)))))
% 6.68/6.98 (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 ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_real (@ P X3)) (@ G X3)) tptp.zero_zero_real))) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat)) (P (-> tptp.real Bool))) (=> (@ tptp.finite_finite_real A2) (= (@ (@ tptp.groups1300246762558778688al_rat G) (@ tptp.collect_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.member_real X3) A2) (@ P X3))))) (@ (@ tptp.groups1300246762558778688al_rat (lambda ((X3 tptp.real)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G X3)) tptp.zero_zero_rat))) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat)) (P (-> tptp.nat Bool))) (=> (@ tptp.finite_finite_nat A2) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (@ P X3))))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((X3 tptp.nat)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G X3)) tptp.zero_zero_rat))) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat)) (P (-> tptp.int Bool))) (=> (@ tptp.finite_finite_int A2) (= (@ (@ tptp.groups3906332499630173760nt_rat G) (@ tptp.collect_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (@ P X3))))) (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((X3 tptp.int)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G X3)) tptp.zero_zero_rat))) A2)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (P (-> tptp.complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ (@ tptp.groups5058264527183730370ex_rat G) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (@ P X3))))) (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((X3 tptp.complex)) (@ (@ (@ tptp.if_rat (@ P X3)) (@ G X3)) tptp.zero_zero_rat))) A2)))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.bit_se2000444600071755411sk_int N)) tptp.zero_zero_int))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.bit0 N)) (@ tptp.bit1 (@ tptp.bitM N)))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (= (= (@ (@ tptp.groups8097168146408367636l_real F) A2) tptp.zero_zero_real) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (= (@ F X3) tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (= (= (@ (@ tptp.groups8778361861064173332t_real F) A2) tptp.zero_zero_real) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (= (= (@ (@ tptp.groups5808333547571424918x_real F) A2) tptp.zero_zero_real) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_real))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (= (= (@ (@ tptp.groups1300246762558778688al_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (= (= (@ (@ tptp.groups2906978787729119204at_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (= (= (@ (@ tptp.groups3906332499630173760nt_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (= (= (@ (@ tptp.groups5058264527183730370ex_rat F) A2) tptp.zero_zero_rat) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_rat))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real A2) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (= (= (@ (@ tptp.groups1935376822645274424al_nat F) A2) tptp.zero_zero_nat) (forall ((X3 tptp.real)) (=> (@ (@ tptp.member_real X3) A2) (= (@ F X3) tptp.zero_zero_nat))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (= (= (@ (@ tptp.groups4541462559716669496nt_nat F) A2) tptp.zero_zero_nat) (forall ((X3 tptp.int)) (=> (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.zero_zero_nat))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.zero_zero_nat) (forall ((X3 tptp.complex)) (=> (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.zero_zero_nat))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X6)))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X6)))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups8778361861064173332t_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_complex) (T tptp.set_int) (G (-> tptp.int tptp.real)) (I (-> tptp.int tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X6)))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups8778361861064173332t_real G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_complex) (T tptp.set_complex) (G (-> tptp.complex tptp.real)) (I (-> tptp.complex tptp.complex)) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) T) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G X6)))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups5808333547571424918x_real F) S)) (@ (@ tptp.groups5808333547571424918x_real G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_nat) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X6)))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_nat) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X6)))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_nat) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.nat)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X6)))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) S)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (T tptp.set_nat) (G (-> tptp.nat tptp.rat)) (I (-> tptp.nat tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_nat T) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X6)))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S) (exists ((Xa tptp.nat)) (and (@ (@ tptp.member_nat Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S)) (@ (@ tptp.groups2906978787729119204at_rat G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (T tptp.set_int) (G (-> tptp.int tptp.rat)) (I (-> tptp.int tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite_finite_int T) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X6)))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S) (exists ((Xa tptp.int)) (and (@ (@ tptp.member_int Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S)) (@ (@ tptp.groups3906332499630173760nt_rat G) T))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (T tptp.set_complex) (G (-> tptp.complex tptp.rat)) (I (-> tptp.complex tptp.int)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S) (=> (@ tptp.finite3207457112153483333omplex T) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) T) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ G X6)))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S) (exists ((Xa tptp.complex)) (and (@ (@ tptp.member_complex Xa) T) (= (@ I Xa) X6) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G Xa)))))) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups3906332499630173760nt_rat F) S)) (@ (@ tptp.groups5058264527183730370ex_rat G) T))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_real (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_real (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_rat (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_rat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_nat (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_nat (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ tptp.finite_finite_nat A2) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) A2) (@ (@ tptp.ord_less_int (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups3539618377306564664at_int F) A2)) (@ (@ tptp.groups3539618377306564664at_int G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.int)) (G (-> tptp.complex tptp.int))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) A2) (@ (@ tptp.ord_less_int (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups5690904116761175830ex_int F) A2)) (@ (@ tptp.groups5690904116761175830ex_int G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.int)) (G (-> tptp.int tptp.int))) (=> (@ tptp.finite_finite_int A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_int (@ F X6)) (@ G X6)))) (=> (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) A2) (@ (@ tptp.ord_less_int (@ F X4)) (@ G X4)))) (@ (@ tptp.ord_less_int (@ (@ tptp.groups4538972089207619220nt_int F) A2)) (@ (@ tptp.groups4538972089207619220nt_int G) A2)))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ (@ R4 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups2073611262835488442omplex H2) S2)) (@ (@ tptp.groups2073611262835488442omplex G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.complex tptp.complex Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.complex))) (=> (@ (@ R4 tptp.zero_zero_complex) tptp.zero_zero_complex) (=> (forall ((X15 tptp.complex) (Y15 tptp.complex) (X23 tptp.complex) (Y23 tptp.complex)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_complex X15) Y15)) (@ (@ tptp.plus_plus_complex X23) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups3049146728041665814omplex H2) S2)) (@ (@ tptp.groups3049146728041665814omplex G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.real tptp.real Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ (@ R4 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups8778361861064173332t_real H2) S2)) (@ (@ tptp.groups8778361861064173332t_real G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.real tptp.real Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.real)) (G (-> tptp.complex tptp.real))) (=> (@ (@ R4 tptp.zero_zero_real) tptp.zero_zero_real) (=> (forall ((X15 tptp.real) (Y15 tptp.real) (X23 tptp.real) (Y23 tptp.real)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_real X15) Y15)) (@ (@ tptp.plus_plus_real X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups5808333547571424918x_real H2) S2)) (@ (@ tptp.groups5808333547571424918x_real G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ (@ R4 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups2906978787729119204at_rat H2) S2)) (@ (@ tptp.groups2906978787729119204at_rat G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ (@ R4 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups3906332499630173760nt_rat H2) S2)) (@ (@ tptp.groups3906332499630173760nt_rat G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.rat tptp.rat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ (@ R4 tptp.zero_zero_rat) tptp.zero_zero_rat) (=> (forall ((X15 tptp.rat) (Y15 tptp.rat) (X23 tptp.rat) (Y23 tptp.rat)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_rat X15) Y15)) (@ (@ tptp.plus_plus_rat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups5058264527183730370ex_rat H2) S2)) (@ (@ tptp.groups5058264527183730370ex_rat G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_int) (H2 (-> tptp.int tptp.nat)) (G (-> tptp.int tptp.nat))) (=> (@ (@ R4 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite_finite_int S2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups4541462559716669496nt_nat H2) S2)) (@ (@ tptp.groups4541462559716669496nt_nat G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.nat tptp.nat Bool)) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.nat)) (G (-> tptp.complex tptp.nat))) (=> (@ (@ R4 tptp.zero_zero_nat) tptp.zero_zero_nat) (=> (forall ((X15 tptp.nat) (Y15 tptp.nat) (X23 tptp.nat) (Y23 tptp.nat)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_nat X15) Y15)) (@ (@ tptp.plus_plus_nat X23) Y23)))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups5693394587270226106ex_nat H2) S2)) (@ (@ tptp.groups5693394587270226106ex_nat G) S2))))))))
% 6.68/6.98 (assert (forall ((R4 (-> tptp.int tptp.int Bool)) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.int)) (G (-> tptp.nat tptp.int))) (=> (@ (@ R4 tptp.zero_zero_int) tptp.zero_zero_int) (=> (forall ((X15 tptp.int) (Y15 tptp.int) (X23 tptp.int) (Y23 tptp.int)) (=> (and (@ (@ R4 X15) X23) (@ (@ R4 Y15) Y23)) (@ (@ R4 (@ (@ tptp.plus_plus_int X15) Y15)) (@ (@ tptp.plus_plus_int X23) Y23)))) (=> (@ tptp.finite_finite_nat S2) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S2) (@ (@ R4 (@ H2 X6)) (@ G X6)))) (@ (@ R4 (@ (@ tptp.groups3539618377306564664at_int H2) S2)) (@ (@ tptp.groups3539618377306564664at_int G) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_real (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups5808333547571424918x_real F) A2)) (@ (@ tptp.groups5808333547571424918x_real G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.real)) (G (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_real (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8778361861064173332t_real F) A2)) (@ (@ tptp.groups8778361861064173332t_real G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_real (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups8097168146408367636l_real F) A2)) (@ (@ tptp.groups8097168146408367636l_real G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (= A2 tptp.bot_bot_set_complex)) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups5058264527183730370ex_rat F) A2)) (@ (@ tptp.groups5058264527183730370ex_rat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (F (-> tptp.nat tptp.rat)) (G (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat A2) (=> (not (= A2 tptp.bot_bot_set_nat)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups2906978787729119204at_rat F) A2)) (@ (@ tptp.groups2906978787729119204at_rat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (F (-> tptp.int tptp.rat)) (G (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int A2) (=> (not (= A2 tptp.bot_bot_set_int)) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups3906332499630173760nt_rat F) A2)) (@ (@ tptp.groups3906332499630173760nt_rat G) A2)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real A2) (=> (not (= A2 tptp.bot_bot_set_real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_rat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_rat (@ (@ tptp.groups1300246762558778688al_rat F) A2)) (@ (@ tptp.groups1300246762558778688al_rat G) A2)))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2)))))))
% 6.68/6.98 (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 ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2)))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_nat (@ F X6)) (@ G X6)))) (@ (@ tptp.ord_less_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2)))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_real) (T4 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.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_real) (T4 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.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups3049146728041665814omplex H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_int) (T4 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.complex)) (H2 (-> tptp.real tptp.complex))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S2 tptp.set_int) (I (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T3 tptp.set_int) (G (-> tptp.int tptp.complex)) (H2 (-> tptp.int tptp.complex))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups3049146728041665814omplex G) S2) (@ (@ tptp.groups3049146728041665814omplex H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_real) (T4 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.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_real) (T4 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.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8778361861064173332t_real H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_real) (T4 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.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_real S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real S2) S4)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T4)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (@ (@ tptp.member_real (@ I B5)) (@ (@ tptp.minus_minus_set_real S2) S4)))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_int) (T4 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.real)) (H2 (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_real T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_real (@ J A5)) (@ (@ tptp.minus_minus_set_real T3) T4)))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_int) (T4 tptp.set_int) (S2 tptp.set_int) (I (-> tptp.int tptp.int)) (J (-> tptp.int tptp.int)) (T3 tptp.set_int) (G (-> tptp.int tptp.real)) (H2 (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite_finite_int T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_int (@ J A5)) (@ (@ tptp.minus_minus_set_int T3) T4)))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) (@ (@ tptp.minus_minus_set_int T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.int)) (=> (@ (@ tptp.member_int B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S2) (@ (@ tptp.groups8778361861064173332t_real H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S4 tptp.set_int) (T4 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.real)) (H2 (-> tptp.complex tptp.real))) (=> (@ tptp.finite_finite_int S4) (=> (@ tptp.finite3207457112153483333omplex T4) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (= (@ I (@ J A5)) A5))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) (@ (@ tptp.minus_minus_set_int S2) S4)) (@ (@ tptp.member_complex (@ J A5)) (@ (@ tptp.minus_811609699411566653omplex T3) T4)))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (= (@ J (@ I B5)) B5))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex T3) T4)) (@ (@ tptp.member_int (@ I B5)) (@ (@ tptp.minus_minus_set_int S2) S4)))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S4) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) T4) (= (@ H2 B5) tptp.zero_zero_real))) (=> (forall ((A5 tptp.int)) (=> (@ (@ tptp.member_int A5) S2) (= (@ H2 (@ J A5)) (@ G A5)))) (= (@ (@ tptp.groups8778361861064173332t_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3)))))))))))))
% 6.68/6.98 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.real)) (B3 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) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.real)) (B3 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) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.real)) (B3 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) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_real (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (B3 tptp.rat) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (B3 tptp.rat) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) B3) (=> (@ (@ tptp.member_nat I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (B3 tptp.rat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (B3 tptp.rat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_rat (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.nat)) (B3 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) B3) (=> (@ (@ tptp.member_real I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.nat)) (B3 tptp.nat) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S) B3) (=> (@ (@ tptp.member_int I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.nat)) (B3 tptp.nat) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S) B3) (=> (@ (@ tptp.member_complex I) S) (@ (@ tptp.ord_less_eq_nat (@ F I)) B3)))))))
% 6.68/6.98 (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)))))))
% 6.68/6.98 (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)))))))
% 6.68/6.98 (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)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_real) (F (-> tptp.real tptp.rat)) (I tptp.real)) (=> (@ tptp.finite_finite_real S) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_real I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_nat) (F (-> tptp.nat tptp.rat)) (I tptp.nat)) (=> (@ tptp.finite_finite_nat S) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_nat I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.rat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups3906332499630173760nt_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.rat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat F) S) tptp.zero_zero_rat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_rat)))))))
% 6.68/6.98 (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)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_int) (F (-> tptp.int tptp.nat)) (I tptp.int)) (=> (@ tptp.finite_finite_int S) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups4541462559716669496nt_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_int I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((S tptp.set_complex) (F (-> tptp.complex tptp.nat)) (I tptp.complex)) (=> (@ tptp.finite3207457112153483333omplex S) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) S) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (=> (= (@ (@ tptp.groups5693394587270226106ex_nat F) S) tptp.zero_zero_nat) (=> (@ (@ tptp.member_complex I) S) (= (@ F I) tptp.zero_zero_nat)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.68/6.98 (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 ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.68/6.98 (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 ((X3 tptp.complex)) (= (@ G X3) tptp.zero_zero_real))))) (@ _let_1 A2))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ tptp.collect_int (lambda ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ tptp.collect_complex (lambda ((X3 tptp.complex)) (= (@ G X3) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.68/6.98 (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 ((X3 tptp.int)) (= (@ G X3) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.68/6.98 (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 ((X3 tptp.complex)) (= (@ G X3) tptp.zero_zero_nat))))) (@ _let_1 A2))))))
% 6.68/6.98 (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 ((X3 tptp.complex)) (= (@ G X3) tptp.zero_zero_int))))) (@ _let_1 A2))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (= (@ G X3) tptp.zero_zero_complex))))) (@ _let_1 A2))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (= (@ G X3) tptp.zero_zero_rat))))) (@ _let_1 A2))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.ord_less_nat N) (@ tptp.bit_se2002935070580805687sk_nat N)))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.bit0 N)) (@ tptp.suc (@ tptp.numeral_numeral_nat (@ tptp.bitM N))))))
% 6.68/6.98 (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)))))))))
% 6.68/6.98 (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)))))))))
% 6.68/6.98 (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)))))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_real) (I tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_real I6) (=> (@ (@ tptp.member_real I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups1300246762558778688al_rat F) I6)))))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_nat) (I tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_nat I6) (=> (@ (@ tptp.member_nat I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups2906978787729119204at_rat F) I6)))))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups3906332499630173760nt_rat F) I6)))))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.ord_less_rat tptp.zero_zero_rat))) (=> (@ 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_rat tptp.zero_zero_rat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5058264527183730370ex_rat F) I6)))))))))
% 6.68/6.98 (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)))))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_int) (I tptp.int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ tptp.finite_finite_int I6) (=> (@ (@ tptp.member_int I) I6) (=> (@ _let_1 (@ F I)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_complex) (I tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ 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_nat tptp.zero_zero_nat) (@ F I4)))) (@ _let_1 (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups5808333547571424918x_real F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8778361861064173332t_real F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F I4)))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.groups8097168146408367636l_real F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups5058264527183730370ex_rat F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat I6) (=> (not (= I6 tptp.bot_bot_set_nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups2906978787729119204at_rat F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups3906332499630173760nt_rat F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F I4)))) (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.groups1300246762558778688al_rat F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex I6) (=> (not (= I6 tptp.bot_bot_set_complex)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups5693394587270226106ex_nat F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ tptp.finite_finite_int I6) (=> (not (= I6 tptp.bot_bot_set_int)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups4541462559716669496nt_nat F) I6)))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ tptp.finite_finite_real I6) (=> (not (= I6 tptp.bot_bot_set_real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F I4)))) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.groups1935376822645274424al_nat F) I6)))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat)) (=> (not (@ tptp.finite_finite_nat A2)) (= (@ tptp.nat_set_encode A2) tptp.zero_zero_nat))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num (@ tptp.bitM N)) tptp.one) (@ tptp.bit0 N))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_num tptp.one) (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X6) tptp.zero_zero_complex))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5754745047067104278omplex G) T3) (@ (@ tptp.groups5754745047067104278omplex H2) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X6) tptp.zero_zero_real))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups8097168146408367636l_real G) T3) (@ (@ tptp.groups8097168146408367636l_real H2) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_real))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5808333547571424918x_real G) T3) (@ (@ tptp.groups5808333547571424918x_real H2) S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) T3) (@ (@ tptp.groups1300246762558778688al_rat H2) S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) T3) (@ (@ tptp.groups5058264527183730370ex_rat H2) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X6) tptp.zero_zero_nat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) T3) (@ (@ tptp.groups1935376822645274424al_nat H2) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_nat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) T3) (@ (@ tptp.groups5693394587270226106ex_nat H2) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ G X6) tptp.zero_zero_int))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups1932886352136224148al_int G) T3) (@ (@ tptp.groups1932886352136224148al_int H2) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_int))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) T3) (@ (@ tptp.groups5690904116761175830ex_int H2) S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X6) tptp.zero_zero_complex))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups2073611262835488442omplex G) T3) (@ (@ tptp.groups2073611262835488442omplex H2) S2))))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X6) tptp.zero_zero_complex))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5754745047067104278omplex G) S2) (@ (@ tptp.groups5754745047067104278omplex H2) T3))))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X6) tptp.zero_zero_real))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups8097168146408367636l_real G) S2) (@ (@ tptp.groups8097168146408367636l_real H2) T3))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X6) tptp.zero_zero_real))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5808333547571424918x_real G) S2) (@ (@ tptp.groups5808333547571424918x_real H2) T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_real) (S2 tptp.set_real) (H2 (-> tptp.real tptp.rat)) (G (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real T3) (=> (@ (@ tptp.ord_less_eq_set_real S2) T3) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X6) tptp.zero_zero_rat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups1300246762558778688al_rat G) S2) (@ (@ tptp.groups1300246762558778688al_rat H2) T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (H2 (-> tptp.complex tptp.rat)) (G (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X6) tptp.zero_zero_rat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5058264527183730370ex_rat G) S2) (@ (@ tptp.groups5058264527183730370ex_rat H2) T3))))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X6) tptp.zero_zero_nat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups1935376822645274424al_nat G) S2) (@ (@ tptp.groups1935376822645274424al_nat H2) T3))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X6) tptp.zero_zero_nat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5693394587270226106ex_nat G) S2) (@ (@ tptp.groups5693394587270226106ex_nat H2) T3))))))))
% 6.68/6.98 (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 ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real T3) S2)) (= (@ H2 X6) tptp.zero_zero_int))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups1932886352136224148al_int G) S2) (@ (@ tptp.groups1932886352136224148al_int H2) T3))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ H2 X6) tptp.zero_zero_int))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups5690904116761175830ex_int G) S2) (@ (@ tptp.groups5690904116761175830ex_int H2) T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (H2 (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.complex))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ H2 X6) tptp.zero_zero_complex))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S2) (= (@ G X6) (@ H2 X6)))) (= (@ (@ tptp.groups2073611262835488442omplex G) S2) (@ (@ tptp.groups2073611262835488442omplex H2) T3))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_nat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X6) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (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 ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X6) tptp.zero_zero_int))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X6) tptp.zero_zero_complex))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X6) tptp.zero_zero_real))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (= (@ _let_1 T3) (@ _let_1 S2))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_complex) (S2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex T3) (=> (@ (@ tptp.ord_le211207098394363844omplex S2) T3) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_nat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (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 ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex T3) S2)) (= (@ G X6) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X6) tptp.zero_zero_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_nat) (S2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat T3) (=> (@ (@ tptp.ord_less_eq_set_nat S2) T3) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (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 ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat T3) S2)) (= (@ G X6) tptp.zero_zero_int))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.complex))) (let ((_let_1 (@ tptp.groups3049146728041665814omplex G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X6) tptp.zero_zero_complex))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X6) tptp.zero_zero_real))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (assert (forall ((T3 tptp.set_int) (S2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int T3) (=> (@ (@ tptp.ord_less_eq_set_int S2) T3) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int T3) S2)) (= (@ G X6) tptp.zero_zero_rat))) (= (@ _let_1 S2) (@ _let_1 T3))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 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 B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 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 B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_int))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 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 B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_int))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_int))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex H2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C4) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) (@ (@ tptp.minus_minus_set_nat C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.nat)) (=> (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (=> (= (@ _let_2 C4) (@ _let_1 C4)) (= (@ _let_2 A2) (@ _let_1 B3))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 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 B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_real))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_real))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 tptp.set_real) (G (-> tptp.real tptp.rat)) (H2 (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat H2))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real C4) (=> (@ (@ tptp.ord_less_eq_set_real A2) C4) (=> (@ (@ tptp.ord_less_eq_set_real B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (H2 (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat H2))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex C4) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) C4) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_rat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_rat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 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 B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_nat))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_nat))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_real) (A2 tptp.set_real) (B3 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 B3) C4) (=> (forall ((A5 tptp.real)) (=> (@ (@ tptp.member_real A5) (@ (@ tptp.minus_minus_set_real C4) A2)) (= (@ G A5) tptp.zero_zero_int))) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real C4) B3)) (= (@ H2 B5) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_complex) (A2 tptp.set_complex) (B3 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 B3) C4) (=> (forall ((A5 tptp.complex)) (=> (@ (@ tptp.member_complex A5) (@ (@ tptp.minus_811609699411566653omplex C4) A2)) (= (@ G A5) tptp.zero_zero_int))) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex C4) B3)) (= (@ H2 B5) tptp.zero_zero_int))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((C4 tptp.set_nat) (A2 tptp.set_nat) (B3 tptp.set_nat) (G (-> tptp.nat tptp.complex)) (H2 (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.groups2073611262835488442omplex H2))) (let ((_let_2 (@ tptp.groups2073611262835488442omplex G))) (=> (@ tptp.finite_finite_nat C4) (=> (@ (@ tptp.ord_less_eq_set_nat A2) C4) (=> (@ (@ tptp.ord_less_eq_set_nat B3) C4) (=> (forall ((A5 tptp.nat)) (=> (@ (@ tptp.member_nat A5) (@ (@ tptp.minus_minus_set_nat C4) A2)) (= (@ G A5) tptp.zero_zero_complex))) (=> (forall ((B5 tptp.nat)) (=> (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat C4) B3)) (= (@ H2 B5) tptp.zero_zero_complex))) (= (= (@ _let_2 A2) (@ _let_1 B3)) (= (@ _let_2 C4) (@ _let_1 C4))))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 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 B3) A2) (=> (@ tptp.finite_finite_nat A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (G (-> tptp.int tptp.int))) (let ((_let_1 (@ tptp.groups4538972089207619220nt_int G))) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (=> (@ tptp.finite_finite_int A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat A2) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (B3 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 B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (B3 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 B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat F))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_int) (B3 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 B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (F (-> tptp.complex tptp.complex))) (let ((_let_1 (@ tptp.groups7754918857620584856omplex F))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_complex (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((A2 tptp.set_nat) (B3 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 B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F B5)))) (@ (@ tptp.ord_less_eq_real (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (forall ((B5 tptp.nat)) (=> (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B3) A2)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F B5)))) (@ (@ tptp.ord_less_eq_rat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F B5)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (forall ((B5 tptp.real)) (=> (@ (@ tptp.member_real B5) (@ (@ tptp.minus_minus_set_real B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (forall ((B5 tptp.complex)) (=> (@ (@ tptp.member_complex B5) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (forall ((B5 tptp.nat)) (=> (@ (@ tptp.member_nat B5) (@ (@ tptp.minus_minus_set_nat B3) A2)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F B5)))) (@ (@ tptp.ord_less_eq_int (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.bitM N)) (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 N))) tptp.one_one_complex))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.bitM N)) (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 N))) tptp.one_one_real))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.bitM N)) (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 N))) tptp.one_one_rat))))
% 6.68/6.98 (assert (forall ((N tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.bitM N)) (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))) tptp.one_one_int))))
% 6.68/6.98 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.numera6620942414471956472nteger (@ tptp.bitM W))))))
% 6.68/6.98 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_nat (@ tptp.bitM W))))))
% 6.68/6.98 (assert (forall ((W tptp.num)) (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.numeral_numeral_int (@ tptp.bitM W))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F B)) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) B3) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (@ (@ tptp.ord_less_real (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B3) A2)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ F B)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) B3) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (@ (@ tptp.ord_less_rat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F B)) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) B3) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (@ (@ tptp.ord_less_nat (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_real) (A2 tptp.set_real) (B tptp.real) (F (-> tptp.real tptp.int))) (let ((_let_1 (@ tptp.groups1932886352136224148al_int F))) (=> (@ tptp.finite_finite_real B3) (=> (@ (@ tptp.ord_less_eq_set_real A2) B3) (=> (@ (@ tptp.member_real B) (@ (@ tptp.minus_minus_set_real B3) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X6)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (B tptp.complex) (F (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex A2) B3) (=> (@ (@ tptp.member_complex B) (@ (@ tptp.minus_811609699411566653omplex B3) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X6)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (B tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat A2) B3) (=> (@ (@ tptp.member_nat B) (@ (@ tptp.minus_minus_set_nat B3) A2)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ F B)) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) B3) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ F X6)))) (@ (@ tptp.ord_less_int (@ _let_1 A2)) (@ _let_1 B3))))))))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (= (@ tptp.suc (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.98 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_nat (@ tptp.bit_se2002935070580805687sk_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.code_integer)) (A (-> tptp.complex tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups6621422865394947399nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups6621422865394947399nteger (lambda ((I5 tptp.complex)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.code_integer)) (A (-> tptp.real tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups7713935264441627589nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7713935264441627589nteger (lambda ((I5 tptp.real)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.98 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.code_integer)) (A (-> tptp.nat tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups7501900531339628137nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7501900531339628137nteger (lambda ((I5 tptp.nat)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.code_integer)) (A (-> tptp.int tptp.code_integer)) (B tptp.code_integer) (Delta tptp.code_integer)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) (@ X I4)))) (=> (= (@ (@ tptp.groups7873554091576472773nteger X) I6) tptp.one_one_Code_integer) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ A I4)) B))) Delta))) (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.abs_abs_Code_integer (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.groups7873554091576472773nteger (lambda ((I5 tptp.int)) (@ (@ tptp.times_3573771949741848930nteger (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.real)) (A (-> tptp.complex tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups5808333547571424918x_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.real)) (A (-> tptp.real tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8097168146408367636l_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8097168146408367636l_real (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((I6 tptp.set_int) (X (-> tptp.int tptp.real)) (A (-> tptp.int tptp.real)) (B tptp.real) (Delta tptp.real)) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X I4)))) (=> (= (@ (@ tptp.groups8778361861064173332t_real X) I6) tptp.one_one_real) (=> (forall ((I4 tptp.int)) (=> (@ (@ tptp.member_int I4) I6) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ tptp.groups8778361861064173332t_real (lambda ((I5 tptp.int)) (@ (@ tptp.times_times_real (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((I6 tptp.set_complex) (X (-> tptp.complex tptp.rat)) (A (-> tptp.complex tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I4)))) (=> (= (@ (@ tptp.groups5058264527183730370ex_rat X) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.complex)) (=> (@ (@ tptp.member_complex I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((I5 tptp.complex)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((I6 tptp.set_real) (X (-> tptp.real tptp.rat)) (A (-> tptp.real tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I4)))) (=> (= (@ (@ tptp.groups1300246762558778688al_rat X) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.real)) (=> (@ (@ tptp.member_real I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups1300246762558778688al_rat (lambda ((I5 tptp.real)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((I6 tptp.set_nat) (X (-> tptp.nat tptp.rat)) (A (-> tptp.nat tptp.rat)) (B tptp.rat) (Delta tptp.rat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ X I4)))) (=> (= (@ (@ tptp.groups2906978787729119204at_rat X) I6) tptp.one_one_rat) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.member_nat I4) I6) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ A I4)) B))) Delta))) (@ (@ tptp.ord_less_eq_rat (@ tptp.abs_abs_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ A I5)) (@ X I5)))) I6)) B))) Delta))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2119862282449309892nteger N)) (= N tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2002935070580805687sk_nat N)) (= N tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int N)) (= N tptp.zero_zero_nat))))
% 6.68/6.99 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.bit_se2000444600071755411sk_int (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))))
% 6.68/6.99 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 6.68/6.99 (assert (= tptp.bit_se2002935070580805687sk_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))
% 6.68/6.99 (assert (= tptp.bit_se2000444600071755411sk_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_int))))
% 6.68/6.99 (assert (= tptp.unique5026877609467782581ep_nat (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((Q5 tptp.nat) (R5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_nat L))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat _let_2) R5)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat R5) _let_2))) (@ (@ tptp.product_Pair_nat_nat _let_1) R5)))))) __flatten_var_0))))
% 6.68/6.99 (assert (= tptp.unique5024387138958732305ep_int (lambda ((L tptp.num) (__flatten_var_0 tptp.product_prod_int_int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numeral_numeral_int L))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_eq_int _let_2) R5)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.minus_minus_int R5) _let_2))) (@ (@ tptp.product_Pair_int_int _let_1) R5)))))) __flatten_var_0))))
% 6.68/6.99 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (or (= N2 tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat M3) N2))) (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) M3)) (@ (@ 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 M3) N2)) N2))))))
% 6.68/6.99 (assert (forall ((X32 tptp.num)) (= (@ tptp.size_num (@ tptp.bit1 X32)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X32)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_Code_integer (= N2 tptp.zero_zero_nat)) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide6298287555418463151nteger A3) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A3) _let_1)))))))
% 6.68/6.99 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_int A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A3) _let_1)))))))
% 6.68/6.99 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) (@ (@ tptp.divide_divide_nat A3) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A3) _let_1)))))))
% 6.68/6.99 (assert (forall ((X22 tptp.num)) (= (@ tptp.size_num (@ tptp.bit0 X22)) (@ (@ tptp.plus_plus_nat (@ tptp.size_num X22)) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (= tptp.tanh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X3)))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real tptp.one_one_real) _let_1)) (@ (@ tptp.plus_plus_real tptp.one_one_real) _let_1))))))
% 6.68/6.99 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 tptp.zero_zero_int) (= L tptp.zero_zero_int))) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= K2 _let_2)) L) (@ (@ (@ tptp.if_int (= L _let_2)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) A) A)))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) A) A)))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (let ((_let_2 (@ _let_1 B))) (= (@ _let_1 _let_2) _let_2)))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) B) _let_1))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B))) (= (@ (@ tptp.bit_se727722235901077358nd_nat _let_1) B) _let_1))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc8763457246119570046nteger) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc127349428274296955eger_o C) P5))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc1908205239877642774nteger) (C (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool))) (=> (forall ((A5 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc8603105652947943368nteger A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc6253627499356882019eger_o C) P5))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc2285326912895808259nt_int) (C (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (forall ((A5 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (=> (= P5 (@ (@ tptp.produc5700946648718959541nt_int A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc1573362020775583542_int_o C) P5))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc7773217078559923341nt_int) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool))) (=> (forall ((A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (=> (= P5 (@ (@ tptp.produc4305682042979456191nt_int A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc2558449545302689196_int_o C) P5))))
% 6.68/6.99 (assert (forall ((P5 tptp.product_prod_int_int) (C (-> tptp.int tptp.int Bool))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ C A5) B5))) (@ (@ tptp.produc4947309494688390418_int_o C) P5))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ F A) B) (@ (@ tptp.produc127349428274296955eger_o F) (@ (@ tptp.produc6137756002093451184nteger A) B)))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ F A) B) (@ (@ tptp.produc6253627499356882019eger_o F) (@ (@ tptp.produc8603105652947943368nteger A) B)))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ F A) B) (@ (@ tptp.produc1573362020775583542_int_o F) (@ (@ tptp.produc5700946648718959541nt_int A) B)))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ F A) B) (@ (@ tptp.produc2558449545302689196_int_o F) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ F A) B) (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.68/6.99 (assert (forall ((P5 tptp.product_prod_int_int) (Z tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc8580519160106071146omplex C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.product_prod_int_int) (Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc6452406959799940328t_real C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.product_prod_int_int) (Z tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4251311855443802252et_nat C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.product_prod_int_int) (Z tptp.int) (C (-> tptp.int tptp.int tptp.set_int))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ tptp.member_int Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc73460835934605544et_int C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.product_prod_int_int) (Z tptp.set_nat) (C (-> tptp.int tptp.int tptp.set_set_nat))) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int A5) B5)) (@ (@ tptp.member_set_nat Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_set_nat Z) (@ (@ tptp.produc5233655623923918146et_nat C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc8763457246119570046nteger) (Z tptp.complex) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex))) (=> (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2592262431452330817omplex C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc8763457246119570046nteger) (Z tptp.real) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real))) (=> (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (@ (@ tptp.member_real Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_real Z) (@ (@ tptp.produc815715089573277247t_real C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc8763457246119570046nteger) (Z tptp.nat) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat))) (=> (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (@ (@ tptp.member_nat Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_nat Z) (@ (@ tptp.produc3558942015123893603et_nat C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc8763457246119570046nteger) (Z tptp.int) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int))) (=> (forall ((A5 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger A5) B5)) (@ (@ tptp.member_int Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_int Z) (@ (@ tptp.produc8604463032469472703et_int C) P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.produc7773217078559923341nt_int) (Z tptp.complex) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_complex))) (=> (forall ((A5 (-> tptp.int tptp.option6357759511663192854e_term)) (B5 tptp.product_prod_int_int)) (=> (= P5 (@ (@ tptp.produc4305682042979456191nt_int A5) B5)) (@ (@ tptp.member_complex Z) (@ (@ C A5) B5)))) (@ (@ tptp.member_complex Z) (@ (@ tptp.produc7959293469001253456omplex C) P5)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8580519160106071146omplex C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc6452406959799940328t_real C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc4251311855443802252et_nat C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (C (-> tptp.int tptp.int tptp.set_int)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc73460835934605544et_int C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.set_nat) (C (-> tptp.int tptp.int tptp.set_set_nat)) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.member_set_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc5233655623923918146et_nat C) (@ (@ tptp.product_Pair_int_int A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc2592262431452330817omplex C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.real) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_real Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc815715089573277247t_real C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_nat Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc3558942015123893603et_nat C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (let ((_let_1 (@ tptp.member_int Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc8604463032469472703et_int C) (@ (@ tptp.produc6137756002093451184nteger A) B)))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_complex)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.member_complex Z))) (=> (@ _let_1 (@ (@ C A) B)) (@ _let_1 (@ (@ tptp.produc7959293469001253456omplex C) (@ (@ tptp.produc4305682042979456191nt_int A) B)))))))
% 6.68/6.99 (assert (forall ((P5 tptp.product_prod_nat_nat) (C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (X tptp.product_prod_nat_nat)) (=> (forall ((A5 tptp.nat) (B5 tptp.nat)) (=> (= (@ (@ tptp.product_Pair_nat_nat A5) B5) P5) (@ (@ (@ C A5) B5) X))) (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P5) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.zero_zero_nat) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) A) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.zero_zero_int) X) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) tptp.zero_zero_int) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 A)) (@ _let_1 B))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 A)) (@ _let_1 B))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) K) tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int tptp.zero_zero_nat) A) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat tptp.zero_zero_nat) A) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (= (@ tptp.exp_complex tptp.zero_zero_complex) tptp.one_one_complex))
% 6.68/6.99 (assert (= (@ tptp.exp_real tptp.zero_zero_real) tptp.one_one_real))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A) A)))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int tptp.one_one_int)) A) A)))
% 6.68/6.99 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) A)))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) (@ tptp.uminus_uminus_int tptp.one_one_int)) A)))
% 6.68/6.99 (assert (forall ((X tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger X) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) X)))
% 6.68/6.99 (assert (forall ((X tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int X) (@ tptp.uminus_uminus_int tptp.one_one_int)) X)))
% 6.68/6.99 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((L2 tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) tptp.one_one_nat) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real X) tptp.one_one_real) (= X tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) tptp.zero_zero_int) (and (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) tptp.zero_zero_int) (= N tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) tptp.zero_zero_nat) (= N tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) tptp.one_one_nat) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.exp_real X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.bit_se2119862282449309892nteger N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.exp_real (@ tptp.ln_ln_real X)) X) (@ (@ tptp.ord_less_real tptp.zero_zero_real) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) tptp.one_one_nat) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.complex))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2073611262835488442omplex G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_complex)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_complex (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_rat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_int)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_nat)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_4 (@ _let_3 (@ _let_2 _let_1)))) (let ((_let_5 (@ (@ tptp.ord_less_nat _let_1) M))) (and (=> _let_5 (= _let_4 tptp.zero_zero_real)) (=> (not _let_5) (= _let_4 (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1745604003318907178nteger N) tptp.one_one_Code_integer) (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) tptp.one_one_int) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) tptp.one_one_nat) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N)))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5)))) A2) tptp.zero_zero_complex))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5)))) A2) tptp.zero_zero_rat))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) (@ C tptp.zero_zero_nat))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5)))) A2) tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit0 Y))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se1745604003318907178nteger N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N) A)) (or (= N tptp.zero_zero_nat) (@ _let_1 A))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.complex)) (D (-> tptp.nat tptp.complex))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) (@ (@ tptp.divide1717551699836669952omplex (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ C I5)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) I5))) (@ D I5)))) A2) tptp.zero_zero_complex))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.rat)) (D (-> tptp.nat tptp.rat))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5))) (@ D I5)))) A2) (@ (@ tptp.divide_divide_rat (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ C I5)) (@ (@ tptp.power_power_rat tptp.zero_zero_rat) I5))) (@ D I5)))) A2) tptp.zero_zero_rat))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (C (-> tptp.nat tptp.real)) (D (-> tptp.nat tptp.real))) (let ((_let_1 (and (@ tptp.finite_finite_nat A2) (@ (@ tptp.member_nat tptp.zero_zero_nat) A2)))) (and (=> _let_1 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) (@ (@ tptp.divide_divide_real (@ C tptp.zero_zero_nat)) (@ D tptp.zero_zero_nat)))) (=> (not _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ C I5)) (@ (@ tptp.power_power_real tptp.zero_zero_real) I5))) (@ D I5)))) A2) tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc tptp.zero_zero_nat)) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 X))) (@ tptp.numeral_numeral_int (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int X)) (@ tptp.numeral_numeral_int Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat X)) (@ tptp.numeral_numeral_nat Y)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se1745604003318907178nteger M) _let_1) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2923211474154528505it_int M) _let_1) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se2925701944663578781it_nat M) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_nat N) M))) _let_1)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger _let_1))) (= (@ (@ tptp.bit_se1745604003318907178nteger N) _let_2) (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (= (@ (@ tptp.bit_se2923211474154528505it_int N) _let_2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat _let_1)) N))) _let_2))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) _let_1) (@ (@ tptp.times_times_nat (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.ord_less_eq_nat _let_1) N))) _let_1)))))
% 6.68/6.99 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int A3) (@ tptp.bit_se2000444600071755411sk_int N2)))))
% 6.68/6.99 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat A3) (@ tptp.bit_se2002935070580805687sk_nat N2)))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ tptp.ring_1_of_int_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int L2)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.ring_1_of_int_int K)) (@ tptp.ring_1_of_int_int (@ _let_1 K))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int B) C))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ _let_1 B)) C) (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat B) C))))))
% 6.68/6.99 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int B2) A3))))
% 6.68/6.99 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.bit_se727722235901077358nd_nat B2) A3))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.bit_se725231765392027082nd_int B))) (let ((_let_2 (@ tptp.bit_se725231765392027082nd_int A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (A tptp.nat) (C tptp.nat)) (let ((_let_1 (@ tptp.bit_se727722235901077358nd_nat B))) (let ((_let_2 (@ tptp.bit_se727722235901077358nd_nat A))) (= (@ _let_1 (@ _let_2 C)) (@ _let_2 (@ _let_1 C)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.plus_plus_int (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_int A) B))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ (@ tptp.plus_plus_nat (@ _let_1 A)) (@ _let_1 B))) (@ _let_1 (@ (@ tptp.plus_plus_nat A) B))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.nat) (B tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat M))) (let ((_let_2 (@ tptp.bit_se2925701944663578781it_nat N))) (=> (= (@ _let_2 A) (@ _let_2 B)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 A) (@ _let_1 B))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (Q2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat M) Q2)) (@ (@ tptp.bit_se2925701944663578781it_nat N) Q2)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M)))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (not (= (@ tptp.exp_complex X) tptp.zero_zero_complex))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (not (= (@ tptp.exp_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (C (-> tptp.int tptp.int tptp.set_complex)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc8580519160106071146omplex C) P5)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.real) (C (-> tptp.int tptp.int tptp.set_real)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc6452406959799940328t_real C) P5)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.nat) (C (-> tptp.int tptp.int tptp.set_nat)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc4251311855443802252et_nat C) P5)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (C (-> tptp.int tptp.int tptp.set_int)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc73460835934605544et_int C) P5)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.set_nat) (C (-> tptp.int tptp.int tptp.set_set_nat)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.member_set_nat Z) (@ (@ tptp.produc5233655623923918146et_nat C) P5)) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ (@ tptp.member_set_nat Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_complex)) (P5 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc2592262431452330817omplex C) P5)) (not (forall ((X6 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger X6) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.real) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_real)) (P5 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_real Z) (@ (@ tptp.produc815715089573277247t_real C) P5)) (not (forall ((X6 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger X6) Y5)) (not (@ (@ tptp.member_real Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.nat) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_nat)) (P5 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_nat Z) (@ (@ tptp.produc3558942015123893603et_nat C) P5)) (not (forall ((X6 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger X6) Y5)) (not (@ (@ tptp.member_nat Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger tptp.set_int)) (P5 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.member_int Z) (@ (@ tptp.produc8604463032469472703et_int C) P5)) (not (forall ((X6 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger X6) Y5)) (not (@ (@ tptp.member_int Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int tptp.set_complex)) (P5 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.member_complex Z) (@ (@ tptp.produc7959293469001253456omplex C) P5)) (not (forall ((X6 (-> tptp.int tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int)) (=> (= P5 (@ (@ tptp.produc4305682042979456191nt_int X6) Y5)) (not (@ (@ tptp.member_complex Z) (@ (@ C X6) Y5)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ _let_1 K))) (@ _let_1 (@ tptp.uminus_uminus_int K))))))
% 6.68/6.99 (assert (forall ((A2 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex A2))) (= (@ (@ tptp.times_times_complex _let_1) A2) (@ (@ tptp.times_times_complex A2) _let_1)))))
% 6.68/6.99 (assert (forall ((A2 tptp.real)) (let ((_let_1 (@ tptp.exp_real A2))) (= (@ (@ tptp.times_times_real _let_1) A2) (@ (@ tptp.times_times_real A2) _let_1)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.times_times_int K) L2))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ (@ tptp.minus_minus_int (@ _let_1 K)) (@ _let_1 L2))) (@ _let_1 (@ (@ tptp.minus_minus_int K) L2))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int) (L2 tptp.int) (R tptp.int) (S tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ tptp.bit_concat_bit N))) (= (= (@ (@ _let_2 K) L2) (@ (@ _let_2 R) S)) (and (= (@ _let_1 K) (@ _let_1 R)) (= L2 S)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (B tptp.int)) (let ((_let_1 (@ tptp.bit_concat_bit N))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) B)) (@ _let_1 B)))))
% 6.68/6.99 (assert (forall ((C (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (P5 tptp.produc8763457246119570046nteger)) (=> (@ (@ tptp.produc127349428274296955eger_o C) P5) (not (forall ((X6 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc6137756002093451184nteger X6) Y5)) (not (@ (@ C X6) Y5))))))))
% 6.68/6.99 (assert (forall ((C (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (P5 tptp.produc1908205239877642774nteger)) (=> (@ (@ tptp.produc6253627499356882019eger_o C) P5) (not (forall ((X6 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (Y5 tptp.produc8923325533196201883nteger)) (=> (= P5 (@ (@ tptp.produc8603105652947943368nteger X6) Y5)) (not (@ (@ C X6) Y5))))))))
% 6.68/6.99 (assert (forall ((C (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P5 tptp.produc2285326912895808259nt_int)) (=> (@ (@ tptp.produc1573362020775583542_int_o C) P5) (not (forall ((X6 (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int)) (=> (= P5 (@ (@ tptp.produc5700946648718959541nt_int X6) Y5)) (not (@ (@ C X6) Y5))))))))
% 6.68/6.99 (assert (forall ((C (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (P5 tptp.produc7773217078559923341nt_int)) (=> (@ (@ tptp.produc2558449545302689196_int_o C) P5) (not (forall ((X6 (-> tptp.int tptp.option6357759511663192854e_term)) (Y5 tptp.product_prod_int_int)) (=> (= P5 (@ (@ tptp.produc4305682042979456191nt_int X6) Y5)) (not (@ (@ C X6) Y5))))))))
% 6.68/6.99 (assert (forall ((C (-> tptp.int tptp.int Bool)) (P5 tptp.product_prod_int_int)) (=> (@ (@ tptp.produc4947309494688390418_int_o C) P5) (not (forall ((X6 tptp.int) (Y5 tptp.int)) (=> (= P5 (@ (@ tptp.product_Pair_int_int X6) Y5)) (not (@ (@ C X6) Y5))))))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.code_integer tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.code_integer tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ tptp.produc127349428274296955eger_o F) (@ (@ tptp.produc6137756002093451184nteger A) B)) (@ (@ F A) B))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term) tptp.produc8923325533196201883nteger Bool)) (A (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (B tptp.produc8923325533196201883nteger)) (=> (@ (@ tptp.produc6253627499356882019eger_o F) (@ (@ tptp.produc8603105652947943368nteger A) B)) (@ (@ F A) B))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.produc8551481072490612790e_term tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ tptp.produc1573362020775583542_int_o F) (@ (@ tptp.produc5700946648718959541nt_int A) B)) (@ (@ F A) B))))
% 6.68/6.99 (assert (forall ((F (-> (-> tptp.int tptp.option6357759511663192854e_term) tptp.product_prod_int_int Bool)) (A (-> tptp.int tptp.option6357759511663192854e_term)) (B tptp.product_prod_int_int)) (=> (@ (@ tptp.produc2558449545302689196_int_o F) (@ (@ tptp.produc4305682042979456191nt_int A) B)) (@ (@ F A) B))))
% 6.68/6.99 (assert (forall ((F (-> tptp.int tptp.int Bool)) (A tptp.int) (B tptp.int)) (=> (@ (@ tptp.produc4947309494688390418_int_o F) (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ F A) B))))
% 6.68/6.99 (assert (forall ((C (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (P5 tptp.product_prod_nat_nat) (Z tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o C) P5) Z) (not (forall ((X6 tptp.nat) (Y5 tptp.nat)) (=> (= P5 (@ (@ tptp.product_Pair_nat_nat X6) Y5)) (not (@ (@ (@ C X6) Y5) Z))))))))
% 6.68/6.99 (assert (forall ((R4 (-> tptp.nat tptp.nat tptp.product_prod_nat_nat Bool)) (A tptp.nat) (B tptp.nat) (C tptp.product_prod_nat_nat)) (=> (@ (@ (@ tptp.produc8739625826339149834_nat_o R4) (@ (@ tptp.product_Pair_nat_nat A) B)) C) (@ (@ (@ R4 A) B) C))))
% 6.68/6.99 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer))) (= (= (@ (@ tptp.bit_se3949692690581998587nteger A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (= (@ (@ tptp.bit_se725231765392027082nd_int A) B) _let_1) (and (= A _let_1) (= B _let_1))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X6 tptp.real)) (= (@ tptp.exp_real X6) Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.exp_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (not (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) tptp.zero_zero_real))))
% 6.68/6.99 (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 ((X6 tptp.nat)) (let ((_let_1 (@ tptp.suc X6))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.68/6.99 (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 ((X6 tptp.nat)) (let ((_let_1 (@ tptp.suc X6))) (=> (@ (@ tptp.member_nat _let_1) A2) (= (@ F _let_1) (@ G _let_1))))) (= (@ (@ tptp.groups6591440286371151544t_real F) A2) (@ (@ tptp.groups6591440286371151544t_real G) A2))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int M) K)) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_eq_int Y) Z) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Y))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) X))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int X) Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)))) (let ((_let_2 (@ tptp.bit_ri631733984087533419it_int N))) (= (= (@ _let_2 A) (@ _let_2 B)) (= (@ _let_1 A) (@ _let_1 B)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int N) K))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (not (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_int K))) (= (@ _let_1 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ _let_1 tptp.zero_zero_int)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_ri631733984087533419it_int M))) (let ((_let_2 (@ tptp.bit_se2923211474154528505it_int N))) (= (@ _let_1 (@ _let_2 A)) (@ (@ (@ (@ tptp.if_int_int (@ (@ tptp.ord_less_eq_nat N) M)) _let_2) _let_1) A))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)) (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)) (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ (@ tptp.times_times_complex X) Y) (@ (@ tptp.times_times_complex Y) X)) (= (@ tptp.exp_complex (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (= (@ (@ tptp.times_times_real X) Y) (@ (@ tptp.times_times_real Y) X)) (= (@ tptp.exp_real (@ (@ tptp.plus_plus_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real Y))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.exp_complex X)) (@ tptp.exp_complex Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.exp_real X)) (@ tptp.exp_real Y)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4203085406695923979it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se4205575877204974255it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7879613467334960850it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se7882103937844011126it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2159334234014336723it_int M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (let ((_let_2 (@ _let_1 A))) (let ((_let_3 (@ tptp.bit_se2161824704523386999it_nat M))) (let ((_let_4 (@ _let_1 (@ _let_3 A)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_nat N) M))) (and (=> _let_5 (= _let_4 _let_2)) (=> (not _let_5) (= _let_4 (@ _let_3 _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (F (-> tptp.complex tptp.nat))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) A2) (@ (@ tptp.ord_less_eq_nat (@ G X6)) (@ F X6)))) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((X3 tptp.complex)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups5693394587270226106ex_nat F) A2)) (@ (@ tptp.groups5693394587270226106ex_nat G) A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (F (-> tptp.real tptp.nat))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_nat (@ G X6)) (@ F X6)))) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat F) A2)) (@ (@ tptp.groups1935376822645274424al_nat G) A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_set_nat) (G (-> tptp.set_nat tptp.nat)) (F (-> tptp.set_nat tptp.nat))) (=> (forall ((X6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X6) A2) (@ (@ tptp.ord_less_eq_nat (@ G X6)) (@ F X6)))) (= (@ (@ tptp.groups8294997508430121362at_nat (lambda ((X3 tptp.set_nat)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups8294997508430121362at_nat F) A2)) (@ (@ tptp.groups8294997508430121362at_nat G) A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (F (-> tptp.int tptp.nat))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) A2) (@ (@ tptp.ord_less_eq_nat (@ G X6)) (@ F X6)))) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat F) A2)) (@ (@ tptp.groups4541462559716669496nt_nat G) A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (G (-> tptp.nat tptp.nat)) (F (-> tptp.nat tptp.nat))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_eq_nat (@ G X6)) (@ F X6)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ F X3)) (@ G X3)))) A2) (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat F) A2)) (@ (@ tptp.groups3542108847815614940at_nat G) A2))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (K tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat M) K)) (@ (@ tptp.plus_plus_nat N) K))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat I5) K)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.68/6.99 (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 ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (= (@ F X3) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) A2) (=> (not (= X3 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.68/6.99 (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 ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (= (@ F X3) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) A2) (=> (not (= X3 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.68/6.99 (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 ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (= (@ F X3) (@ tptp.suc tptp.zero_zero_nat)) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A2) (=> (not (= X3 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.nat)) (A2 tptp.set_nat) (N tptp.nat)) (=> (= (@ (@ tptp.groups3542108847815614940at_nat F) A2) (@ tptp.suc N)) (exists ((X6 tptp.nat)) (and (@ (@ tptp.member_nat X6) A2) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ F X6)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_real tptp.one_one_real) (@ tptp.exp_real X)))))
% 6.68/6.99 (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 ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) A2) (= (@ F X3) tptp.one_one_nat) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) A2) (=> (not (= X3 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (= (@ (@ tptp.groups5693394587270226106ex_nat F) A2) tptp.one_one_nat) (exists ((X3 tptp.complex)) (and (@ (@ tptp.member_complex X3) A2) (= (@ F X3) tptp.one_one_nat) (forall ((Y3 tptp.complex)) (=> (@ (@ tptp.member_complex Y3) A2) (=> (not (= X3 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.68/6.99 (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 ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) A2) (= (@ F X3) tptp.one_one_nat) (forall ((Y3 tptp.nat)) (=> (@ (@ tptp.member_nat Y3) A2) (=> (not (= X3 Y3)) (= (@ F Y3) tptp.zero_zero_nat))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int M))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ tptp.suc N)) (= (@ _let_1 (@ (@ tptp.bit_ri631733984087533419it_int N) A)) (@ _let_1 A))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) K))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (Z tptp.int) (Ya tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int Y) Ya)) Z)))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (Z tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (=> (@ (@ tptp.ord_less_int Y) Z) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) Z)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (= (= (@ _let_1 K) (@ tptp.bit_se2000444600071755411sk_int N)) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) tptp.zero_zero_int)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.times_times_real (@ tptp.exp_real X)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.times_times_complex (@ tptp.exp_complex X)) (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X))) tptp.one_one_complex)))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 tptp.zero_zero_int)) (= (@ _let_1 (@ (@ tptp.minus_minus_int K) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_complex (@ _let_1 M)) (@ (@ tptp.groups2073611262835488442omplex _let_1) I6))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_rat (@ _let_1 M)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) I6))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_int (@ _let_1 M)) (@ (@ tptp.groups3539618377306564664at_int _let_1) I6))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (M tptp.nat) (I6 tptp.set_nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.plus_plus_nat M) I5)))) I6) (@ (@ tptp.times_times_real (@ _let_1 M)) (@ (@ tptp.groups6591440286371151544t_real _let_1) I6))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups3542108847815614940at_nat G) _let_1) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I5)))) _let_1)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat N) M))) (= (@ (@ tptp.groups6591440286371151544t_real G) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat M) N)) I5)))) _let_1)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (C tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) C)))) tptp.zero_zero_complex))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.one_one_nat) N) (= (@ (@ tptp.groups7754918857620584856omplex (lambda ((X3 tptp.complex)) X3)) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) tptp.one_one_complex)))) tptp.zero_zero_complex))))
% 6.68/6.99 (assert (forall ((A tptp.code_integer) (B tptp.code_integer)) (let ((_let_1 (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se3949692690581998587nteger A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se727722235901077358nd_nat A) B)) (or (@ _let_1 A) (@ _let_1 B))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat F))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ (@ tptp.ord_le211207098394363844omplex B3) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat F))) (=> (@ tptp.finite_finite_int B3) (=> (@ (@ tptp.ord_less_eq_set_int B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (@ tptp.finite_finite_nat B3) (=> (@ (@ tptp.ord_less_eq_set_nat B3) A2) (= (@ _let_1 (@ (@ tptp.minus_minus_set_nat A2) B3)) (@ (@ tptp.minus_minus_nat (@ _let_1 A2)) (@ _let_1 B3))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ tptp.exp_real X)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.complex)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2073611262835488442omplex F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_complex) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.rat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_rat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.int)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_int) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.nat)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_nat) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real F))) (=> (= (@ F tptp.zero_zero_nat) tptp.zero_zero_real) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) K)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) K)))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) (or (@ _let_1 K) (@ _let_1 L2))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_rat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_int (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_nat (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_3 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_3 (@ _let_2 _let_1)) (@ (@ tptp.plus_plus_real (@ _let_3 (@ _let_2 N))) (@ G _let_1))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) Y) (exists ((X6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X6) (@ (@ tptp.ord_less_eq_real X6) (@ (@ tptp.minus_minus_real Y) tptp.one_one_real)) (= (@ tptp.exp_real X6) Y))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_rat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_int (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_nat (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.plus_plus_real (@ G M)) (@ _let_1 (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_rat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_int (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_nat (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_3 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_2 (@ _let_1 _let_3)) (@ (@ tptp.plus_plus_real (@ G _let_3)) (@ _let_2 (@ _let_1 N))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ tptp.ln_ln_real X)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real Y)) X)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real Y)) Y)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) X))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.groups2906978787729119204at_rat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G M)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.groups3539618377306564664at_int G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G M)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_nat (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G M)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real G) _let_1)) (@ G (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G M)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) _let_1)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_rat (@ F _let_1)) (@ F M)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_int (@ F _let_1)) (@ F M)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_1) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc I5))) (@ F I5)))) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.minus_minus_real (@ F _let_1)) (@ F M)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (= tptp.bit_se1745604003318907178nteger (lambda ((N2 tptp.nat) (A3 tptp.code_integer)) (@ (@ tptp.modulo364778990260209775nteger A3) (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (A3 tptp.int)) (@ (@ tptp.modulo_modulo_int A3) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (A3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat A3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger tptp.one_one_Code_integer) A) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) A) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat tptp.one_one_nat) A) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.code_integer)) (= (@ (@ tptp.bit_se3949692690581998587nteger A) tptp.one_one_Code_integer) (@ (@ tptp.modulo364778990260209775nteger A) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.bit_se725231765392027082nd_int A) tptp.one_one_int) (@ (@ tptp.modulo_modulo_int A) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat A) tptp.one_one_nat) (@ (@ tptp.modulo_modulo_nat A) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M) (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) M) M))))
% 6.68/6.99 (assert (= tptp.bit_se2925701944663578781it_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.rat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups2906978787729119204at_rat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_rat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.int)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3539618377306564664at_int G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.nat)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups3542108847815614940at_nat G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (G (-> tptp.nat tptp.real)) (P5 tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (let ((_let_2 (@ _let_1 P5))) (let ((_let_3 (@ _let_1 tptp.one_one_nat))) (let ((_let_4 (@ tptp.groups6591440286371151544t_real G))) (let ((_let_5 (@ tptp.set_or1269000886237332187st_nat M))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_3) (= (@ _let_4 (@ _let_5 _let_2)) (@ (@ tptp.plus_plus_real (@ _let_4 (@ _let_5 N))) (@ _let_4 (@ (@ tptp.set_or1269000886237332187st_nat _let_3) _let_2))))))))))))
% 6.68/6.99 (assert (= tptp.bit_se2923211474154528505it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.modulo_modulo_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (= tptp.nat_set_encode (@ tptp.groups3542108847815614940at_nat (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (= tptp.tanh_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.exp_real (@ tptp.uminus_uminus_real X3)))) (let ((_let_2 (@ tptp.exp_real X3))) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_2) _let_1)) (@ (@ tptp.plus_plus_real _let_2) _let_1)))))))
% 6.68/6.99 (assert (= tptp.tanh_complex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ tptp.exp_complex (@ tptp.uminus1482373934393186551omplex X3)))) (let ((_let_2 (@ tptp.exp_complex X3))) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex _let_2) _let_1)) (@ (@ tptp.plus_plus_complex _let_2) _let_1)))))))
% 6.68/6.99 (assert (= (@ tptp.size_num tptp.one) tptp.zero_zero_nat))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (= (= (@ (@ tptp.bit_se1745604003318907178nteger N) A) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.dvd_dvd_Code_integer (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) N)) A))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) A) tptp.zero_zero_int) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) A))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.nat)) (= (= (@ (@ tptp.bit_se2925701944663578781it_nat N) A) tptp.zero_zero_nat) (@ (@ tptp.dvd_dvd_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) A))))
% 6.68/6.99 (assert (= tptp.adjust_div (@ tptp.produc8211389475949308722nt_int (lambda ((Q5 tptp.int) (R5 tptp.int)) (@ (@ tptp.plus_plus_int Q5) (@ tptp.zero_n2684676970156552555ol_int (not (= R5 tptp.zero_zero_int))))))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit0 K))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 K))) (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) M)) M) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) M))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1))) _let_1)))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) K) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) K))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex _let_1)) Z)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.68/6.99 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) Z)) (@ (@ tptp.power_power_real (@ tptp.exp_real Z)) (@ tptp.numeral_numeral_nat _let_1))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.complex))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_complex (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_complex)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_rat)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_int (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_int)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_2 (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) (@ (@ tptp.minus_minus_real (@ F M)) (@ F (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))) (=> (not _let_2) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.plus_plus_nat K2) tptp.one_one_nat))))) _let_1) tptp.zero_zero_real)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_rat (@ F N)) (@ F M))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.int))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_int (@ F N)) (@ F M))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (F (-> tptp.nat tptp.real))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F K2)) (@ F (@ (@ tptp.minus_minus_nat K2) tptp.one_one_nat))))) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.minus_minus_real (@ F N)) (@ F M))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) K)))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K)))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.bit_se2923211474154528505it_int N))) (let ((_let_2 (@ _let_1 K))) (=> (not (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.plus_plus_int K) tptp.one_one_int)) (@ (@ tptp.plus_plus_int tptp.one_one_int) _let_2)))))))
% 6.68/6.99 (assert (= tptp.divmod_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.divide_divide_nat M3) N2)) (@ (@ tptp.modulo_modulo_nat M3) N2)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (= (@ (@ tptp.bit_se2923211474154528505it_int N) K) (@ tptp.bit_se2000444600071755411sk_int N)) (@ (@ tptp.dvd_dvd_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) tptp.one_one_int) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) tptp.one_one_nat) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.power_power_int X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int tptp.one_one_int) X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_int (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real tptp.one_one_real) X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N))) (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.rat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_rat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.int)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_int (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_nat (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ _let_1 M)) (@ tptp.suc (@ _let_1 N)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5))) (@ (@ tptp.plus_plus_real (@ G _let_1)) (@ G (@ tptp.suc _let_1)))))) (@ (@ tptp.set_or1269000886237332187st_nat M) N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se1745604003318907178nteger _let_1) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_Code_integer)))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) tptp.one_one_int)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se1745604003318907178nteger (@ tptp.suc N)) A) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.bit_se1745604003318907178nteger N) (@ (@ tptp.divide6298287555418463151nteger A) _let_1))) _let_1)) (@ (@ tptp.modulo364778990260209775nteger A) _let_1))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ (@ tptp.divide_divide_int A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_int A) _let_1))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.suc N)) A) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ (@ tptp.divide_divide_nat A) _let_1))) _let_1)) (@ (@ tptp.modulo_modulo_nat A) _let_1))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int _let_1) K) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.minus_minus_int K) _let_1)))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.plus_plus_int K) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.68/6.99 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N2)) (@ (@ tptp.plus_plus_int K2) _let_1))) _let_1)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.minus_minus_nat (@ _let_1 N)) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ tptp.collect_nat (lambda ((Q5 tptp.nat)) (@ (@ tptp.ord_less_nat Q5) N))))))))
% 6.68/6.99 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K2)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.68/6.99 (assert (forall ((A tptp.code_integer) (N tptp.nat)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se1745604003318907178nteger N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_Code_integer _let_1) A))) (=> (= (@ (@ tptp.divide6298287555418463151nteger A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_z3403309356797280102nteger)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_8373710615458151222nteger (@ (@ tptp.power_8256067586552552935nteger _let_1) N)) tptp.one_one_Code_integer))))))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2923211474154528505it_int N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_int _let_1) A))) (=> (= (@ (@ tptp.divide_divide_int A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_int)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int _let_1) N)) tptp.one_one_int))))))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.bit_se2925701944663578781it_nat N) A))) (let ((_let_3 (@ (@ tptp.dvd_dvd_nat _let_1) A))) (=> (= (@ (@ tptp.divide_divide_nat A) _let_1) A) (and (=> _let_3 (= _let_2 tptp.zero_zero_nat)) (=> (not _let_3) (= _let_2 (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat _let_1) N)) tptp.one_one_nat))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ tptp.suc N))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_int (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_int K))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat L2)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 K))) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.pred_numeral L2)) (@ tptp.numeral_numeral_nat K))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.exp_real X)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_1) X))))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (=> (@ (@ tptp.ord_less_eq_int K) _let_1) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int K)) (@ (@ tptp.minus_minus_int _let_1) K)))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat I5) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ tptp.suc N)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat N) D)))) _let_1)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.plus_plus_real tptp.one_one_real) X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ tptp.numeral_numeral_real _let_1)))) (@ tptp.exp_real X))))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 X)) (not (@ _let_2 Xa2)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_5 (and (@ (@ tptp.member_int X) _let_4) (@ (@ tptp.member_int Xa2) _let_4)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (and (=> _let_5 (= Y (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_5) (= Y (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_1)) (@ (@ tptp.divide_divide_int Xa2) _let_1)))))))))))))))
% 6.68/6.99 (assert (= tptp.bit_se725231765392027082nd_int (lambda ((K2 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 K2)) (not (@ _let_2 L)))))) (let ((_let_4 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (@ (@ (@ tptp.if_int (and (@ (@ tptp.member_int K2) _let_4) (@ (@ tptp.member_int L) _let_4))) (@ tptp.uminus_uminus_int _let_3)) (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K))))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (X tptp.complex)) (let ((_let_1 (@ tptp.power_power_complex X))) (let ((_let_2 (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X tptp.one_one_complex))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_complex)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_complex tptp.one_one_complex) X)))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (X tptp.rat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X tptp.one_one_rat))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_rat)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_rat tptp.one_one_rat) X)))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))) (let ((_let_3 (= X tptp.one_one_real))) (let ((_let_4 (@ (@ tptp.ord_less_nat N) M))) (and (=> _let_4 (= _let_2 tptp.zero_zero_real)) (=> (not _let_4) (and (=> _let_3 (= _let_2 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 M)) (@ _let_1 (@ tptp.suc N)))) (@ (@ tptp.minus_minus_real tptp.one_one_real) X)))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one)))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.log _let_1) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real _let_1))) (@ tptp.ln_ln_real X)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) (@ tptp.semiri8010041392384452111omplex N)) (= M N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) (@ tptp.semiri5074537144036343181t_real N)) (= M N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) (@ tptp.semiri681578069525770553at_rat N)) (= M N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) (@ tptp.semiri1316708129612266289at_nat N)) (= M N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.semiri1314217659103216013at_int N)) (= M N))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (= (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.insert_complex X) A2)) B3) (and (@ (@ tptp.member_complex X) B3) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (= (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.insert_real X) A2)) B3) (and (@ (@ tptp.member_real X) B3) (@ (@ tptp.ord_less_eq_set_real A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B3 tptp.set_set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.insert_set_nat X) A2)) B3) (and (@ (@ tptp.member_set_nat X) B3) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.insert_nat X) A2)) B3) (and (@ (@ tptp.member_nat X) B3) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (= (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.insert_int X) A2)) B3) (and (@ (@ tptp.member_int X) B3) (@ (@ tptp.ord_less_eq_set_int A2) B3)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (V tptp.num)) (= (= (@ tptp.semiri1314217659103216013at_int M) (@ tptp.numeral_numeral_int V)) (= M (@ tptp.numeral_numeral_nat V)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger N))) (= (@ tptp.abs_abs_Code_integer _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ tptp.abs_abs_real _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ tptp.abs_abs_rat _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ tptp.abs_abs_int _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (= (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B3 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) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (B3 tptp.set_complex) (A2 tptp.set_complex)) (=> (@ (@ tptp.member_complex X) B3) (= (@ (@ tptp.minus_811609699411566653omplex (@ (@ tptp.insert_complex X) A2)) B3) (@ (@ tptp.minus_811609699411566653omplex A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (B3 tptp.set_real) (A2 tptp.set_real)) (=> (@ (@ tptp.member_real X) B3) (= (@ (@ tptp.minus_minus_set_real (@ (@ tptp.insert_real X) A2)) B3) (@ (@ tptp.minus_minus_set_real A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.set_nat) (B3 tptp.set_set_nat) (A2 tptp.set_set_nat)) (=> (@ (@ tptp.member_set_nat X) B3) (= (@ (@ tptp.minus_2163939370556025621et_nat (@ (@ tptp.insert_set_nat X) A2)) B3) (@ (@ tptp.minus_2163939370556025621et_nat A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (B3 tptp.set_int) (A2 tptp.set_int)) (=> (@ (@ tptp.member_int X) B3) (= (@ (@ tptp.minus_minus_set_int (@ (@ tptp.insert_int X) A2)) B3) (@ (@ tptp.minus_minus_set_int A2) B3)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (=> (@ (@ tptp.member_nat X) B3) (= (@ (@ tptp.minus_minus_set_nat (@ (@ tptp.insert_nat X) A2)) B3) (@ (@ tptp.minus_minus_set_nat A2) B3)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) (@ tptp.semiri1314217659103216013at_int M))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex M) tptp.zero_zero_complex) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real M) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat M) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat M) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int M) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_complex (@ tptp.semiri8010041392384452111omplex N)) (= tptp.zero_zero_nat N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_real (@ tptp.semiri5074537144036343181t_real N)) (= tptp.zero_zero_nat N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_rat (@ tptp.semiri681578069525770553at_rat N)) (= tptp.zero_zero_nat N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_nat (@ tptp.semiri1316708129612266289at_nat N)) (= tptp.zero_zero_nat N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.zero_zero_int (@ tptp.semiri1314217659103216013at_int N)) (= tptp.zero_zero_nat N))))
% 6.68/6.99 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.zero_zero_nat) tptp.zero_zero_complex))
% 6.68/6.99 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.zero_zero_nat) tptp.zero_zero_rat))
% 6.68/6.99 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.zero_zero_nat) tptp.zero_zero_nat))
% 6.68/6.99 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.numeral_numeral_nat N)) (@ tptp.numera6690914467698888265omplex N))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_real N))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_rat N))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (A tptp.nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= _let_1 (@ (@ tptp.insert_nat A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (A tptp.real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= _let_1 (@ (@ tptp.insert_real A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= _let_1 (@ (@ tptp.insert_int A) A2)) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (A2 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (= (= (@ (@ tptp.insert_nat A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_nat A2) _let_1))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (A2 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (= (= (@ (@ tptp.insert_real A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_real A2) _let_1))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (A2 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (= (= (@ (@ tptp.insert_int A) A2) _let_1) (and (= A B) (@ (@ tptp.ord_less_eq_set_int A2) _let_1))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat M) N)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.68/6.99 (assert (= (@ tptp.semiri8010041392384452111omplex tptp.one_one_nat) tptp.one_one_complex))
% 6.68/6.99 (assert (= (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat) tptp.one_one_real))
% 6.68/6.99 (assert (= (@ tptp.semiri681578069525770553at_rat tptp.one_one_nat) tptp.one_one_rat))
% 6.68/6.99 (assert (= (@ tptp.semiri1316708129612266289at_nat tptp.one_one_nat) tptp.one_one_nat))
% 6.68/6.99 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_complex (@ tptp.semiri8010041392384452111omplex N)) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_real (@ tptp.semiri5074537144036343181t_real N)) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_rat (@ tptp.semiri681578069525770553at_rat N)) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_nat (@ tptp.semiri1316708129612266289at_nat N)) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= tptp.one_one_int (@ tptp.semiri1314217659103216013at_int N)) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex N) tptp.one_one_complex) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real N) tptp.one_one_real) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat N) tptp.one_one_rat) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat N) tptp.one_one_nat) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int N) tptp.one_one_int) (= N tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat A) A) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int A) A) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (= (@ (@ tptp.set_or1222579329274155063t_real A) A) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat) (C tptp.nat)) (= (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat C) tptp.bot_bot_set_nat)) (and (= A B) (= B C)))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int)) (= (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int C) tptp.bot_bot_set_int)) (and (= A B) (= B C)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (= (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real C) tptp.bot_bot_set_real)) (and (= A B) (= B C)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real A2))) (= (@ tptp.finite_finite_real (@ _let_1 (@ (@ tptp.insert_real A) B3))) (@ tptp.finite_finite_real (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int A2))) (= (@ tptp.finite_finite_int (@ _let_1 (@ (@ tptp.insert_int A) B3))) (@ tptp.finite_finite_int (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex A2))) (= (@ tptp.finite3207457112153483333omplex (@ _let_1 (@ (@ tptp.insert_complex A) B3))) (@ tptp.finite3207457112153483333omplex (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat A2))) (= (@ tptp.finite_finite_nat (@ _let_1 (@ (@ tptp.insert_nat A) B3))) (@ tptp.finite_finite_nat (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex M)) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real M)) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat M)) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat M)) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.power_power_nat M) N)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int M)) N))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W) (@ tptp.semiri8010041392384452111omplex X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W) (@ tptp.semiri5074537144036343181t_real X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W) (@ tptp.semiri681578069525770553at_rat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W) (@ tptp.semiri1316708129612266289at_nat X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W) (@ tptp.semiri1314217659103216013at_int X)) (= (@ (@ tptp.power_power_nat B) W) X))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex X) (@ (@ tptp.power_power_complex (@ tptp.semiri8010041392384452111omplex B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real X) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat X) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1316708129612266289at_nat X) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int X) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (= X (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (= (@ (@ tptp.log A) tptp.one_one_real) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.pred_numeral (@ tptp.inc K)) (@ tptp.numeral_numeral_nat K))))
% 6.68/6.99 (assert (forall ((P Bool)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n1201886186963655149omplex P))))
% 6.68/6.99 (assert (forall ((P Bool)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n3304061248610475627l_real P))))
% 6.68/6.99 (assert (forall ((P Bool)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2052037380579107095ol_rat P))))
% 6.68/6.99 (assert (forall ((P Bool)) (let ((_let_1 (@ tptp.zero_n2687167440665602831ol_nat P))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((P Bool)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n2684676970156552555ol_int P))))
% 6.68/6.99 (assert (forall ((P Bool)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.zero_n2687167440665602831ol_nat P)) (@ tptp.zero_n356916108424825756nteger P))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int) (= M tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc M)) (@ (@ tptp.plus_plus_complex tptp.one_one_complex) (@ tptp.semiri8010041392384452111omplex M)))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M)) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real M)))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc M)) (@ (@ tptp.plus_plus_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat M)))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc M)) (@ (@ tptp.plus_plus_nat tptp.one_one_nat) (@ tptp.semiri1316708129612266289at_nat M)))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc M)) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat X) A2)) (= (@ _let_1 (@ (@ tptp.insert_nat X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (not (@ (@ tptp.member_real X) A2)) (= (@ _let_1 (@ (@ tptp.insert_real X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (not (@ (@ tptp.member_int X) A2)) (= (@ _let_1 (@ (@ tptp.insert_int X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 A2))))))))
% 6.68/6.99 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.numeral_numeral_real W)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat (@ tptp.numeral_numeral_nat W)) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (W tptp.num)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.numeral_numeral_real W)) (@ (@ tptp.ord_less_nat N) (@ tptp.numeral_numeral_nat W)))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real N)) (@ tptp.semiri5074537144036343181t_real M)) (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat N)) M))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (B tptp.complex)) (= (@ (@ tptp.ord_le211207098394363844omplex A2) (@ tptp.uminus8566677241136511917omplex (@ (@ tptp.insert_complex B) tptp.bot_bot_set_complex))) (not (@ (@ tptp.member_complex B) A2)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_set_nat) (B tptp.set_nat)) (= (@ (@ tptp.ord_le6893508408891458716et_nat A2) (@ tptp.uminus613421341184616069et_nat (@ (@ tptp.insert_set_nat B) tptp.bot_bot_set_set_nat))) (not (@ (@ tptp.member_set_nat B) A2)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (B tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat A2) (@ tptp.uminus5710092332889474511et_nat (@ (@ tptp.insert_nat B) tptp.bot_bot_set_nat))) (not (@ (@ tptp.member_nat B) A2)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (B tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.uminus612125837232591019t_real (@ (@ tptp.insert_real B) tptp.bot_bot_set_real))) (not (@ (@ tptp.member_real B) A2)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (B tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int A2) (@ tptp.uminus1532241313380277803et_int (@ (@ tptp.insert_int B) tptp.bot_bot_set_int))) (not (@ (@ tptp.member_int B) A2)))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) A) tptp.one_one_real)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y)))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) A))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_real A) X)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_2 X) (= (@ _let_2 (@ (@ tptp.log A) X)) (@ _let_1 X))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N) (@ tptp.semiri8010041392384452111omplex Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N) (@ tptp.semiri5074537144036343181t_real Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N) (@ tptp.semiri681578069525770553at_rat Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= _let_1 (@ tptp.semiri1316708129612266289at_nat Y)) (= _let_1 Y)))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.nat)) (= (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) (@ tptp.semiri1314217659103216013at_int Y)) (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) Y))))
% 6.68/6.99 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri8010041392384452111omplex Y) (@ (@ tptp.power_power_complex (@ tptp.numera6690914467698888265omplex X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.68/6.99 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri5074537144036343181t_real Y) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.68/6.99 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri681578069525770553at_rat Y) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.68/6.99 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N))) (= (= (@ tptp.semiri1316708129612266289at_nat Y) _let_1) (= Y _let_1)))))
% 6.68/6.99 (assert (forall ((Y tptp.nat) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.semiri1314217659103216013at_int Y) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) (= Y (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (W tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat B) W)) X))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B tptp.nat) (W tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int B)) W)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat B) W)))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.int)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) A))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real A) X))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log A) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.log A) X)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex N))) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger N))) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat N))) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_real (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real M))) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc M))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc M))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_complex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex M))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc M))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger M))) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc M))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.plus_plus_rat (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat M))) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc M))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.numeral_numeral_real M)) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real (@ tptp.inc M)))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.inc M)))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.numera6690914467698888265omplex M)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex (@ tptp.inc M)))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.numera6620942414471956472nteger M)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger (@ tptp.inc M)))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.numeral_numeral_rat M)) (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat (@ tptp.inc M)))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.numeral_numeral_real N)) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (@ tptp.numera6690914467698888265omplex N)) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) (@ tptp.numera6620942414471956472nteger N)) (@ tptp.uminus1351360451143612070nteger (@ tptp.numera6620942414471956472nteger (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.minus_minus_rat (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ tptp.numeral_numeral_rat N)) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat (@ tptp.inc N))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.power_power_real A) B)) (@ tptp.semiri5074537144036343181t_real B))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.power_power_real (@ tptp.semiri5074537144036343181t_real X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.power_power_rat (@ tptp.semiri681578069525770553at_rat X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ (@ tptp.power_power_nat (@ tptp.semiri1316708129612266289at_nat X)) N)) (or (@ _let_1 X) (= N tptp.zero_zero_nat))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.power_power_int (@ tptp.semiri1314217659103216013at_int X)) N)) (or (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) X) (= N tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se727722235901077358nd_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.modulo_modulo_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_nat X) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat N)) (@ _let_1 N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N)))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat X)) (@ _let_1 X)))))
% 6.68/6.99 (assert (forall ((I tptp.num) (N tptp.nat) (X tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)) X))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat X)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N))) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1316708129612266289at_nat X)) _let_1) (@ (@ tptp.ord_less_eq_nat X) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (I tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int X)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int I)) N)) (@ (@ tptp.ord_less_eq_nat X) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat I)) N)))))
% 6.68/6.99 (assert (forall ((A2 (-> tptp.int tptp.int Bool)) (B3 (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.ord_le6741204236512500942_int_o A2) B3) (@ (@ tptp.ord_le2843351958646193337nt_int (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o A2))) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o B3))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.68/6.99 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real N3)))))
% 6.68/6.99 (assert (forall ((X tptp.rat)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat X) (@ tptp.semiri681578069525770553at_rat N3)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex X))) (= (@ (@ tptp.times_times_complex _let_1) Y) (@ (@ tptp.times_times_complex Y) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real X))) (= (@ (@ tptp.times_times_real _let_1) Y) (@ (@ tptp.times_times_real Y) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat X))) (= (@ (@ tptp.times_times_rat _let_1) Y) (@ (@ tptp.times_times_rat Y) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat X))) (= (@ (@ tptp.times_times_nat _let_1) Y) (@ (@ tptp.times_times_nat Y) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int X))) (= (@ (@ tptp.times_times_int _let_1) Y) (@ (@ tptp.times_times_int Y) _let_1)))))
% 6.68/6.99 (assert (forall ((C4 tptp.set_nat) (D4 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ tptp.insert_nat A))) (=> (@ (@ tptp.ord_less_eq_set_nat C4) D4) (@ (@ tptp.ord_less_eq_set_nat (@ _let_1 C4)) (@ _let_1 D4))))))
% 6.68/6.99 (assert (forall ((C4 tptp.set_real) (D4 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ tptp.insert_real A))) (=> (@ (@ tptp.ord_less_eq_set_real C4) D4) (@ (@ tptp.ord_less_eq_set_real (@ _let_1 C4)) (@ _let_1 D4))))))
% 6.68/6.99 (assert (forall ((C4 tptp.set_int) (D4 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ tptp.insert_int A))) (=> (@ (@ tptp.ord_less_eq_set_int C4) D4) (@ (@ tptp.ord_less_eq_set_int (@ _let_1 C4)) (@ _let_1 D4))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (A2 tptp.set_complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ _let_1 (@ (@ tptp.insert_complex X) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A2 tptp.set_real) (B3 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) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.set_nat) (A2 tptp.set_set_nat) (B3 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) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (A2 tptp.set_nat) (B3 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) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (A2 tptp.set_int) (B3 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) B3)) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_set_nat B3) (@ (@ tptp.insert_nat A) B3))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_real) (A tptp.real)) (@ (@ tptp.ord_less_eq_set_real B3) (@ (@ tptp.insert_real A) B3))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_int) (A tptp.int)) (@ (@ tptp.ord_less_eq_set_int B3) (@ (@ tptp.insert_int A) B3))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (B tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_set_nat A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_nat B) B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (B tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_set_real A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_real B) B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (B tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_set_int A2))) (=> (@ _let_1 B3) (@ _let_1 (@ (@ tptp.insert_int B) B3))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.bit_se2923211474154528505it_int N) (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se2925701944663578781it_nat N) M)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit_se2925701944663578781it_nat N))) (= (@ _let_1 (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat (@ _let_1 M))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.bit_se727722235901077358nd_nat M) N)) (@ (@ tptp.bit_se727722235901077358nd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (B3 tptp.set_complex) (A2 tptp.set_complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A2) B3))) (let ((_let_2 (@ tptp.insert_complex X))) (let ((_let_3 (@ (@ tptp.minus_811609699411566653omplex (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_complex X) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (B3 tptp.set_real) (A2 tptp.set_real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A2) B3))) (let ((_let_2 (@ tptp.insert_real X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_real (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_real X) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.set_nat) (B3 tptp.set_set_nat) (A2 tptp.set_set_nat)) (let ((_let_1 (@ (@ tptp.minus_2163939370556025621et_nat A2) B3))) (let ((_let_2 (@ tptp.insert_set_nat X))) (let ((_let_3 (@ (@ tptp.minus_2163939370556025621et_nat (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_set_nat X) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (B3 tptp.set_int) (A2 tptp.set_int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A2) B3))) (let ((_let_2 (@ tptp.insert_int X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_int (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_int X) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (B3 tptp.set_nat) (A2 tptp.set_nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A2) B3))) (let ((_let_2 (@ tptp.insert_nat X))) (let ((_let_3 (@ (@ tptp.minus_minus_set_nat (@ _let_2 A2)) B3))) (let ((_let_4 (@ (@ tptp.member_nat X) B3))) (and (=> _let_4 (= _let_3 _let_1)) (=> (not _let_4) (= _let_3 (@ _let_2 _let_1))))))))))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (not (forall ((M4 tptp.nat) (N3 tptp.nat)) (not (= Z (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (= _let_1 (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log B) _let_1)))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ring_1_of_int_real X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ tptp.ring_1_of_int_rat X)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)))) (= (@ _let_1 (@ tptp.ring_1_of_int_int X)) (@ _let_1 X)))))
% 6.68/6.99 (assert (forall ((P (-> tptp.num Bool)) (X tptp.num)) (=> (@ P tptp.one) (=> (forall ((X6 tptp.num)) (=> (@ P X6) (@ P (@ tptp.inc X6)))) (@ P X)))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.plus_plus_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ tptp.inc (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (N tptp.nat) (M tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real B) N)) M) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) M))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ (@ tptp.log (@ (@ tptp.power_power_real A) N)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_1 X)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.semiri5074537144036343181t_real N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ tptp.semiri681578069525770553at_rat N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ tptp.semiri1316708129612266289at_nat N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.semiri1314217659103216013at_int N))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) tptp.zero_zero_rat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (not (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri8010041392384452111omplex (@ tptp.suc N)) tptp.zero_zero_complex))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N)) tptp.zero_zero_rat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1316708129612266289at_nat (@ tptp.suc N)) tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (not (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_3 (@ tptp.divide_divide_nat A))) (= (@ _let_3 (@ (@ tptp.times_times_nat _let_2) _let_1)) (@ (@ tptp.divide_divide_nat (@ _let_3 _let_2)) _let_1)))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_3 (@ tptp.divide_divide_int A))) (= (@ _let_3 (@ (@ tptp.times_times_int _let_2) _let_1)) (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) _let_1)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((I tptp.nat) (J tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I) J) (@ (@ tptp.ord_less_eq_rat (@ tptp.semiri681578069525770553at_rat I)) (@ tptp.semiri681578069525770553at_rat J)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_Code_integer (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.dvd_dvd_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.dvd_dvd_nat M) N))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (or (= A2 tptp.bot_bot_set_nat) (= A2 _let_1))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))) (=> (@ (@ tptp.ord_less_eq_set_real A2) _let_1) (or (= A2 tptp.bot_bot_set_real) (= A2 _let_1))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))) (=> (@ (@ tptp.ord_less_eq_set_int A2) _let_1) (or (= A2 tptp.bot_bot_set_int) (= A2 _let_1))))))
% 6.68/6.99 (assert (forall ((X8 tptp.set_nat) (A tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat))) (= (@ (@ tptp.ord_less_eq_set_nat X8) _let_1) (or (= X8 tptp.bot_bot_set_nat) (= X8 _let_1))))))
% 6.68/6.99 (assert (forall ((X8 tptp.set_real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real A) tptp.bot_bot_set_real))) (= (@ (@ tptp.ord_less_eq_set_real X8) _let_1) (or (= X8 tptp.bot_bot_set_real) (= X8 _let_1))))))
% 6.68/6.99 (assert (forall ((X8 tptp.set_int) (A tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int A) tptp.bot_bot_set_int))) (= (@ (@ tptp.ord_less_eq_set_int X8) _let_1) (or (= X8 tptp.bot_bot_set_int) (= X8 _let_1))))))
% 6.68/6.99 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.zero_zero_nat) tptp.zero_zero_int))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.numeral_numeral_nat N)) (@ tptp.numeral_numeral_int N))))
% 6.68/6.99 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (= A B) (= (@ (@ tptp.set_or1269000886237332187st_nat A) B) (@ (@ tptp.insert_nat A) tptp.bot_bot_set_nat)))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (=> (= A B) (= (@ (@ tptp.set_or1266510415728281911st_int A) B) (@ (@ tptp.insert_int A) tptp.bot_bot_set_int)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (=> (= A B) (= (@ (@ tptp.set_or1222579329274155063t_real A) B) (@ (@ tptp.insert_real A) tptp.bot_bot_set_real)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.insert_complex X))) (=> (not (@ (@ tptp.member_complex X) A2)) (= (@ (@ tptp.minus_811609699411566653omplex (@ _let_1 A2)) (@ _let_1 tptp.bot_bot_set_complex)) A2)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_int (@ _let_2 (@ _let_1 tptp.bot_bot_set_int))) B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_real (@ _let_2 (@ _let_1 tptp.bot_bot_set_real))) B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 (@ _let_1 tptp.bot_bot_set_nat))) B3))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (A2 tptp.set_complex)) (let ((_let_1 (@ tptp.insert_complex A))) (=> (@ (@ tptp.member_complex A) A2) (= (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))) A2)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (A tptp.int) (B3 tptp.set_int)) (let ((_let_1 (@ tptp.insert_int A))) (let ((_let_2 (@ tptp.minus_minus_set_int A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_int (@ _let_2 B3)) (@ _let_1 tptp.bot_bot_set_int)))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (A tptp.real) (B3 tptp.set_real)) (let ((_let_1 (@ tptp.insert_real A))) (let ((_let_2 (@ tptp.minus_minus_set_real A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_real (@ _let_2 B3)) (@ _let_1 tptp.bot_bot_set_real)))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (B3 tptp.set_nat)) (let ((_let_1 (@ tptp.insert_nat A))) (let ((_let_2 (@ tptp.minus_minus_set_nat A2))) (= (@ _let_2 (@ _let_1 B3)) (@ (@ tptp.minus_minus_set_nat (@ _let_2 B3)) (@ _let_1 tptp.bot_bot_set_nat)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.ord_less_eq_nat M) N))))
% 6.68/6.99 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (B3 tptp.set_complex) (X tptp.complex) (C4 tptp.set_complex)) (let ((_let_1 (@ tptp.minus_811609699411566653omplex B3))) (let ((_let_2 (@ tptp.ord_le211207098394363844omplex A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_complex X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_complex X) A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (B3 tptp.set_real) (X tptp.real) (C4 tptp.set_real)) (let ((_let_1 (@ tptp.minus_minus_set_real B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_real A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_real X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_real X) A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_set_nat) (B3 tptp.set_set_nat) (X tptp.set_nat) (C4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.minus_2163939370556025621et_nat B3))) (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))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (B3 tptp.set_nat) (X tptp.nat) (C4 tptp.set_nat)) (let ((_let_1 (@ tptp.minus_minus_set_nat B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_nat A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_nat X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_nat X) A2))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (B3 tptp.set_int) (X tptp.int) (C4 tptp.set_int)) (let ((_let_1 (@ tptp.minus_minus_set_int B3))) (let ((_let_2 (@ tptp.ord_less_eq_set_int A2))) (= (@ _let_2 (@ _let_1 (@ (@ tptp.insert_int X) C4))) (and (@ _let_2 (@ _let_1 C4)) (not (@ (@ tptp.member_int X) A2))))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (= K (@ tptp.semiri1314217659103216013at_int N3))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.semiri4939895301339042750nteger M)) (@ tptp.semiri4939895301339042750nteger N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (Z tptp.int)) (= (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) Z)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat M) N))) Z))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat N) M)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat A) B)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat A) B)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.68/6.99 (assert (= (@ tptp.semiri1314217659103216013at_int tptp.one_one_nat) tptp.one_one_int))
% 6.68/6.99 (assert (= tptp.ord_less_eq_int (lambda ((W3 tptp.int) (Z3 tptp.int)) (exists ((N2 tptp.nat)) (= Z3 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int N2)))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat A) B)) (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4216267220026989637d_enat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_ma741700101516333627d_enat (@ tptp.semiri4216267220026989637d_enat X)) (@ tptp.semiri4216267220026989637d_enat Y)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri4939895301339042750nteger (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_Code_integer (@ tptp.semiri4939895301339042750nteger X)) (@ tptp.semiri4939895301339042750nteger Y)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_real (@ tptp.semiri5074537144036343181t_real X)) (@ tptp.semiri5074537144036343181t_real Y)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_rat (@ tptp.semiri681578069525770553at_rat X)) (@ tptp.semiri681578069525770553at_rat Y)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_nat (@ tptp.semiri1316708129612266289at_nat X)) (@ tptp.semiri1316708129612266289at_nat Y)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.ord_max_nat X) Y)) (@ (@ tptp.ord_max_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat A) B)) (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (= M (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (= (@ tptp.semiri5074537144036343181t_real N) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.68/6.99 (assert (= tptp.ord_less_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.68/6.99 (assert (= tptp.ord_less_eq_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit_se2002935070580805687sk_nat N))) (= (@ tptp.semiri1316708129612266289at_nat _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.bit_se2002935070580805687sk_nat N)) (@ tptp.bit_se2000444600071755411sk_int N))))
% 6.68/6.99 (assert (= (@ tptp.inc tptp.one) (@ tptp.bit0 tptp.one)))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit1 X)) (@ tptp.bit0 (@ tptp.inc X)))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ tptp.inc (@ tptp.bit0 X)) (@ tptp.bit1 X))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (B tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real M))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.power_power_real B) N)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) _let_1)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (Y tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) X) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_rat Y) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N3)) X))))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.plus_plus_num X) tptp.one) (@ tptp.inc X))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.inc (@ tptp.bitM N)) (@ tptp.bit0 N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_nat (@ tptp.semiri1316708129612266289at_nat M)) (@ tptp.semiri1316708129612266289at_nat N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int M)) (@ tptp.semiri1314217659103216013at_int N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.bitM (@ tptp.inc N)) (@ tptp.bit1 N))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.rat))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X6 tptp.complex) (S5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_complex X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.rat))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X6 tptp.nat) (S5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S5) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_nat X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.rat))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X6 tptp.int) (S5 tptp.set_int)) (=> (@ tptp.finite_finite_int S5) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_int X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.rat))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X6 tptp.real) (S5 tptp.set_real)) (=> (@ tptp.finite_finite_real S5) (=> (forall ((Y2 tptp.real)) (=> (@ (@ tptp.member_real Y2) S5) (@ (@ tptp.ord_less_eq_rat (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_real X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool)) (F (-> tptp.complex tptp.num))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((X6 tptp.complex) (S5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S5) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_complex X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool)) (F (-> tptp.nat tptp.num))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((X6 tptp.nat) (S5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S5) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S5) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_nat X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool)) (F (-> tptp.int tptp.num))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((X6 tptp.int) (S5 tptp.set_int)) (=> (@ tptp.finite_finite_int S5) (=> (forall ((Y2 tptp.int)) (=> (@ (@ tptp.member_int Y2) S5) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_int X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool)) (F (-> tptp.real tptp.num))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((X6 tptp.real) (S5 tptp.set_real)) (=> (@ tptp.finite_finite_real S5) (=> (forall ((Y2 tptp.real)) (=> (@ (@ tptp.member_real Y2) S5) (@ (@ tptp.ord_less_eq_num (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_real X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (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 ((X6 tptp.complex) (S5 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex S5) (=> (forall ((Y2 tptp.complex)) (=> (@ (@ tptp.member_complex Y2) S5) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_complex X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (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 ((X6 tptp.nat) (S5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S5) (=> (forall ((Y2 tptp.nat)) (=> (@ (@ tptp.member_nat Y2) S5) (@ (@ tptp.ord_less_eq_nat (@ F Y2)) (@ F X6)))) (=> (@ P S5) (@ P (@ (@ tptp.insert_nat X6) S5)))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ (@ tptp.ord_less_real X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) A7) (@ (@ tptp.ord_less_rat X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) A7) (@ (@ tptp.ord_less_num X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ (@ tptp.ord_less_nat X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ (@ tptp.ord_less_int X4) B5))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((B5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ (@ tptp.ord_less_real B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_real B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_rat) (P (-> tptp.set_rat Bool))) (=> (@ tptp.finite_finite_rat A2) (=> (@ P tptp.bot_bot_set_rat) (=> (forall ((B5 tptp.rat) (A7 tptp.set_rat)) (=> (@ tptp.finite_finite_rat A7) (=> (forall ((X4 tptp.rat)) (=> (@ (@ tptp.member_rat X4) A7) (@ (@ tptp.ord_less_rat B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_rat B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_num) (P (-> tptp.set_num Bool))) (=> (@ tptp.finite_finite_num A2) (=> (@ P tptp.bot_bot_set_num) (=> (forall ((B5 tptp.num) (A7 tptp.set_num)) (=> (@ tptp.finite_finite_num A7) (=> (forall ((X4 tptp.num)) (=> (@ (@ tptp.member_num X4) A7) (@ (@ tptp.ord_less_num B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_num B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((B5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ (@ tptp.ord_less_nat B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_nat B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((B5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ (@ tptp.ord_less_int B5) X4))) (=> (@ P A7) (@ P (@ (@ tptp.insert_int B5) A7)))))) (@ P A2))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex X) (@ tptp.semiri8010041392384452111omplex N))) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real X) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.complex)) (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) X)) (@ (@ tptp.power_power_complex (@ tptp.exp_complex X)) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (= (@ tptp.exp_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) (@ (@ tptp.power_power_real (@ tptp.exp_real X)) N))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_real (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat 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_rat (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (G (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat 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_rat (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat 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_rat (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat 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_rat (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_real X) A2)))) (let ((_let_4 (@ (@ tptp.member_real X) A2))) (=> (@ tptp.finite_finite_real A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_int X) A2)))) (let ((_let_4 (@ (@ tptp.member_int X) A2))) (=> (@ tptp.finite_finite_int A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ _let_1 (@ (@ tptp.insert_complex X) A2)))) (let ((_let_4 (@ (@ tptp.member_complex X) A2))) (=> (@ tptp.finite3207457112153483333omplex A2) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ tptp.plus_plus_nat (@ G X)) _let_2)))))))))))
% 6.68/6.99 (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 ((A5 tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A5))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A5) F4)))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A5))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A5) F4)))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A5))) (=> (@ tptp.finite_finite_nat F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_nat A5) F4)))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A5))) (=> (@ tptp.finite_finite_real F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_real A5) F4)))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A5))) (=> (@ tptp.finite_finite_int F4) (=> (@ _let_1 A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_int A5) F4)))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.set_nat) (F4 tptp.set_set_nat)) (let ((_let_1 (@ tptp.member_set_nat A5))) (=> (@ tptp.finite1152437895449049373et_nat F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le6893508408891458716et_nat F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_set_nat A5) F4))))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.complex) (F4 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex A5))) (=> (@ tptp.finite3207457112153483333omplex F4) (=> (@ _let_1 A2) (=> (@ (@ tptp.ord_le211207098394363844omplex F4) A2) (=> (not (@ _let_1 F4)) (=> (@ P F4) (@ P (@ (@ tptp.insert_complex A5) F4))))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.nat) (F4 tptp.set_nat)) (let ((_let_1 (@ tptp.member_nat A5))) (=> (@ 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 A5) F4))))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.real) (F4 tptp.set_real)) (let ((_let_1 (@ tptp.member_real A5))) (=> (@ 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 A5) F4))))))))) (@ P F3)))))))
% 6.68/6.99 (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 ((A5 tptp.int) (F4 tptp.set_int)) (let ((_let_1 (@ tptp.member_int A5))) (=> (@ 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 A5) F4))))))))) (@ P F3)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (forall ((Y2 tptp.real)) (exists ((N3 tptp.nat)) (@ (@ tptp.ord_less_real Y2) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) X)))))))
% 6.68/6.99 (assert (= tptp.ln_ln_real (@ tptp.log (@ tptp.exp_real tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((M tptp.int)) (=> (forall ((N3 tptp.nat)) (not (= M (@ tptp.semiri1314217659103216013at_int N3)))) (not (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (not (= M (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))))))))))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.set_complex Bool)) (A2 tptp.set_complex)) (=> (@ X8 A2) (=> (forall ((A7 tptp.set_complex)) (=> (@ X8 A7) (exists ((X4 tptp.complex)) (let ((_let_1 (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex)))) (and (@ (@ tptp.member_complex X4) A7) (or (@ X8 _let_1) (not (@ tptp.finite3207457112153483333omplex _let_1)))))))) (not (@ tptp.finite3207457112153483333omplex A2))))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.set_int Bool)) (A2 tptp.set_int)) (=> (@ X8 A2) (=> (forall ((A7 tptp.set_int)) (=> (@ X8 A7) (exists ((X4 tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int)))) (and (@ (@ tptp.member_int X4) A7) (or (@ X8 _let_1) (not (@ tptp.finite_finite_int _let_1)))))))) (not (@ tptp.finite_finite_int A2))))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.set_real Bool)) (A2 tptp.set_real)) (=> (@ X8 A2) (=> (forall ((A7 tptp.set_real)) (=> (@ X8 A7) (exists ((X4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real)))) (and (@ (@ tptp.member_real X4) A7) (or (@ X8 _let_1) (not (@ tptp.finite_finite_real _let_1)))))))) (not (@ tptp.finite_finite_real A2))))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.set_nat Bool)) (A2 tptp.set_nat)) (=> (@ X8 A2) (=> (forall ((A7 tptp.set_nat)) (=> (@ X8 A7) (exists ((X4 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat)))) (and (@ (@ tptp.member_nat X4) A7) (or (@ X8 _let_1) (not (@ tptp.finite_finite_nat _let_1)))))))) (not (@ tptp.finite_finite_nat A2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat A2) (=> (@ P A2) (=> (forall ((A5 tptp.set_nat) (A7 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A7) (=> (@ (@ tptp.member_set_nat A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A7) (@ (@ tptp.insert_set_nat A5) tptp.bot_bot_set_set_nat))))))) (@ P tptp.bot_bot_set_set_nat))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ P A2) (=> (forall ((A5 tptp.complex) (A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (@ (@ tptp.member_complex A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex A5) tptp.bot_bot_set_complex))))))) (@ P tptp.bot_bot_set_complex))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int A2) (=> (@ P A2) (=> (forall ((A5 tptp.int) (A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (@ (@ tptp.member_int A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int A5) tptp.bot_bot_set_int))))))) (@ P tptp.bot_bot_set_int))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real A2) (=> (@ P A2) (=> (forall ((A5 tptp.real) (A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (@ (@ tptp.member_real A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real A5) tptp.bot_bot_set_real))))))) (@ P tptp.bot_bot_set_real))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat A2) (=> (@ P A2) (=> (forall ((A5 tptp.nat) (A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (@ (@ tptp.member_nat A5) A7) (=> (@ P A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat A5) tptp.bot_bot_set_nat))))))) (@ P tptp.bot_bot_set_nat))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B3 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))) B3) (@ (@ tptp.ord_less_eq_set_real A2) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B3 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))) B3) (@ (@ tptp.ord_less_eq_set_nat A2) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B3 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))) B3) (@ (@ tptp.ord_less_eq_set_int A2) (@ _let_1 B3))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.ord_le211207098394363844omplex A2))) (let ((_let_2 (@ (@ tptp.member_complex X) A2))) (let ((_let_3 (@ tptp.insert_complex X))) (= (@ _let_1 (@ _let_3 B3)) (and (=> _let_2 (@ (@ tptp.ord_le211207098394363844omplex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B3 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 B3)) (and (=> _let_2 (@ (@ tptp.ord_le6893508408891458716et_nat (@ (@ tptp.minus_2163939370556025621et_nat A2) (@ _let_3 tptp.bot_bot_set_set_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B3 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 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B3 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 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B3 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 B3)) (and (=> _let_2 (@ (@ tptp.ord_less_eq_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ _let_1 B3)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_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))) (and (=> _let_4 (= _let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2)))))))))
% 6.68/6.99 (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)))))))))
% 6.68/6.99 (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)))))))))
% 6.68/6.99 (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)))))))))
% 6.68/6.99 (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)))))))))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc A)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))
% 6.68/6.99 (assert (= tptp.ord_less_int (lambda ((W3 tptp.int) (Z3 tptp.int)) (exists ((N2 tptp.nat)) (= Z3 (@ (@ tptp.plus_plus_int W3) (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N2))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int M))) (and (= N tptp.zero_zero_nat) (= M tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((D tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.dvd_dvd_nat D) N) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) D)) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real D))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (not (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3)))))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.times_times_num X))) (= (@ _let_1 (@ tptp.inc Y)) (@ (@ tptp.plus_plus_num (@ _let_1 Y)) X)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) M) (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log B) X) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 B))))))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ tptp.numera6690914467698888265omplex (@ tptp.inc X)) (@ (@ tptp.plus_plus_complex (@ tptp.numera6690914467698888265omplex X)) tptp.one_one_complex))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_real (@ tptp.inc X)) (@ (@ tptp.plus_plus_real (@ tptp.numeral_numeral_real X)) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_rat (@ tptp.inc X)) (@ (@ tptp.plus_plus_rat (@ tptp.numeral_numeral_rat X)) tptp.one_one_rat))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_nat (@ tptp.inc X)) (@ (@ tptp.plus_plus_nat (@ tptp.numeral_numeral_nat X)) tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ tptp.numeral_numeral_int (@ tptp.inc X)) (@ (@ tptp.plus_plus_int (@ tptp.numeral_numeral_int X)) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((A tptp.code_integer) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri4939895301339042750nteger M))) (let ((_let_2 (@ tptp.modulo364778990260209775nteger A))) (let ((_let_3 (@ tptp.semiri4939895301339042750nteger N))) (let ((_let_4 (@ tptp.times_3573771949741848930nteger _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_p5714425477246183910nteger (@ _let_4 (@ (@ tptp.modulo364778990260209775nteger (@ (@ tptp.divide6298287555418463151nteger A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat M))) (let ((_let_2 (@ tptp.modulo_modulo_nat A))) (let ((_let_3 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_4 (@ tptp.times_times_nat _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_nat (@ _let_4 (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.divide_divide_nat A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int M))) (let ((_let_2 (@ tptp.modulo_modulo_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_4 (@ tptp.times_times_int _let_1))) (= (@ _let_2 (@ _let_4 _let_3)) (@ (@ tptp.plus_plus_int (@ _let_4 (@ (@ tptp.modulo_modulo_int (@ (@ tptp.divide_divide_int A) _let_1)) _let_3))) (@ _let_2 _let_1)))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ tptp.semiri8010041392384452111omplex M)) (@ tptp.semiri8010041392384452111omplex (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri8010041392384452111omplex N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri5074537144036343181t_real N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.divide_divide_nat M) N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ tptp.semiri681578069525770553at_rat M)) (@ tptp.semiri681578069525770553at_rat (@ (@ tptp.modulo_modulo_nat M) N)))) (@ tptp.semiri681578069525770553at_rat N)))))
% 6.68/6.99 (assert (forall ((P (-> tptp.set_set_nat Bool)) (B3 tptp.set_set_nat)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_set_nat) (=> (=> (not (@ tptp.finite1152437895449049373et_nat B3)) _let_1) (=> (forall ((A7 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A7) (=> (not (= A7 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A7) B3) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A7) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A7) (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))))) (@ P A7)))))) _let_1))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.set_complex Bool)) (B3 tptp.set_complex)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_complex) (=> (=> (not (@ tptp.finite3207457112153483333omplex B3)) _let_1) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))) (@ P A7)))))) _let_1))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.set_real Bool)) (B3 tptp.set_real)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_real) (=> (=> (not (@ tptp.finite_finite_real B3)) _let_1) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))) (@ P A7)))))) _let_1))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.set_nat Bool)) (B3 tptp.set_nat)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_nat) (=> (=> (not (@ tptp.finite_finite_nat B3)) _let_1) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))) (@ P A7)))))) _let_1))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.set_int Bool)) (B3 tptp.set_int)) (let ((_let_1 (@ P B3))) (=> (@ P tptp.bot_bot_set_int) (=> (=> (not (@ tptp.finite_finite_int B3)) _let_1) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))) (@ P A7)))))) _let_1))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_set_nat) (P (-> tptp.set_set_nat Bool))) (=> (@ tptp.finite1152437895449049373et_nat B3) (=> (@ P tptp.bot_bot_set_set_nat) (=> (forall ((A7 tptp.set_set_nat)) (=> (@ tptp.finite1152437895449049373et_nat A7) (=> (not (= A7 tptp.bot_bot_set_set_nat)) (=> (@ (@ tptp.ord_le6893508408891458716et_nat A7) B3) (=> (forall ((X4 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X4) A7) (@ P (@ (@ tptp.minus_2163939370556025621et_nat A7) (@ (@ tptp.insert_set_nat X4) tptp.bot_bot_set_set_nat))))) (@ P A7)))))) (@ P B3))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex B3) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((A7 tptp.set_complex)) (=> (@ tptp.finite3207457112153483333omplex A7) (=> (not (= A7 tptp.bot_bot_set_complex)) (=> (@ (@ tptp.ord_le211207098394363844omplex A7) B3) (=> (forall ((X4 tptp.complex)) (=> (@ (@ tptp.member_complex X4) A7) (@ P (@ (@ tptp.minus_811609699411566653omplex A7) (@ (@ tptp.insert_complex X4) tptp.bot_bot_set_complex))))) (@ P A7)))))) (@ P B3))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real B3) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((A7 tptp.set_real)) (=> (@ tptp.finite_finite_real A7) (=> (not (= A7 tptp.bot_bot_set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A7) B3) (=> (forall ((X4 tptp.real)) (=> (@ (@ tptp.member_real X4) A7) (@ P (@ (@ tptp.minus_minus_set_real A7) (@ (@ tptp.insert_real X4) tptp.bot_bot_set_real))))) (@ P A7)))))) (@ P B3))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat B3) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((A7 tptp.set_nat)) (=> (@ tptp.finite_finite_nat A7) (=> (not (= A7 tptp.bot_bot_set_nat)) (=> (@ (@ tptp.ord_less_eq_set_nat A7) B3) (=> (forall ((X4 tptp.nat)) (=> (@ (@ tptp.member_nat X4) A7) (@ P (@ (@ tptp.minus_minus_set_nat A7) (@ (@ tptp.insert_nat X4) tptp.bot_bot_set_nat))))) (@ P A7)))))) (@ P B3))))))
% 6.68/6.99 (assert (forall ((B3 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int B3) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((A7 tptp.set_int)) (=> (@ tptp.finite_finite_int A7) (=> (not (= A7 tptp.bot_bot_set_int)) (=> (@ (@ tptp.ord_less_eq_set_int A7) B3) (=> (forall ((X4 tptp.int)) (=> (@ (@ tptp.member_int X4) A7) (@ P (@ (@ tptp.minus_minus_set_int A7) (@ (@ tptp.insert_int X4) tptp.bot_bot_set_int))))) (@ P A7)))))) (@ P B3))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (exists ((N3 tptp.nat)) (and (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= K (@ tptp.semiri1314217659103216013at_int N3)))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) K) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (=> (not (= K tptp.zero_zero_int)) (=> (forall ((N3 tptp.nat)) (=> (= K (@ tptp.semiri1314217659103216013at_int N3)) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3)))))))))
% 6.68/6.99 (assert (= tptp.ord_less_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N2)) tptp.one_one_real)) (@ tptp.semiri5074537144036343181t_real M3)))))
% 6.68/6.99 (assert (= tptp.ord_less_eq_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real M3)) tptp.one_one_real)))))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ tptp.suc N)))) tptp.zero_zero_int)))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (P (-> tptp.set_complex Bool))) (=> (@ tptp.finite3207457112153483333omplex S2) (=> (@ P tptp.bot_bot_set_complex) (=> (forall ((T5 tptp.set_complex)) (=> (@ (@ tptp.ord_less_set_complex T5) S2) (=> (@ P T5) (exists ((X4 tptp.complex)) (and (@ (@ tptp.member_complex X4) (@ (@ tptp.minus_811609699411566653omplex S2) T5)) (@ P (@ (@ tptp.insert_complex X4) T5))))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_int) (P (-> tptp.set_int Bool))) (=> (@ tptp.finite_finite_int S2) (=> (@ P tptp.bot_bot_set_int) (=> (forall ((T5 tptp.set_int)) (=> (@ (@ tptp.ord_less_set_int T5) S2) (=> (@ P T5) (exists ((X4 tptp.int)) (and (@ (@ tptp.member_int X4) (@ (@ tptp.minus_minus_set_int S2) T5)) (@ P (@ (@ tptp.insert_int X4) T5))))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_real) (P (-> tptp.set_real Bool))) (=> (@ tptp.finite_finite_real S2) (=> (@ P tptp.bot_bot_set_real) (=> (forall ((T5 tptp.set_real)) (=> (@ (@ tptp.ord_less_set_real T5) S2) (=> (@ P T5) (exists ((X4 tptp.real)) (and (@ (@ tptp.member_real X4) (@ (@ tptp.minus_minus_set_real S2) T5)) (@ P (@ (@ tptp.insert_real X4) T5))))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat) (P (-> tptp.set_nat Bool))) (=> (@ tptp.finite_finite_nat S2) (=> (@ P tptp.bot_bot_set_nat) (=> (forall ((T5 tptp.set_nat)) (=> (@ (@ tptp.ord_less_set_nat T5) S2) (=> (@ P T5) (exists ((X4 tptp.nat)) (and (@ (@ tptp.member_nat X4) (@ (@ tptp.minus_minus_set_nat S2) T5)) (@ P (@ (@ tptp.insert_nat X4) T5))))))) (@ P S2))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (B3 tptp.set_complex)) (let ((_let_1 (@ tptp.member_complex X))) (let ((_let_2 (@ _let_1 A2))) (let ((_let_3 (@ tptp.insert_complex X))) (let ((_let_4 (@ _let_1 B3))) (let ((_let_5 (@ tptp.ord_less_set_complex A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_complex (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_3 tptp.bot_bot_set_complex))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le211207098394363844omplex A2) B3)))))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_set_nat) (X tptp.set_nat) (B3 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 B3))) (let ((_let_5 (@ tptp.ord_less_set_set_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (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))) B3)) (=> (not _let_2) (@ (@ tptp.ord_le6893508408891458716et_nat A2) B3)))))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (B3 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 B3))) (let ((_let_5 (@ tptp.ord_less_set_real A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_real (@ (@ tptp.minus_minus_set_real A2) (@ _let_3 tptp.bot_bot_set_real))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_real A2) B3)))))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (X tptp.nat) (B3 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 B3))) (let ((_let_5 (@ tptp.ord_less_set_nat A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_nat (@ (@ tptp.minus_minus_set_nat A2) (@ _let_3 tptp.bot_bot_set_nat))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_nat A2) B3)))))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (B3 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 B3))) (let ((_let_5 (@ tptp.ord_less_set_int A2))) (= (@ _let_5 (@ _let_3 B3)) (and (=> _let_4 (@ _let_5 B3)) (=> (not _let_4) (and (=> _let_2 (@ (@ tptp.ord_less_set_int (@ (@ tptp.minus_minus_set_int A2) (@ _let_3 tptp.bot_bot_set_int))) B3)) (=> (not _let_2) (@ (@ tptp.ord_less_eq_set_int A2) B3)))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (= (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT (@ tptp.suc N)) X)) (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.nat)) (= (@ tptp.set_nat2 (@ (@ tptp.replicate_nat (@ tptp.suc N)) X)) (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.int)) (= (@ tptp.set_int2 (@ (@ tptp.replicate_int (@ tptp.suc N)) X)) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (= (@ tptp.set_real2 (@ (@ tptp.replicate_real (@ tptp.suc N)) X)) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_nat M) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat _let_1)) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real M))) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.vEBT_VEBT)) (let ((_let_1 (@ tptp.set_VEBT_VEBT2 (@ (@ tptp.replicate_VEBT_VEBT N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bo8194388402131092736T_VEBT)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_VEBT_VEBT X) tptp.bot_bo8194388402131092736T_VEBT))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.nat)) (let ((_let_1 (@ tptp.set_nat2 (@ (@ tptp.replicate_nat N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_nat)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_nat X) tptp.bot_bot_set_nat))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.int)) (let ((_let_1 (@ tptp.set_int2 (@ (@ tptp.replicate_int N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_int)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.set_real2 (@ (@ tptp.replicate_real N) X)))) (let ((_let_2 (= N tptp.zero_zero_nat))) (and (=> _let_2 (= _let_1 tptp.bot_bot_set_real)) (=> (not _let_2) (= _let_1 (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int B))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int A))) (let ((_let_3 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat A) B)))) (let ((_let_4 (@ (@ tptp.ord_less_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 tptp.zero_zero_int)) (=> (not _let_4) (= _let_3 (@ (@ tptp.minus_minus_int _let_2) _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (D tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real D))) (= (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real X)) _let_1) (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat X) D))) (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.modulo_modulo_nat X) D))) _let_1))))))
% 6.68/6.99 (assert (forall ((M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.set_or1266510415728281911st_int M))) (let ((_let_2 (@ (@ tptp.plus_plus_int tptp.one_one_int) N))) (=> (@ (@ tptp.ord_less_eq_int M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_int _let_2) (@ _let_1 N))))))))
% 6.68/6.99 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_set_int (@ (@ tptp.ord_less_int J3) I5)) tptp.bot_bot_set_int) (@ (@ tptp.insert_int I5) (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3))))))
% 6.68/6.99 (assert (forall ((E tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3)))) E)))))))
% 6.68/6.99 (assert (forall ((E tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) E) (not (forall ((N3 tptp.nat)) (not (@ (@ tptp.ord_less_rat (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.semiri681578069525770553at_rat (@ tptp.suc N3)))) E)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.plus_plus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_rat (@ tptp.semiri681578069525770553at_rat N)) (@ (@ tptp.power_power_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int N)) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (=> (@ _let_2 Y) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.minus_minus_real (@ _let_1 X)) (@ _let_1 Y)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real M))) (@ _let_1 (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.divide_divide_rat tptp.one_one_rat))) (=> (@ (@ tptp.ord_less_eq_nat N) M) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_rat (@ _let_1 (@ tptp.semiri681578069525770553at_rat M))) (@ _let_1 (@ tptp.semiri681578069525770553at_rat N))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_complex (@ tptp.exp_complex (@ (@ tptp.divide1717551699836669952omplex X) (@ tptp.semiri8010041392384452111omplex N)))) N) (@ tptp.exp_complex X)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.power_power_real (@ tptp.exp_real (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N)))) N) (@ tptp.exp_real X)))))
% 6.68/6.99 (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 ((M4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M4) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M4)) X)) C))) (= X tptp.zero_zero_real)))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.real))) (let ((_let_1 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.nat))) (let ((_let_1 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (X tptp.complex) (G (-> tptp.complex tptp.int))) (let ((_let_1 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (=> (@ (@ tptp.member_complex X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_1 (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex X) tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.real))) (let ((_let_1 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (X tptp.int) (G (-> tptp.int tptp.nat))) (let ((_let_1 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (=> (@ (@ tptp.member_int X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int X) tptp.bot_bot_set_int))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (X tptp.real) (G (-> tptp.real tptp.nat))) (let ((_let_1 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (=> (@ (@ tptp.member_real X) A2) (= (@ _let_1 A2) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_1 (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real X) tptp.bot_bot_set_real))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.real)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5808333547571424918x_real G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.rat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5058264527183730370ex_rat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.nat)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5693394587270226106ex_nat G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (G (-> tptp.complex tptp.int)) (X tptp.complex)) (let ((_let_1 (@ tptp.insert_complex X))) (let ((_let_2 (@ tptp.groups5690904116761175830ex_int G))) (=> (@ tptp.finite3207457112153483333omplex A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_int (@ G X)) (@ _let_2 (@ (@ tptp.minus_811609699411566653omplex A2) (@ _let_1 tptp.bot_bot_set_complex))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.real)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups8778361861064173332t_real G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.rat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups3906332499630173760nt_rat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (G (-> tptp.int tptp.nat)) (X tptp.int)) (let ((_let_1 (@ tptp.insert_int X))) (let ((_let_2 (@ tptp.groups4541462559716669496nt_nat G))) (=> (@ tptp.finite_finite_int A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_int A2) (@ _let_1 tptp.bot_bot_set_int))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups8097168146408367636l_real G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_real (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.rat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1300246762558778688al_rat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_rat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (G (-> tptp.real tptp.nat)) (X tptp.real)) (let ((_let_1 (@ tptp.insert_real X))) (let ((_let_2 (@ tptp.groups1935376822645274424al_nat G))) (=> (@ tptp.finite_finite_real A2) (= (@ _let_2 (@ _let_1 A2)) (@ (@ tptp.plus_plus_nat (@ G X)) (@ _let_2 (@ (@ tptp.minus_minus_set_real A2) (@ _let_1 tptp.bot_bot_set_real))))))))))
% 6.68/6.99 (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))))))))))
% 6.68/6.99 (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))))))))))
% 6.68/6.99 (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))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_complex) (A tptp.complex) (F (-> tptp.complex tptp.rat))) (let ((_let_1 (@ tptp.groups5058264527183730370ex_rat 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_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_int) (A tptp.int) (F (-> tptp.int tptp.rat))) (let ((_let_1 (@ tptp.groups3906332499630173760nt_rat 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_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (A tptp.real) (F (-> tptp.real tptp.rat))) (let ((_let_1 (@ tptp.groups1300246762558778688al_rat 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_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.68/6.99 (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))))))))))
% 6.68/6.99 (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))))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (A tptp.nat) (F (-> tptp.nat tptp.rat))) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat 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_rat _let_2) (@ F A)))) (=> (not _let_4) (= _let_3 _let_2))))))))))
% 6.68/6.99 (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))))))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (=> (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (not (forall ((N3 tptp.nat)) (=> (= K (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N3))) (not (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3))))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.int Bool)) (X tptp.nat) (Y tptp.nat)) (= (@ P (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat X) Y))) (and (=> (@ (@ tptp.ord_less_eq_nat Y) X) (@ P (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int X)) (@ tptp.semiri1314217659103216013at_int Y)))) (=> (@ (@ tptp.ord_less_nat X) Y) (@ P tptp.zero_zero_int))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real X))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) X)))) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.ln_ln_real X))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.real)) (C (-> tptp.complex tptp.real))) (let ((_let_1 (@ (@ tptp.groups5808333547571424918x_real C) (@ (@ tptp.minus_811609699411566653omplex 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)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5808333547571424918x_real (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.rat)) (C (-> tptp.complex tptp.rat))) (let ((_let_1 (@ (@ tptp.groups5058264527183730370ex_rat C) (@ (@ tptp.minus_811609699411566653omplex 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.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5058264527183730370ex_rat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.nat)) (C (-> tptp.complex tptp.nat))) (let ((_let_1 (@ (@ tptp.groups5693394587270226106ex_nat C) (@ (@ tptp.minus_811609699411566653omplex 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)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5693394587270226106ex_nat (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (A tptp.complex) (B (-> tptp.complex tptp.int)) (C (-> tptp.complex tptp.int))) (let ((_let_1 (@ (@ tptp.groups5690904116761175830ex_int C) (@ (@ tptp.minus_811609699411566653omplex 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)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_int (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups5690904116761175830ex_int (lambda ((K2 tptp.complex)) (@ (@ (@ tptp.if_int (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.real)) (C (-> tptp.int tptp.real))) (let ((_let_1 (@ (@ tptp.groups8778361861064173332t_real C) (@ (@ tptp.minus_minus_set_int 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.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8778361861064173332t_real (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.rat)) (C (-> tptp.int tptp.rat))) (let ((_let_1 (@ (@ tptp.groups3906332499630173760nt_rat C) (@ (@ tptp.minus_minus_set_int 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.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups3906332499630173760nt_rat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_int) (A tptp.int) (B (-> tptp.int tptp.nat)) (C (-> tptp.int tptp.nat))) (let ((_let_1 (@ (@ tptp.groups4541462559716669496nt_nat C) (@ (@ tptp.minus_minus_set_int 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.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((K2 tptp.int)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.real)) (C (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.groups8097168146408367636l_real C) (@ (@ tptp.minus_minus_set_real 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.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_real (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups8097168146408367636l_real (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_real (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.rat)) (C (-> tptp.real tptp.rat))) (let ((_let_1 (@ (@ tptp.groups1300246762558778688al_rat 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.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_rat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1300246762558778688al_rat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_rat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_real) (A tptp.real) (B (-> tptp.real tptp.nat)) (C (-> tptp.real tptp.nat))) (let ((_let_1 (@ (@ tptp.groups1935376822645274424al_nat C) (@ (@ tptp.minus_minus_set_real 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)) (@ B K2)) (@ C K2)))) S2) (@ (@ tptp.plus_plus_nat (@ B A)) _let_1))) (=> (not _let_2) (= (@ (@ tptp.groups1935376822645274424al_nat (lambda ((K2 tptp.real)) (@ (@ (@ tptp.if_nat (= K2 A)) (@ B K2)) (@ C K2)))) S2) _let_1))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.log A) X) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.ln_ln_real A))) (@ (@ tptp.log B) X)))))))))))
% 6.68/6.99 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.real))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups5808333547571424918x_real F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.real))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ 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 X6)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8778361861064173332t_real F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ 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 X6)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_real (@ F I)) (@ (@ tptp.groups8097168146408367636l_real F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.rat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups5058264527183730370ex_rat F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.rat))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups3906332499630173760nt_rat F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.rat))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups1300246762558778688al_rat F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.nat) (A2 tptp.set_nat) (F (-> tptp.nat tptp.rat))) (=> (@ (@ tptp.member_nat I) A2) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) (@ (@ tptp.minus_minus_set_nat A2) (@ (@ tptp.insert_nat I) tptp.bot_bot_set_nat))) (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ F X6)))) (=> (@ tptp.finite_finite_nat A2) (@ (@ tptp.ord_less_eq_rat (@ F I)) (@ (@ tptp.groups2906978787729119204at_rat F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.complex) (A2 tptp.set_complex) (F (-> tptp.complex tptp.nat))) (=> (@ (@ tptp.member_complex I) A2) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) (@ (@ tptp.minus_811609699411566653omplex A2) (@ (@ tptp.insert_complex I) tptp.bot_bot_set_complex))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (=> (@ tptp.finite3207457112153483333omplex A2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups5693394587270226106ex_nat F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.int) (A2 tptp.set_int) (F (-> tptp.int tptp.nat))) (=> (@ (@ tptp.member_int I) A2) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) (@ (@ tptp.minus_minus_set_int A2) (@ (@ tptp.insert_int I) tptp.bot_bot_set_int))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (=> (@ tptp.finite_finite_int A2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups4541462559716669496nt_nat F) A2)))))))
% 6.68/6.99 (assert (forall ((I tptp.real) (A2 tptp.set_real) (F (-> tptp.real tptp.nat))) (=> (@ (@ tptp.member_real I) A2) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.minus_minus_set_real A2) (@ (@ tptp.insert_real I) tptp.bot_bot_set_real))) (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) (@ F X6)))) (=> (@ tptp.finite_finite_real A2) (@ (@ tptp.ord_less_eq_nat (@ F I)) (@ (@ tptp.groups1935376822645274424al_nat F) A2)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X)) tptp.one_one_real)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real X) tptp.one_one_real)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 6.68/6.99 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (or (= M3 tptp.zero_zero_nat) (= N2 tptp.zero_zero_nat))) tptp.zero_zero_nat) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.68/6.99 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (and (not (@ _let_2 M3)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se727722235901077358nd_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (D tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (let ((_let_2 (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_complex A) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_complex (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex)) (@ (@ tptp.plus_plus_complex (@ _let_2 A)) (@ (@ tptp.times_times_complex _let_1) D))))))))
% 6.68/6.99 (assert (forall ((A tptp.rat) (D tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (let ((_let_2 (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_rat A) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_rat (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat)) (@ (@ tptp.plus_plus_rat (@ _let_2 A)) (@ (@ tptp.times_times_rat _let_1) D))))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (let ((_let_2 (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ _let_2 A)) (@ (@ tptp.times_times_int _let_1) D))))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (let ((_let_2 (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ _let_2 A)) (@ (@ tptp.times_times_nat _let_1) D))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (D tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (= (@ _let_2 (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_real A) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N))) (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (@ (@ tptp.plus_plus_real (@ _let_2 A)) (@ (@ tptp.times_times_real _let_1) D))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (D tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_int A) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int _let_1) A)) (@ (@ tptp.times_times_int _let_2) D)))) _let_1))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (D tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat A) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat I5)) D)))) (@ (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat _let_1) A)) (@ (@ tptp.times_times_nat _let_2) D)))) _let_1))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri8010041392384452111omplex N))) (= (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2073611262835488442omplex tptp.semiri8010041392384452111omplex) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_complex _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri681578069525770553at_rat N))) (= (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups2906978787729119204at_rat tptp.semiri681578069525770553at_rat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_rat _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (= (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.groups6591440286371151544t_real tptp.semiri5074537144036343181t_real) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N))) (@ (@ tptp.times_times_real _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.plus_plus_real tptp.one_one_real))) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) X))) (@ (@ tptp.power_power_real (@ _let_1 X)) N))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (let ((_let_2 (@ tptp.power_power_complex X))) (let ((_let_3 (@ (@ tptp.groups2073611262835488442omplex _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_complex (@ tptp.semiri8010041392384452111omplex N)) tptp.one_one_complex))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_rat (@ tptp.semiri681578069525770553at_rat N)) tptp.one_one_rat))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ (@ tptp.times_times_rat (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (let ((_let_2 (@ tptp.power_power_real X))) (let ((_let_3 (@ (@ tptp.groups6591440286371151544t_real _let_2) (@ (@ tptp.set_or1269000886237332187st_nat M) (@ (@ tptp.plus_plus_nat M) N))))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ (@ tptp.plus_plus_real (@ tptp.semiri5074537144036343181t_real N)) tptp.one_one_real))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ _let_2 M)) (@ _let_1 (@ _let_2 (@ tptp.suc N))))) (@ _let_1 X)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.semiri5074537144036343181t_real N))) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) _let_1))) N)) (@ tptp.exp_real (@ tptp.uminus_uminus_real X))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.log (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit0 tptp.one))))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ _let_1 X) (@ (@ tptp.times_times_real (@ _let_1 (@ tptp.exp_real tptp.one_one_real))) (@ tptp.ln_ln_real X)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int N))) (= (@ (@ tptp.groups3539618377306564664at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))) (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri1316708129612266289at_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat tptp.semiri1316708129612266289at_nat) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (= tptp.semiri8010041392384452111omplex (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_complex (= N2 tptp.zero_zero_nat)) tptp.zero_zero_complex) (@ (@ tptp.produc1917071388513777916omplex (lambda ((M3 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.semiri8010041392384452111omplex M3)))) (@ (@ (@ tptp.if_complex (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_complex _let_1) tptp.one_one_complex))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (= tptp.semiri5074537144036343181t_real (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ tptp.produc1703576794950452218t_real (lambda ((M3 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real M3)))) (@ (@ (@ tptp.if_real (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (= tptp.semiri681578069525770553at_rat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_rat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_rat) (@ (@ tptp.produc6207742614233964070at_rat (lambda ((M3 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_rat (@ tptp.numeral_numeral_rat (@ tptp.bit0 tptp.one))) (@ tptp.semiri681578069525770553at_rat M3)))) (@ (@ (@ tptp.if_rat (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_rat _let_1) tptp.one_one_rat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.semiri1316708129612266289at_nat M3)))) (@ (@ (@ tptp.if_nat (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.if_int (= N2 tptp.zero_zero_nat)) tptp.zero_zero_int) (@ (@ tptp.produc6840382203811409530at_int (lambda ((M3 tptp.nat) (Q5 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.semiri1314217659103216013at_int M3)))) (@ (@ (@ tptp.if_int (= Q5 tptp.zero_zero_nat)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.divmod_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))))))
% 6.68/6.99 (assert (forall ((H2 tptp.real) (Z tptp.real) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)))) (let ((_let_4 (@ tptp.power_power_real Z))) (let ((_let_5 (@ (@ tptp.plus_plus_real Z) H2))) (=> (not (= H2 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real _let_5)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real _let_5) N)) (@ _let_4 N))) H2)) (@ _let_3 (@ _let_4 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V7735802525324610683m_real H2)))))))))))))
% 6.68/6.99 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (K5 tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (let ((_let_2 (@ _let_1 (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_3 (@ tptp.power_power_complex Z))) (let ((_let_4 (@ (@ tptp.plus_plus_complex Z) H2))) (=> (not (= H2 tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) K5) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex _let_4)) K5) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex _let_4) N)) (@ _let_3 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_3 _let_2))))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ tptp.semiri5074537144036343181t_real _let_2))) (@ (@ tptp.power_power_real K5) (@ _let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ tptp.real_V1022390504157884413omplex H2))))))))))))
% 6.68/6.99 (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 ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat N2) tptp.one_one_nat))))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) tptp.one_one_real)) (@ tptp.suc N2))))))))))
% 6.68/6.99 (assert (forall ((H2 tptp.complex) (Z tptp.complex) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_complex Z))) (=> (not (= H2 tptp.zero_zero_complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_complex H2) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P2 tptp.nat)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) Q5)) (@ (@ tptp.power_power_complex Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P2))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.68/6.99 (assert (forall ((H2 tptp.rat) (Z tptp.rat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_rat Z))) (=> (not (= H2 tptp.zero_zero_rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_rat H2) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P2 tptp.nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) Q5)) (@ (@ tptp.power_power_rat Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P2))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.68/6.99 (assert (forall ((H2 tptp.real) (Z tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))) (let ((_let_2 (@ tptp.power_power_real Z))) (=> (not (= H2 tptp.zero_zero_real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) N)) (@ _let_2 N))) H2)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ _let_2 _let_1))) (@ (@ tptp.times_times_real H2) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((Q5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) Q5)) (@ (@ tptp.power_power_real Z) (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Q5))))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))) P2))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat X) (@ tptp.set_ord_lessThan_nat Y)) (= X Y))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (= (= (@ tptp.set_ord_lessThan_int X) (@ tptp.set_ord_lessThan_int Y)) (= X Y))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.set_or5984915006950818249n_real X) (@ tptp.set_or5984915006950818249n_real Y)) (= X Y))))
% 6.68/6.99 (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))))
% 6.68/6.99 (assert (forall ((I tptp.rat) (K tptp.rat)) (= (@ (@ tptp.member_rat I) (@ tptp.set_ord_lessThan_rat K)) (@ (@ tptp.ord_less_rat I) K))))
% 6.68/6.99 (assert (forall ((I tptp.num) (K tptp.num)) (= (@ (@ tptp.member_num I) (@ tptp.set_ord_lessThan_num K)) (@ (@ tptp.ord_less_num I) K))))
% 6.68/6.99 (assert (forall ((I tptp.nat) (K tptp.nat)) (= (@ (@ tptp.member_nat I) (@ tptp.set_ord_lessThan_nat K)) (@ (@ tptp.ord_less_nat I) K))))
% 6.68/6.99 (assert (forall ((I tptp.int) (K tptp.int)) (= (@ (@ tptp.member_int I) (@ tptp.set_ord_lessThan_int K)) (@ (@ tptp.ord_less_int I) K))))
% 6.68/6.99 (assert (forall ((I tptp.real) (K tptp.real)) (= (@ (@ tptp.member_real I) (@ tptp.set_or5984915006950818249n_real K)) (@ (@ tptp.ord_less_real I) K))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_lessThan_nat K))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ tptp.ord_less_eq_set_rat (@ tptp.set_ord_lessThan_rat X)) (@ tptp.set_ord_lessThan_rat Y)) (@ (@ tptp.ord_less_eq_rat X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ tptp.ord_less_eq_set_num (@ tptp.set_ord_lessThan_num X)) (@ tptp.set_ord_lessThan_num Y)) (@ (@ tptp.ord_less_eq_num X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ tptp.ord_less_eq_set_nat (@ tptp.set_ord_lessThan_nat X)) (@ tptp.set_ord_lessThan_nat Y)) (@ (@ tptp.ord_less_eq_nat X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.ord_less_eq_set_int (@ tptp.set_ord_lessThan_int X)) (@ tptp.set_ord_lessThan_int Y)) (@ (@ tptp.ord_less_eq_int X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_set_real (@ tptp.set_or5984915006950818249n_real X)) (@ tptp.set_or5984915006950818249n_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.68/6.99 (assert (= (@ tptp.set_ord_lessThan_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups2906978787729119204at_rat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3539618377306564664at_int G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups3542108847815614940at_nat G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.groups6591440286371151544t_real G))) (= (@ _let_1 (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ _let_1 (@ tptp.set_ord_lessThan_nat N))) (@ G N))))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat))) (= (@ (@ tptp.minus_minus_set_nat _let_1) (@ tptp.set_ord_lessThan_nat K)) _let_1))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (let ((_let_1 (@ (@ tptp.insert_int K) tptp.bot_bot_set_int))) (= (@ (@ tptp.minus_minus_set_int _let_1) (@ tptp.set_ord_lessThan_int K)) _let_1))))
% 6.68/6.99 (assert (forall ((K tptp.real)) (let ((_let_1 (@ (@ tptp.insert_real K) tptp.bot_bot_set_real))) (= (@ (@ tptp.minus_minus_set_real _let_1) (@ tptp.set_or5984915006950818249n_real K)) _let_1))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.complex))) (= (@ tptp.suminf_complex (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_complex (@ F N2)) (@ (@ tptp.power_power_complex tptp.zero_zero_complex) N2)))) (@ F tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real))) (= (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real tptp.zero_zero_real) N2)))) (@ F tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (N tptp.nat)) (=> (@ tptp.finite_finite_nat A2) (=> (not (@ (@ tptp.member_nat N) A2)) (= (@ tptp.nat_set_encode (@ (@ tptp.insert_nat N) A2)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ tptp.nat_set_encode A2)))))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.pred_numeral K))) (= (@ tptp.set_ord_lessThan_nat (@ tptp.numeral_numeral_nat K)) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_lessThan_nat _let_1))))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ (@ tptp.insert_nat K) (@ tptp.set_ord_lessThan_nat K)))))
% 6.68/6.99 (assert (forall ((X tptp.int)) (not (= (@ tptp.set_ord_lessThan_int X) tptp.bot_bot_set_int))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (not (= (@ tptp.set_or5984915006950818249n_real X) tptp.bot_bot_set_real))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (not (@ tptp.finite_finite_int (@ tptp.set_ord_lessThan_int A)))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (not (@ tptp.finite_finite_real (@ tptp.set_or5984915006950818249n_real A)))))
% 6.68/6.99 (assert (= tptp.set_or890127255671739683et_nat (lambda ((U2 tptp.set_nat)) (@ tptp.collect_set_nat (lambda ((X3 tptp.set_nat)) (@ (@ tptp.ord_less_set_nat X3) U2))))))
% 6.68/6.99 (assert (= tptp.set_ord_lessThan_rat (lambda ((U2 tptp.rat)) (@ tptp.collect_rat (lambda ((X3 tptp.rat)) (@ (@ tptp.ord_less_rat X3) U2))))))
% 6.68/6.99 (assert (= tptp.set_ord_lessThan_num (lambda ((U2 tptp.num)) (@ tptp.collect_num (lambda ((X3 tptp.num)) (@ (@ tptp.ord_less_num X3) U2))))))
% 6.68/6.99 (assert (= tptp.set_ord_lessThan_nat (lambda ((U2 tptp.nat)) (@ tptp.collect_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.ord_less_nat X3) U2))))))
% 6.68/6.99 (assert (= tptp.set_ord_lessThan_int (lambda ((U2 tptp.int)) (@ tptp.collect_int (lambda ((X3 tptp.int)) (@ (@ tptp.ord_less_int X3) U2))))))
% 6.68/6.99 (assert (= tptp.set_or5984915006950818249n_real (lambda ((U2 tptp.real)) (@ tptp.collect_real (lambda ((X3 tptp.real)) (@ (@ tptp.ord_less_real X3) U2))))))
% 6.68/6.99 (assert (forall ((N tptp.extended_enat)) (= (= (@ tptp.set_or8419480210114673929d_enat N) tptp.bot_bo7653980558646680370d_enat) (= N tptp.bot_bo4199563552545308370d_enat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.bot_bot_nat))))
% 6.68/6.99 (assert (forall ((M tptp.rat) (N tptp.rat)) (= (@ (@ tptp.ord_less_set_rat (@ tptp.set_ord_lessThan_rat M)) (@ tptp.set_ord_lessThan_rat N)) (@ (@ tptp.ord_less_rat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.ord_less_set_num (@ tptp.set_ord_lessThan_num M)) (@ tptp.set_ord_lessThan_num N)) (@ (@ tptp.ord_less_num M) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_set_nat (@ tptp.set_ord_lessThan_nat M)) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.ord_less_nat M) N))))
% 6.68/6.99 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_set_int (@ tptp.set_ord_lessThan_int M)) (@ tptp.set_ord_lessThan_int N)) (@ (@ tptp.ord_less_int M) N))))
% 6.68/6.99 (assert (forall ((M tptp.real) (N tptp.real)) (= (@ (@ tptp.ord_less_set_real (@ tptp.set_or5984915006950818249n_real M)) (@ tptp.set_or5984915006950818249n_real N)) (@ (@ tptp.ord_less_real M) N))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex X))) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.68/6.99 (assert (forall ((B tptp.complex) (A tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex B) A))) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex A))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (= (@ tptp.set_ord_lessThan_nat N) tptp.bot_bot_set_nat) (= N tptp.zero_zero_nat))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (let ((_let_2 (@ tptp.suc N))) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.set_or1269000886237332187st_nat M) N) (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat M))) (let ((_let_2 (@ tptp.suc N))) (=> (@ (@ tptp.ord_less_eq_nat M) _let_2) (= (@ _let_1 _let_2) (@ (@ tptp.insert_nat _let_2) (@ _let_1 N))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.insert_nat M) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc M)) N)) (@ (@ tptp.set_or1269000886237332187st_nat M) N)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real X))) (@ tptp.exp_real (@ tptp.real_V7735802525324610683m_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex X))) (@ tptp.exp_real (@ tptp.real_V1022390504157884413omplex X)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups3542108847815614940at_nat G) _let_1)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real G) _let_1)))))
% 6.68/6.99 (assert (forall ((Q (-> tptp.int tptp.nat)) (P (-> tptp.int tptp.nat)) (N tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_int N))) (=> (forall ((X6 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ Q X6)) (@ P X6))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups4541462559716669496nt_nat P) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat Q) _let_1)) (@ (@ tptp.groups4541462559716669496nt_nat (lambda ((X3 tptp.int)) (@ (@ tptp.minus_minus_nat (@ P X3)) (@ Q X3)))) _let_1))))))
% 6.68/6.99 (assert (forall ((Q (-> tptp.real tptp.nat)) (P (-> tptp.real tptp.nat)) (N tptp.real)) (let ((_let_1 (@ tptp.set_or5984915006950818249n_real N))) (=> (forall ((X6 tptp.real)) (@ (@ tptp.ord_less_eq_nat (@ Q X6)) (@ P X6))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups1935376822645274424al_nat P) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat Q) _let_1)) (@ (@ tptp.groups1935376822645274424al_nat (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_nat (@ P X3)) (@ Q X3)))) _let_1))))))
% 6.68/6.99 (assert (forall ((Q (-> tptp.nat tptp.nat)) (P (-> tptp.nat tptp.nat)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (=> (forall ((X6 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ Q X6)) (@ P X6))) (= (@ (@ tptp.minus_minus_nat (@ (@ tptp.groups3542108847815614940at_nat P) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat Q) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ P X3)) (@ Q X3)))) _let_1))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.rat)) (N tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_rat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.int)) (N tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_int (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_nat (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) (@ (@ tptp.plus_plus_real (@ G tptp.zero_zero_nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ tptp.suc I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F (@ tptp.suc N2))) (@ F N2)))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F M)) (@ F tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.rat)) (M tptp.nat)) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_rat (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.int)) (M tptp.nat)) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_int (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (M tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ F (@ tptp.suc N2))))) (@ tptp.set_ord_lessThan_nat M)) (@ (@ tptp.minus_minus_real (@ F tptp.zero_zero_nat)) (@ F M)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.complex)) (N tptp.nat) (R tptp.complex)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.groups2073611262835488442omplex F) _let_1)) (@ (@ tptp.times_times_complex (@ tptp.semiri8010041392384452111omplex N)) R)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_complex (@ F I5)) R))) _let_1)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.rat)) (N tptp.nat) (R tptp.rat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.groups2906978787729119204at_rat F) _let_1)) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) R)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_rat (@ F I5)) R))) _let_1)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.int)) (N tptp.nat) (R tptp.int)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.groups3539618377306564664at_int F) _let_1)) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) R)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_int (@ F I5)) R))) _let_1)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (N tptp.nat) (R tptp.real)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.groups6591440286371151544t_real F) _let_1)) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) R)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F I5)) R))) _let_1)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.nat)) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real G) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((K2 tptp.nat)) (@ G (@ tptp.suc K2)))) (@ tptp.set_ord_lessThan_nat N)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex X))) (= (@ (@ tptp.minus_minus_complex (@ _let_1 N)) 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 N)))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (= (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_int X))) (= (@ (@ tptp.minus_minus_int (@ _let_1 N)) 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 N)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_real X))) (= (@ (@ tptp.minus_minus_real (@ _let_1 N)) 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 N)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N 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 N)) (@ (@ tptp.times_times_complex (@ _let_2 X)) (@ (@ tptp.groups2073611262835488442omplex _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (let ((_let_2 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_2 (@ _let_1 N)) (@ (@ tptp.times_times_rat (@ _let_2 X)) (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N 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 N)) (@ (@ tptp.times_times_int (@ _let_2 X)) (@ (@ tptp.groups3539618377306564664at_int _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N 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 N)) (@ (@ tptp.times_times_real (@ _let_2 X)) (@ (@ tptp.groups6591440286371151544t_real _let_1) (@ tptp.set_ord_lessThan_nat N))))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N 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 N)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.minus_minus_complex (@ _let_1 N)) tptp.one_one_complex)) (@ (@ tptp.minus_minus_complex X) tptp.one_one_complex)))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat X))) (=> (not (= X tptp.one_one_rat)) (= (@ (@ tptp.groups2906978787729119204at_rat _let_1) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.divide_divide_rat (@ (@ tptp.minus_minus_rat (@ _let_1 N)) tptp.one_one_rat)) (@ (@ tptp.minus_minus_rat X) tptp.one_one_rat)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N 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 N)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_1 N)) tptp.one_one_real)) (@ (@ tptp.minus_minus_real X) tptp.one_one_real)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ tptp.topolo6980174941875973593q_real (@ tptp.power_power_real X))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N 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 N)))) (let ((_let_4 (= X tptp.one_one_complex))) (and (=> _let_4 (= _let_3 (@ tptp.semiri8010041392384452111omplex N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide1717551699836669952omplex (@ _let_1 (@ _let_2 N))) (@ _let_1 X)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (let ((_let_2 (@ tptp.power_power_rat X))) (let ((_let_3 (@ (@ tptp.groups2906978787729119204at_rat _let_2) (@ tptp.set_ord_lessThan_nat N)))) (let ((_let_4 (= X tptp.one_one_rat))) (and (=> _let_4 (= _let_3 (@ tptp.semiri681578069525770553at_rat N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_rat (@ _let_1 (@ _let_2 N))) (@ _let_1 X)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N 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 N)))) (let ((_let_4 (= X tptp.one_one_real))) (and (=> _let_4 (= _let_3 (@ tptp.semiri5074537144036343181t_real N))) (=> (not _let_4) (= _let_3 (@ (@ tptp.divide_divide_real (@ _let_1 (@ _let_2 N))) (@ _let_1 X)))))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (H2 tptp.complex) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2073611262835488442omplex (lambda ((P2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_complex Z))) (@ (@ tptp.minus_minus_complex (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) (@ (@ tptp.minus_minus_nat M) P2))) (@ _let_1 P2))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2073611262835488442omplex (lambda ((P2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P2))) (let ((_let_2 (@ tptp.power_power_complex Z))) (@ (@ tptp.times_times_complex (@ _let_2 P2)) (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex (@ (@ tptp.plus_plus_complex Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.68/6.99 (assert (forall ((Z tptp.rat) (H2 tptp.rat) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_rat Z))) (@ (@ tptp.minus_minus_rat (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) (@ (@ tptp.minus_minus_nat M) P2))) (@ _let_1 P2))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P2))) (let ((_let_2 (@ tptp.power_power_rat Z))) (@ (@ tptp.times_times_rat (@ _let_2 P2)) (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat (@ (@ tptp.plus_plus_rat Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (H2 tptp.int) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups3539618377306564664at_int (lambda ((P2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_int Z))) (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) (@ (@ tptp.minus_minus_nat M) P2))) (@ _let_1 P2))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups3539618377306564664at_int (lambda ((P2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P2))) (let ((_let_2 (@ tptp.power_power_int Z))) (@ (@ tptp.times_times_int (@ _let_2 P2)) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ (@ tptp.plus_plus_int Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.68/6.99 (assert (forall ((Z tptp.real) (H2 tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat M))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((P2 tptp.nat)) (let ((_let_1 (@ tptp.power_power_real Z))) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) (@ (@ tptp.minus_minus_nat M) P2))) (@ _let_1 P2))) (@ _let_1 M))))) _let_1) (@ (@ tptp.groups6591440286371151544t_real (lambda ((P2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat M) P2))) (let ((_let_2 (@ tptp.power_power_real Z))) (@ (@ tptp.times_times_real (@ _let_2 P2)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real Z) H2)) _let_1)) (@ _let_2 _let_1))))))) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex Y) N)) (@ (@ tptp.times_times_complex (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5)))) (@ (@ tptp.power_power_complex X) I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (N tptp.nat) (Y tptp.rat)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.power_power_rat Y) N)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5)))) (@ (@ tptp.power_power_rat X) I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (= (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.power_power_int Y) N)) (@ (@ tptp.times_times_int (@ (@ tptp.minus_minus_int X) Y)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5)))) (@ (@ tptp.power_power_int X) I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (= (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real Y) N)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real X) Y)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5)))) (@ (@ tptp.power_power_real X) I5)))) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat) (Y tptp.complex)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ 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 ((P2 tptp.nat)) (@ (@ tptp.times_times_complex (@ (@ tptp.power_power_complex X) P2)) (@ (@ tptp.power_power_complex Y) (@ (@ tptp.minus_minus_nat N) P2))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (N tptp.nat) (Y tptp.rat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.power_power_rat X) _let_1)) (@ (@ tptp.power_power_rat Y) _let_1)) (@ (@ tptp.times_times_rat (@ (@ tptp.minus_minus_rat X) Y)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((P2 tptp.nat)) (@ (@ tptp.times_times_rat (@ (@ tptp.power_power_rat X) P2)) (@ (@ tptp.power_power_rat Y) (@ (@ tptp.minus_minus_nat N) P2))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ 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 ((P2 tptp.nat)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int X) P2)) (@ (@ tptp.power_power_int Y) (@ (@ tptp.minus_minus_nat N) P2))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ 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 ((P2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real X) P2)) (@ (@ tptp.power_power_real Y) (@ (@ tptp.minus_minus_nat N) P2))))) (@ tptp.set_ord_lessThan_nat _let_1)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Z tptp.nat)) (let ((_let_1 (@ tptp.nat_set_decode Z))) (=> (not (@ (@ tptp.member_nat N) _let_1)) (= (@ tptp.nat_set_decode (@ (@ tptp.plus_plus_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) Z)) (@ (@ tptp.insert_nat N) _let_1))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.rat)) (K5 tptp.rat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_rat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) K5) (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.groups2906978787729119204at_rat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_rat (@ tptp.semiri681578069525770553at_rat N)) K5))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.int)) (K5 tptp.int) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_int (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K5) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.groups3539618377306564664at_int F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int N)) K5))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.nat)) (K5 tptp.nat) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_nat (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_nat tptp.zero_zero_nat) K5) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat N)) K5))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (F (-> tptp.nat tptp.real)) (K5 tptp.real) (K tptp.nat)) (=> (forall ((P7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat P7) N) (@ (@ tptp.ord_less_eq_real (@ F P7)) K5))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) K5) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) K5))))))
% 6.68/6.99 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) _let_1)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_1)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_complex tptp.one_one_complex))) (= (@ _let_1 (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.times_times_complex (@ _let_1 X)) (@ (@ tptp.groups2073611262835488442omplex (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_complex X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.68/6.99 (assert (forall ((X tptp.rat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_rat tptp.one_one_rat))) (= (@ _let_1 (@ (@ tptp.power_power_rat X) N)) (@ (@ tptp.times_times_rat (@ _let_1 X)) (@ (@ tptp.groups2906978787729119204at_rat (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_rat X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_int tptp.one_one_int))) (= (@ _let_1 (@ (@ tptp.power_power_int X) N)) (@ (@ tptp.times_times_int (@ _let_1 X)) (@ (@ tptp.groups3539618377306564664at_int (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_int X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_real tptp.one_one_real))) (= (@ _let_1 (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc I5))))) (@ tptp.set_ord_lessThan_nat N)))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real)) (N tptp.nat)) (let ((_let_1 (@ tptp.set_ord_lessThan_nat N))) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) (@ F I5)) (@ G I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ F (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)))) _let_1)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ G (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) I5)) tptp.one_one_nat)))) _let_1))))))
% 6.68/6.99 (assert (forall ((Z tptp.real)) (let ((_let_1 (@ tptp.real_V7735802525324610683m_real Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ tptp.exp_real Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real _let_1) (@ (@ tptp.divide_divide_real tptp.one_one_real) _let_2)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ tptp.exp_complex Z))) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real _let_2) _let_1))))))))
% 6.68/6.99 (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))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real A) _let_1)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real A)) _let_1)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex A) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.numeral_numeral_real W)))))
% 6.68/6.99 (assert (forall ((W tptp.num) (A tptp.real)) (let ((_let_1 (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)))) (= (@ tptp.real_V7735802525324610683m_real (@ _let_1 A)) (@ _let_1 (@ tptp.real_V7735802525324610683m_real A))))))
% 6.68/6.99 (assert (forall ((W tptp.num) (A tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex W)) A)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real W)) (@ tptp.real_V1022390504157884413omplex A)))))
% 6.68/6.99 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real (@ tptp.uminus_uminus_real _let_1)) _let_1))))
% 6.68/6.99 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (@ tptp.numeral_numeral_real W))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.68/6.99 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.real_V7735802525324610683m_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (= (= (@ tptp.real_V1022390504157884413omplex X) tptp.zero_zero_real) (= X tptp.zero_zero_complex))))
% 6.68/6.99 (assert (= (@ tptp.real_V7735802525324610683m_real tptp.one_one_real) tptp.one_one_real))
% 6.68/6.99 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.one_one_complex) tptp.one_one_real))
% 6.68/6.99 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real W))) (= (@ tptp.real_V7735802525324610683m_real _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((W tptp.num)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.numera6690914467698888265omplex W)) (@ tptp.numeral_numeral_real W))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V7735802525324610683m_real X)) (not (= X tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X)) (not (= X tptp.zero_zero_complex)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) A)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) A)))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (not (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.real_V1022390504157884413omplex X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_real) (F (-> tptp.real tptp.complex)) (G (-> tptp.real tptp.real))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X6))) (@ G X6)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups5754745047067104278omplex F) S2))) (@ (@ tptp.groups8097168146408367636l_real G) S2)))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_set_nat) (F (-> tptp.set_nat tptp.complex)) (G (-> tptp.set_nat tptp.real))) (=> (forall ((X6 tptp.set_nat)) (=> (@ (@ tptp.member_set_nat X6) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X6))) (@ G X6)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups8255218700646806128omplex F) S2))) (@ (@ tptp.groups5107569545109728110t_real G) S2)))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_int) (F (-> tptp.int tptp.complex)) (G (-> tptp.int tptp.real))) (=> (forall ((X6 tptp.int)) (=> (@ (@ tptp.member_int X6) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X6))) (@ G X6)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups3049146728041665814omplex F) S2))) (@ (@ tptp.groups8778361861064173332t_real G) S2)))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.complex)) (G (-> tptp.nat tptp.real))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X6))) (@ G X6)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_complex) (F (-> tptp.complex tptp.complex)) (G (-> tptp.complex tptp.real))) (=> (forall ((X6 tptp.complex)) (=> (@ (@ tptp.member_complex X6) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ F X6))) (@ G X6)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) S2))) (@ (@ tptp.groups5808333547571424918x_real G) S2)))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat) (F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.member_nat X6) S2) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ F X6))) (@ G X6)))) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) S2))) (@ (@ tptp.groups6591440286371151544t_real G) S2)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N)) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.complex)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups2073611262835488442omplex F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))))
% 6.68/6.99 (assert (forall ((F (-> tptp.complex tptp.complex)) (A2 tptp.set_complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.groups7754918857620584856omplex F) A2))) (@ (@ tptp.groups5808333547571424918x_real (lambda ((I5 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ F I5)))) A2))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (A2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.groups6591440286371151544t_real F) A2))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ tptp.real_V7735802525324610683m_real (@ F I5)))) A2))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ tptp.uminus_uminus_real X)) Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ tptp.uminus1482373934393186551omplex X)) Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y)))))
% 6.68/6.99 (assert (forall ((B tptp.real) (A tptp.real)) (=> (not (= B tptp.zero_zero_real)) (= (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.divide_divide_real A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))))))
% 6.68/6.99 (assert (forall ((B tptp.complex) (A tptp.complex)) (=> (not (= B tptp.zero_zero_complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.divide1717551699836669952omplex A) B)) (@ (@ tptp.divide_divide_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))))))
% 6.68/6.99 (assert (forall ((W tptp.real) (N tptp.nat) (Z tptp.real)) (=> (= (@ (@ tptp.power_power_real W) N) (@ (@ tptp.power_power_real Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V7735802525324610683m_real W) (@ tptp.real_V7735802525324610683m_real Z))))))
% 6.68/6.99 (assert (forall ((W tptp.complex) (N tptp.nat) (Z tptp.complex)) (=> (= (@ (@ tptp.power_power_complex W) N) (@ (@ tptp.power_power_complex Z) N)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.real_V1022390504157884413omplex W) (@ tptp.real_V1022390504157884413omplex Z))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real R) S))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex Y)) S) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real R) S))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex X) Y))) (@ (@ tptp.times_times_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.68/6.99 (assert (forall ((X tptp.real) (R tptp.real) (Y tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real X)) R) (=> (@ (@ 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 R) S))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (R tptp.real) (Y tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex X)) R) (=> (@ (@ 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 R) S))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.power_power_real X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V7735802525324610683m_real X)) N))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.power_power_complex X) N))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex X)) N))))
% 6.68/6.99 (assert (forall ((A tptp.real) (R tptp.real) (B tptp.real) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (R tptp.real) (B tptp.complex) (S tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex A)) R) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) S) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) (@ (@ tptp.plus_plus_real R) S))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real X) Y))) E))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex X) Y))) E))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) C)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B))) C) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex B)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) C)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real X)) (@ tptp.real_V7735802525324610683m_real Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))) E))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex) (E tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y))) E) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))) E))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (E1 tptp.real) (Z tptp.real) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_real X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex) (E1 tptp.real) (Z tptp.complex) (E22 tptp.real)) (let ((_let_1 (@ tptp.minus_minus_complex X))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Y))) E1) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Y) Z))) E22) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ _let_1 Z))) (@ (@ tptp.plus_plus_real E1) E22)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real Y)) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real X) Y))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Y)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X) Y))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.plus_plus_real A) B)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex A) B)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.68/6.99 (assert (forall ((W tptp.real) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_real W) N) tptp.one_one_real) (or (= (@ tptp.real_V7735802525324610683m_real W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((W tptp.complex) (N tptp.nat)) (=> (= (@ (@ tptp.power_power_complex W) N) tptp.one_one_complex) (or (= (@ tptp.real_V1022390504157884413omplex W) tptp.one_one_real) (= N tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real (@ (@ tptp.plus_plus_real A) B)) (@ (@ tptp.plus_plus_real C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) C))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real B) D))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex) (C tptp.complex) (D tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.plus_plus_complex A) B)) (@ (@ tptp.plus_plus_complex C) D)))) (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) C))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex B) D))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V7735802525324610683m_real A)) (@ tptp.real_V7735802525324610683m_real B)))) (@ tptp.real_V7735802525324610683m_real (@ (@ tptp.minus_minus_real A) B)))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex A)) (@ tptp.real_V1022390504157884413omplex B)))) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex A) B)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (= (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_real) (= (@ tptp.real_V7735802525324610683m_real X) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (=> (= (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) tptp.one_one_complex) (= (@ tptp.real_V1022390504157884413omplex X) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (W tptp.complex) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex W)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex (@ (@ tptp.power_power_complex Z) M)) (@ (@ tptp.power_power_complex W) M)))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex Z) W))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real tptp.zero_zero_real) M3)))) (@ tptp.set_ord_lessThan_nat (@ tptp.suc N))) tptp.one_one_real)))
% 6.68/6.99 (assert (= (@ tptp.cos_coeff tptp.zero_zero_nat) tptp.one_one_real))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.68/6.99 (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)))))))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_eq_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int N)) tptp.one_one_int))))))))
% 6.68/6.99 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B))))))
% 6.68/6.99 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim7802044766580827645g_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B))))))
% 6.68/6.99 (assert (not (= tptp.pi tptp.zero_zero_real)))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) tptp.pi))
% 6.68/6.99 (assert (not (@ (@ tptp.ord_less_real tptp.pi) tptp.zero_zero_real)))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) tptp.pi))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ F N3))) (@ G N3))))) (=> (@ tptp.summable_real G) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.suminf_real F))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ tptp.abs_abs_real (@ F N2))))))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (not (= (@ (@ tptp.divide_divide_real tptp.pi) _let_1) _let_1))))
% 6.68/6.99 (assert (not (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) _let_1)))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (Z tptp.real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F I4)) tptp.one_one_real)) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F I4))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Z) (=> (@ (@ tptp.ord_less_real Z) tptp.one_one_real) (@ tptp.summable_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ F I5)) (@ (@ tptp.power_power_real Z) I5))))))))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) tptp.pi))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.arctan Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (= (@ tptp.arctan tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arctan Y))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arctan Y))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.bit0 _let_1))) (let ((_let_3 (@ tptp.bit1 tptp.one))) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_1))) (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_3)))))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real _let_3)) (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 _let_2))))))))) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_2)))))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.divide_divide_real tptp.one_one_real))) (let ((_let_2 (@ tptp.bit0 tptp.one))) (let ((_let_3 (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_2)))) (= (@ (@ tptp.divide_divide_real tptp.pi) _let_3) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real _let_3) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 _let_2)))))) (@ tptp.arctan (@ _let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit1 (@ tptp.bit0 (@ tptp.bit1 (@ tptp.bit1 tptp.one))))))))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (K tptp.nat)) (=> (@ tptp.summable_real F) (=> (forall ((D3 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))) D3))) (let ((_let_2 (@ tptp.plus_plus_nat K))) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ F (@ _let_2 _let_1))) (@ F (@ _let_2 (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))))))) (@ (@ tptp.ord_less_real (@ (@ tptp.groups6591440286371151544t_real F) (@ tptp.set_ord_lessThan_nat K))) (@ tptp.suminf_real F))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim7802044766580827645g_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) _let_2)) tptp.one_one_nat))))) tptp.one_one_int))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)))) tptp.pi)) (@ tptp.numeral_numeral_real _let_1))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) M))))) (@ tptp.numeral_numeral_real _let_1))) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (let ((_let_3 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_2 K)) (not (@ _let_2 L2)))))) (let ((_let_4 (@ (@ tptp.bit_se725231765392027082nd_int K) L2))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int K) _let_5) (@ (@ tptp.member_int L2) _let_5)))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int K) L2)) (and (=> _let_6 (= _let_4 (@ tptp.uminus_uminus_int _let_3))) (=> (not _let_6) (= _let_4 (@ (@ tptp.plus_plus_int _let_3) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int K) _let_1)) (@ (@ tptp.divide_divide_int L2) _let_1))))))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_3 (@ tptp.dvd_dvd_int _let_2))) (let ((_let_4 (@ tptp.zero_n2684676970156552555ol_int (and (not (@ _let_3 X)) (not (@ _let_3 Xa2)))))) (let ((_let_5 (@ (@ tptp.insert_int tptp.zero_zero_int) (@ (@ tptp.insert_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.bot_bot_set_int)))) (let ((_let_6 (and (@ (@ tptp.member_int X) _let_5) (@ (@ tptp.member_int Xa2) _let_5)))) (=> (= (@ (@ tptp.bit_se725231765392027082nd_int X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_6 (= Y (@ tptp.uminus_uminus_int _let_4))) (=> (not _let_6) (= Y (@ (@ tptp.plus_plus_int _let_4) (@ (@ tptp.times_times_int _let_2) (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.divide_divide_int X) _let_2)) (@ (@ tptp.divide_divide_int Xa2) _let_2))))))) (not _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (not (= X tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (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 ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))
% 6.68/6.99 (assert (= (@ tptp.sin_real tptp.pi) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.sin_real X))))
% 6.68/6.99 (assert (= (@ tptp.cos_real tptp.pi) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real tptp.pi) X)) (@ tptp.uminus_uminus_real (@ tptp.cos_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real X) tptp.pi)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.68/6.99 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.one_one_real))
% 6.68/6.99 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_real))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cos_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.sin_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.cos_real X))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.semiri5074537144036343181t_real N))) tptp.pi)) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) X)) (@ tptp.uminus_uminus_real (@ tptp.sin_real X)))))
% 6.68/6.99 (assert (forall ((N tptp.int)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((N tptp.int)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.ring_1_of_int_real N))) tptp.one_one_real)))
% 6.68/6.99 (assert (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi)) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((N tptp.int)) (let ((_let_1 (@ tptp.cos_real (@ (@ tptp.times_times_real tptp.pi) (@ tptp.ring_1_of_int_real N))))) (let ((_let_2 (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (and (=> _let_2 (= _let_1 tptp.one_one_real)) (=> (not _let_2) (= _let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (exists ((R2 tptp.real) (A5 tptp.real)) (let ((_let_1 (@ tptp.times_times_real R2))) (and (= X (@ _let_1 (@ tptp.cos_real A5))) (= Y (@ _let_1 (@ tptp.sin_real A5))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= (@ tptp.abs_abs_real (@ tptp.cos_real X)) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (exists ((Y5 tptp.real)) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) Y5) (@ (@ tptp.ord_less_eq_real Y5) tptp.pi) (= (@ tptp.sin_real Y5) (@ tptp.sin_real X)) (= (@ tptp.cos_real Y5) (@ tptp.cos_real X))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) (@ tptp.abs_abs_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (not (= (@ tptp.cos_real (@ tptp.arctan X)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.sin_real X)) (@ tptp.sin_real Y))) (@ (@ tptp.times_times_real (@ tptp.cos_real X)) (@ tptp.cos_real Y))))) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real X)) (@ tptp.sin_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.sin_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (=> (= (@ tptp.cos_real X) (@ tptp.cos_real Y)) (= X Y)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_2 Y) (=> (@ _let_1 tptp.pi) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ _let_1 X))))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.cos_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.sin_real X))) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.cos_real X))) tptp.one_one_real)))
% 6.68/6.99 (assert (not (= (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.pi) (= (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)) (@ (@ tptp.ord_less_real Y) X)))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (@ (@ tptp.ord_less_real (@ tptp.cos_real X)) (@ tptp.cos_real Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_real X) tptp.pi) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.pi) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) tptp.pi))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.pi) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.plus_plus_real X))) (= (@ tptp.cos_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc M))) tptp.pi)) _let_1))) (@ tptp.uminus_uminus_real (@ tptp.sin_real (@ _let_2 (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real M)) tptp.pi)) _let_1)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.68/6.99 (assert (exists ((X6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X6) (@ (@ tptp.ord_less_eq_real X6) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X6) tptp.zero_zero_real) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real Y2) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real Y2) tptp.zero_zero_real)) (= Y2 X6))))))
% 6.68/6.99 (assert (@ (@ tptp.ord_less_eq_real (@ tptp.cos_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cos_real Y)) (@ tptp.cos_real X)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X6) (@ (@ tptp.ord_less_eq_real X6) tptp.pi) (= (@ tptp.cos_real X6) Y) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2) (@ (@ tptp.ord_less_eq_real Y2) tptp.pi) (= (@ tptp.cos_real Y2) Y)) (= Y2 X6)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (= X (@ tptp.cos_real T6)) (= Y (@ tptp.sin_real T6))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.times_times_real _let_1) _let_1)) (@ tptp.semiri2265585572941072030t_real (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)) tptp.one_one_real) (not (forall ((T6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (=> (@ (@ tptp.ord_less_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (=> (= X (@ tptp.cos_real T6)) (not (= Y (@ tptp.sin_real T6))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.sin_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.cos_real (@ (@ tptp.times_times_real _let_1) X))) tptp.one_one_real))))))
% 6.68/6.99 (assert (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit1 tptp.one))))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cos_real X)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_2) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ _let_1 Y)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (=> (= (@ tptp.sin_real X) (@ tptp.sin_real Y)) (= X Y))))))))))
% 6.68/6.99 (assert (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (exists ((X3 tptp.int)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.cos_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ 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 N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.pi) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.sin_real Y)) (@ tptp.sin_real X))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_eq_real Y) _let_1) (= (@ (@ tptp.ord_less_real (@ tptp.sin_real X)) (@ tptp.sin_real Y)) (@ (@ tptp.ord_less_real X) Y))))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (exists ((X6 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X6) (@ (@ tptp.ord_less_eq_real X6) _let_1) (= (@ tptp.sin_real X6) Y) (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) Y2) (@ (@ tptp.ord_less_eq_real Y2) _let_1) (= (@ tptp.sin_real Y2) Y)) (= Y2 X6)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cos_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.one_one_real) (or (exists ((X3 tptp.nat)) (= X (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))) (exists ((X3 tptp.nat)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real X3)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.pi))))))))
% 6.68/6.99 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.bit_and_int_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((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) A12)))))
% 6.68/6.99 (assert (forall ((H2 tptp.real) (F (-> tptp.real tptp.real)) (J (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (exists ((B8 tptp.real)) (= (@ F H2) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ J M3)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real B8) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real H2) N)) (@ tptp.semiri2265585572941072030t_real N)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ 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 N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.cos_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ 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 N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.exp_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X) M3)) (@ tptp.semiri2265585572941072030t_real M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ tptp.exp_real T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((I5 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) I5)) (= X (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I5)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sin_real X) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real X) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.68/6.99 (assert (= tptp.cos_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ tptp.semiri2265585572941072030t_real N2))) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.cos_real X) tptp.zero_zero_real) (exists ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N3)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N3)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.cos_real X) tptp.zero_zero_real) (or (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (and (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) N2)) (= X (@ tptp.uminus_uminus_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N2)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ 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 N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ 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_eq_real T6) X) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ 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 N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ 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 N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (exists ((T6 tptp.real)) (= (@ tptp.sin_real X) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ 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 N))) tptp.pi)))) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))
% 6.68/6.99 (assert (= tptp.sin_coeff (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat))) _let_1))) (@ tptp.semiri2265585572941072030t_real N2)))))))
% 6.68/6.99 (assert (= (@ tptp.sin_coeff tptp.zero_zero_nat) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat N) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.ord_less_eq_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) M) (=> (@ (@ tptp.ord_less_nat M) N) (@ (@ tptp.ord_less_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat tptp.one_one_nat) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.dvd_dvd_nat M) (@ tptp.semiri1408675320244567234ct_nat N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc M))) (let ((_let_2 (@ (@ tptp.minus_minus_nat _let_1) N))) (=> (@ (@ tptp.ord_less_nat N) _let_1) (= (@ tptp.semiri1408675320244567234ct_nat _let_2) (@ (@ tptp.times_times_nat _let_2) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat M) N)))))))))
% 6.68/6.99 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) R)))) (@ (@ tptp.power_power_nat N) R)))))
% 6.68/6.99 (assert (forall ((A0 tptp.int) (A12 tptp.int) (P (-> tptp.int tptp.int Bool))) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int A0) A12)) (=> (forall ((I4 tptp.int) (J2 tptp.int)) (=> (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int I4) J2)) (=> (=> (@ (@ tptp.ord_less_eq_int I4) J2) (@ (@ P (@ (@ tptp.plus_plus_int I4) tptp.one_one_int)) J2)) (@ (@ P I4) J2)))) (@ (@ P A0) A12)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.real_V1022390504157884413omplex Z) tptp.one_one_real) (not (forall ((T6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (=> (@ (@ tptp.ord_less_real T6) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (not (= Z (@ (@ tptp.complex2 (@ tptp.cos_real T6)) (@ tptp.sin_real T6)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.sin_real X))))
% 6.68/6.99 (assert (= (@ tptp.tan_real tptp.pi) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) tptp.pi)) (@ tptp.tan_real X))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.num)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi))) (@ tptp.tan_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (I tptp.int)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real I)) tptp.pi))) (@ tptp.tan_real X))))
% 6.68/6.99 (assert (forall ((T tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 (@ tptp.cos_real T)) (@ tptp.sin_real T))) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.tan_real X))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.minus_minus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real A) C)) (@ (@ tptp.minus_minus_real B) D)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.numera6690914467698888265omplex W)) (and (= A (@ tptp.numeral_numeral_real W)) (= B tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.zero_zero_complex) (and (= A tptp.zero_zero_real) (= B tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= tptp.zero_zero_complex (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real A) C)) (@ (@ tptp.plus_plus_real B) D)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (W tptp.num)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))) (and (= A (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real W))) (= B tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.times_times_real B))) (let ((_let_2 (@ tptp.times_times_real A))) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 C) D)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_2 C)) (@ _let_1 D))) (@ (@ tptp.plus_plus_real (@ _let_2 D)) (@ _let_1 C))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) tptp.one_one_complex) (and (= A tptp.one_one_real) (= B tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= tptp.one_one_complex (@ (@ tptp.complex2 tptp.one_one_real) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (= (@ (@ tptp.complex2 A) B) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) (and (= A (@ tptp.uminus_uminus_real tptp.one_one_real)) (= B tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) tptp.one_one_real))
% 6.68/6.99 (assert (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.suc N2)))) tptp.one_one_real))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (exists ((X6 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) X6) (@ (@ tptp.ord_less_real X6) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real Y) (@ tptp.tan_real X6)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (exists ((X6 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X6) (@ (@ tptp.ord_less_real X6) _let_1) (= (@ tptp.tan_real X6) Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real X))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 X) (=> (@ _let_1 _let_2) (=> (@ _let_3 Y) (=> (@ (@ tptp.ord_less_real Y) _let_2) (= (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ _let_1 Y)))))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_3 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)))) (=> (@ _let_3 Y) (=> (@ _let_1 _let_2) (=> (@ _let_3 X) (=> (@ (@ tptp.ord_less_real X) _let_2) (= (@ _let_1 X) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y) (=> (@ (@ tptp.ord_less_real Y) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (@ (@ tptp.ord_less_real (@ tptp.tan_real Y)) (@ tptp.tan_real X))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (exists ((X6 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X6) (@ (@ tptp.ord_less_real X6) _let_1) (= (@ tptp.tan_real X6) Y) (forall ((Y2 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Y2) (@ (@ tptp.ord_less_real Y2) _let_1) (= (@ tptp.tan_real Y2) Y)) (= Y2 X6)))))))))
% 6.68/6.99 (assert (= (@ tptp.tan_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (@ tptp.uminus_uminus_real tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (= (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.tan_real Y)) (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) Y)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real)) (=> (@ (@ tptp.sums_real G) X) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) tptp.zero_zero_real) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) X))))
% 6.68/6.99 (assert (forall ((G (-> tptp.nat tptp.real)) (X tptp.real) (F (-> tptp.nat tptp.real)) (Y tptp.real)) (=> (@ (@ tptp.sums_real G) X) (=> (@ (@ tptp.sums_real F) Y) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_real (@ (@ tptp.dvd_dvd_nat _let_1) N2)) (@ F (@ (@ tptp.divide_divide_nat N2) _let_1))) (@ G (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat N2) tptp.one_one_nat)) _let_1)))))) (@ (@ tptp.plus_plus_real X) Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.tan_real X)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (exists ((X6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X6) (@ (@ tptp.ord_less_real X6) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (= (@ tptp.tan_real X6) Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.tan_real X)) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)))) (=> (@ _let_2 X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (@ _let_2 Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (= (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_real Y) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.tan_real X)) (@ tptp.tan_real Y))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one))))) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ tptp.tan_real X))) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (=> (= (@ tptp.tan_real X) Y) (= (@ tptp.arctan Y) X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_real X) _let_1) (= (@ tptp.arctan (@ tptp.tan_real X)) X))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arctan Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_real _let_1) _let_2) (= (@ tptp.tan_real _let_1) Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (exists ((Z5 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) Z5) (@ (@ tptp.ord_less_real Z5) _let_1) (= (@ tptp.tan_real Z5) X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.sums_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ tptp.semiri2265585572941072030t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.cos_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim7802044766580827645g_real (@ (@ tptp.log B) X)) (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int)) (and (@ (@ tptp.ord_less_real (@ _let_1 (@ tptp.semiri5074537144036343181t_real K))) X) (@ (@ tptp.ord_less_eq_real X) (@ _let_1 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.plus_plus_nat K) tptp.one_one_nat)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.tan_real X))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real X) (@ (@ tptp.divide_divide_real _let_2) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real _let_2) (@ tptp.numeral_numeral_nat _let_1)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ tptp.sqrt X) (@ tptp.sqrt Y)) (= X Y))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.68/6.99 (assert (= (@ tptp.sqrt tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_real X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.sqrt X) tptp.one_one_real) (= X tptp.one_one_real))))
% 6.68/6.99 (assert (= (@ tptp.sqrt tptp.one_one_real) tptp.one_one_real))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) A)) (not (= X tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real) (= A tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (= (@ _let_1 (@ tptp.sqrt Y)) (@ _let_1 Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_real A) B))))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (let ((_let_1 (@ tptp.sqrt A))) (= (@ (@ tptp.times_times_real _let_1) _let_1) (@ tptp.abs_abs_real A)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) X)) (@ tptp.abs_abs_real X))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) (@ tptp.numeral_numeral_real _let_1))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) A) (= (= (@ (@ tptp.powr_real A) X) tptp.one_one_real) (= X tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.powr_real X) tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) tptp.one_one_real) X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.ord_less_eq_real A) B))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_real M))) (= (@ (@ tptp.powr_real _let_1) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real _let_1) (@ tptp.numeral_numeral_nat N))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_1 X) (= (@ (@ tptp.powr_real A) (@ (@ tptp.log A) X)) X)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (@ (@ tptp.log A) (@ (@ tptp.powr_real A) Y)) Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.abs_abs_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.numeral_numeral_real N)) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))) (= (@ (@ tptp.power_power_real (@ tptp.sqrt _let_2)) _let_1) _let_2)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ (@ tptp.powr_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real _let_1))) (@ tptp.abs_abs_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.sqrt X)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (K tptp.nat)) (= (@ tptp.sqrt (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ tptp.sqrt X)) K))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ tptp.sqrt (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (= (@ (@ tptp.powr_real (@ _let_1 A)) B) (@ _let_1 (@ (@ tptp.times_times_real A) B))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) (@ tptp.sqrt Y)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (not (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real A) X)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.powr_real X) Y))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (= (@ tptp.sqrt X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_real (@ _let_1 A)) (@ _let_1 B)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real A) B))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ _let_1 A)) (@ _let_1 B)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (@ _let_1 (@ tptp.sqrt X))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real Y) A)) (@ (@ tptp.powr_real X) A)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real A))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (=> (not (= A tptp.one_one_real)) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y) (@ _let_1 (@ (@ tptp.powr_real X) Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (@ _let_1 (@ (@ tptp.powr_real X) A)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) A) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) B))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 A) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real X) A)) tptp.one_one_real)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.divide_divide_real X) Y)) A) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (A tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.powr_real (@ (@ tptp.times_times_real X) Y)) A) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real X) A)) (@ (@ tptp.powr_real Y) A))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real X) _let_1) _let_1)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real X) Y))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt X)) (@ tptp.sqrt Y))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real X) X)) (@ (@ tptp.times_times_real Y) Y))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (C tptp.real)) (let ((_let_1 (@ tptp.powr_real B))) (= (@ (@ tptp.divide_divide_real A) (@ _let_1 C)) (@ (@ tptp.times_times_real A) (@ _let_1 (@ tptp.uminus_uminus_real C)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real)) (=> (not (= A tptp.zero_zero_real)) (= (@ (@ tptp.log (@ (@ tptp.powr_real A) B)) X) (@ (@ tptp.divide_divide_real (@ (@ tptp.log A) X)) B)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.ln_ln_real (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ tptp.ln_ln_real X))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (B tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (not (= X tptp.zero_zero_real)) (= (@ _let_1 (@ (@ tptp.powr_real X) Y)) (@ (@ tptp.times_times_real Y) (@ _let_1 X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt X)))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt _let_1)) _let_1)))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) N)))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_real X) (@ tptp.sqrt Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.powr_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.times_times_real X) (@ _let_1 Y)) (@ _let_1 (@ (@ tptp.plus_plus_real tptp.one_one_real) Y)))))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ tptp.sqrt _let_1))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.powr_real B) Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.log B) X)) Y))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real B) Y)) X) (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.log B) X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt X)) Y)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (=> (= (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) X) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ tptp.sqrt X) Y)))))
% 6.68/6.99 (assert (forall ((U tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) U) (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) U))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) X) (= Y tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (= (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) Y) (= X tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real Y) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (C tptp.real) (B tptp.real) (D tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real A) C)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real B) D)) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real C) _let_1)) (@ (@ tptp.power_power_real D) _let_1))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt Y)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real X) A)) A))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.powr_real (@ tptp.ln_ln_real X)) A)) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real A) A)) X))))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_2)) _let_2)))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.times_times_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.plus_plus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) Y)))))))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real Y) (@ _let_1 X)) (@ _let_1 (@ (@ tptp.divide_divide_real (@ (@ tptp.powr_real B) Y)) X))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_real (@ tptp.sqrt X)) Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_2 X) (=> (@ _let_2 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real X) Y))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.power_power_real (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.dvd_dvd_nat _let_2) N) (= (@ tptp.sqrt (@ _let_3 N)) (@ _let_3 (@ (@ tptp.divide_divide_nat N) _let_2)))))))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.tan_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.sqrt X)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (= tptp.arsinh_real (lambda ((X3 tptp.real)) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X3) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.bit1 tptp.one))) (= (@ tptp.cos_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1)))) (@ (@ tptp.divide_divide_real (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit1 tptp.one)))) (= (@ tptp.sin_real (@ (@ tptp.divide_divide_real tptp.pi) _let_1)) (@ (@ tptp.divide_divide_real (@ tptp.sqrt _let_1)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.log B))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 B) (=> (not (= B tptp.one_one_real)) (=> (@ _let_2 X) (= (@ (@ tptp.minus_minus_real (@ _let_1 X)) Y) (@ _let_1 (@ (@ tptp.times_times_real X) (@ (@ tptp.powr_real B) (@ tptp.uminus_uminus_real Y))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.complex2 X) Y)) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.dvd_dvd_nat _let_1) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.sqrt X)) N) (@ (@ tptp.power_power_real X) (@ (@ tptp.divide_divide_nat N) _let_1))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real) (Ya tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.sqrt (@ (@ tptp.times_times_real (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real Xa2) _let_1)) (@ (@ tptp.power_power_real Ya) _let_1))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ (@ tptp.ord_less_eq_real (@ tptp.sqrt (@ (@ tptp.times_times_real X) Y))) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) Y)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.num)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.powr_real X) (@ tptp.uminus_uminus_real (@ tptp.numeral_numeral_real N))) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat N)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_1)) (@ (@ tptp.power_power_real Y) _let_1)))))) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ (@ tptp.divide_divide_real U) (@ tptp.sqrt (@ tptp.numeral_numeral_real _let_1))))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) _let_3) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real Y)) _let_3) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (= (@ tptp.arcosh_real X) (@ tptp.ln_ln_real (@ (@ tptp.plus_plus_real X) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cos_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sin_real (@ tptp.arctan X)) (@ (@ tptp.divide_divide_real X) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (U tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (let ((_let_4 (@ (@ tptp.divide_divide_real U) (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_real X) _let_4) (=> (@ (@ tptp.ord_less_real Y) _let_4) (=> (@ _let_3 X) (=> (@ _let_3 Y) (@ (@ tptp.ord_less_real (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) _let_2)) (@ (@ tptp.power_power_real Y) _let_2)))) U)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sin_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= _let_1 (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.cos_real X)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.68/6.99 (assert (= tptp.arctan (lambda ((X3 tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.plus_plus_real tptp.one_one_real))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.arctan (@ (@ tptp.divide_divide_real X3) (@ _let_2 (@ tptp.sqrt (@ _let_2 (@ (@ tptp.power_power_real X3) (@ tptp.numeral_numeral_nat _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real _let_1))) (= (@ tptp.cos_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real (@ tptp.tan_real X)) (@ tptp.numeral_numeral_nat _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_mint X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) X) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Mi2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_mint_rel) _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.vEBT_VEBT) (Y tptp.option_nat)) (=> (= (@ tptp.vEBT_vebt_maxt X) Y) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) X) (=> (forall ((A5 Bool) (B5 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf A5) B5))) (=> (= X _let_1) (=> (and (=> B5 (= Y (@ tptp.some_nat tptp.one_one_nat))) (=> (not B5) (and (=> A5 (= Y (@ tptp.some_nat tptp.zero_zero_nat))) (=> (not A5) (= Y tptp.none_nat))))) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (=> (forall ((Uu2 tptp.nat) (Uv2 tptp.list_VEBT_VEBT) (Uw2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uu2) Uv2) Uw2))) (=> (= X _let_1) (=> (= Y tptp.none_nat) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))) (not (forall ((Mi2 tptp.nat) (Ma2 tptp.nat) (Ux2 tptp.nat) (Uy2 tptp.list_VEBT_VEBT) (Uz2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat (@ (@ tptp.product_Pair_nat_nat Mi2) Ma2))) Ux2) Uy2) Uz2))) (=> (= X _let_1) (=> (= Y (@ tptp.some_nat Ma2)) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_vebt_maxt_rel) _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (exists ((A5 tptp.complex) (R2 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ tptp.exp_complex A5))))))
% 6.68/6.99 (assert (= tptp.real_V4546457046886955230omplex (lambda ((R5 tptp.real)) (@ (@ tptp.complex2 R5) tptp.zero_zero_real))))
% 6.68/6.99 (assert (= tptp.real_V4546457046886955230omplex (lambda ((X3 tptp.real)) (@ (@ tptp.complex2 X3) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (Xa2 tptp.real)) (= (= (@ (@ tptp.complex2 X) Y) (@ tptp.real_V4546457046886955230omplex Xa2)) (and (= X Xa2) (= Y tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ _let_1 X)) (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.times_times_real X) R)) (@ (@ tptp.times_times_real Y) R)))))
% 6.68/6.99 (assert (forall ((R tptp.real) (X tptp.real) (Y tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 X) Y)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real R) X)) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real) (R tptp.real)) (= (@ (@ tptp.plus_plus_complex (@ (@ tptp.complex2 X) Y)) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real X) R)) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arcsin X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos Y)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real Y) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arccos X)) (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))))
% 6.68/6.99 (assert (= (@ tptp.arcsin tptp.zero_zero_real) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.arccos tptp.one_one_real) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.arccos (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.pi))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y)))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (= (@ tptp.sin_real (@ tptp.arcsin Y)) Y)))))
% 6.68/6.99 (assert (= (@ tptp.arccos tptp.zero_zero_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (= (@ tptp.arcsin tptp.one_one_real) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (= (@ tptp.arcsin (@ tptp.uminus_uminus_real tptp.one_one_real)) (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real)) (= (= (@ tptp.arccos X) (@ tptp.arccos Y)) (= X Y)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_eq_real Y) X))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arcsin (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ tptp.arcsin X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (= (@ tptp.arcsin X) (@ tptp.arcsin Y)) (= X Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.arccos Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arccos Y)) (@ tptp.arccos X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arccos X)) (@ tptp.arccos Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) tptp.pi)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real X)) X)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ (@ tptp.ord_less_real (@ tptp.arcsin X)) (@ tptp.arcsin Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real Y)) tptp.one_one_real) (= (@ tptp.cos_real (@ tptp.arccos Y)) Y))))
% 6.68/6.99 (assert (forall ((Theta tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real Theta))) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.arccos (@ tptp.cos_real Theta)) _let_1)))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) tptp.pi)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.sin_real (@ tptp.arccos X)) tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.pi)) X) (= (@ tptp.arccos (@ tptp.cos_real X)) (@ tptp.uminus_uminus_real X))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (not (= (@ tptp.cos_real (@ tptp.arcsin X)) tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arccos Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.cos_real _let_1) Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (= (@ tptp.arccos (@ tptp.uminus_uminus_real X)) (@ (@ tptp.minus_minus_real tptp.pi) (@ tptp.arccos X))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arccos Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_real _let_2) _let_1))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (let ((_let_2 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) _let_2) (@ (@ tptp.ord_less_eq_real _let_2) _let_1))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin Y)) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.arcsin Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X) (=> (@ (@ tptp.ord_less_eq_real X) _let_1) (= (@ tptp.arcsin (@ tptp.sin_real X)) X))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ _let_1 (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ _let_1 (@ tptp.arcsin X)) (@ (@ tptp.ord_less_eq_real (@ tptp.sin_real Y)) X))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real X))) (let ((_let_2 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ _let_1 tptp.one_one_real) (=> (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) _let_2)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) (@ (@ tptp.divide_divide_real tptp.pi) _let_2)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.arcsin X)) Y) (@ _let_1 (@ tptp.sin_real Y)))))))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi) (= (@ tptp.sin_real _let_1) Y)))))))
% 6.68/6.99 (assert (forall ((Y tptp.real)) (let ((_let_1 (@ tptp.arcsin Y))) (let ((_let_2 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real tptp.one_one_real)) Y) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.one_one_real) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_2)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) _let_2) (= (@ tptp.sin_real _let_1) Y))))))))
% 6.68/6.99 (assert (forall ((Theta tptp.real)) (not (forall ((K3 tptp.int)) (not (= (@ tptp.arccos (@ tptp.cos_real Theta)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Theta) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real K3)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))))))))
% 6.68/6.99 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))))) tptp.one_one_complex))
% 6.68/6.99 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.numera6690914467698888265omplex (@ tptp.bit0 tptp.one))) (@ tptp.real_V4546457046886955230omplex tptp.pi))) tptp.imaginary_unit)) tptp.one_one_complex))
% 6.68/6.99 (assert (= tptp.binomial (lambda ((N2 tptp.nat) (K2 tptp.nat)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N2) K2))) (let ((_let_2 (@ tptp.ord_less_nat N2))) (@ (@ (@ tptp.if_nat (@ _let_2 K2)) tptp.zero_zero_nat) (@ (@ (@ tptp.if_nat (@ _let_2 (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K2))) (@ (@ tptp.binomial N2) _let_1)) (@ (@ tptp.divide_divide_nat (@ (@ (@ (@ tptp.set_fo2584398358068434914at_nat tptp.times_times_nat) (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)) N2) tptp.one_one_nat)) (@ tptp.semiri1408675320244567234ct_nat K2)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) N) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) (@ tptp.suc tptp.zero_zero_nat)) N)))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.binomial tptp.zero_zero_nat) (@ tptp.suc K)) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat) (@ (@ tptp.ord_less_nat N) K))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.binomial N))) (= (@ (@ tptp.binomial (@ tptp.suc N)) _let_1) (@ (@ tptp.plus_plus_nat (@ _let_2 K)) (@ _let_2 _let_1)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.zero_zero_nat) tptp.one_one_nat)))
% 6.68/6.99 (assert (= (@ tptp.real_V1022390504157884413omplex tptp.imaginary_unit) tptp.one_one_real))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (@ _let_1 (@ _let_1 X)) (@ tptp.uminus1482373934393186551omplex X)))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (= (@ (@ tptp.divide1717551699836669952omplex X) tptp.imaginary_unit) (@ (@ tptp.times_times_complex (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)) (@ (@ tptp.ord_less_eq_nat K) N))))
% 6.68/6.99 (assert (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) tptp.imaginary_unit) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (N tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex N))) (= (@ (@ tptp.divide1717551699836669952omplex Z) (@ (@ tptp.times_times_complex _let_1) tptp.imaginary_unit)) (@ (@ tptp.divide1717551699836669952omplex (@ tptp.uminus1482373934393186551omplex (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z))) _let_1)))))
% 6.68/6.99 (assert (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.68/6.99 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex tptp.pi)) tptp.imaginary_unit)) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.68/6.99 (assert (= (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex tptp.pi))) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.power_power_complex tptp.imaginary_unit) (@ (@ tptp.times_times_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.power_power_complex (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.binomial N) tptp.one_one_nat) N)))
% 6.68/6.99 (assert (not (= tptp.imaginary_unit tptp.zero_zero_complex)))
% 6.68/6.99 (assert (not (= tptp.imaginary_unit tptp.one_one_complex)))
% 6.68/6.99 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.numera6690914467698888265omplex W)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K) (= (@ (@ tptp.binomial N) K) tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (let ((_let_2 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial _let_1) _let_2)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) K)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial _let_2) _let_1)) _let_1))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ _let_1 K) (@ _let_1 (@ (@ tptp.minus_minus_nat N) K)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (R tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat M))) (let ((_let_2 (@ _let_1 R))) (let ((_let_3 (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) K)))) (let ((_let_4 (@ _let_1 K))) (= (@ (@ tptp.times_times_nat (@ _let_3 _let_4)) (@ (@ tptp.binomial _let_4) K)) (@ (@ tptp.times_times_nat (@ _let_3 K)) (@ (@ tptp.binomial _let_2) M)))))))))
% 6.68/6.99 (assert (forall ((R tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat R) N) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) R)) (@ (@ tptp.power_power_nat N) R)))))
% 6.68/6.99 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.times_times_complex tptp.imaginary_unit))) (= (= (@ _let_1 W) Z) (= W (@ tptp.uminus1482373934393186551omplex (@ _let_1 Z)))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.binomial N) K)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat A) B))))) (let ((_let_2 (@ tptp.suc A))) (= (@ (@ tptp.times_times_nat _let_2) (@ _let_1 _let_2)) (@ (@ tptp.times_times_nat (@ tptp.suc B)) (@ _let_1 A)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (let ((_let_2 (@ tptp.suc N))) (= (@ (@ tptp.binomial _let_2) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat _let_2) (@ (@ tptp.binomial N) K))) _let_1))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) M) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.times_times_nat (@ _let_1 M)) (@ (@ tptp.binomial M) K)) (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K)) (@ (@ tptp.minus_minus_nat M) K)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat N))) (= (@ (@ tptp.times_times_nat (@ _let_1 K)) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ _let_1 tptp.one_one_nat)) K))))))
% 6.68/6.99 (assert (forall ((W tptp.num)) (not (= tptp.imaginary_unit (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W))))))
% 6.68/6.99 (assert (= tptp.imaginary_unit (@ (@ tptp.complex2 tptp.zero_zero_real) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (= (@ (@ tptp.complex2 X) Y) tptp.imaginary_unit) (and (= X tptp.zero_zero_real) (= Y tptp.one_one_real)))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.binomial N) _let_1)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) K))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ (@ tptp.complex2 A) B)) tptp.imaginary_unit) (@ (@ tptp.complex2 (@ tptp.uminus_uminus_real B)) A))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K)))) (@ (@ tptp.binomial N) K)) (@ tptp.semiri1408675320244567234ct_nat N)))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K)) (@ _let_1 (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_eq_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) K) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_eq_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.binomial N) K)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_2 N) (=> (@ _let_2 K) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.plus_plus_nat (@ _let_1 (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat))) (@ _let_1 K)))))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (@ (@ tptp.times_times_nat K) (@ (@ tptp.binomial N) K)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)) (@ (@ tptp.minus_minus_nat K) tptp.one_one_nat)))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K) N) (= (@ (@ tptp.binomial N) K) (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat K)) (@ tptp.semiri1408675320244567234ct_nat (@ (@ tptp.minus_minus_nat N) K))))))))
% 6.68/6.99 (assert (forall ((R tptp.real)) (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.complex2 tptp.zero_zero_real) R))))
% 6.68/6.99 (assert (forall ((R tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) tptp.imaginary_unit) (@ (@ tptp.complex2 tptp.zero_zero_real) R))))
% 6.68/6.99 (assert (= tptp.complex2 (lambda ((A3 tptp.real) (B2 tptp.real)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex A3)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) (@ (@ tptp.divide_divide_nat N) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 (@ tptp.suc K)))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K6)) N) (@ (@ tptp.ord_less_nat (@ _let_1 K)) (@ _let_1 K6)))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (K6 tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.binomial N))) (=> (@ (@ tptp.ord_less_nat K) K6) (=> (@ (@ tptp.ord_less_eq_nat N) (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) K)) (=> (@ (@ tptp.ord_less_eq_nat K6) N) (@ (@ tptp.ord_less_nat (@ _let_1 K6)) (@ _let_1 K))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.divide_divide_nat N) _let_1))) (let ((_let_3 (@ tptp.binomial N))) (=> (not (@ (@ tptp.dvd_dvd_nat _let_1) N)) (= (@ _let_3 (@ tptp.suc _let_2)) (@ _let_3 _let_2))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) (let ((_let_2 (@ tptp.suc K))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.binomial N) _let_2) (@ (@ tptp.plus_plus_nat (@ _let_1 _let_2)) (@ _let_1 K))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.binomial N) _let_1) (@ (@ tptp.divide_divide_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) _let_1)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (exists ((R2 tptp.real) (A5 tptp.real)) (= Z (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R2)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A5))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A5)))))))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A))))) tptp.one_one_real)))
% 6.68/6.99 (assert (forall ((R tptp.real) (A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex R)) (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.cos_real A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sin_real A)))))) (@ tptp.abs_abs_real R))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real (@ tptp.numeral_numeral_real (@ tptp.bit0 _let_1))) N)) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.semiri5074537144036343181t_real N)))) (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat _let_1)) N)) N)))))))
% 6.68/6.99 (assert (= (@ tptp.arg (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (= (@ tptp.csqrt tptp.imaginary_unit) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.plus_plus_complex tptp.one_one_complex) tptp.imaginary_unit)) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (= (@ tptp.arg tptp.imaginary_unit) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (@ tptp.finite_finite_nat (@ tptp.set_ord_atMost_nat K))))
% 6.68/6.99 (assert (= (@ tptp.csqrt tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.csqrt Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 6.68/6.99 (assert (= (@ tptp.csqrt tptp.one_one_complex) tptp.one_one_complex))
% 6.68/6.99 (assert (= (@ tptp.set_ord_atMost_nat tptp.zero_zero_nat) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.power_power_complex (@ tptp.csqrt Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z)))
% 6.68/6.99 (assert (= tptp.set_ord_atMost_nat (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc K)) (@ tptp.set_ord_atMost_nat K))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat K))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat K))) (= (@ tptp.set_ord_atMost_nat _let_1) (@ (@ tptp.insert_nat _let_1) (@ tptp.set_ord_atMost_nat (@ tptp.pred_numeral K)))))))
% 6.68/6.99 (assert (= (@ tptp.arg tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((R tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat R) K2)) K2))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ tptp.suc (@ (@ tptp.plus_plus_nat R) N))) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat N) M)) tptp.one_one_nat)) M))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.plus_plus_nat N))) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat N) J3)) N))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat (@ _let_1 M)) tptp.one_one_nat)) (@ _let_1 tptp.one_one_nat))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.binomial (@ (@ tptp.minus_minus_nat N) K2)) (@ (@ tptp.minus_minus_nat M) K2)))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.binomial (@ tptp.suc N)) M)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (R tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.binomial M) K2)) (@ (@ tptp.binomial N) (@ (@ tptp.minus_minus_nat R) K2))))) (@ tptp.set_ord_atMost_nat R)) (@ (@ tptp.binomial (@ (@ tptp.plus_plus_nat M) N)) R))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt X)) (@ tptp.csqrt (@ tptp.real_V4546457046886955230omplex X))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial N)) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat) (N tptp.nat)) (= (@ (@ tptp.power_power_nat (@ (@ tptp.plus_plus_nat A) B)) N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.times_times_nat (@ tptp.semiri1316708129612266289at_nat (@ (@ tptp.binomial N) K2))) (@ (@ tptp.power_power_nat A) K2))) (@ (@ tptp.power_power_nat B) (@ (@ tptp.minus_minus_nat N) K2))))) (@ tptp.set_ord_atMost_nat N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (A (-> tptp.nat tptp.nat)) (N tptp.nat) (B (-> tptp.nat tptp.nat)) (X tptp.nat)) (=> (forall ((I4 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M) I4) (= (@ A I4) tptp.zero_zero_nat))) (=> (forall ((J2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) J2) (= (@ B J2) tptp.zero_zero_nat))) (= (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ (@ tptp.power_power_nat X) I5)))) (@ tptp.set_ord_atMost_nat M))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((J3 tptp.nat)) (@ (@ tptp.times_times_nat (@ B J3)) (@ (@ tptp.power_power_nat X) J3)))) (@ tptp.set_ord_atMost_nat N))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((R5 tptp.nat)) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.times_times_nat (@ A K2)) (@ B (@ (@ tptp.minus_minus_nat R5) K2))))) (@ tptp.set_ord_atMost_nat R5))) (@ (@ tptp.power_power_nat X) R5)))) (@ tptp.set_ord_atMost_nat (@ (@ tptp.plus_plus_nat M) N))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.power_power_nat (@ (@ tptp.binomial N) K2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.binomial (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.times_times_nat _let_1) M))) (= (@ (@ tptp.groups3542108847815614940at_nat (@ tptp.binomial (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat))) (@ tptp.set_ord_atMost_nat M)) (@ (@ tptp.power_power_nat _let_1) _let_2))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat I5) (@ (@ tptp.binomial N) I5)))) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.times_times_nat N) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))))))
% 6.68/6.99 (assert (= tptp.semiri1316708129612266289at_nat (lambda ((N2 tptp.nat)) N2)))
% 6.68/6.99 (assert (= tptp.real_V1485227260804924795R_real tptp.times_times_real))
% 6.68/6.99 (assert (forall ((R tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.times_times_real R))) (= (@ (@ tptp.real_V2046097035970521341omplex R) (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ _let_1 A)) (@ _let_1 B))))))
% 6.68/6.99 (assert (= (@ tptp.cis (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ tptp.uminus1482373934393186551omplex tptp.imaginary_unit)))
% 6.68/6.99 (assert (forall ((B tptp.nat) (K tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) K) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N)) (and (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (= (@ tptp.real_V1022390504157884413omplex (@ tptp.cis A)) tptp.one_one_real)))
% 6.68/6.99 (assert (= (@ tptp.cis tptp.zero_zero_real) tptp.one_one_complex))
% 6.68/6.99 (assert (= (@ tptp.cis tptp.pi) (@ tptp.uminus1482373934393186551omplex tptp.one_one_complex)))
% 6.68/6.99 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int (@ tptp.numeral_numeral_int A)) (@ tptp.numeral_numeral_int B)))))
% 6.68/6.99 (assert (= (@ tptp.cis (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.imaginary_unit))
% 6.68/6.99 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B))) (@ (@ tptp.divide_divide_int tptp.one_one_int) (@ tptp.numeral_numeral_int B)))))
% 6.68/6.99 (assert (= (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) tptp.one_one_complex))
% 6.68/6.99 (assert (forall ((A tptp.num) (B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real (@ tptp.numeral_numeral_real A)) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int A))) (@ tptp.numeral_numeral_int B)))))
% 6.68/6.99 (assert (forall ((B tptp.num)) (= (@ tptp.archim6058952711729229775r_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.numeral_numeral_real B)))) (@ (@ tptp.divide_divide_int (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.numeral_numeral_int B)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.sqrt (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (not (= (@ tptp.cis A) tptp.zero_zero_complex))))
% 6.68/6.99 (assert (= tptp.divide_divide_real (lambda ((X3 tptp.real) (Y3 tptp.real)) (@ (@ tptp.times_times_real X3) (@ tptp.inverse_inverse_real Y3)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.times_times_complex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.plus_plus_real A) B)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (= (@ (@ tptp.divide1717551699836669952omplex (@ tptp.cis A)) (@ tptp.cis B)) (@ tptp.cis (@ (@ tptp.minus_minus_real A) B)))))
% 6.68/6.99 (assert (forall ((Y tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (= (@ (@ tptp.powr_real (@ tptp.inverse_inverse_real Y)) A) (@ tptp.inverse_inverse_real (@ (@ tptp.powr_real Y) A))))))
% 6.68/6.99 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ tptp.ord_less_real _let_1) X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.plus_plus_real _let_1) tptp.one_one_real)) (= (@ tptp.archim6058952711729229775r_real X) N))))))
% 6.68/6.99 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real R) (@ (@ tptp.plus_plus_real (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R))) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.68/6.99 (assert (forall ((R tptp.real)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.minus_minus_real R) tptp.one_one_real)) (@ tptp.ring_1_of_int_real (@ tptp.archim6058952711729229775r_real R)))))
% 6.68/6.99 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (N tptp.nat)) (= (@ (@ tptp.power_power_complex (@ tptp.cis A)) N) (@ tptp.cis (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)))))
% 6.68/6.99 (assert (forall ((P (-> tptp.real Bool)) (E tptp.real)) (=> (forall ((D3 tptp.real) (E2 tptp.real)) (=> (@ (@ tptp.ord_less_real D3) E2) (=> (@ P D3) (@ P E2)))) (=> (forall ((N3 tptp.nat)) (=> (not (= N3 tptp.zero_zero_nat)) (@ P (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N3))))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (@ P E))))))
% 6.68/6.99 (assert (forall ((E tptp.real)) (= (@ (@ tptp.ord_less_real tptp.zero_zero_real) E) (exists ((N2 tptp.nat)) (let ((_let_1 (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real N2)))) (and (not (= N2 tptp.zero_zero_nat)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (@ (@ tptp.ord_less_real _let_1) E)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.sqrt X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.divide_divide_real _let_1) X) (@ tptp.inverse_inverse_real _let_1))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.ln_ln_real (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ tptp.ln_ln_real X))))))
% 6.68/6.99 (assert (forall ((N tptp.int) (X tptp.real)) (let ((_let_1 (@ tptp.ring_1_of_int_real N))) (=> (@ (@ 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) N))))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.divide_divide_real A) (@ tptp.ring_1_of_int_real B))) (@ (@ tptp.divide_divide_int (@ tptp.archim6058952711729229775r_real A)) B)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.log A))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_2 A) (=> (not (= A tptp.one_one_real)) (=> (@ _let_2 X) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))))))
% 6.68/6.99 (assert (= tptp.cis (lambda ((B2 tptp.real)) (@ tptp.exp_complex (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex B2))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real _let_1) (@ tptp.inverse_inverse_real _let_1))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) (@ tptp.inverse_inverse_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.inverse_inverse_real (@ tptp.tan_real X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real X) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.exp_real X))) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_1) (@ tptp.inverse_inverse_real _let_1))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (B tptp.real) (K tptp.int)) (let ((_let_1 (@ tptp.powr_real B))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) B) (= (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log B) X)) K) (and (@ (@ tptp.ord_less_eq_real (@ _let_1 (@ tptp.ring_1_of_int_real K))) X) (@ (@ tptp.ord_less_real X) (@ _let_1 (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int K) tptp.one_one_int)))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_nat _let_1))) (let ((_let_3 (@ tptp.log (@ tptp.numeral_numeral_real _let_1)))) (=> (@ (@ tptp.ord_less_eq_nat _let_2) N) (= (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real N))) (@ (@ tptp.plus_plus_int (@ tptp.archim6058952711729229775r_real (@ _let_3 (@ tptp.semiri5074537144036343181t_real (@ (@ tptp.divide_divide_nat N) _let_2))))) tptp.one_one_int))))))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (N tptp.nat) (K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat B))) (=> (@ (@ tptp.ord_less_eq_nat (@ _let_1 N)) K) (=> (@ (@ tptp.ord_less_nat K) (@ _let_1 (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat))) (=> (@ (@ tptp.ord_less_eq_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) B) (= (@ tptp.archim6058952711729229775r_real (@ (@ tptp.log (@ tptp.semiri5074537144036343181t_real B)) (@ tptp.semiri5074537144036343181t_real K))) (@ tptp.semiri1314217659103216013at_int N))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ tptp.sin_real X)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ tptp.sin_coeff M3)) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))))) (@ (@ tptp.times_times_real (@ tptp.inverse_inverse_real (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real X)) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_betw_nat_complex (lambda ((K2 tptp.nat)) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) (@ tptp.semiri5074537144036343181t_real K2))) (@ tptp.semiri5074537144036343181t_real N))))) (@ tptp.set_ord_lessThan_nat N)) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) tptp.one_one_complex)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.sinh_real X) tptp.zero_zero_real) (= X tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.sinh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sinh_real X)) (@ _let_1 X)))))
% 6.68/6.99 (assert (= tptp.divide1717551699836669952omplex (lambda ((X3 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.times_times_complex X3) (@ tptp.invers8013647133539491842omplex Y3)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ tptp.semiri1408675320244567234ct_nat M) (@ (@ tptp.times_times_nat (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc N)) M)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.divide_divide_nat (@ tptp.semiri1408675320244567234ct_nat M)) (@ tptp.semiri1408675320244567234ct_nat N)) (@ (@ tptp.groups708209901874060359at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or1269000886237332187st_nat (@ (@ tptp.plus_plus_nat N) tptp.one_one_nat)) M))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real A) _let_1)) (@ (@ tptp.power_power_real B) _let_1)))) (= (@ tptp.invers8013647133539491842omplex (@ (@ tptp.complex2 A) B)) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real A) _let_2)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real B)) _let_2)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.sinh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (forall ((X tptp.vEBT_VEBT) (Y Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (= (@ tptp.vEBT_VEBT_minNull X) Y) (=> (@ _let_2 X) (=> (=> (= X _let_1) (=> Y (not (@ _let_2 _let_1)))) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (=> (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (=> Y (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X _let_1) (=> (not Y) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real (@ tptp.sinh_real X)) (@ tptp.cosh_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (not (= (@ tptp.cosh_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.cosh_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_eq_real X) Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real Y))) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ _let_1 tptp.zero_zero_real) (= (@ (@ tptp.ord_less_eq_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ _let_1 X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ tptp.cosh_real X))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real Y) tptp.zero_zero_real) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real Y) X))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y)) (@ (@ tptp.ord_less_real X) Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ tptp.cosh_real X)) (@ tptp.cosh_real Y))))))
% 6.68/6.99 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ (@ tptp.groups705719431365010083at_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat I) J)) (@ (@ tptp.groups1705073143266064639nt_int (lambda ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int J))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ tptp.arcosh_real (@ tptp.cosh_real X)) X))))
% 6.68/6.99 (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 ((X3 tptp.int)) X3)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int I)) (@ tptp.semiri1314217659103216013at_int _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ tptp.cosh_real (@ tptp.ln_ln_real X)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real X) (@ tptp.inverse_inverse_real X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (forall ((X tptp.vEBT_VEBT)) (=> (not (@ tptp.vEBT_VEBT_minNull X)) (=> (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) X) (=> (forall ((Uv2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf true) Uv2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (=> (forall ((Uu2 Bool)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf Uu2) true))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))) (not (forall ((Uz2 tptp.product_prod_nat_nat) (Va3 tptp.nat) (Vb2 tptp.list_VEBT_VEBT) (Vc2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node (@ tptp.some_P7363390416028606310at_nat Uz2)) Va3) Vb2) Vc2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ tptp.vEBT_Leaf false) false))) (let ((_let_2 (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel))) (=> (@ tptp.vEBT_VEBT_minNull X) (=> (@ _let_2 X) (=> (=> (= X _let_1) (not (@ _let_2 _let_1))) (not (forall ((Uw2 tptp.nat) (Ux2 tptp.list_VEBT_VEBT) (Uy2 tptp.vEBT_VEBT)) (let ((_let_1 (@ (@ (@ (@ tptp.vEBT_Node tptp.none_P5556105721700978146at_nat) Uw2) Ux2) Uy2))) (=> (= X _let_1) (not (@ (@ tptp.accp_VEBT_VEBT tptp.vEBT_V6963167321098673237ll_rel) _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ (@ (@ tptp.bij_be1856998921033663316omplex (@ tptp.times_times_complex (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.root N) (@ tptp.real_V1022390504157884413omplex C)))) (@ tptp.cis (@ (@ tptp.divide_divide_real (@ tptp.arg C)) (@ tptp.semiri5074537144036343181t_real N)))))) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) tptp.one_one_complex)))) (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) C))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X) (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.cot_real X)) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= tptp.int_ge_less_than (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z6) (@ (@ tptp.ord_less_int Z6) Z3))))))))
% 6.68/6.99 (assert (= tptp.int_ge_less_than2 (lambda ((D2 tptp.int)) (@ tptp.collec213857154873943460nt_int (@ tptp.produc4947309494688390418_int_o (lambda ((Z6 tptp.int) (Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int D2) Z3) (@ (@ tptp.ord_less_int Z6) Z3))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.root N) tptp.zero_zero_real) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root (@ tptp.suc tptp.zero_zero_nat)) X) X)))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ _let_1 X) (@ _let_1 Y)) (= X Y))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.root tptp.zero_zero_nat) X) tptp.zero_zero_real)))
% 6.68/6.99 (assert (= (@ tptp.cot_real tptp.pi) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.zero_zero_real) (= X tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_real X) Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)) (@ (@ tptp.ord_less_eq_real X) Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (= (@ (@ tptp.root N) X) tptp.one_one_real) (= X tptp.one_one_real)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) tptp.one_one_real) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_real X) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_real X) tptp.one_one_real)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N) X)) tptp.one_one_real) (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.one_one_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.root N) Y)) (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.cot_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) tptp.pi)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.cot_real (@ (@ tptp.plus_plus_real X) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))) (@ tptp.cot_real X))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.inverse_inverse_real X)) (@ tptp.inverse_inverse_real (@ _let_1 X))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.divide_divide_real X) Y)) (@ (@ tptp.divide_divide_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root M))) (let ((_let_2 (@ tptp.root N))) (= (@ _let_1 (@ _let_2 X)) (@ _let_2 (@ _let_1 X)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (X tptp.real)) (= (@ (@ tptp.root (@ (@ tptp.times_times_nat M) N)) X) (@ (@ tptp.root M) (@ (@ tptp.root N) X)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ (@ tptp.times_times_real X) Y)) (@ (@ tptp.times_times_real (@ _let_1 X)) (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (= (@ _let_1 (@ tptp.uminus_uminus_real X)) (@ tptp.uminus_uminus_real (@ _let_1 X))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real X) Y) (@ (@ tptp.ord_less_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (Y tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real X) Y) (@ (@ tptp.ord_less_eq_real (@ _let_1 X)) (@ _let_1 Y)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (K tptp.nat)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ (@ tptp.power_power_real X) K)) (@ (@ tptp.power_power_real (@ _let_1 X)) K))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ _let_1 (@ tptp.abs_abs_real X)) (@ tptp.abs_abs_real (@ _let_1 X)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ _let_1 X) (@ _let_1 (@ (@ tptp.root N) X)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.ord_less_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N) X)))))))
% 6.68/6.99 (assert (= tptp.sqrt (@ tptp.root (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.abs_abs_real (@ (@ tptp.root N) (@ (@ tptp.power_power_real Y) N))) (@ tptp.abs_abs_real Y)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ (@ tptp.root N) X))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_nat N) N4) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.ord_less_real (@ (@ tptp.root N) X)) (@ (@ tptp.root N4) X))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ tptp.ord_less_eq_real tptp.one_one_real) X) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.root N4) X)) (@ (@ tptp.root N) X)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y) (=> (= (@ (@ tptp.power_power_real Y) N) X) (= (@ (@ tptp.root N) X) Y))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.power_power_real (@ (@ tptp.root N) X)) N) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (= (@ (@ tptp.power_power_real Y) N) X) (= (@ (@ tptp.root N) X) Y)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (= (@ (@ tptp.root N) (@ (@ tptp.power_power_real X) N)) X))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (N4 tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_eq_nat N) N4) (=> (@ (@ 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 N) X)) (@ (@ tptp.root N4) X))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (B tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ tptp.ln_ln_real (@ (@ tptp.root N) B)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real B)) (@ tptp.semiri5074537144036343181t_real N)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ tptp.log B))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) A) (= (@ _let_1 (@ (@ tptp.root N) A)) (@ (@ tptp.divide_divide_real (@ _let_1 A)) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (B tptp.real) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) B) (= (@ (@ tptp.log (@ (@ tptp.root N) B)) X) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.log B) X)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= (@ (@ tptp.root N) X) (@ (@ tptp.powr_real X) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_real X) (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ _let_1 (@ tptp.cot_real X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ tptp.tan_real (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) X)) (@ tptp.cot_real X))))
% 6.68/6.99 (assert (= tptp.arctan (lambda ((Y3 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_real X3) _let_1) (= (@ tptp.tan_real X3) Y3))))))))
% 6.68/6.99 (assert (= tptp.arcsin (lambda ((Y3 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (and (@ (@ tptp.ord_less_eq_real (@ tptp.uminus_uminus_real _let_1)) X3) (@ (@ tptp.ord_less_eq_real X3) _let_1) (= (@ tptp.sin_real X3) Y3))))))))
% 6.68/6.99 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (let ((_let_1 (@ tptp.suc N2))) (@ (@ tptp.minus_minus_int (@ (@ tptp.bit_se2923211474154528505it_int _let_1) K2)) (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2))))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat M) N)))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.times_times_int _let_2))) (let ((_let_4 (@ tptp.sgn_sgn_int K))) (let ((_let_5 (@ (@ tptp.times_times_int _let_4) (@ tptp.semiri1314217659103216013at_int M)))) (let ((_let_6 (@ (@ tptp.modulo_modulo_int _let_5) (@ _let_3 (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_7 (= _let_4 _let_2))) (let ((_let_8 (or (= _let_2 tptp.zero_zero_int) (= _let_4 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_8 (= _let_6 _let_5)) (=> (not _let_8) (and (=> _let_7 (= _let_6 (@ _let_3 _let_1))) (=> (not _let_7) (= _let_6 (@ _let_3 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.times_times_nat N) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))) _let_1)))))))))))))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int) (R tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int K) (@ tptp.sgn_sgn_int R))) (or (@ _let_1 K) (= R tptp.zero_zero_int))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (R tptp.int) (K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int L2))) (= (@ _let_1 (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R)) K)) (or (@ _let_1 K) (= R tptp.zero_zero_int))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (R tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int L2) (@ tptp.sgn_sgn_int R))) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.68/6.99 (assert (forall ((R tptp.int) (L2 tptp.int) (K tptp.int)) (= (@ (@ tptp.dvd_dvd_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int R)) L2)) K) (and (@ (@ tptp.dvd_dvd_int L2) K) (=> (= R tptp.zero_zero_int) (= K tptp.zero_zero_int))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.bit_ri631733984087533419it_int N) K)) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_ri631733984087533419it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.bit_se1146084159140164899it_int K) N))))
% 6.68/6.99 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.suc N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) N))))
% 6.68/6.99 (assert (forall ((W tptp.num) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.suc N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) N)))))
% 6.68/6.99 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 W)))) (@ tptp.numeral_numeral_nat N)) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) (@ tptp.pred_numeral N)))))
% 6.68/6.99 (assert (forall ((W tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 W)))) (@ tptp.numeral_numeral_nat N)) (not (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.numeral_numeral_int W)) (@ tptp.pred_numeral N))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se725231765392027082nd_int K) L2)) N) (and (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat) (L4 tptp.int)) (not (= K (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int L4)) (@ tptp.semiri1314217659103216013at_int N3))))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2)) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K)) tptp.one_one_int)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (@ (@ tptp.dvd_dvd_int L2) K)) (= (@ tptp.sgn_sgn_int (@ (@ tptp.modulo_modulo_int K) L2)) (@ tptp.sgn_sgn_int L2))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.ln_ln_real X) (@ tptp.the_real (lambda ((X3 tptp.real)) false))))))
% 6.68/6.99 (assert (= tptp.sgn_sgn_int (lambda ((I5 tptp.int)) (@ (@ (@ tptp.if_int (= I5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) I5)) tptp.one_one_int) (@ tptp.uminus_uminus_int tptp.one_one_int))))))
% 6.68/6.99 (assert (forall ((V tptp.int) (K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (let ((_let_3 (@ tptp.times_times_int (@ tptp.sgn_sgn_int V)))) (=> (not (= V tptp.zero_zero_int)) (= (@ (@ tptp.divide_divide_int (@ _let_3 _let_2)) (@ _let_3 _let_1)) (@ (@ tptp.divide_divide_int _let_2) _let_1))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat) (K tptp.int)) (=> (@ (@ tptp.ord_less_nat N) M) (=> (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.bit_se2923211474154528505it_int M) K))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.dvd_dvd_int L2) K) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int K)) (@ tptp.sgn_sgn_int L2))) (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ (@ tptp.bit_concat_bit M) K) L2)) N) (or (and (@ (@ tptp.ord_less_nat N) M) (@ (@ tptp.bit_se1146084159140164899it_int K) N)) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) (@ (@ tptp.minus_minus_nat N) M)))))))
% 6.68/6.99 (assert (= tptp.bit_ri631733984087533419it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ (@ tptp.bit_concat_bit N2) K2) (@ tptp.uminus_uminus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (not (forall ((N3 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (forall ((M2 tptp.nat)) (let ((_let_1 (@ tptp.bit_se1146084159140164899it_int K))) (=> (@ (@ tptp.ord_less_eq_nat N3) M2) (= (@ _let_1 M2) (@ _let_1 N3))))) (not (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N3) (= (@ _let_1 (@ (@ tptp.minus_minus_nat N3) tptp.one_one_nat)) (not (@ _let_1 N3)))))))))))
% 6.68/6.99 (assert (= tptp.bit_se1146084159140164899it_int (lambda ((K2 tptp.int) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_int _let_1) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int _let_1) N2))))))))
% 6.68/6.99 (assert (= tptp.arccos (lambda ((Y3 tptp.real)) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) tptp.pi) (= (@ tptp.cos_real X3) Y3)))))))
% 6.68/6.99 (assert (forall ((R tptp.int) (L2 tptp.int) (K tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.sgn_sgn_int R) (@ tptp.sgn_sgn_int L2)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R)) (@ tptp.abs_abs_int L2)) (=> (= K (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q2) L2)) R)) (@ (@ (@ tptp.eucl_rel_int K) L2) (@ (@ tptp.product_Pair_int_int Q2) R)))))))
% 6.68/6.99 (assert (forall ((A12 tptp.int) (A23 tptp.int) (A32 tptp.product_prod_int_int)) (=> (@ (@ (@ tptp.eucl_rel_int A12) A23) A32) (=> (=> (= A23 tptp.zero_zero_int) (not (= A32 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A12)))) (=> (forall ((Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) tptp.zero_zero_int)) (=> (not (= A23 tptp.zero_zero_int)) (not (= A12 (@ (@ tptp.times_times_int Q3) A23)))))) (not (forall ((R2 tptp.int) (Q3 tptp.int)) (=> (= A32 (@ (@ tptp.product_Pair_int_int Q3) R2)) (=> (= (@ tptp.sgn_sgn_int R2) (@ tptp.sgn_sgn_int A23)) (=> (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R2)) (@ tptp.abs_abs_int A23)) (not (= A12 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q3) A23)) R2)))))))))))))
% 6.68/6.99 (assert (= tptp.eucl_rel_int (lambda ((A1 tptp.int) (A22 tptp.int) (A33 tptp.product_prod_int_int)) (or (exists ((K2 tptp.int)) (and (= A1 K2) (= A22 tptp.zero_zero_int) (= A33 (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) K2)))) (exists ((L tptp.int) (K2 tptp.int) (Q5 tptp.int)) (and (= A1 K2) (= A22 L) (= A33 (@ (@ tptp.product_Pair_int_int Q5) tptp.zero_zero_int)) (not (= L tptp.zero_zero_int)) (= K2 (@ (@ tptp.times_times_int Q5) L)))) (exists ((R5 tptp.int) (L tptp.int) (K2 tptp.int) (Q5 tptp.int)) (and (= A1 K2) (= A22 L) (= A33 (@ (@ tptp.product_Pair_int_int Q5) R5)) (= (@ tptp.sgn_sgn_int R5) (@ tptp.sgn_sgn_int L)) (@ (@ tptp.ord_less_int (@ tptp.abs_abs_int R5)) (@ tptp.abs_abs_int L)) (= K2 (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int Q5) L)) R5))))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (not (= L2 tptp.zero_zero_int)) (=> (not (= (@ tptp.sgn_sgn_int K) (@ tptp.sgn_sgn_int L2))) (= (@ (@ tptp.divide_divide_int K) L2) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int (@ (@ tptp.divide_divide_int (@ tptp.abs_abs_int K)) (@ tptp.abs_abs_int L2)))) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L2) K)))))))))
% 6.68/6.99 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.plus_plus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.bit_se1146084159140164899it_int K2) N2)))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.68/6.99 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.minus_minus_int K2) (@ (@ tptp.times_times_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K2) N2))) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2))))))
% 6.68/6.99 (assert (= (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real))))))
% 6.68/6.99 (assert (= tptp.pi (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.the_real (lambda ((X3 tptp.real)) (and (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X3) (@ (@ tptp.ord_less_eq_real X3) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (= (@ tptp.cos_real X3) tptp.zero_zero_real)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se2923211474154528505it_int (@ tptp.suc N)) K) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)) (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.bit_se1146084159140164899it_int K) N)))) (@ (@ tptp.bit_se2923211474154528505it_int N) K)))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int) (N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.divide_divide_nat M) N))) (let ((_let_2 (@ tptp.sgn_sgn_int L2))) (let ((_let_3 (@ tptp.sgn_sgn_int K))) (let ((_let_4 (@ (@ tptp.divide_divide_int (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int M))) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int N))))) (let ((_let_5 (= _let_3 _let_2))) (let ((_let_6 (or (= _let_2 tptp.zero_zero_int) (= _let_3 tptp.zero_zero_int) (= N tptp.zero_zero_nat)))) (and (=> _let_6 (= _let_4 tptp.zero_zero_int)) (=> (not _let_6) (and (=> _let_5 (= _let_4 (@ tptp.semiri1314217659103216013at_int _let_1))) (=> (not _let_5) (= _let_4 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_nat N) M)))))))))))))))))))
% 6.68/6.99 (assert (= tptp.modulo_modulo_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L))) (let ((_let_2 (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 _let_1))))) (let ((_let_3 (@ tptp.sgn_sgn_int L))) (let ((_let_4 (@ tptp.times_times_int _let_3))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) _let_3)) (@ _let_4 _let_2)) (@ _let_4 (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int _let_1) (@ tptp.zero_n2684676970156552555ol_int (not (@ (@ tptp.dvd_dvd_int L) K2))))) _let_2)))))))))))
% 6.68/6.99 (assert (= tptp.divide_divide_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_nat (@ tptp.nat2 (@ tptp.abs_abs_int K2))) (@ tptp.nat2 (@ tptp.abs_abs_int L))))) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ (@ tptp.if_int (= (@ tptp.sgn_sgn_int K2) (@ tptp.sgn_sgn_int L))) (@ tptp.semiri1314217659103216013at_int _let_1)) (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.plus_plus_nat _let_1) (@ tptp.zero_n2687167440665602831ol_nat (not (@ (@ tptp.dvd_dvd_int L) K2))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (I tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real I)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) I))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 I)))) (=> (not _let_3) (= _let_2 (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int I)))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.sgn_sgn_real X)) (@ _let_1 X)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.sgn_sgn_real X)) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_nat K))))
% 6.68/6.99 (assert (= (@ tptp.nat2 tptp.one_one_int) (@ tptp.suc tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 Z) tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((I tptp.int)) (= (= (@ tptp.nat2 I) tptp.zero_zero_nat) (@ (@ tptp.ord_less_eq_int I) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (and (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (@ (@ tptp.ord_less_int W) Z)))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.uminus_uminus_int (@ tptp.semiri1314217659103216013at_int N))) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (let ((_let_1 (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (and (=> _let_2 (= _let_1 Z)) (=> (not _let_2) (= _let_1 tptp.zero_zero_int)))))))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z))))
% 6.68/6.99 (assert (forall ((V tptp.num) (V3 tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) (@ tptp.numeral_numeral_nat V3)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) (@ tptp.numeral_numeral_int V3))))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (X tptp.num) (N tptp.nat)) (= (= (@ tptp.nat2 Y) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (= Y (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (Y tptp.int)) (= (= (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N) (@ tptp.nat2 Y)) (= (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N) Y))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))) A) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real A)))))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (= (@ (@ tptp.ord_less_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int tptp.one_one_int) Z))))
% 6.68/6.99 (assert (forall ((V tptp.num)) (= (@ (@ tptp.minus_minus_nat (@ tptp.numeral_numeral_nat V)) tptp.one_one_nat) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.numeral_numeral_int V)) tptp.one_one_int)))))
% 6.68/6.99 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.68/6.99 (assert (forall ((X tptp.num) (N tptp.nat) (A tptp.int)) (= (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ tptp.nat2 A)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)) A))))
% 6.68/6.99 (assert (forall ((A tptp.int) (X tptp.num) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 A)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat X)) N)) (@ (@ tptp.ord_less_eq_int A) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int X)) N)))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.nat2 K)) N) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.suc N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) N) (= N tptp.zero_zero_nat))))
% 6.68/6.99 (assert (= tptp.zero_zero_nat (@ tptp.nat2 tptp.zero_zero_int)))
% 6.68/6.99 (assert (= tptp.numeral_numeral_nat (lambda ((I5 tptp.num)) (@ tptp.nat2 (@ tptp.numeral_numeral_int I5)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int X) Y) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y)))))
% 6.68/6.99 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (exists ((X7 tptp.nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.nat Bool))) (exists ((X3 tptp.int)) (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P4 (@ tptp.nat2 X3)))))))
% 6.68/6.99 (assert (= (lambda ((P3 (-> tptp.nat Bool))) (forall ((X7 tptp.nat)) (@ P3 X7))) (lambda ((P4 (-> tptp.nat Bool))) (forall ((X3 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X3) (@ P4 (@ tptp.nat2 X3)))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (= (@ tptp.nat2 Z) (@ tptp.nat2 Z7)) (= Z Z7)))))))
% 6.68/6.99 (assert (= tptp.one_one_nat (@ tptp.nat2 tptp.one_one_int)))
% 6.68/6.99 (assert (= tptp.bit_se4205575877204974255it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se4203085406695923979it_int M3) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.nat2 (@ tptp.bit_se2000444600071755411sk_int N)) (@ tptp.bit_se2002935070580805687sk_nat N))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (not (@ (@ tptp.bit_se1148574629649215175it_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.sgn_sgn_real (@ (@ tptp.root N) X)) (@ tptp.sgn_sgn_real X)))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (W tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Z) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (@ (@ tptp.ord_less_nat M) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int (@ tptp.semiri1314217659103216013at_int M)) Z))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 X)) N) (@ (@ tptp.ord_less_eq_int X) (@ tptp.semiri1314217659103216013at_int N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (Z tptp.int)) (= (= (@ tptp.semiri1314217659103216013at_int M) Z) (and (= M (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)))))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 Z)) Z))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B))) (@ (@ tptp.plus_plus_nat A) B))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.minus_minus_nat N) M)) (@ tptp.semiri1314217659103216013at_int (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int N)) (@ tptp.semiri1314217659103216013at_int M)))))))
% 6.68/6.99 (assert (forall ((W tptp.int) (Z tptp.int)) (= (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.times_times_int W) Z))) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.abs_abs_int W))) (@ tptp.nat2 (@ tptp.abs_abs_int Z))))))
% 6.68/6.99 (assert (= tptp.bit_se727722235901077358nd_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.68/6.99 (assert (= tptp.plus_plus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.68/6.99 (assert (= tptp.times_times_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.times_times_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.ord_less_eq_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.nat2 (@ tptp.archim7802044766580827645g_real X))))))
% 6.68/6.99 (assert (= tptp.minus_minus_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.68/6.99 (assert (= tptp.divide_divide_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.divide_divide_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.68/6.99 (assert (= tptp.modulo_modulo_nat (lambda ((A3 tptp.nat) (B2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int (@ tptp.semiri1314217659103216013at_int A3)) (@ tptp.semiri1314217659103216013at_int B2))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (=> (not (= Z tptp.zero_zero_complex)) (= (@ tptp.cis (@ tptp.arg Z)) (@ tptp.sgn_sgn_complex Z)))))
% 6.68/6.99 (assert (= tptp.sgn_sgn_real (lambda ((A3 tptp.real)) (@ (@ (@ tptp.if_real (= A3 tptp.zero_zero_real)) tptp.zero_zero_real) (@ (@ (@ tptp.if_real (@ (@ tptp.ord_less_real tptp.zero_zero_real) A3)) tptp.one_one_real) (@ tptp.uminus_uminus_real tptp.one_one_real))))))
% 6.68/6.99 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_int W) Z)))))
% 6.68/6.99 (assert (forall ((W tptp.int) (Z tptp.int)) (=> (or (@ (@ tptp.ord_less_int tptp.zero_zero_int) W) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 W)) (@ tptp.nat2 Z)) (@ (@ tptp.ord_less_eq_int W) Z)))))
% 6.68/6.99 (assert (forall ((W tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= (@ tptp.nat2 W) M) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (W tptp.int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W))) (= (= M (@ tptp.nat2 W)) (and (=> _let_1 (= W (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.nat Bool)) (I tptp.int)) (= (@ P (@ tptp.nat2 I)) (and (forall ((N2 tptp.nat)) (=> (= I (@ tptp.semiri1314217659103216013at_int N2)) (@ P N2))) (=> (@ (@ tptp.ord_less_int I) tptp.zero_zero_int) (@ P tptp.zero_zero_nat))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.ord_less_eq_nat N) (@ tptp.nat2 K)) (@ (@ tptp.ord_less_eq_int (@ tptp.semiri1314217659103216013at_int N)) K)))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 Z) (=> (@ _let_1 Z7) (= (@ tptp.nat2 (@ (@ tptp.plus_plus_int Z) Z7)) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7))))))
% 6.68/6.99 (assert (= tptp.suc (lambda ((A3 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ tptp.semiri1314217659103216013at_int A3)) tptp.one_one_int)))))
% 6.68/6.99 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z7) (=> (@ (@ tptp.ord_less_eq_int Z7) Z) (= (@ tptp.nat2 (@ (@ tptp.minus_minus_int Z) Z7)) (@ (@ tptp.minus_minus_nat (@ tptp.nat2 Z)) (@ tptp.nat2 Z7)))))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (@ (@ tptp.ord_less_eq_nat (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.plus_plus_int K) L2)))) (@ (@ tptp.plus_plus_nat (@ tptp.nat2 (@ tptp.abs_abs_int K))) (@ tptp.nat2 (@ tptp.abs_abs_int L2))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Y) (= (@ tptp.nat2 (@ (@ tptp.divide_divide_int X) Y)) (@ (@ tptp.divide_divide_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.nat2 (@ (@ tptp.power_power_int Z) N)) (@ (@ tptp.power_power_nat (@ tptp.nat2 Z)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X) tptp.zero_zero_real) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (= (@ tptp.nat2 (@ (@ tptp.modulo_modulo_int X) Y)) (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 X)) (@ tptp.nat2 Y))))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.divide_divide_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (A tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real X)) A) (@ (@ tptp.ord_less_eq_nat X) (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real A))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.abs_abs_int L2))) (let ((_let_2 (@ tptp.abs_abs_int K))) (= (@ (@ tptp.modulo_modulo_int _let_2) _let_1) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.modulo_modulo_nat (@ tptp.nat2 _let_2)) (@ tptp.nat2 _let_1))))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K)) (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.bit_se2925701944663578781it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se2923211474154528505it_int N) K))))))
% 6.68/6.99 (assert (= (@ tptp.nat2 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.suc (@ tptp.suc tptp.zero_zero_nat))))
% 6.68/6.99 (assert (forall ((A tptp.real) (N tptp.nat) (X tptp.real) (B tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real A)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real A)) N)) X) (=> (= X (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real B)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real B)) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= A B))))))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z) (= (@ tptp.suc (@ tptp.nat2 Z)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int tptp.one_one_int) Z))))))
% 6.68/6.99 (assert (forall ((W tptp.int) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) W) (= (@ (@ tptp.ord_less_nat (@ tptp.nat2 W)) M) (@ (@ tptp.ord_less_int W) (@ tptp.semiri1314217659103216013at_int M))))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (Z7 tptp.int)) (=> (@ (@ tptp.ord_less_eq_int Z) tptp.zero_zero_int) (= (@ tptp.nat2 (@ (@ tptp.times_times_int Z) Z7)) (@ (@ tptp.times_times_nat (@ tptp.nat2 (@ tptp.uminus_uminus_int Z))) (@ tptp.nat2 (@ tptp.uminus_uminus_int Z7)))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (let ((_let_1 (@ tptp.nat2 (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat A) B))) (and (=> _let_2 (= _let_1 (@ (@ tptp.minus_minus_nat B) A))) (=> (not _let_2) (= _let_1 (@ (@ tptp.minus_minus_nat A) B))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.semiri5074537144036343181t_real N)) X) (=> (@ (@ tptp.ord_less_real X) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N))) (= (@ tptp.nat2 (@ tptp.archim6058952711729229775r_real X)) N)))))
% 6.68/6.99 (assert (forall ((Z7 tptp.int) (Z tptp.int)) (let ((_let_1 (@ (@ tptp.minus_minus_int Z) Z7))) (let ((_let_2 (@ tptp.nat2 Z))) (let ((_let_3 (@ (@ tptp.minus_minus_nat _let_2) (@ tptp.nat2 Z7)))) (let ((_let_4 (@ (@ tptp.ord_less_int Z7) tptp.zero_zero_int))) (and (=> _let_4 (= _let_3 _let_2)) (=> (not _let_4) (= _let_3 (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_less_int _let_1) tptp.zero_zero_int)) tptp.zero_zero_nat) (@ tptp.nat2 _let_1)))))))))))
% 6.68/6.99 (assert (= tptp.bit_se1148574629649215175it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (not (@ (@ tptp.dvd_dvd_nat _let_1) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat _let_1) N2))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Y tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.root N) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y)) N))) Y))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ (@ tptp.root N) X))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real _let_1)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real _let_1)) N)) X)))))
% 6.68/6.99 (assert (forall ((Z tptp.int) (M tptp.nat)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) Z))) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.nat2 Z)) M) (and (=> _let_1 (@ (@ tptp.dvd_dvd_int Z) (@ tptp.semiri1314217659103216013at_int M))) (=> (not _let_1) (= M tptp.zero_zero_nat)))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (X tptp.real)) (=> (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis X)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.pi) (= (@ tptp.arg Z) X))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.real Bool)) (N tptp.nat) (X tptp.real)) (= (@ P (@ (@ tptp.root N) X)) (and (=> (= N tptp.zero_zero_nat) (@ P tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (forall ((Y3 tptp.real)) (=> (= (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y3)) N)) X) (@ P Y3))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.arg Z))) (=> (not (= Z tptp.zero_zero_complex)) (and (= (@ tptp.sgn_sgn_complex Z) (@ tptp.cis _let_1)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) tptp.pi))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K) (= (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat _let_1)) (@ tptp.nat2 K)) (@ (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int _let_1)) K))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.int)) (let ((_let_1 (@ tptp.power_power_real X))) (let ((_let_2 (@ (@ tptp.powr_real X) (@ tptp.ring_1_of_int_real N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) N))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (and (=> _let_3 (= _let_2 (@ _let_1 (@ tptp.nat2 N)))) (=> (not _let_3) (= _let_2 (@ tptp.inverse_inverse_real (@ _let_1 (@ tptp.nat2 (@ tptp.uminus_uminus_int N)))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (= (@ tptp.arctan (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.minus_minus_real (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real X)) tptp.pi)) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.arctan X))))))
% 6.68/6.99 (assert (= tptp.arg (lambda ((Z3 tptp.complex)) (@ (@ (@ tptp.if_real (= Z3 tptp.zero_zero_complex)) tptp.zero_zero_real) (@ tptp.fChoice_real (lambda ((A3 tptp.real)) (and (= (@ tptp.sgn_sgn_complex Z3) (@ tptp.cis A3)) (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.pi)) A3) (@ (@ tptp.ord_less_eq_real A3) tptp.pi))))))))
% 6.68/6.99 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (or (= K2 _let_2) (= L _let_2))) _let_2) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ (@ tptp.ord_max_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) (and (@ _let_1 K) (@ _let_1 L2))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) tptp.zero_zero_int) (or (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int)))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int _let_1) tptp.one_one_int) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se1409905431419307370or_int K) L2)) N) (or (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N)))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (K tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) L2) (@ (@ tptp.ord_less_eq_int K) (@ (@ tptp.bit_se1409905431419307370or_int K) L2)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se1409905431419307370or_int X) Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se725231765392027082nd_int X) Y)) (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) (@ (@ tptp.plus_plus_int X) Y))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se1409905431419307370or_int X) Y)) _let_1)))))))
% 6.68/6.99 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (or (not (@ _let_2 K2)) (not (@ _let_2 L))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bitM N)))))))
% 6.68/6.99 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cis (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_complex))))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))) (= (@ (@ tptp.bit_se1412395901928357646or_nat _let_1) (@ tptp.suc tptp.zero_zero_nat)) _let_1))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bit0 N)))))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) (@ tptp.bitM N)))))))
% 6.68/6.99 (assert (= (@ (@ tptp.bit_or_not_num_neg tptp.one) tptp.one) tptp.one))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) tptp.one) (@ tptp.bit0 tptp.one))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit1 M)) (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) tptp.one) tptp.one)))
% 6.68/6.99 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit1 M))) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit0 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit1 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.68/6.99 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg tptp.one) (@ tptp.bit0 M)) (@ tptp.bit1 M))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_or_not_num_neg (@ tptp.bit1 N)) (@ tptp.bit0 M)) (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N) M)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (= (= (@ tptp.sin_real (@ (@ tptp.times_times_real X) tptp.pi)) tptp.zero_zero_real) (@ (@ tptp.member_real X) tptp.ring_1_Ints_real))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= Xa2 tptp.one))) (let ((_let_2 (=> _let_1 (not (= Y tptp.one))))) (let ((_let_3 (= X tptp.one))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y) (=> (=> _let_3 _let_2) (=> (=> _let_3 (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y (@ tptp.bit1 M4)))))) (=> (=> _let_3 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (not (= Y _let_1)))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit0 N3))) (=> _let_1 (not (= Y (@ tptp.bit0 tptp.one))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (=> (=> (exists ((N3 tptp.num)) (= X (@ tptp.bit1 N3))) _let_2) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit0 M4)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (=> (= Xa2 (@ tptp.bit1 M4)) (not (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4)))))))))))))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((N tptp.real)) (=> (@ (@ tptp.member_real N) tptp.ring_1_Ints_real) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi)) N)) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se1412395901928357646or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))))
% 6.68/6.99 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (or (not (@ _let_2 M3)) (not (@ _let_2 N2))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.68/6.99 (assert (= tptp.bit_se1412395901928357646or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.ord_max_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se1412395901928357646or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Xa2 tptp.num) (Y tptp.num)) (let ((_let_1 (= X tptp.one))) (let ((_let_2 (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel))) (=> (= (@ (@ tptp.bit_or_not_num_neg X) Xa2) Y) (=> (@ _let_2 (@ (@ tptp.product_Pair_num_num X) Xa2)) (=> (=> _let_1 (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ _let_2 (@ (@ tptp.product_Pair_num_num tptp.one) tptp.one)))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit1 M4)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (=> _let_1 (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y _let_1) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num tptp.one) _let_1)))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit0 N3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y (@ tptp.bit0 tptp.one)) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit0 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bit0 (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit0 N3)) _let_1))))))))) (=> (forall ((N3 tptp.num)) (let ((_let_1 (@ tptp.bit1 N3))) (=> (= X _let_1) (=> (= Xa2 tptp.one) (=> (= Y tptp.one) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num _let_1) tptp.one)))))))) (=> (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit0 M4))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))) (not (forall ((N3 tptp.num)) (=> (= X (@ tptp.bit1 N3)) (forall ((M4 tptp.num)) (let ((_let_1 (@ tptp.bit1 M4))) (=> (= Xa2 _let_1) (=> (= Y (@ tptp.bitM (@ (@ tptp.bit_or_not_num_neg N3) M4))) (not (@ (@ tptp.accp_P3113834385874906142um_num tptp.bit_or3848514188828904588eg_rel) (@ (@ tptp.product_Pair_num_num (@ tptp.bit1 N3)) _let_1))))))))))))))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_nat (@ (@ tptp.plus_plus_nat N) (@ tptp.zero_n2687167440665602831ol_nat _let_1))) (@ tptp.zero_n2687167440665602831ol_nat (not _let_1)))))))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y)))))
% 6.68/6.99 (assert (forall ((Y tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 Y))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 Y)))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit1 X)))))
% 6.68/6.99 (assert (forall ((X tptp.num)) (= (@ (@ tptp.bit_se6528837805403552850or_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 X))) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 X)))))
% 6.68/6.99 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ (@ tptp.if_nat (= M3 tptp.zero_zero_nat)) N2) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) M3) (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.modulo_modulo_nat M3) _let_1)) (@ (@ tptp.modulo_modulo_nat N2) _let_1))) _let_1)) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1))))))))))
% 6.68/6.99 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_nat _let_1))) (@ (@ tptp.plus_plus_nat (@ tptp.zero_n2687167440665602831ol_nat (not (= (not (@ _let_2 M3)) (not (@ _let_2 N2)))))) (@ (@ tptp.times_times_nat _let_1) (@ (@ tptp.bit_se6528837805403552850or_nat (@ (@ tptp.divide_divide_nat M3) _let_1)) (@ (@ tptp.divide_divide_nat N2) _let_1)))))))))
% 6.68/6.99 (assert (forall ((Bs tptp.list_o)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.ord_less_int (@ (@ (@ tptp.groups9116527308978886569_o_int tptp.zero_n2684676970156552555ol_int) _let_1) Bs)) (@ (@ tptp.power_power_int _let_1) (@ tptp.size_size_list_o Bs))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ _let_1 K)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se545348938243370406it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (L2 tptp.int)) (= (@ (@ (@ tptp.bit_concat_bit N) tptp.zero_zero_int) L2) (@ (@ tptp.bit_se545348938243370406it_int N) L2))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) (= (@ _let_1 K) (@ _let_1 L2))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) tptp.zero_zero_int) (not (= (@ (@ tptp.ord_less_int K) tptp.zero_zero_int) (@ (@ tptp.ord_less_int L2) tptp.zero_zero_int))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))))
% 6.68/6.99 (assert (forall ((K tptp.int) (L2 tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se6526347334894502574or_int K) L2)) N) (not (= (@ (@ tptp.bit_se1146084159140164899it_int K) N) (@ (@ tptp.bit_se1146084159140164899it_int L2) N))))))
% 6.68/6.99 (assert (= tptp.bit_se2159334234014336723it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se6526347334894502574or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se547839408752420682it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se545348938243370406it_int N) K)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (=> (@ _let_1 X) (=> (@ _let_1 Y) (@ _let_1 (@ (@ tptp.bit_se6526347334894502574or_int X) Y)))))))
% 6.68/6.99 (assert (= tptp.bit_se7882103937844011126it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se1412395901928357646or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 6.68/6.99 (assert (= tptp.bit_se2161824704523386999it_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.bit_se6528837805403552850or_nat N2) (@ (@ tptp.bit_se547839408752420682it_nat M3) tptp.one_one_nat)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ (@ tptp.bit_se545348938243370406it_int M) K)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1146084159140164899it_int K) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.68/6.99 (assert (= tptp.bit_se6528837805403552850or_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ tptp.nat2 (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.semiri1314217659103216013at_int M3)) (@ tptp.semiri1314217659103216013at_int N2))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (Q2 tptp.nat) (N tptp.nat)) (= (@ (@ tptp.bit_se1148574629649215175it_nat (@ (@ tptp.bit_se547839408752420682it_nat M) Q2)) N) (and (@ (@ tptp.ord_less_eq_nat M) N) (@ (@ tptp.bit_se1148574629649215175it_nat Q2) (@ (@ tptp.minus_minus_nat N) M))))))
% 6.68/6.99 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (@ (@ tptp.plus_plus_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.68/6.99 (assert (= tptp.bit_concat_bit (lambda ((N2 tptp.nat) (K2 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se2923211474154528505it_int N2) K2)) (@ (@ tptp.bit_se545348938243370406it_int N2) L)))))
% 6.68/6.99 (assert (= tptp.bit_se7879613467334960850it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int K2) (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int)))))
% 6.68/6.99 (assert (= tptp.bit_se547839408752420682it_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.times_times_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (= tptp.bit_se545348938243370406it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.times_times_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se545348938243370406it_int N) (@ tptp.uminus_uminus_int tptp.one_one_int)) (@ tptp.uminus_uminus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.nat) (Y tptp.int)) (let ((_let_1 (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) X) (=> (@ (@ tptp.ord_less_int X) _let_1) (=> (@ (@ tptp.ord_less_int Y) _let_1) (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se6526347334894502574or_int X) Y)) _let_1)))))))
% 6.68/6.99 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.dvd_dvd_int _let_1))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (not (= (not (@ _let_2 K2)) (not (@ _let_2 L)))))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))
% 6.68/6.99 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.uminus_uminus_int tptp.one_one_int))) (@ (@ (@ tptp.if_int (= K2 _let_2)) (@ tptp.bit_ri7919022796975470100ot_int L)) (@ (@ (@ tptp.if_int (= L _let_2)) (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ (@ (@ tptp.if_int (= K2 tptp.zero_zero_int)) L) (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ tptp.plus_plus_int (@ tptp.abs_abs_int (@ (@ tptp.minus_minus_int (@ (@ tptp.modulo_modulo_int K2) _let_1)) (@ (@ tptp.modulo_modulo_int L) _let_1)))) (@ (@ tptp.times_times_int _let_1) (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.divide_divide_int K2) _let_1)) (@ (@ tptp.divide_divide_int L) _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.divide_divide_nat (@ (@ tptp.minus_minus_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat))) (@ (@ tptp.times_times_nat M) (@ (@ tptp.minus_minus_nat M) tptp.one_one_nat)))) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_int (@ tptp.bit_ri7919022796975470100ot_int K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) K))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (= (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.bit_ri7919022796975470100ot_int K)) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) (@ tptp.suc M)) (@ (@ tptp.insert_nat M) tptp.bot_bot_set_nat))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int _let_2)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.minus_minus_int _let_2) tptp.one_one_int)) (@ (@ tptp.minus_minus_int _let_1) tptp.one_one_int))))))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int K)) N) (not (@ (@ tptp.bit_se1146084159140164899it_int K) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (forall ((X3 tptp.nat)) (=> (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool))) (= (exists ((M3 tptp.nat)) (and (@ (@ tptp.ord_less_nat M3) N) (@ P M3))) (exists ((X3 tptp.nat)) (and (@ (@ tptp.member_nat X3) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ P X3))))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat L2) (@ tptp.suc U)) (@ (@ tptp.set_or1269000886237332187st_nat L2) U))))
% 6.68/6.99 (assert (= tptp.set_ord_lessThan_nat (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat M) tptp.zero_zero_nat) tptp.bot_bot_set_nat)))
% 6.68/6.99 (assert (= tptp.bit_se1409905431419307370or_int (lambda ((K2 tptp.int) (L tptp.int)) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) (@ tptp.bit_ri7919022796975470100ot_int L))))))
% 6.68/6.99 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (@ (@ tptp.minus_minus_int (@ tptp.uminus_uminus_int K2)) tptp.one_one_int))))
% 6.68/6.99 (assert (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) tptp.zero_zero_int))
% 6.68/6.99 (assert (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat N) (@ _let_1 N))))))
% 6.68/6.99 (assert (= tptp.bit_se4203085406695923979it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se545348938243370406it_int N2) tptp.one_one_int))))))
% 6.68/6.99 (assert (= tptp.bit_se6526347334894502574or_int (lambda ((K2 tptp.int) (L tptp.int)) (@ (@ tptp.bit_se1409905431419307370or_int (@ (@ tptp.bit_se725231765392027082nd_int K2) (@ tptp.bit_ri7919022796975470100ot_int L))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int K2)) L)))))
% 6.68/6.99 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.finite_finite_nat N4))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.divide_divide_int (@ tptp.bit_ri7919022796975470100ot_int K)) _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K) _let_1))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))))) (= (@ _let_1 (@ tptp.bit_ri7919022796975470100ot_int K)) (not (@ _let_1 K))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))) (= (@ (@ tptp.bit_se725231765392027082nd_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) _let_1))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int))) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.nat)) (= (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.uminus_uminus_int K)) N) (@ (@ tptp.bit_se1146084159140164899it_int (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.minus_minus_int K) tptp.one_one_int))) N))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg N) M))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ tptp.numeral_numeral_int (@ (@ tptp.bit_or_not_num_neg M) N)) (@ tptp.uminus_uminus_int (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.suc N)))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat M) N))) (and (=> _let_3 (= _let_2 (@ (@ tptp.insert_nat N) (@ _let_1 N)))) (=> (not _let_3) (= _let_2 tptp.bot_bot_set_nat))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.groups708209901874060359at_nat tptp.suc) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ tptp.semiri1408675320244567234ct_nat N))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.numeral_numeral_int (@ tptp.bit0 M)))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int tptp.one_one_int) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) tptp.zero_zero_int)))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int tptp.one_one_int)) (@ tptp.bit_ri7919022796975470100ot_int tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (K tptp.num)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat M))) (let ((_let_2 (@ _let_1 (@ tptp.numeral_numeral_nat K)))) (let ((_let_3 (@ tptp.pred_numeral K))) (let ((_let_4 (@ (@ tptp.ord_less_eq_nat M) _let_3))) (and (=> _let_4 (= _let_2 (@ (@ tptp.insert_nat _let_3) (@ _let_1 _let_3)))) (=> (not _let_4) (= _let_2 tptp.bot_bot_set_nat)))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N)))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit0 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc tptp.zero_zero_nat)) N) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int (@ tptp.bit1 M))) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ tptp.plus_plus_int tptp.one_one_int) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.bit_se1409905431419307370or_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))))))))
% 6.68/6.99 (assert (= tptp.bit_ri7919022796975470100ot_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one)))) (@ (@ tptp.plus_plus_int (@ tptp.zero_n2684676970156552555ol_int (@ (@ tptp.dvd_dvd_int _let_1) K2))) (@ (@ tptp.times_times_int _let_1) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.divide_divide_int K2) _let_1))))))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))) (= (@ (@ tptp.groups3542108847815614940at_nat _let_1) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) K)) (@ (@ tptp.minus_minus_nat (@ _let_1 K)) tptp.one_one_nat)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A (-> tptp.nat tptp.nat)) (B (-> tptp.nat tptp.nat))) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ A I4)) (@ A J2))))) (=> (forall ((I4 tptp.nat) (J2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat I4) J2) (=> (@ (@ tptp.ord_less_nat J2) N) (@ (@ tptp.ord_less_eq_nat (@ B J2)) (@ B I4))))) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat N) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_nat (@ A I5)) (@ B I5)))) _let_1))) (@ (@ tptp.times_times_nat (@ (@ tptp.groups3542108847815614940at_nat A) _let_1)) (@ (@ tptp.groups3542108847815614940at_nat B) _let_1))))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.68/6.99 (assert (forall ((U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int L2) (@ (@ tptp.plus_plus_int U) tptp.one_one_int)) (@ (@ tptp.set_or1266510415728281911st_int L2) U))))
% 6.68/6.99 (assert (= tptp.topolo4055970368930404560y_real (lambda ((X2 (-> tptp.nat tptp.real))) (forall ((J3 tptp.nat)) (exists ((M8 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M8) N2) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ X2 M3)) (@ X2 N2)))) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc J3)))))))))))))
% 6.68/6.99 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.size_size_VEBT_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.size_size_VEBT_VEBT) X13)) (@ tptp.size_size_VEBT_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((X11 tptp.option4927543243414619207at_nat) (X12 tptp.nat) (X13 tptp.list_VEBT_VEBT) (X14 tptp.vEBT_VEBT)) (= (@ tptp.vEBT_size_VEBT (@ (@ (@ (@ tptp.vEBT_Node X11) X12) X13) X14)) (@ (@ tptp.plus_plus_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.size_list_VEBT_VEBT tptp.vEBT_size_VEBT) X13)) (@ tptp.vEBT_size_VEBT X14))) (@ tptp.suc tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (= tptp.vEBT_VEBT_valid tptp.vEBT_invar_vebt))
% 6.68/6.99 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_invar_vebt T) D) (@ (@ tptp.vEBT_VEBT_valid T) D))))
% 6.68/6.99 (assert (forall ((T tptp.vEBT_VEBT) (D tptp.nat)) (=> (@ (@ tptp.vEBT_VEBT_valid T) D) (@ (@ tptp.vEBT_invar_vebt T) D))))
% 6.68/6.99 (assert (forall ((Uu Bool) (Uv Bool) (D tptp.nat)) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ tptp.vEBT_Leaf Uu) Uv)) D) (= D tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((X21 Bool) (X222 Bool)) (= (@ tptp.vEBT_size_VEBT (@ (@ tptp.vEBT_Leaf X21) X222)) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (= tptp.code_Target_positive tptp.numeral_numeral_int))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.csqrt Z)) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))
% 6.68/6.99 (assert (forall ((V tptp.num)) (= (@ tptp.re (@ tptp.numera6690914467698888265omplex V)) (@ tptp.numeral_numeral_real V))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.re Z)) (@ tptp.numeral_numeral_real W)))))
% 6.68/6.99 (assert (forall ((Y tptp.complex)) (=> (not (= Y tptp.zero_zero_complex)) (=> (= (@ tptp.re Y) tptp.zero_zero_real) (= (@ tptp.cos_real (@ tptp.arg Y)) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= (@ tptp.re tptp.imaginary_unit) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.re X)) (@ tptp.real_V1022390504157884413omplex X))))
% 6.68/6.99 (assert (= (@ tptp.re tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.re tptp.one_one_complex) tptp.one_one_real))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.68/6.99 (assert (forall ((R tptp.real) (X tptp.complex)) (= (@ tptp.re (@ (@ tptp.real_V2046097035970521341omplex R) X)) (@ (@ tptp.times_times_real R) (@ tptp.re X)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.re X)) (@ tptp.re Y)))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re (@ tptp.csqrt Z)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.real_V1022390504157884413omplex Z))) (let ((_let_2 (@ tptp.re Z))) (= (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real _let_1) _let_2)) tptp.zero_zero_real) (= _let_2 (@ tptp.uminus_uminus_real _let_1)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.cos_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.re (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.68/6.99 (assert (= tptp.csqrt (lambda ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re Z3))) (let ((_let_3 (@ tptp.real_V1022390504157884413omplex Z3))) (let ((_let_4 (@ tptp.im Z3))) (@ (@ tptp.complex2 (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real _let_3) _let_2)) _let_1))) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_4 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_4))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real _let_3) _let_2)) _let_1)))))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.im Z))) (= (@ tptp.im (@ tptp.csqrt Z)) (@ (@ tptp.times_times_real (@ (@ (@ tptp.if_real (= _let_1 tptp.zero_zero_real)) tptp.one_one_real) (@ tptp.sgn_sgn_real _let_1))) (@ tptp.sqrt (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.re Z))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real _let_1) tptp.zero_zero_real) (= (@ tptp.csqrt X) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt (@ tptp.abs_abs_real _let_1))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri5044797733671781792omplex N)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (= (@ tptp.im (@ tptp.ring_17405671764205052669omplex Z)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.im (@ tptp.semiri8010041392384452111omplex N)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((Z tptp.real)) (= (@ tptp.im (@ tptp.real_V4546457046886955230omplex Z)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.power_power_complex X) N)) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((V tptp.num)) (= (@ tptp.im (@ tptp.numera6690914467698888265omplex V)) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.re Z))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (=> (= (@ tptp.im X) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_real (@ tptp.re X)) N)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex tptp.imaginary_unit) Z)) (@ tptp.uminus_uminus_real (@ tptp.im Z)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (W tptp.num)) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex Z) (@ tptp.numera6690914467698888265omplex W))) (@ (@ tptp.divide_divide_real (@ tptp.im Z)) (@ tptp.numeral_numeral_real W)))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.re X))) (=> (= (@ tptp.im X) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) _let_1) (= (@ tptp.csqrt X) (@ tptp.real_V4546457046886955230omplex (@ tptp.sqrt _let_1))))))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.im X))) (=> (or (@ (@ tptp.ord_less_real _let_1) tptp.zero_zero_real) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.re X)))) (= (@ tptp.csqrt (@ tptp.uminus1482373934393186551omplex X)) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.csqrt X)))))))
% 6.68/6.99 (assert (= (@ tptp.im tptp.imaginary_unit) tptp.one_one_real))
% 6.68/6.99 (assert (= (@ tptp.im tptp.zero_zero_complex) tptp.zero_zero_real))
% 6.68/6.99 (assert (= (@ tptp.im tptp.one_one_complex) tptp.zero_zero_real))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.68/6.99 (assert (forall ((R tptp.real) (X tptp.complex)) (= (@ tptp.im (@ (@ tptp.real_V2046097035970521341omplex R) X)) (@ (@ tptp.times_times_real R) (@ tptp.im X)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_real (@ tptp.im X)) (@ tptp.im Y)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.ring_1_Ints_complex) (and (= (@ tptp.im Z) tptp.zero_zero_real) (exists ((I5 tptp.int)) (= (@ tptp.re Z) (@ tptp.ring_1_of_int_real I5)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.real_V1022390504157884413omplex X))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.im Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.re Y))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.im Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.re Z))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.re Z) tptp.zero_zero_real) (= (@ tptp.real_V1022390504157884413omplex Z) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (=> (= (@ tptp.abs_abs_real (@ tptp.re Z)) (@ tptp.real_V1022390504157884413omplex Z)) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.im X) (@ tptp.im Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.re X))) (@ tptp.abs_abs_real (@ tptp.re Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (=> (= (@ tptp.re X) (@ tptp.re Y)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex X)) (@ tptp.real_V1022390504157884413omplex Y)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ tptp.im X))) (@ tptp.abs_abs_real (@ tptp.im Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.re (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.re X)) (@ tptp.re Y))) (@ (@ tptp.times_times_real (@ tptp.im X)) (@ tptp.im Y))))))
% 6.68/6.99 (assert (= tptp.plus_plus_complex (lambda ((X3 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.plus_plus_real (@ tptp.re X3)) (@ tptp.re Y3))) (@ (@ tptp.plus_plus_real (@ tptp.im X3)) (@ tptp.im Y3))))))
% 6.68/6.99 (assert (= tptp.real_V2046097035970521341omplex (lambda ((R5 tptp.real) (X3 tptp.complex)) (let ((_let_1 (@ tptp.times_times_real R5))) (@ (@ tptp.complex2 (@ _let_1 (@ tptp.re X3))) (@ _let_1 (@ tptp.im X3)))))))
% 6.68/6.99 (assert (= tptp.minus_minus_complex (lambda ((X3 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ tptp.re X3)) (@ tptp.re Y3))) (@ (@ tptp.minus_minus_real (@ tptp.im X3)) (@ tptp.im Y3))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.csqrt Z))) (let ((_let_2 (@ tptp.re _let_1))) (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (and (= _let_2 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im _let_1))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ tptp.real_V1022390504157884413omplex Z)) (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (A tptp.real)) (= (@ tptp.sin_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) A)) (@ tptp.im (@ (@ tptp.power_power_complex (@ tptp.cis A)) N)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.re (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.cos_real (@ tptp.im Z))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ tptp.exp_complex Z)) (@ (@ tptp.times_times_real (@ tptp.exp_real (@ tptp.re Z))) (@ tptp.sin_real (@ tptp.im Z))))))
% 6.68/6.99 (assert (forall ((A tptp.complex)) (= A (@ (@ tptp.plus_plus_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.re A))) (@ (@ tptp.times_times_complex tptp.imaginary_unit) (@ tptp.real_V4546457046886955230omplex (@ tptp.im A)))))))
% 6.68/6.99 (assert (= tptp.times_times_complex (lambda ((X3 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.re Y3))) (let ((_let_2 (@ tptp.times_times_real (@ tptp.im X3)))) (let ((_let_3 (@ tptp.im Y3))) (let ((_let_4 (@ tptp.times_times_real (@ tptp.re X3)))) (@ (@ tptp.complex2 (@ (@ tptp.minus_minus_real (@ _let_4 _let_1)) (@ _let_2 _let_3))) (@ (@ tptp.plus_plus_real (@ _let_4 _let_3)) (@ _let_2 _let_1))))))))))
% 6.68/6.99 (assert (= tptp.exp_complex (lambda ((Z3 tptp.complex)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ tptp.exp_real (@ tptp.re Z3)))) (@ tptp.cis (@ tptp.im Z3))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) _let_1) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1))))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.im (@ (@ tptp.power_power_complex X) (@ tptp.numeral_numeral_nat _let_1))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real _let_1)) (@ tptp.re X))) (@ tptp.im X))))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ tptp.re (@ (@ tptp.power_power_complex X) _let_1)) (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (= Z tptp.zero_zero_complex) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)) tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z3)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z3)) _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.re X))) (= (@ tptp.re (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real _let_2) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_2) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im X)) _let_1))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (not (= Z tptp.zero_zero_complex)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real (@ tptp.re X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.im X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.68/6.99 (assert (forall ((W tptp.complex) (Z tptp.complex)) (let ((_let_1 (@ tptp.re W))) (=> (= (@ (@ tptp.power_power_complex W) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) Z) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im W)))) (= (@ tptp.csqrt Z) W))))))
% 6.68/6.99 (assert (forall ((B tptp.complex)) (let ((_let_1 (@ tptp.re B))) (=> (or (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_1) (and (= _let_1 tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ tptp.im B)))) (= (@ tptp.csqrt (@ (@ tptp.power_power_complex B) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) B)))))
% 6.68/6.99 (assert (forall ((X tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X))) (= (@ tptp.im (@ tptp.invers8013647133539491842omplex X)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re X)) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1))))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y))) (let ((_let_3 (@ tptp.re Y))) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex X) Y)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ (@ tptp.times_times_real (@ tptp.im X)) _let_3)) (@ (@ tptp.times_times_real (@ tptp.re X)) _let_2))) (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.plus_plus_real (@ tptp.abs_abs_real (@ tptp.re Z))) (@ tptp.abs_abs_real (@ tptp.im Z)))) (@ (@ tptp.times_times_real (@ tptp.sqrt (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ tptp.real_V1022390504157884413omplex Z)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.real_V1022390504157884413omplex Z))) (=> (not (= Z tptp.zero_zero_complex)) (= (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.re Z)) _let_2)) _let_1)) (@ (@ tptp.power_power_real (@ (@ tptp.divide_divide_real (@ tptp.im Z)) _let_2)) _let_1)) tptp.one_one_real))))))
% 6.68/6.99 (assert (= tptp.invers8013647133539491842omplex (lambda ((X3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im X3))) (let ((_let_3 (@ tptp.re X3))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real _let_3) _let_4)) (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_4)))))))))
% 6.68/6.99 (assert (= tptp.divide1717551699836669952omplex (lambda ((X3 tptp.complex) (Y3 tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.im Y3))) (let ((_let_3 (@ tptp.re Y3))) (let ((_let_4 (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real _let_3) _let_1)) (@ (@ tptp.power_power_real _let_2) _let_1)))) (let ((_let_5 (@ tptp.times_times_real (@ tptp.re X3)))) (let ((_let_6 (@ tptp.times_times_real (@ tptp.im X3)))) (@ (@ tptp.complex2 (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ _let_5 _let_3)) (@ _let_6 _let_2))) _let_4)) (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ _let_6 _let_3)) (@ _let_5 _let_2))) _let_4)))))))))))
% 6.68/6.99 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.uminus_uminus_real (@ tptp.re R))) (@ tptp.im Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((R tptp.complex) (Z tptp.complex)) (=> (@ (@ tptp.member_complex R) tptp.real_V2521375963428798218omplex) (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex R) Z)) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real (@ tptp.re R)) (@ tptp.re Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((Y tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y) X) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.68/6.99 (assert (forall ((Y tptp.complex) (X tptp.complex)) (=> (@ (@ tptp.member_complex Y) tptp.real_V2521375963428798218omplex) (=> (@ (@ tptp.member_complex X) tptp.real_V2521375963428798218omplex) (= (= X (@ (@ tptp.times_times_complex tptp.imaginary_unit) Y)) (and (= X tptp.zero_zero_complex) (= Y tptp.zero_zero_complex)))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.member_complex Z) tptp.real_V2521375963428798218omplex) (= (@ tptp.im Z) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.member_complex (@ (@ tptp.complex2 X) tptp.zero_zero_real)) tptp.real_V2521375963428798218omplex)))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.minus_minus_complex Z) (@ tptp.cnj Z)) (@ (@ tptp.times_times_complex (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.im Z)))) tptp.imaginary_unit))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (= (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real (@ tptp.re Z)) _let_1)) (@ (@ tptp.power_power_real (@ tptp.im Z)) _let_1)))))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.times_times_complex X) Y)) (@ (@ tptp.times_times_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.68/6.99 (assert (= (@ tptp.cnj tptp.zero_zero_complex) tptp.zero_zero_complex))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.zero_zero_complex) (= Z tptp.zero_zero_complex))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (= (@ tptp.cnj Z) tptp.one_one_complex) (= Z tptp.one_one_complex))))
% 6.68/6.99 (assert (= (@ tptp.cnj tptp.one_one_complex) tptp.one_one_complex))
% 6.68/6.99 (assert (forall ((X tptp.complex) (N tptp.nat)) (= (@ tptp.cnj (@ (@ tptp.power_power_complex X) N)) (@ (@ tptp.power_power_complex (@ tptp.cnj X)) N))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.plus_plus_complex X) Y)) (@ (@ tptp.plus_plus_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.68/6.99 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.numera6690914467698888265omplex W))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ tptp.cnj (@ (@ tptp.minus_minus_complex X) Y)) (@ (@ tptp.minus_minus_complex (@ tptp.cnj X)) (@ tptp.cnj Y)))))
% 6.68/6.99 (assert (forall ((W tptp.num)) (let ((_let_1 (@ tptp.uminus1482373934393186551omplex (@ tptp.numera6690914467698888265omplex W)))) (= (@ tptp.cnj _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.im (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) tptp.zero_zero_real)))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (= (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B)) tptp.zero_zero_real) (= (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))) tptp.zero_zero_real))))
% 6.68/6.99 (assert (= tptp.real_V1022390504157884413omplex (lambda ((Z3 tptp.complex)) (@ tptp.sqrt (@ tptp.re (@ (@ tptp.times_times_complex Z3) (@ tptp.cnj Z3)))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.re (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ tptp.ord_less_eq_real tptp.zero_zero_real))) (= (@ _let_1 (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) (@ _let_1 (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B))))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (= (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.divide1717551699836669952omplex A) B))) tptp.zero_zero_real) (@ (@ tptp.ord_less_eq_real (@ tptp.im (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) tptp.zero_zero_real))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z))) (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))
% 6.68/6.99 (assert (forall ((A tptp.complex) (B tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex A) (@ tptp.cnj B)))) (let ((_let_2 (@ tptp.ord_less_real tptp.zero_zero_real))) (let ((_let_3 (@ (@ tptp.divide1717551699836669952omplex A) B))) (and (= (@ _let_2 (@ tptp.re _let_3)) (@ _let_2 (@ tptp.re _let_1))) (= (@ _let_2 (@ tptp.im _let_3)) (@ _let_2 (@ tptp.im _let_1)))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex Z)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (@ (@ tptp.times_times_complex Z) (@ tptp.cnj Z)))))
% 6.68/6.99 (assert (forall ((Z tptp.complex)) (= (@ (@ tptp.plus_plus_complex Z) (@ tptp.cnj Z)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re Z))))))
% 6.68/6.99 (assert (= tptp.divide1717551699836669952omplex (lambda ((A3 tptp.complex) (B2 tptp.complex)) (@ (@ tptp.divide1717551699836669952omplex (@ (@ tptp.times_times_complex A3) (@ tptp.cnj B2))) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.power_power_real (@ tptp.real_V1022390504157884413omplex B2)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((Z tptp.complex) (W tptp.complex)) (let ((_let_1 (@ (@ tptp.times_times_complex Z) (@ tptp.cnj W)))) (= (@ (@ tptp.plus_plus_complex _let_1) (@ (@ tptp.times_times_complex (@ tptp.cnj Z)) W)) (@ tptp.real_V4546457046886955230omplex (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) (@ tptp.re _let_1)))))))
% 6.68/6.99 (assert (= tptp.unique4921790084139445826nteger (lambda ((L tptp.num) (__flatten_var_0 tptp.produc8923325533196201883nteger)) (@ (@ tptp.produc6916734918728496179nteger (lambda ((Q5 tptp.code_integer) (R5 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))) Q5))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger L))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le3102999989581377725nteger _let_2) R5)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger R5) _let_2))) (@ (@ tptp.produc1086072967326762835nteger _let_1) R5)))))) __flatten_var_0))))
% 6.68/6.99 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_lessThan_nat U)) U)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_nat I5) N)))) N)))
% 6.68/6.99 (assert (forall ((U tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.set_ord_atMost_nat U)) (@ tptp.suc U))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or4665077453230672383an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.ord_less_eq_nat I5) N)))) (@ tptp.suc N))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or1269000886237332187st_nat L2) U)) (@ (@ tptp.minus_minus_nat (@ tptp.suc U)) L2))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or1266510415728281911st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.plus_plus_int (@ (@ tptp.minus_minus_int U) L2)) tptp.one_one_int)))))
% 6.68/6.99 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.68/6.99 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.minus_8373710615458151222nteger tptp.zero_z3403309356797280102nteger) L2) (@ tptp.uminus1351360451143612070nteger L2))))
% 6.68/6.99 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger K) tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.99 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.times_3573771949741848930nteger tptp.zero_z3403309356797280102nteger) L2) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.99 (assert (forall ((L2 tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger tptp.zero_z3403309356797280102nteger) L2) L2)))
% 6.68/6.99 (assert (forall ((K tptp.code_integer)) (= (@ (@ tptp.plus_p5714425477246183910nteger K) tptp.zero_z3403309356797280102nteger) K)))
% 6.68/6.99 (assert (@ (@ tptp.ord_le3102999989581377725nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.68/6.99 (assert (forall ((X tptp.produc8763457246119570046nteger)) (not (forall ((F2 (-> tptp.code_integer tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I4 tptp.code_integer)) (not (= X (@ (@ tptp.produc6137756002093451184nteger F2) (@ (@ tptp.produc1086072967326762835nteger D3) I4))))))))
% 6.68/6.99 (assert (forall ((X tptp.produc1908205239877642774nteger)) (not (forall ((F2 (-> tptp.produc6241069584506657477e_term tptp.option6357759511663192854e_term)) (D3 tptp.code_integer) (I4 tptp.code_integer)) (not (= X (@ (@ tptp.produc8603105652947943368nteger F2) (@ (@ tptp.produc1086072967326762835nteger D3) I4))))))))
% 6.68/6.99 (assert (= tptp.unique3479559517661332726nteger (lambda ((M3 tptp.num) (N2 tptp.num)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger N2))) (let ((_let_2 (@ tptp.numera6620942414471956472nteger M3))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.68/6.99 (assert (= tptp.sgn_sgn_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger tptp.one_one_Code_integer)) tptp.one_one_Code_integer)))))
% 6.68/6.99 (assert (forall ((Nat tptp.nat)) (= (not (= Nat tptp.zero_zero_nat)) (@ (@ (@ tptp.case_nat_o false) (lambda ((Uu3 tptp.nat)) true)) Nat))))
% 6.68/6.99 (assert (forall ((Nat tptp.nat)) (= (= Nat tptp.zero_zero_nat) (@ (@ (@ tptp.case_nat_o true) (lambda ((Uu3 tptp.nat)) false)) Nat))))
% 6.68/6.99 (assert (= tptp.zero_zero_nat tptp.zero_zero_nat))
% 6.68/6.99 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (not (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M5) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I)))))) tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (@ (@ tptp.member_nat tptp.zero_zero_nat) M5) (= (@ tptp.suc (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M5) (@ (@ tptp.ord_less_nat K2) I)))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M5) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.68/6.99 (assert (forall ((M5 tptp.set_nat) (I tptp.nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat (@ tptp.suc K2)) M5) (@ (@ tptp.ord_less_nat K2) I))))) (@ tptp.finite_card_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (and (@ (@ tptp.member_nat K2) M5) (@ (@ tptp.ord_less_nat K2) (@ tptp.suc I))))))))))
% 6.68/6.99 (assert (forall ((U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U)) (@ tptp.nat2 U))))
% 6.68/6.99 (assert (= tptp.zero_zero_int tptp.zero_zero_int))
% 6.68/6.99 (assert (= tptp.one_one_int tptp.one_one_int))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat) (K tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat K) (@ (@ tptp.plus_plus_nat K) (@ tptp.finite_card_nat A2))))) (=> (@ (@ tptp.ord_less_eq_set_nat A2) _let_1) (= A2 _let_1)))))
% 6.68/6.99 (assert (= tptp.one_one_nat tptp.one_one_nat))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_eq_nat (@ tptp.suc M)) N) (@ (@ (@ tptp.case_nat_o false) (@ tptp.ord_less_eq_nat M)) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat M) _let_1) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat M6) N)))) M)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (let ((_let_1 (@ tptp.suc N))) (= (@ (@ tptp.ord_max_nat _let_1) M) (@ (@ (@ tptp.case_nat_nat _let_1) (lambda ((M6 tptp.nat)) (@ tptp.suc (@ (@ tptp.ord_max_nat N) M6)))) M)))))
% 6.68/6.99 (assert (forall ((N4 tptp.set_nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_set_nat N4) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat N4)) N))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.finite_card_nat S2)))) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) S2))))
% 6.68/6.99 (assert (forall ((C tptp.complex) (N tptp.nat)) (=> (not (= C tptp.zero_zero_complex)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) C)))) N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.finite_card_complex (@ tptp.collect_complex (lambda ((Z3 tptp.complex)) (= (@ (@ tptp.power_power_complex Z3) N) tptp.one_one_complex)))) N))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.minus_minus_nat M))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((K2 tptp.nat)) K2)) (@ _let_1 N))))))
% 6.68/6.99 (assert (= tptp.code_integer_of_int (lambda ((K2 tptp.int)) (let ((_let_1 (@ tptp.bit0 tptp.one))) (let ((_let_2 (@ tptp.numeral_numeral_int _let_1))) (let ((_let_3 (@ (@ tptp.times_3573771949741848930nteger (@ tptp.numera6620942414471956472nteger _let_1)) (@ tptp.code_integer_of_int (@ (@ tptp.divide_divide_int K2) _let_2))))) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_less_int K2) tptp.zero_zero_int)) (@ tptp.uminus1351360451143612070nteger (@ tptp.code_integer_of_int (@ tptp.uminus_uminus_int K2)))) (@ (@ (@ tptp.if_Code_integer (= K2 tptp.zero_zero_int)) tptp.zero_z3403309356797280102nteger) (@ (@ (@ tptp.if_Code_integer (= (@ (@ tptp.modulo_modulo_int K2) _let_2) tptp.zero_zero_int)) _let_3) (@ (@ tptp.plus_p5714425477246183910nteger _let_3) tptp.one_one_Code_integer))))))))))
% 6.68/6.99 (assert (= tptp.abs_abs_Code_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus1351360451143612070nteger K2)) K2))))
% 6.68/6.99 (assert (= (@ tptp.uminus1351360451143612070nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))
% 6.68/6.99 (assert (= tptp.zero_z3403309356797280102nteger (@ tptp.code_integer_of_int tptp.zero_zero_int)))
% 6.68/6.99 (assert (not (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger)))
% 6.68/6.99 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.modulo364778990260209775nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.modulo_modulo_int Xa2) X)))))
% 6.68/6.99 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.plus_p5714425477246183910nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.plus_plus_int Xa2) X)))))
% 6.68/6.99 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.times_3573771949741848930nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.times_times_int Xa2) X)))))
% 6.68/6.99 (assert (= tptp.one_one_Code_integer (@ tptp.code_integer_of_int tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.ord_le3102999989581377725nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ (@ tptp.ord_less_eq_int Xa2) X))))
% 6.68/6.99 (assert (forall ((Xa2 tptp.int) (X tptp.int)) (= (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.code_integer_of_int Xa2)) (@ tptp.code_integer_of_int X)) (@ tptp.code_integer_of_int (@ (@ tptp.minus_minus_int Xa2) X)))))
% 6.68/6.99 (assert (= tptp.code_positive tptp.numera6620942414471956472nteger))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit1 N)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)) tptp.one_one_Code_integer)))))
% 6.68/6.99 (assert (= tptp.code_integer_of_num tptp.numera6620942414471956472nteger))
% 6.68/6.99 (assert (= (@ tptp.code_integer_of_num tptp.one) tptp.one_one_Code_integer))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.code_integer_of_num N))) (= (@ tptp.code_integer_of_num (@ tptp.bit0 N)) (@ (@ tptp.plus_p5714425477246183910nteger _let_1) _let_1)))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.bit0 tptp.one))) (= (@ tptp.code_integer_of_num _let_1) (@ tptp.numera6620942414471956472nteger _let_1))))
% 6.68/6.99 (assert (= tptp.code_int_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_int (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) (@ tptp.uminus_uminus_int (@ tptp.code_int_of_integer (@ tptp.uminus1351360451143612070nteger K2)))) (@ (@ (@ tptp.if_int (= K2 tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_int) (@ (@ tptp.produc1553301316500091796er_int (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ tptp.code_int_of_integer L)))) (@ (@ (@ tptp.if_int (= J3 tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))))))))
% 6.68/6.99 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ tptp.divide6298287555418463151nteger K2) _let_1)) (not (@ (@ tptp.dvd_dvd_Code_integer _let_1) K2)))))))
% 6.68/6.99 (assert (= tptp.code_num_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_num (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.one_one_Code_integer)) tptp.one) (@ (@ tptp.produc7336495610019696514er_num (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_num_of_integer L))) (let ((_let_2 (@ (@ tptp.plus_plus_num _let_1) _let_1))) (@ (@ (@ tptp.if_num (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_num _let_2) tptp.one)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (= (@ tptp.code_int_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_int))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.code_int_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_int K))))
% 6.68/6.99 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.plus_p5714425477246183910nteger X) Xa2)) (@ (@ tptp.plus_plus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.68/6.99 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.times_3573771949741848930nteger X) Xa2)) (@ (@ tptp.times_times_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.68/6.99 (assert (= (@ tptp.code_int_of_integer tptp.one_one_Code_integer) tptp.one_one_int))
% 6.68/6.99 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.minus_8373710615458151222nteger X) Xa2)) (@ (@ tptp.minus_minus_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.68/6.99 (assert (forall ((X tptp.code_integer) (Xa2 tptp.code_integer)) (= (@ tptp.code_int_of_integer (@ (@ tptp.modulo364778990260209775nteger X) Xa2)) (@ (@ tptp.modulo_modulo_int (@ tptp.code_int_of_integer X)) (@ tptp.code_int_of_integer Xa2)))))
% 6.68/6.99 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer K2)) (@ tptp.code_int_of_integer L)))))
% 6.68/6.99 (assert (= tptp.ord_le3102999989581377725nteger (lambda ((X3 tptp.code_integer) (Xa4 tptp.code_integer)) (@ (@ tptp.ord_less_eq_int (@ tptp.code_int_of_integer X3)) (@ tptp.code_int_of_integer Xa4)))))
% 6.68/6.99 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger K2) L)) (@ (@ tptp.modulo364778990260209775nteger K2) L)))))
% 6.68/6.99 (assert (= tptp.code_bit_cut_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_Pro5737122678794959658eger_o (= K2 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc6677183202524767010eger_o tptp.zero_z3403309356797280102nteger) false)) (@ (@ tptp.produc9125791028180074456eger_o (lambda ((R5 tptp.code_integer) (S7 tptp.code_integer)) (@ (@ tptp.produc6677183202524767010eger_o (@ (@ (@ tptp.if_Code_integer (@ (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger) K2)) R5) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger R5)) S7))) (= S7 tptp.one_one_Code_integer)))) (@ (@ tptp.code_divmod_abs K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (= tptp.code_nat_of_integer (lambda ((K2 tptp.code_integer)) (@ (@ (@ tptp.if_nat (@ (@ tptp.ord_le3102999989581377725nteger K2) tptp.zero_z3403309356797280102nteger)) tptp.zero_zero_nat) (@ (@ tptp.produc1555791787009142072er_nat (lambda ((L tptp.code_integer) (J3 tptp.code_integer)) (let ((_let_1 (@ tptp.code_nat_of_integer L))) (let ((_let_2 (@ (@ tptp.plus_plus_nat _let_1) _let_1))) (@ (@ (@ tptp.if_nat (= J3 tptp.zero_z3403309356797280102nteger)) _let_2) (@ (@ tptp.plus_plus_nat _let_2) tptp.one_one_nat)))))) (@ (@ tptp.code_divmod_integer K2) (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one))))))))
% 6.68/6.99 (assert (forall ((K tptp.code_integer)) (= (@ tptp.semiri4939895301339042750nteger (@ tptp.code_nat_of_integer K)) (@ (@ tptp.ord_max_Code_integer tptp.zero_z3403309356797280102nteger) K))))
% 6.68/6.99 (assert (forall ((K tptp.code_integer)) (=> (@ (@ tptp.ord_le3102999989581377725nteger K) tptp.zero_z3403309356797280102nteger) (= (@ tptp.code_nat_of_integer K) tptp.zero_zero_nat))))
% 6.68/6.99 (assert (= (@ tptp.code_nat_of_integer tptp.zero_z3403309356797280102nteger) tptp.zero_zero_nat))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.code_nat_of_integer (@ tptp.numera6620942414471956472nteger K)) (@ tptp.numeral_numeral_nat K))))
% 6.68/6.99 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs tptp.zero_z3403309356797280102nteger) J) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) tptp.zero_z3403309356797280102nteger))))
% 6.68/6.99 (assert (= (@ tptp.code_nat_of_integer tptp.one_one_Code_integer) tptp.one_one_nat))
% 6.68/6.99 (assert (forall ((J tptp.code_integer)) (= (@ (@ tptp.code_divmod_abs J) tptp.zero_z3403309356797280102nteger) (@ (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger) (@ tptp.abs_abs_Code_integer J)))))
% 6.68/6.99 (assert (= tptp.pred (@ (@ tptp.case_nat_nat tptp.zero_zero_nat) (lambda ((X24 tptp.nat)) X24))))
% 6.68/6.99 (assert (= tptp.code_divmod_abs (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ tptp.abs_abs_Code_integer L))) (let ((_let_2 (@ tptp.abs_abs_Code_integer K2))) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.divide6298287555418463151nteger _let_2) _let_1)) (@ (@ tptp.modulo364778990260209775nteger _let_2) _let_1)))))))
% 6.68/6.99 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (let ((_let_3 (@ tptp.ord_le6747313008572928689nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 L)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ _let_3 K2)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S7 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S7 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger L) S7)))))) _let_1))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ tptp.produc6499014454317279255nteger tptp.uminus1351360451143612070nteger) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (@ (@ tptp.ord_le6747313008572928689nteger K2) tptp.zero_z3403309356797280102nteger)) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S7 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S7 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.uminus1351360451143612070nteger L)) S7)))))) _let_1))))))))))))
% 6.68/6.99 (assert (= tptp.binomial (lambda ((N2 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) N2))) (= (@ tptp.finite_card_nat K7) K2))))))))
% 6.68/6.99 (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))))
% 6.68/6.99 (assert (= tptp.archim6058952711729229775r_real (lambda ((X3 tptp.real)) (@ tptp.the_int (lambda ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_real (@ tptp.ring_1_of_int_real Z3)) X3) (@ (@ tptp.ord_less_real X3) (@ tptp.ring_1_of_int_real (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))))
% 6.68/6.99 (assert (= tptp.archim3151403230148437115or_rat (lambda ((X3 tptp.rat)) (@ tptp.the_int (lambda ((Z3 tptp.int)) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat Z3)) X3) (@ (@ tptp.ord_less_rat X3) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int Z3) tptp.one_one_int)))))))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ (@ tptp.modulo_modulo_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_snd_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (let ((_let_1 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (= (@ _let_1 (@ (@ tptp.bit_se8568078237143864401it_int N) K)) (@ _let_1 K)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.ord_less_int (@ (@ tptp.bit_se8568078237143864401it_int N) K)) tptp.zero_zero_int) (@ (@ tptp.ord_less_int K) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.uminus_uminus_int tptp.one_one_int))) (= (@ (@ tptp.bit_se8568078237143864401it_int N) _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_snd_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.modulo_modulo_nat M) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.68/6.99 (assert (forall ((L2 tptp.num) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.numeral_numeral_nat L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 K)))) (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.pred_numeral L2)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.num)) (= (@ (@ tptp.bit_se8568078237143864401it_int (@ tptp.suc N)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 K)))) (@ (@ tptp.bit_se8568078237143864401it_int N) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.inc K)))))))
% 6.68/6.99 (assert (= tptp.ord_less_eq_rat (lambda ((X3 tptp.rat) (Y3 tptp.rat)) (or (@ (@ tptp.ord_less_rat X3) Y3) (= X3 Y3)))))
% 6.68/6.99 (assert (= tptp.abs_abs_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat A3) tptp.zero_zero_rat)) (@ tptp.uminus_uminus_rat A3)) A3))))
% 6.68/6.99 (assert (= tptp.sgn_sgn_rat (lambda ((A3 tptp.rat)) (@ (@ (@ tptp.if_rat (= A3 tptp.zero_zero_rat)) tptp.zero_zero_rat) (@ (@ (@ tptp.if_rat (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) A3)) tptp.one_one_rat) (@ tptp.uminus_uminus_rat tptp.one_one_rat))))))
% 6.68/6.99 (assert (forall ((R tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) R) (not (forall ((S3 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) S3) (forall ((T6 tptp.rat)) (=> (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) T6) (not (= R (@ (@ tptp.plus_plus_rat S3) T6)))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8568078237143864401it_int M) (@ (@ tptp.bit_se545348938243370406it_int N) K)) (@ (@ tptp.bit_se8568078237143864401it_int (@ (@ tptp.minus_minus_nat M) N)) (@ (@ tptp.bit_se545348938243370406it_int (@ (@ tptp.minus_minus_nat N) M)) K)))))
% 6.68/6.99 (assert (= tptp.bit_se8568078237143864401it_int (lambda ((N2 tptp.nat) (K2 tptp.int)) (@ (@ tptp.divide_divide_int K2) (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (forall ((P5 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.inverse_inverse_rat P5)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (B2 tptp.int)) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= A3 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A3)) B2)) (@ tptp.abs_abs_int A3))))) (@ tptp.quotient_of P5)))))
% 6.68/6.99 (assert (forall ((Q2 tptp.int) (P5 tptp.int)) (=> (@ (@ tptp.ord_less_int Q2) tptp.zero_zero_int) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int P5)) (@ tptp.uminus_uminus_int Q2)))))))
% 6.68/6.99 (assert (= tptp.nat_prod_decode_aux (lambda ((K2 tptp.nat) (M3 tptp.nat)) (let ((_let_1 (@ tptp.suc K2))) (@ (@ (@ tptp.if_Pro6206227464963214023at_nat (@ (@ tptp.ord_less_eq_nat M3) K2)) (@ (@ tptp.product_Pair_nat_nat M3) (@ (@ tptp.minus_minus_nat K2) M3))) (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat M3) _let_1)))))))
% 6.68/6.99 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_integer K) L2)) (@ (@ tptp.modulo364778990260209775nteger K) L2))))
% 6.68/6.99 (assert (forall ((K tptp.code_integer) (L2 tptp.code_integer)) (= (@ tptp.produc6174133586879617921nteger (@ (@ tptp.code_divmod_abs K) L2)) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K)) (@ tptp.abs_abs_Code_integer L2)))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((P5 tptp.int)) (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P5) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int))))
% 6.68/6.99 (assert (= (@ tptp.quotient_of tptp.one_one_rat) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.zero_n2687167440665602831ol_nat (= N tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (= (@ tptp.quotient_of tptp.zero_zero_rat) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K))) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.68/6.99 (assert (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat tptp.one_one_rat)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((R tptp.rat)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ tptp.product_snd_int_int (@ tptp.quotient_of R)))))
% 6.68/6.99 (assert (= tptp.divide_divide_rat (lambda ((Q5 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.times_times_rat Q5) (@ tptp.inverse_inverse_rat R5)))))
% 6.68/6.99 (assert (= tptp.minus_minus_rat (lambda ((Q5 tptp.rat) (R5 tptp.rat)) (@ (@ tptp.plus_plus_rat Q5) (@ tptp.uminus_uminus_rat R5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.divide_divide_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C3) B2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.times_times_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.times_times_int A3) B2)) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (K tptp.int)) (= (@ (@ tptp.bit_se8570568707652914677it_nat N) (@ tptp.nat2 K)) (@ tptp.nat2 (@ (@ tptp.bit_se8568078237143864401it_int N) K)))))
% 6.68/6.99 (assert (forall ((R tptp.rat) (N tptp.int) (D tptp.int)) (=> (= (@ tptp.quotient_of R) (@ (@ tptp.product_Pair_int_int N) D)) (= R (@ (@ tptp.divide_divide_rat (@ tptp.ring_1_of_int_rat N)) (@ tptp.ring_1_of_int_rat D))))))
% 6.68/6.99 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.plus_plus_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.rat) (Q2 tptp.rat)) (= (@ tptp.quotient_of (@ (@ tptp.minus_minus_rat P5) Q2)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((B2 tptp.int) (D2 tptp.int)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int B2) C3))) (@ (@ tptp.times_times_int C3) D2))))) (@ tptp.quotient_of Q2)))) (@ tptp.quotient_of P5)))))
% 6.68/6.99 (assert (forall ((R tptp.rat) (P5 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.quotient_of R) (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.68/6.99 (assert (forall ((P5 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.uminus_uminus_rat P5)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A3)) __flatten_var_0))) (@ tptp.quotient_of P5)))))
% 6.68/6.99 (assert (forall ((P5 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.abs_abs_rat P5)) (@ (@ tptp.produc4245557441103728435nt_int (lambda ((A3 tptp.int) (__flatten_var_0 tptp.int)) (@ (@ tptp.product_Pair_int_int (@ tptp.abs_abs_int A3)) __flatten_var_0))) (@ tptp.quotient_of P5)))))
% 6.68/6.99 (assert (forall ((R tptp.product_prod_int_int) (P5 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize R) (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ (@ tptp.ord_less_int tptp.zero_zero_int) Q2))))
% 6.68/6.99 (assert (forall ((Q2 tptp.int) (S tptp.int) (P5 tptp.int) (R tptp.int)) (=> (not (= Q2 tptp.zero_zero_int)) (=> (not (= S tptp.zero_zero_int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int P5) Q2)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int R) S))) (= (@ (@ tptp.times_times_int P5) S) (@ (@ tptp.times_times_int R) Q2)))))))
% 6.68/6.99 (assert (= tptp.bit_se8570568707652914677it_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ (@ tptp.divide_divide_nat M3) (@ (@ tptp.power_power_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)))))
% 6.68/6.99 (assert (= tptp.ord_less_rat (lambda ((P2 tptp.rat) (Q5 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C3) B2)))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P2)))))
% 6.68/6.99 (assert (= tptp.ord_less_eq_rat (lambda ((P2 tptp.rat) (Q5 tptp.rat)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((A3 tptp.int) (C3 tptp.int)) (@ (@ tptp.produc4947309494688390418_int_o (lambda ((B2 tptp.int) (D2 tptp.int)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int A3) D2)) (@ (@ tptp.times_times_int C3) B2)))) (@ tptp.quotient_of Q5)))) (@ tptp.quotient_of P2)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ tptp.suc X))) (let ((_let_2 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (and (=> _let_2 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_2) (= Y (@ (@ tptp.nat_prod_decode_aux _let_1) (@ (@ tptp.minus_minus_nat Xa2) _let_1))))))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int tptp.one_one_int)) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N)))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int tptp.one_one_int) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int tptp.one) N))))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_nat_nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.nat_pr5047031295181774490ux_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ tptp.suc X))) (let ((_let_3 (@ (@ tptp.ord_less_eq_nat Xa2) X))) (=> (= (@ (@ tptp.nat_prod_decode_aux X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_nat_nat Xa2) (@ (@ tptp.minus_minus_nat X) Xa2)))) (=> (not _let_3) (= Y (@ (@ tptp.nat_prod_decode_aux _let_2) (@ (@ tptp.minus_minus_nat Xa2) _let_2))))) (not _let_1))))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int _let_1)) (@ tptp.uminus_uminus_int (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.modulo_modulo_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M))) _let_1) (@ (@ tptp.adjust_mod _let_1) (@ tptp.product_snd_int_int (@ (@ tptp.unique5052692396658037445od_int M) N)))))))
% 6.68/6.99 (assert (= tptp.adjust_mod (lambda ((L tptp.int) (R5 tptp.int)) (@ (@ (@ tptp.if_int (= R5 tptp.zero_zero_int)) tptp.zero_zero_int) (@ (@ tptp.minus_minus_int L) R5)))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ tptp.quotient_of (@ tptp.of_int A)) (@ (@ tptp.product_Pair_int_int A) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) (@ tptp.numeral_numeral_int K))) (@ (@ tptp.divide_divide_rat tptp.one_one_rat) (@ tptp.numeral_numeral_rat K)))))
% 6.68/6.99 (assert (= tptp.bezw (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y3) (@ (@ tptp.modulo_modulo_nat X3) Y3)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= Y3 tptp.zero_zero_nat)) (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X3) Y3)))))))))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) tptp.zero_zero_int)) tptp.zero_zero_rat)))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) A)) tptp.zero_zero_rat)))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.uminus_uminus_int A)) B)) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ (@ tptp.product_Pair_int_int A) B))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.product_Pair_int_int A))) (= (@ tptp.frct (@ _let_1 (@ tptp.uminus_uminus_int B))) (@ tptp.uminus_uminus_rat (@ tptp.frct (@ _let_1 B)))))))
% 6.68/6.99 (assert (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.one_one_int)) tptp.one_one_rat))
% 6.68/6.99 (assert (forall ((P5 tptp.rat)) (= (@ tptp.quotient_of (@ tptp.sgn_sgn_rat P5)) (@ (@ tptp.product_Pair_int_int (@ tptp.sgn_sgn_int (@ tptp.product_fst_int_int (@ tptp.quotient_of P5)))) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) tptp.one_one_int)) (@ tptp.numeral_numeral_rat K))))
% 6.68/6.99 (assert (forall ((K tptp.num) (L2 tptp.num)) (= (@ tptp.frct (@ (@ tptp.product_Pair_int_int (@ tptp.numeral_numeral_int K)) (@ tptp.numeral_numeral_int L2))) (@ (@ tptp.divide_divide_rat (@ tptp.numeral_numeral_rat K)) (@ tptp.numeral_numeral_rat L2)))))
% 6.68/6.99 (assert (forall ((Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw Y) (@ (@ tptp.modulo_modulo_nat X) Y)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) Y) (= (@ (@ tptp.bezw X) Y) (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Y)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_2 (@ tptp.product_snd_int_int _let_1))) (let ((_let_3 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (and (=> _let_3 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_3) (= Y (@ (@ tptp.product_Pair_int_int _let_2) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_1)) (@ (@ tptp.times_times_int _let_2) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2))))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.product_prod_int_int)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.bezw_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (@ (@ tptp.bezw Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))) (let ((_let_3 (@ tptp.product_snd_int_int _let_2))) (let ((_let_4 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.bezw X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_4 (= Y (@ (@ tptp.product_Pair_int_int tptp.one_one_int) tptp.zero_zero_int))) (=> (not _let_4) (= Y (@ (@ tptp.product_Pair_int_int _let_3) (@ (@ tptp.minus_minus_int (@ tptp.product_fst_int_int _let_2)) (@ (@ tptp.times_times_int _let_3) (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.divide_divide_nat X) Xa2)))))))) (not _let_1)))))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.product_fst_nat_nat (@ (@ tptp.divmod_nat M) N)) (@ (@ tptp.divide_divide_nat M) N))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ (@ tptp.divide_divide_nat (@ tptp.suc tptp.zero_zero_nat)) (@ tptp.numeral_numeral_nat K)) (@ tptp.product_fst_nat_nat (@ (@ tptp.unique5055182867167087721od_nat tptp.one) K)))))
% 6.68/6.99 (assert (= tptp.normalize (lambda ((P2 tptp.product_prod_int_int)) (let ((_let_1 (@ tptp.product_snd_int_int P2))) (let ((_let_2 (@ tptp.product_fst_int_int P2))) (let ((_let_3 (@ (@ tptp.gcd_gcd_int _let_2) _let_1))) (let ((_let_4 (@ tptp.uminus_uminus_int _let_3))) (let ((_let_5 (@ tptp.divide_divide_int _let_1))) (let ((_let_6 (@ tptp.divide_divide_int _let_2))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (@ (@ tptp.ord_less_int tptp.zero_zero_int) _let_1)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_3)) (@ _let_5 _let_3))) (@ (@ (@ tptp.if_Pro3027730157355071871nt_int (= _let_1 tptp.zero_zero_int)) (@ (@ tptp.product_Pair_int_int tptp.zero_zero_int) tptp.one_one_int)) (@ (@ tptp.product_Pair_int_int (@ _let_6 _let_4)) (@ _let_5 _let_4)))))))))))))
% 6.68/6.99 (assert (forall ((M tptp.int)) (= (@ (@ tptp.gcd_gcd_int M) tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((M tptp.int) (N tptp.int)) (= (@ (@ tptp.ord_less_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int M) N)) (or (not (= M tptp.zero_zero_int)) (not (= N tptp.zero_zero_int))))))
% 6.68/6.99 (assert (forall ((N tptp.num) (X tptp.int)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (= (@ (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int _let_1)) X) (@ (@ tptp.gcd_gcd_int _let_1) X)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.gcd_gcd_int X))) (= (@ _let_2 (@ tptp.uminus_uminus_int _let_1)) (@ _let_2 _let_1))))))
% 6.68/6.99 (assert (forall ((X tptp.int)) (= (@ (@ tptp.gcd_gcd_int tptp.zero_zero_int) X) (@ tptp.abs_abs_int X))))
% 6.68/6.99 (assert (forall ((X tptp.int)) (= (@ (@ tptp.gcd_gcd_int X) tptp.zero_zero_int) (@ tptp.abs_abs_int X))))
% 6.68/6.99 (assert (forall ((K tptp.int) (M tptp.int) (N tptp.int)) (let ((_let_1 (@ tptp.times_times_int K))) (= (@ (@ tptp.times_times_int (@ tptp.abs_abs_int K)) (@ (@ tptp.gcd_gcd_int M) N)) (@ (@ tptp.gcd_gcd_int (@ _let_1 M)) (@ _let_1 N))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (exists ((U3 tptp.int) (V2 tptp.int)) (= (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int U3) X)) (@ (@ tptp.times_times_int V2) Y)) (@ (@ tptp.gcd_gcd_int X) Y)))))
% 6.68/6.99 (assert (= tptp.gcd_gcd_int (lambda ((X3 tptp.int) (Y3 tptp.int)) (@ (@ tptp.gcd_gcd_int Y3) (@ (@ tptp.modulo_modulo_int X3) Y3)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ (@ tptp.gcd_gcd_int X) Y))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) A) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) A))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.gcd_gcd_int A) B)) B))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int) (P (-> tptp.int Bool))) (let ((_let_1 (@ tptp.gcd_gcd_int X))) (let ((_let_2 (@ P (@ _let_1 Y)))) (let ((_let_3 (@ tptp.uminus_uminus_int Y))) (let ((_let_4 (@ tptp.gcd_gcd_int (@ tptp.uminus_uminus_int X)))) (let ((_let_5 (@ (@ tptp.ord_less_eq_int Y) tptp.zero_zero_int))) (let ((_let_6 (@ (@ tptp.ord_less_eq_int X) tptp.zero_zero_int))) (let ((_let_7 (@ tptp.ord_less_eq_int tptp.zero_zero_int))) (let ((_let_8 (@ _let_7 Y))) (let ((_let_9 (@ _let_7 X))) (=> (=> _let_9 (=> _let_8 _let_2)) (=> (=> _let_9 (=> _let_5 (@ P (@ _let_1 _let_3)))) (=> (=> _let_6 (=> _let_8 (@ P (@ _let_4 Y)))) (=> (=> _let_6 (=> _let_5 (@ P (@ _let_4 _let_3)))) _let_2)))))))))))))))
% 6.68/6.99 (assert (forall ((D tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D))) (= (and (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) D) (@ _let_1 A) (@ _let_1 B) (forall ((E3 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int E3))) (=> (and (@ _let_1 A) (@ _let_1 B)) (@ _let_1 D))))) (= D (@ (@ tptp.gcd_gcd_int A) B))))))
% 6.68/6.99 (assert (forall ((Y tptp.int) (X tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) Y) (= (@ (@ tptp.gcd_gcd_int X) Y) (@ (@ tptp.gcd_gcd_int Y) (@ (@ tptp.modulo_modulo_int X) Y))))))
% 6.68/6.99 (assert (= tptp.gcd_gcd_int (lambda ((K2 tptp.int) (L tptp.int)) (@ tptp.abs_abs_int (@ (@ (@ tptp.if_int (= L tptp.zero_zero_int)) K2) (@ (@ tptp.gcd_gcd_int L) (@ (@ tptp.modulo_modulo_int (@ tptp.abs_abs_int K2)) (@ tptp.abs_abs_int L))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (P (-> tptp.nat Bool)) (M tptp.nat)) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) K3) (@ P K3))) (=> (forall ((K3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat K3) N) (=> (forall ((I2 tptp.nat)) (=> (@ (@ tptp.ord_less_nat K3) I2) (@ P I2))) (@ P K3)))) (@ P M)))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (exists ((R2 (-> tptp.nat tptp.nat))) (and (@ (@ tptp.strict1292158309912662752at_nat R2) (@ tptp.set_ord_lessThan_nat (@ tptp.finite_card_nat S2))) (forall ((N7 tptp.nat)) (=> (@ (@ tptp.ord_less_nat N7) (@ tptp.finite_card_nat S2)) (@ (@ tptp.member_nat (@ R2 N7)) S2))))))))
% 6.68/6.99 (assert (= tptp.code_divmod_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (let ((_let_1 (@ (@ tptp.code_divmod_abs K2) L))) (let ((_let_2 (@ tptp.produc1086072967326762835nteger tptp.zero_z3403309356797280102nteger))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= K2 tptp.zero_z3403309356797280102nteger)) (@ _let_2 tptp.zero_z3403309356797280102nteger)) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= L tptp.zero_z3403309356797280102nteger)) (@ _let_2 K2)) (@ (@ (@ (@ tptp.comp_C1593894019821074884nteger (@ (@ tptp.comp_C8797469213163452608nteger tptp.produc6499014454317279255nteger) tptp.times_3573771949741848930nteger)) tptp.sgn_sgn_Code_integer) L) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= (@ tptp.sgn_sgn_Code_integer K2) (@ tptp.sgn_sgn_Code_integer L))) _let_1) (@ (@ tptp.produc6916734918728496179nteger (lambda ((R5 tptp.code_integer) (S7 tptp.code_integer)) (let ((_let_1 (@ tptp.uminus1351360451143612070nteger R5))) (@ (@ (@ tptp.if_Pro6119634080678213985nteger (= S7 tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger _let_1) tptp.zero_z3403309356797280102nteger)) (@ (@ tptp.produc1086072967326762835nteger (@ (@ tptp.minus_8373710615458151222nteger _let_1) tptp.one_one_Code_integer)) (@ (@ tptp.minus_8373710615458151222nteger (@ tptp.abs_abs_Code_integer L)) S7)))))) _let_1))))))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= (@ (@ tptp.gcd_gcd_nat A) B) tptp.zero_zero_nat) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) A) A)))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (= tptp.zero_zero_nat (@ (@ tptp.gcd_gcd_nat A) B)) (and (= A tptp.zero_zero_nat) (= B tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((A tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat A) tptp.zero_zero_nat) A)))
% 6.68/6.99 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat X) tptp.zero_zero_nat) X)))
% 6.68/6.99 (assert (forall ((X tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat tptp.zero_zero_nat) X) X)))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (= (@ (@ tptp.gcd_gcd_nat M) tptp.one_one_nat) tptp.one_one_nat)))
% 6.68/6.99 (assert (forall ((M tptp.nat)) (let ((_let_1 (@ tptp.suc tptp.zero_zero_nat))) (= (@ (@ tptp.gcd_gcd_nat M) _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) (@ (@ tptp.gcd_gcd_nat M) N)) (or (not (= M tptp.zero_zero_nat)) (not (= N tptp.zero_zero_nat))))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat K))) (= (@ _let_1 (@ (@ tptp.gcd_gcd_nat M) N)) (@ (@ tptp.gcd_gcd_nat (@ _let_1 M)) (@ _let_1 N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) M) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat M) N)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ (@ tptp.gcd_gcd_nat (@ (@ tptp.minus_minus_nat N) M)) N) (@ (@ tptp.gcd_gcd_nat M) N)))))
% 6.68/6.99 (assert (= tptp.gcd_gcd_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.gcd_gcd_nat Y3) (@ (@ tptp.modulo_modulo_nat X3) Y3)))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa2) Y) (and (=> _let_1 (= Y X)) (=> (not _let_1) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2)))))))))
% 6.68/6.99 (assert (= tptp.gcd_gcd_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ (@ tptp.if_nat (= Y3 tptp.zero_zero_nat)) X3) (@ (@ tptp.gcd_gcd_nat Y3) (@ (@ tptp.modulo_modulo_nat X3) Y3))))))
% 6.68/6.99 (assert (forall ((Y tptp.nat) (X tptp.nat)) (=> (not (= Y tptp.zero_zero_nat)) (= (@ (@ tptp.gcd_gcd_nat X) Y) (@ (@ tptp.gcd_gcd_nat Y) (@ (@ tptp.modulo_modulo_nat X) Y))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) A))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (A tptp.nat)) (=> (not (= B tptp.zero_zero_nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.gcd_gcd_nat A) B)) B))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (=> (not (= A tptp.zero_zero_nat)) (exists ((X6 tptp.nat) (Y5 tptp.nat)) (= (@ (@ tptp.times_times_nat A) X6) (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat B) Y5)) (@ (@ tptp.gcd_gcd_nat A) B)))))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (A tptp.nat)) (exists ((X6 tptp.nat) (Y5 tptp.nat)) (let ((_let_1 (@ (@ tptp.gcd_gcd_nat A) B))) (let ((_let_2 (@ tptp.times_times_nat A))) (let ((_let_3 (@ _let_2 Y5))) (let ((_let_4 (@ tptp.times_times_nat B))) (let ((_let_5 (@ _let_4 X6))) (let ((_let_6 (@ _let_4 Y5))) (let ((_let_7 (@ _let_2 X6))) (or (and (@ (@ tptp.ord_less_eq_nat _let_6) _let_7) (= (@ (@ tptp.minus_minus_nat _let_7) _let_6) _let_1)) (and (@ (@ tptp.ord_less_eq_nat _let_3) _let_5) (= (@ (@ tptp.minus_minus_nat _let_5) _let_3) _let_1)))))))))))))
% 6.68/6.99 (assert (= tptp.gcd_gcd_Code_integer (lambda ((K2 tptp.code_integer) (L tptp.code_integer)) (@ tptp.abs_abs_Code_integer (@ (@ (@ tptp.if_Code_integer (= L tptp.zero_z3403309356797280102nteger)) K2) (@ (@ tptp.gcd_gcd_Code_integer L) (@ (@ tptp.modulo364778990260209775nteger (@ tptp.abs_abs_Code_integer K2)) (@ tptp.abs_abs_Code_integer L))))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.bezw X) Y))) (= (@ tptp.semiri1314217659103216013at_int (@ (@ tptp.gcd_gcd_nat X) Y)) (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int (@ tptp.product_fst_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int X))) (@ (@ tptp.times_times_int (@ tptp.product_snd_int_int _let_1)) (@ tptp.semiri1314217659103216013at_int Y)))))))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Xa2 tptp.nat) (Y tptp.nat)) (let ((_let_1 (@ (@ tptp.accp_P4275260045618599050at_nat tptp.gcd_nat_rel) (@ (@ tptp.product_Pair_nat_nat X) Xa2)))) (let ((_let_2 (= Xa2 tptp.zero_zero_nat))) (=> (= (@ (@ tptp.gcd_gcd_nat X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y X)) (=> (not _let_2) (= Y (@ (@ tptp.gcd_gcd_nat Xa2) (@ (@ tptp.modulo_modulo_nat X) Xa2))))) (not _let_1)))))))))
% 6.68/6.99 (assert (= tptp.code_negative (@ (@ tptp.comp_C3531382070062128313er_num tptp.uminus1351360451143612070nteger) tptp.numera6620942414471956472nteger)))
% 6.68/6.99 (assert (= tptp.code_Target_negative (@ (@ tptp.comp_int_int_num tptp.uminus_uminus_int) tptp.numeral_numeral_int)))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or5832277885323065728an_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) (@ (@ tptp.plus_plus_int L2) tptp.one_one_int))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or4662586982721622107an_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or5832277885323065728an_int L2) U))))
% 6.68/6.99 (assert (forall ((N tptp.num) (K tptp.int)) (= (@ (@ tptp.bit_se6526347334894502574or_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) K) (@ tptp.bit_ri7919022796975470100ot_int (@ (@ tptp.bit_se6526347334894502574or_int (@ (@ tptp.neg_numeral_sub_int N) tptp.one)) K)))))
% 6.68/6.99 (assert (forall ((K tptp.int) (N tptp.num)) (let ((_let_1 (@ tptp.bit_se6526347334894502574or_int K))) (= (@ _let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ tptp.bit_ri7919022796975470100ot_int (@ _let_1 (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or5834768355832116004an_nat L2) U)) (@ (@ tptp.minus_minus_nat U) (@ tptp.suc L2)))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or4665077453230672383an_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or5834768355832116004an_nat L2) U))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.member_real (@ tptp.tanh_real X)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.neg_numeral_sub_int (@ tptp.bitM N)) tptp.one) (@ (@ tptp.times_times_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) (@ (@ tptp.neg_numeral_sub_int N) tptp.one)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.compow_nat_nat N) tptp.suc) (@ tptp.plus_plus_nat N))))
% 6.68/6.99 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.ord_max_nat) tptp.zero_zero_nat) (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_eq_nat Y3) X3))) (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.ord_less_nat Y3) X3))))
% 6.68/6.99 (assert (@ (@ (@ (@ tptp.semila1623282765462674594er_nat tptp.gcd_gcd_nat) tptp.zero_zero_nat) tptp.dvd_dvd_nat) (lambda ((M3 tptp.nat) (N2 tptp.nat)) (and (@ (@ tptp.dvd_dvd_nat M3) N2) (not (= M3 N2))))))
% 6.68/6.99 (assert (= (@ tptp.complete_Sup_Sup_nat tptp.bot_bot_set_nat) tptp.zero_zero_nat))
% 6.68/6.99 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.gcd_Gcd_nat (@ (@ tptp.minus_minus_set_nat M5) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat)))))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y3))) (let ((_let_2 (@ tptp.times_times_nat X3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))) Xa2) X)))))
% 6.68/6.99 (assert (forall ((Z tptp.int)) (not (forall ((X6 tptp.nat) (Y5 tptp.nat)) (not (= Z (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat X6) Y5))))))))
% 6.68/6.99 (assert (forall ((N4 tptp.set_nat)) (=> (@ (@ tptp.member_nat tptp.one_one_nat) N4) (= (@ tptp.gcd_Gcd_nat N4) tptp.one_one_nat))))
% 6.68/6.99 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.nat2 (@ tptp.abs_Integ X)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) X))))
% 6.68/6.99 (assert (= tptp.zero_zero_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.zero_zero_nat) tptp.zero_zero_nat))))
% 6.68/6.99 (assert (= tptp.semiri1314217659103216013at_int (lambda ((N2 tptp.nat)) (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat N2) tptp.zero_zero_nat)))))
% 6.68/6.99 (assert (forall ((X tptp.product_prod_nat_nat)) (= (@ tptp.uminus_uminus_int (@ tptp.abs_Integ X)) (@ tptp.abs_Integ (@ (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y3) X3))) X)))))
% 6.68/6.99 (assert (= tptp.one_one_int (@ tptp.abs_Integ (@ (@ tptp.product_Pair_nat_nat tptp.one_one_nat) tptp.zero_zero_nat))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat U2) Y3)))) __flatten_var_0))) Xa2) X))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat U2) Y3)))) __flatten_var_0))) Xa2) X))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) U2)) (@ (@ tptp.plus_plus_nat Y3) V4)))) __flatten_var_0))) Xa2) X)))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat Y3) U2)))) __flatten_var_0))) Xa2) X)))))
% 6.68/6.99 (assert (forall ((K5 tptp.set_int)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) (@ tptp.gcd_Gcd_int K5))))
% 6.68/6.99 (assert (= tptp.ord_less_eq_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y3 tptp.nat) (Z3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat Y3) V4)) (@ (@ tptp.plus_plus_nat U2) Z3)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 6.68/6.99 (assert (= tptp.ord_less_int (lambda ((X3 tptp.int) (Xa4 tptp.int)) (@ (@ (@ tptp.produc8739625826339149834_nat_o (lambda ((Y3 tptp.nat) (Z3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat Y3) V4)) (@ (@ tptp.plus_plus_nat U2) Z3)))) __flatten_var_0))) (@ tptp.rep_Integ X3)) (@ tptp.rep_Integ Xa4)))))
% 6.68/6.99 (assert (= tptp.nat2 (lambda ((X3 tptp.int)) (@ (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat) (@ tptp.rep_Integ X3)))))
% 6.68/6.99 (assert (= tptp.nat_prod_encode (@ tptp.produc6842872674320459806at_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle (@ (@ tptp.plus_plus_nat M3) N2))) M3)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (@ (@ tptp.ord_less_eq_nat A) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.68/6.99 (assert (forall ((B tptp.nat) (A tptp.nat)) (@ (@ tptp.ord_less_eq_nat B) (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat A) B)))))
% 6.68/6.99 (assert (forall ((K tptp.nat) (M tptp.nat)) (= (@ tptp.nat_prod_encode (@ (@ tptp.nat_prod_decode_aux K) M)) (@ (@ tptp.plus_plus_nat (@ tptp.nat_triangle K)) M))))
% 6.68/6.99 (assert (= tptp.uminus_uminus_int (@ (@ (@ tptp.map_fu3667384564859982768at_int tptp.rep_Integ) tptp.abs_Integ) (@ tptp.produc2626176000494625587at_nat (lambda ((X3 tptp.nat) (Y3 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat Y3) X3))))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (let ((_let_1 (@ tptp.times_times_nat Y3))) (let ((_let_2 (@ tptp.times_times_nat X3))) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat (@ _let_2 U2)) (@ _let_1 V4))) (@ (@ tptp.plus_plus_nat (@ _let_2 V4)) (@ _let_1 U2))))))) __flatten_var_0))))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat Y3) U2)))) __flatten_var_0))))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc2626176000494625587at_nat (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.product_Pair_nat_nat (@ (@ tptp.plus_plus_nat X3) U2)) (@ (@ tptp.plus_plus_nat Y3) V4)))) __flatten_var_0))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.num_of_nat (@ tptp.suc N)))) (let ((_let_2 (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N))) (and (=> _let_2 (= _let_1 (@ tptp.inc (@ tptp.num_of_nat N)))) (=> (not _let_2) (= _let_1 tptp.one)))))))
% 6.68/6.99 (assert (forall ((Q2 tptp.num)) (= (@ tptp.num_of_nat (@ tptp.numeral_numeral_nat Q2)) Q2)))
% 6.68/6.99 (assert (= (@ tptp.num_of_nat tptp.zero_zero_nat) tptp.one))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.numeral_numeral_nat (@ tptp.num_of_nat N)) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N) tptp.one_one_nat) (= (@ tptp.num_of_nat N) tptp.one))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat N) N)) (@ tptp.bit0 (@ tptp.num_of_nat N))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ tptp.ord_less_nat tptp.zero_zero_nat))) (=> (@ _let_1 M) (=> (@ _let_1 N) (= (@ tptp.num_of_nat (@ (@ tptp.plus_plus_nat M) N)) (@ (@ tptp.plus_plus_num (@ tptp.num_of_nat M)) (@ tptp.num_of_nat N))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) (@ tptp.suc I))) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or5834768355832116004an_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_nat N) (@ (@ tptp.minus_minus_nat J) I)) (= (@ (@ tptp.nth_nat (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or6659071591806873216st_nat I) J))) N) (@ tptp.suc (@ (@ tptp.plus_plus_nat I) N))))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit1 Y)) (@ (@ tptp.times_times_num (@ tptp.sqr (@ _let_1 Y))) X)))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (@ tptp.finite_finite_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ tptp.finite_card_nat (@ (@ tptp.set_or6659071591806873216st_nat L2) U)) (@ (@ tptp.minus_minus_nat U) L2))))
% 6.68/6.99 (assert (forall ((L2 tptp.nat) (U tptp.nat)) (= (@ (@ tptp.set_or1269000886237332187st_nat (@ tptp.suc L2)) U) (@ (@ tptp.set_or6659071591806873216st_nat L2) U))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit0 N)) (@ tptp.bit0 (@ tptp.bit0 (@ tptp.sqr N))))))
% 6.68/6.99 (assert (= (@ tptp.sqr tptp.one) tptp.one))
% 6.68/6.99 (assert (= tptp.sqr (lambda ((X3 tptp.num)) (@ (@ tptp.times_times_num X3) X3))))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (let ((_let_1 (@ tptp.pow X))) (= (@ _let_1 (@ tptp.bit0 Y)) (@ tptp.sqr (@ _let_1 Y))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ tptp.sqr (@ tptp.bit1 N)) (@ tptp.bit1 (@ tptp.bit0 (@ (@ tptp.plus_plus_num (@ tptp.sqr N)) N))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (let ((_let_1 (@ (@ tptp.divide_divide_int A) B))) (let ((_let_2 (@ (@ tptp.fract A) B))) (and (@ (@ tptp.ord_less_eq_rat (@ tptp.ring_1_of_int_rat _let_1)) _let_2) (@ (@ tptp.ord_less_rat _let_2) (@ tptp.ring_1_of_int_rat (@ (@ tptp.plus_plus_int _let_1) tptp.one_one_int))))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (@ tptp.finite_finite_int (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.times_times_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) C)) (@ (@ tptp.times_times_int B) D)))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int) (C tptp.int) (D tptp.int)) (= (@ (@ tptp.divide_divide_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int B) C)))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ tptp.finite_card_int (@ (@ tptp.set_or6656581121297822940st_int L2) U)) (@ tptp.nat2 (@ (@ tptp.minus_minus_int U) L2)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.68/6.99 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.plus_plus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.68/6.99 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (let ((_let_1 (@ (@ tptp.times_times_int B) D))) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.ord_less_eq_int (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int A) D)) _let_1)) (@ (@ tptp.times_times_int (@ (@ tptp.times_times_int C) B)) _let_1))))))))
% 6.68/6.99 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (@ (@ tptp.minus_minus_rat (@ (@ tptp.fract A) B)) (@ (@ tptp.fract C) D)) (@ (@ tptp.fract (@ (@ tptp.minus_minus_int (@ (@ tptp.times_times_int A) D)) (@ (@ tptp.times_times_int C) B))) (@ (@ tptp.times_times_int B) D)))))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.sgn_sgn_rat (@ (@ tptp.fract A) B)) (@ tptp.ring_1_of_int_rat (@ (@ tptp.times_times_int (@ tptp.sgn_sgn_int A)) (@ tptp.sgn_sgn_int B))))))
% 6.68/6.99 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.one_one_int) (@ tptp.ring_1_of_int_rat K))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int) (P5 tptp.int) (Q2 tptp.int)) (let ((_let_1 (@ (@ tptp.fract A) B))) (=> (= (@ tptp.quotient_of _let_1) (@ (@ tptp.product_Pair_int_int P5) Q2)) (= (@ (@ tptp.fract P5) Q2) _let_1)))))
% 6.68/6.99 (assert (= tptp.one_one_rat (@ (@ tptp.fract tptp.one_one_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract tptp.zero_zero_int) K) tptp.zero_zero_rat)))
% 6.68/6.99 (assert (forall ((K tptp.int)) (= (@ (@ tptp.fract K) tptp.zero_zero_int) tptp.zero_zero_rat)))
% 6.68/6.99 (assert (forall ((C tptp.int) (A tptp.int) (B tptp.int)) (let ((_let_1 (@ tptp.times_times_int C))) (=> (not (= C tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ _let_1 A)) (@ _let_1 B)) (@ (@ tptp.fract A) B))))))
% 6.68/6.99 (assert (forall ((B tptp.int) (D tptp.int) (A tptp.int) (C tptp.int)) (=> (not (= B tptp.zero_zero_int)) (=> (not (= D tptp.zero_zero_int)) (= (= (@ (@ tptp.fract A) B) (@ (@ tptp.fract C) D)) (= (@ (@ tptp.times_times_int A) D) (@ (@ tptp.times_times_int C) B)))))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (= (@ (@ tptp.fract (@ tptp.semiri1314217659103216013at_int K)) tptp.one_one_int) (@ tptp.semiri681578069525770553at_rat K))))
% 6.68/6.99 (assert (forall ((A tptp.int)) (= (@ (@ tptp.fract A) tptp.zero_zero_int) (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((A tptp.int) (C tptp.int)) (let ((_let_1 (@ tptp.fract tptp.zero_zero_int))) (= (@ _let_1 A) (@ _let_1 C)))))
% 6.68/6.99 (assert (forall ((P (-> tptp.rat Bool)) (Q2 tptp.rat)) (=> (forall ((A5 tptp.int) (B5 tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B5) (@ P (@ (@ tptp.fract A5) B5)))) (@ P Q2))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int) (P5 tptp.int) (Q2 tptp.int)) (=> (= (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)) (@ (@ tptp.product_Pair_int_int P5) Q2)) (= (@ (@ tptp.fract P5) Q2) (@ (@ tptp.fract A) B)))))
% 6.68/6.99 (assert (= tptp.zero_zero_rat (@ (@ tptp.fract tptp.zero_zero_int) tptp.one_one_int)))
% 6.68/6.99 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.numeral_numeral_int W)) tptp.one_one_int) (@ tptp.numeral_numeral_rat W))))
% 6.68/6.99 (assert (= tptp.numeral_numeral_rat (lambda ((K2 tptp.num)) (@ (@ tptp.fract (@ tptp.numeral_numeral_int K2)) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.set_or1266510415728281911st_int (@ (@ tptp.plus_plus_int L2) tptp.one_one_int)) U) (@ (@ tptp.set_or6656581121297822940st_int L2) U))))
% 6.68/6.99 (assert (forall ((A tptp.int) (B tptp.int)) (= (@ tptp.quotient_of (@ (@ tptp.fract A) B)) (@ tptp.normalize (@ (@ tptp.product_Pair_int_int A) B)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (let ((_let_1 (@ tptp.ord_less_int tptp.zero_zero_int))) (=> (@ _let_1 B) (= (@ (@ tptp.ord_less_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ _let_1 A))))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_int A) tptp.zero_zero_int)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_int B) A)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_int A) B)))))
% 6.68/6.99 (assert (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int tptp.one_one_int)) tptp.one_one_int) (@ tptp.uminus_uminus_rat tptp.one_one_rat)))
% 6.68/6.99 (assert (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.fract (@ (@ tptp.plus_plus_int M) N)) N) (@ (@ tptp.plus_plus_rat (@ (@ tptp.fract M) N)) tptp.one_one_rat)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.zero_zero_rat) (@ (@ tptp.ord_less_eq_int A) tptp.zero_zero_int)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.zero_zero_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) A)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat (@ (@ tptp.fract A) B)) tptp.one_one_rat) (@ (@ tptp.ord_less_eq_int A) B)))))
% 6.68/6.99 (assert (forall ((B tptp.int) (A tptp.int)) (=> (@ (@ tptp.ord_less_int tptp.zero_zero_int) B) (= (@ (@ tptp.ord_less_eq_rat tptp.one_one_rat) (@ (@ tptp.fract A) B)) (@ (@ tptp.ord_less_eq_int B) A)))))
% 6.68/6.99 (assert (forall ((W tptp.num)) (= (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int W))) tptp.one_one_int) (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat W)))))
% 6.68/6.99 (assert (forall ((K tptp.num)) (= (@ tptp.uminus_uminus_rat (@ tptp.numeral_numeral_rat K)) (@ (@ tptp.fract (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int K))) tptp.one_one_int))))
% 6.68/6.99 (assert (forall ((C tptp.nat) (Y tptp.nat) (X tptp.nat)) (let ((_let_1 (@ (@ tptp.set_or4665077453230672383an_nat X) Y))) (let ((_let_2 (@ (@ tptp.ord_less_nat X) Y))) (let ((_let_3 (@ (@ tptp.ord_less_nat C) Y))) (and (=> _let_3 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.set_or4665077453230672383an_nat (@ (@ tptp.minus_minus_nat X) C)) (@ (@ tptp.minus_minus_nat Y) C)))) (=> (not _let_3) (and (=> _let_2 (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) (@ (@ tptp.insert_nat tptp.zero_zero_nat) tptp.bot_bot_set_nat))) (=> (not _let_2) (= (@ (@ tptp.image_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.minus_minus_nat I5) C))) _let_1) tptp.bot_bot_set_nat))))))))))
% 6.68/6.99 (assert (= tptp.semiri1316708129612266289at_nat tptp.id_nat))
% 6.68/6.99 (assert (forall ((M5 tptp.set_nat) (N4 tptp.set_nat)) (= (@ (@ (@ tptp.bij_betw_nat_nat tptp.suc) M5) N4) (= (@ (@ tptp.image_nat_nat tptp.suc) M5) N4))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat U2) Y3)))) __flatten_var_0))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_nat)) (not (@ (@ tptp.member_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) A2)))))
% 6.68/6.99 (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 ((X3 tptp.nat) (Y3 tptp.nat) (__flatten_var_0 tptp.product_prod_nat_nat)) (@ (@ tptp.produc6081775807080527818_nat_o (lambda ((U2 tptp.nat) (V4 tptp.nat)) (@ (@ tptp.ord_less_nat (@ (@ tptp.plus_plus_nat X3) V4)) (@ (@ tptp.plus_plus_nat U2) Y3)))) __flatten_var_0))))))
% 6.68/6.99 (assert (= tptp.nat2 (@ (@ (@ tptp.map_fu2345160673673942751at_nat tptp.rep_Integ) tptp.id_nat) (@ tptp.produc6842872674320459806at_nat tptp.minus_minus_nat))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N)) (@ (@ tptp.set_or1269000886237332187st_nat tptp.one_one_nat) (@ tptp.suc N)))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or1269000886237332187st_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (let ((_let_1 (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat))) (= (@ _let_1 (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ _let_1 N)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_lessThan_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_lessThan_nat N))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ tptp.set_ord_atMost_nat (@ tptp.suc N)) (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) (@ tptp.set_ord_atMost_nat N))))))
% 6.68/6.99 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_lessThan_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.68/6.99 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atMost_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.68/6.99 (assert (= tptp.comple4887499456419720421f_real (lambda ((X2 tptp.set_real)) (@ tptp.uminus_uminus_real (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_real_real tptp.uminus_uminus_real) X2))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or1269000886237332187st_nat A) B)) (@ (@ tptp.set_or1266510415728281911st_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.68/6.99 (assert (forall ((A tptp.nat) (B tptp.nat)) (= (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ (@ tptp.set_or4665077453230672383an_nat A) B)) (@ (@ tptp.set_or4662586982721622107an_int (@ tptp.semiri1314217659103216013at_int A)) (@ tptp.semiri1314217659103216013at_int B)))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (@ tptp.summable_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ X8 I4))) (= (@ tptp.suminf_real X8) (@ tptp.comple1385675409528146559p_real (@ (@ tptp.image_nat_real (lambda ((I5 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real X8) (@ tptp.set_ord_lessThan_nat I5)))) tptp.top_top_set_nat)))))))
% 6.68/6.99 (assert (forall ((L2 tptp.int) (U tptp.int)) (= (@ (@ tptp.image_int_int (lambda ((X3 tptp.int)) (@ (@ tptp.plus_plus_int X3) L2))) (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) (@ (@ tptp.minus_minus_int U) L2))) (@ (@ tptp.set_or4662586982721622107an_int L2) U))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.image_nat_nat (lambda ((M3 tptp.nat)) (@ (@ tptp.modulo_modulo_nat M3) N))) tptp.top_top_set_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) N)))))
% 6.68/6.99 (assert (forall ((U tptp.int)) (=> (@ (@ tptp.ord_less_eq_int tptp.zero_zero_int) U) (= (@ (@ tptp.set_or4662586982721622107an_int tptp.zero_zero_int) U) (@ (@ tptp.image_nat_int tptp.semiri1314217659103216013at_int) (@ tptp.set_ord_lessThan_nat (@ tptp.nat2 U)))))))
% 6.68/6.99 (assert (= tptp.top_top_set_nat (@ (@ tptp.insert_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat))))
% 6.68/6.99 (assert (= (@ tptp.finite410649719033368117t_unit tptp.top_to1996260823553986621t_unit) tptp.one_one_nat))
% 6.68/6.99 (assert (= (@ tptp.finite_card_o tptp.top_top_set_o) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (let ((_let_1 (@ (@ tptp.image_real_real (@ tptp.times_times_real A)) tptp.top_top_set_real))) (let ((_let_2 (= A tptp.zero_zero_real))) (and (=> _let_2 (= _let_1 (@ (@ tptp.insert_real tptp.zero_zero_real) tptp.bot_bot_set_real))) (=> (not _let_2) (= _let_1 tptp.top_top_set_real)))))))
% 6.68/6.99 (assert (= tptp.root (lambda ((N2 tptp.nat) (X3 tptp.real)) (@ (@ (@ tptp.if_real (= N2 tptp.zero_zero_nat)) tptp.zero_zero_real) (@ (@ (@ tptp.the_in5290026491893676941l_real tptp.top_top_set_real) (lambda ((Y3 tptp.real)) (@ (@ tptp.times_times_real (@ tptp.sgn_sgn_real Y3)) (@ (@ tptp.power_power_real (@ tptp.abs_abs_real Y3)) N2)))) X3)))))
% 6.68/6.99 (assert (= (@ tptp.finite_card_char tptp.top_top_set_char) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))
% 6.68/6.99 (assert (= tptp.top_top_set_char (@ (@ tptp.image_nat_char tptp.unique3096191561947761185of_nat) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one)))))))))))))
% 6.68/6.99 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((C tptp.char)) (@ (@ tptp.ord_less_nat (@ tptp.comm_s629917340098488124ar_nat C)) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.68/6.99 (assert (= (@ (@ tptp.image_char_nat tptp.comm_s629917340098488124ar_nat) tptp.top_top_set_char) (@ (@ tptp.set_or4665077453230672383an_nat tptp.zero_zero_nat) (@ tptp.numeral_numeral_nat (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 (@ tptp.bit0 tptp.one))))))))))))
% 6.68/6.99 (assert (forall ((B0 Bool) (B1 Bool) (B22 Bool) (B32 Bool) (B42 Bool) (B52 Bool) (B62 Bool) (B72 Bool)) (let ((_let_1 (@ tptp.numera6620942414471956472nteger (@ tptp.bit0 tptp.one)))) (= (@ tptp.integer_of_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 B0) B1) B22) B32) B42) B52) B62) B72)) (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ (@ tptp.plus_p5714425477246183910nteger (@ (@ tptp.times_3573771949741848930nteger (@ tptp.zero_n356916108424825756nteger B72)) _let_1)) (@ tptp.zero_n356916108424825756nteger B62))) _let_1)) (@ tptp.zero_n356916108424825756nteger B52))) _let_1)) (@ tptp.zero_n356916108424825756nteger B42))) _let_1)) (@ tptp.zero_n356916108424825756nteger B32))) _let_1)) (@ tptp.zero_n356916108424825756nteger B22))) _let_1)) (@ tptp.zero_n356916108424825756nteger B1))) _let_1)) (@ tptp.zero_n356916108424825756nteger B0))))))
% 6.68/6.99 (assert (forall ((X1 Bool) (X22 Bool) (X32 Bool) (X42 Bool) (X52 Bool) (X62 Bool) (X72 Bool) (X82 Bool)) (= (@ tptp.size_char (@ (@ (@ (@ (@ (@ (@ (@ tptp.char2 X1) X22) X32) X42) X52) X62) X72) X82)) tptp.zero_zero_nat)))
% 6.68/6.99 (assert (forall ((C tptp.char)) (= (@ tptp.comm_s629917340098488124ar_nat (@ tptp.ascii_of C)) (@ (@ tptp.bit_se2925701944663578781it_nat (@ tptp.numeral_numeral_nat (@ tptp.bit1 (@ tptp.bit1 tptp.one)))) (@ tptp.comm_s629917340098488124ar_nat C)))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat (@ tptp.suc K))) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_lessThan_nat K))) (@ (@ tptp.cons_nat K) tptp.nil_nat)))))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat _let_1)) (@ (@ tptp.append_nat (@ tptp.linord2614967742042102400et_nat (@ tptp.set_ord_atMost_nat K))) (@ (@ tptp.cons_nat _let_1) tptp.nil_nat))))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (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 ((X6 tptp.nat) (Xs3 tptp.list_nat)) (=> (= X (@ (@ tptp.cons_nat X6) Xs3)) (not (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X6) (@ tptp.nat_list_encode Xs3)))))))))))))
% 6.68/6.99 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (Js tptp.list_int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_int J3) I5)) Js) (@ (@ (@ tptp.upto_aux I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int)) (@ (@ tptp.cons_int J3) Js))))))
% 6.68/6.99 (assert (= tptp.sup_su3973961784419623482d_enat tptp.ord_ma741700101516333627d_enat))
% 6.68/6.99 (assert (= tptp.sup_sup_nat tptp.ord_max_nat))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (assert (= (@ tptp.nat_list_encode tptp.nil_nat) tptp.zero_zero_nat))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (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 ((X6 tptp.nat) (Xs3 tptp.list_nat)) (let ((_let_1 (@ (@ tptp.cons_nat X6) Xs3))) (=> (= X _let_1) (=> (= Y (@ tptp.suc (@ tptp.nat_prod_encode (@ (@ tptp.product_Pair_nat_nat X6) (@ tptp.nat_list_encode Xs3))))) (not (@ (@ tptp.accp_list_nat tptp.nat_list_encode_rel) _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.accp_P1096762738010456898nt_int tptp.upto_rel) (@ (@ tptp.product_Pair_int_int X) Xa2)))) (let ((_let_2 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (=> _let_1 (not (=> (and (=> _let_2 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_2) (= Y tptp.nil_int))) (not _let_1)))))))))
% 6.68/6.99 (assert (forall ((I tptp.int) (J tptp.int)) (= (= (@ (@ tptp.upto I) J) tptp.nil_int) (@ (@ tptp.ord_less_int J) I))))
% 6.68/6.99 (assert (forall ((I tptp.int) (J tptp.int)) (= (= tptp.nil_int (@ (@ tptp.upto I) J)) (@ (@ tptp.ord_less_int J) I))))
% 6.68/6.99 (assert (forall ((J tptp.int) (I tptp.int)) (=> (@ (@ tptp.ord_less_int J) I) (= (@ (@ tptp.upto I) J) tptp.nil_int))))
% 6.68/6.99 (assert (forall ((I tptp.int)) (= (@ (@ tptp.upto I) I) (@ (@ tptp.cons_int I) tptp.nil_int))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.numeral_numeral_int M))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_int N))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N)))) (let ((_let_2 (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int M)))) (let ((_let_3 (@ (@ tptp.upto _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_eq_int _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_int _let_2) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int _let_2) tptp.one_one_int)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_int)))))))))
% 6.68/6.99 (assert (= tptp.upto_aux (lambda ((I5 tptp.int) (J3 tptp.int) (__flatten_var_0 tptp.list_int)) (@ (@ tptp.append_int (@ (@ tptp.upto I5) J3)) __flatten_var_0))))
% 6.68/6.99 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.upto_aux I5) J3) tptp.nil_int))))
% 6.68/6.99 (assert (forall ((I tptp.int) (J tptp.int)) (@ tptp.distinct_int (@ (@ tptp.upto I) J))))
% 6.68/6.99 (assert (= tptp.set_or1266510415728281911st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) J3)))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (assert (= tptp.set_or4662586982721622107an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto I5) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.68/6.99 (assert (= tptp.set_or6656581121297822940st_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3)))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Xa2 tptp.int) (Y tptp.list_int)) (let ((_let_1 (@ (@ tptp.ord_less_eq_int X) Xa2))) (=> (= (@ (@ tptp.upto X) Xa2) Y) (and (=> _let_1 (= Y (@ (@ tptp.cons_int X) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int X) tptp.one_one_int)) Xa2)))) (=> (not _let_1) (= Y tptp.nil_int)))))))
% 6.68/6.99 (assert (= tptp.upto (lambda ((I5 tptp.int) (J3 tptp.int)) (@ (@ (@ tptp.if_list_int (@ (@ tptp.ord_less_eq_int I5) J3)) (@ (@ tptp.cons_int I5) (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) J3))) tptp.nil_int))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (assert (= tptp.set_or5832277885323065728an_int (lambda ((I5 tptp.int) (J3 tptp.int)) (@ tptp.set_int2 (@ (@ tptp.upto (@ (@ tptp.plus_plus_int I5) tptp.one_one_int)) (@ (@ tptp.minus_minus_int J3) tptp.one_one_int))))))
% 6.68/6.99 (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)))))))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.root N))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))))) (let ((_let_3 (= D4 _let_2))) (let ((_let_4 (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) _let_3)) (=> (=> _let_4 (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D4 (@ tptp.uminus_uminus_real _let_2)))) (=> (=> (not _let_4) _let_3) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (= (@ F X) (@ F Y5)))) (= L2 tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.minus_minus_real X) H4))) (@ F X)))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.minus_minus_real X) H4))))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) K))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (K tptp.real)) (=> (not (= A B)) (=> (forall ((X6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) K) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))) (= (@ (@ tptp.divide_divide_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ (@ tptp.minus_minus_real B) A)) K)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (Y tptp.real)) (=> (forall ((X6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))) (= (@ F X) (@ F Y)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F (@ (@ tptp.plus_plus_real X) H4))) (@ F X)))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F (@ (@ tptp.plus_plus_real X) H4))))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ tptp.inverse_inverse_real X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (X tptp.real) (Y tptp.real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.member_real X) _let_1) (=> (@ (@ tptp.member_real Y) _let_1) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)))) (= (@ F X) (@ F Y)))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S2)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.plus_plus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S2)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F _let_1)) (@ F X)))))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (S2 tptp.set_real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) S2)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((D3 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) D3) (forall ((H4 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real X) H4))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H4) (=> (@ (@ tptp.member_real _let_1) S2) (=> (@ (@ tptp.ord_less_real H4) D3) (@ (@ tptp.ord_less_real (@ F X)) (@ F _let_1)))))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X6) (=> (@ (@ tptp.ord_less_eq_real X6) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X6)) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))))) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z5) (@ (@ tptp.ord_less_real Z5) B) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) (@ F5 Z5)))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X6) (=> (@ (@ tptp.ord_less_eq_real X6) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_real (@ F B)) (@ F A))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X6) (=> (@ (@ tptp.ord_less_eq_real X6) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2)))))) (@ (@ tptp.ord_less_real (@ F A)) (@ F B))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X6)) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ G2 X6)))) (=> (@ (@ tptp.ord_less_eq_real A) B) (@ (@ tptp.ord_less_eq_real (@ G A)) (@ G B)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X6) (=> (@ (@ tptp.ord_less_eq_real X6) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real Y2) tptp.zero_zero_real)))))) (@ (@ tptp.ord_less_eq_real (@ F B)) (@ F A))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) X6) (=> (@ (@ tptp.ord_less_eq_real X6) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) Y2)))))) (@ (@ tptp.ord_less_eq_real (@ F A)) (@ F B))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (V (-> tptp.real tptp.real)) (K tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (=> (not (= A B)) (=> (forall ((X6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real V) K) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))) (= (@ V (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real A) B)) _let_1)) (@ (@ tptp.divide_divide_real (@ (@ tptp.plus_plus_real (@ V A)) (@ V B))) _let_1)))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (@ (@ tptp.ord_less_eq_real (@ F X)) (@ F Y5)))) (= L2 tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (X tptp.real) (D tptp.real)) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L2) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X) Y5))) D) (@ (@ tptp.ord_less_eq_real (@ F Y5)) (@ F X)))) (= L2 tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.ln_ln_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) X)) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real) (S tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real X3) N))) (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real X) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat))))) (@ (@ tptp.topolo2177554685111907308n_real X) S))))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ G X3)) N))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ G X)) (@ (@ tptp.minus_minus_nat N) tptp.one_one_nat)))) M)) _let_1)))))
% 6.68/6.99 (assert (forall ((Z tptp.real) (R tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) Z) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((Z3 tptp.real)) (@ (@ tptp.powr_real Z3) R))) (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real Z) (@ (@ tptp.minus_minus_real R) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real Z) tptp.top_top_set_real)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ tptp.log B)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.times_times_real (@ tptp.ln_ln_real B)) X))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.powr_real (@ G X3)) R))) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real R) (@ (@ tptp.powr_real _let_2) (@ (@ tptp.minus_minus_real R) (@ tptp.semiri5074537144036343181t_real tptp.one_one_nat))))) M)) _let_1)))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (M tptp.real) (X tptp.real) (F (-> tptp.real tptp.real)) (R tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ G X))) (let ((_let_3 (@ F X))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real G) M) _let_1) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) _let_2) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) R) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ tptp.powr_real (@ G X3)) (@ F X3)))) (@ (@ tptp.times_times_real (@ (@ tptp.powr_real _let_2) _let_3)) (@ (@ tptp.plus_plus_real (@ (@ tptp.times_times_real R) (@ tptp.ln_ln_real _let_2))) (@ (@ tptp.divide_divide_real (@ (@ tptp.times_times_real M) _let_3)) _let_2)))) _let_1)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) (@ (@ tptp.divide_divide_real (@ tptp.inverse_inverse_real (@ tptp.sqrt X))) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.nat tptp.real)) (F5 (-> tptp.real tptp.nat tptp.real)) (X0 tptp.real) (A tptp.real) (B tptp.real) (L5 (-> tptp.nat tptp.real))) (let ((_let_1 (@ F5 X0))) (=> (forall ((N3 tptp.nat)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ (@ F X3) N3))) (@ (@ F5 X0) N3)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real))) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (@ tptp.summable_real (@ F X6)))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real A) B)) (=> (@ tptp.summable_real _let_1) (=> (@ tptp.summable_real L5) (=> (forall ((N3 tptp.nat) (X6 tptp.real) (Y5 tptp.real)) (let ((_let_1 (@ (@ tptp.set_or1633881224788618240n_real A) B))) (=> (@ (@ tptp.member_real X6) _let_1) (=> (@ (@ tptp.member_real Y5) _let_1) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real (@ (@ F X6) N3)) (@ (@ F Y5) N3)))) (@ (@ tptp.times_times_real (@ L5 N3)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X6) Y5)))))))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ tptp.suminf_real (@ F X3)))) (@ tptp.suminf_real _let_1)) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arctan) (@ tptp.inverse_inverse_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arsinh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.plus_plus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2))))
% 6.68/6.99 (assert (forall ((X tptp.real) (D4 tptp.real)) (let ((_let_1 (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ tptp.inverse_inverse_real (@ tptp.sqrt X)))) (=> (not (= X tptp.zero_zero_real)) (=> (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (= D4 (@ (@ tptp.divide_divide_real _let_2) _let_1))) (=> (=> (@ (@ tptp.ord_less_real X) tptp.zero_zero_real) (= D4 (@ (@ tptp.divide_divide_real (@ tptp.uminus_uminus_real _let_2)) _let_1))) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.sqrt) D4) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcosh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.sqrt (@ (@ tptp.minus_minus_real (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_real)))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.artanh_real) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.topolo2177554685111907308n_real X) A2)))))
% 6.68/6.99 (assert (forall ((R4 tptp.real) (F (-> tptp.nat tptp.real)) (X0 tptp.real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R4)) R4)) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X6) N2)))))) (=> (@ (@ tptp.member_real X0) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real R4)) R4)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) R4) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((X3 tptp.real)) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ F N2)) (@ (@ tptp.power_power_real X3) (@ tptp.suc N2))))))) (@ tptp.suminf_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.times_times_real (@ F N2)) (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))) (@ (@ tptp.power_power_real X0) N2))))) (@ (@ tptp.topolo2177554685111907308n_real X0) tptp.top_top_set_real)))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) X) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arccos) (@ tptp.inverse_inverse_real (@ tptp.uminus_uminus_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.has_fi5821293074295781190e_real tptp.arcsin) (@ tptp.inverse_inverse_real (@ tptp.sqrt (@ (@ tptp.minus_minus_real tptp.one_one_real) (@ (@ tptp.power_power_real X) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))
% 6.68/6.99 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (and (= (@ Diff tptp.zero_zero_nat) F) (forall ((M4 tptp.nat) (X6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X6)) (@ (@ tptp.topolo2177554685111907308n_real X6) 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))
% 6.68/6.99 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (X tptp.real) (N tptp.nat)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (X6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X6)) (@ (@ tptp.topolo2177554685111907308n_real X6) 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (=> (not (= X tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real _let_1) (@ tptp.inverse_inverse_real (@ (@ tptp.times_times_real (@ tptp.semiri5074537144036343181t_real N)) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)))))))
% 6.68/6.99 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real H2) tptp.zero_zero_real) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real H2) T6) (@ (@ tptp.ord_less_eq_real T6) tptp.zero_zero_real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.68/6.99 (assert (forall ((H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N)))))))))))
% 6.68/6.99 (assert (forall ((H2 tptp.real) (N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) H2) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real H2) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real H2) N))))))))))))
% 6.68/6.99 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (not (= X tptp.zero_zero_real)) (=> (forall ((M4 tptp.nat) (X6 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) X6)) (@ (@ tptp.topolo2177554685111907308n_real X6) 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N)))))))))))))
% 6.68/6.99 (assert (forall ((Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (N tptp.nat) (X tptp.real)) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real T6)) (@ tptp.abs_abs_real X))) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) 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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real X) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real X) N))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_real A) C) (=> (@ (@ tptp.ord_less_eq_real C) B) (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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real A) C)) N)))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ (@ tptp.ord_less_eq_real A) C) (=> (@ (@ tptp.ord_less_real C) B) (exists ((T6 tptp.real)) (and (@ (@ tptp.ord_less_real C) T6) (@ (@ tptp.ord_less_real T6) B) (= (@ F B) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real B) C)) N)))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (Diff (-> tptp.nat tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (A tptp.real) (B tptp.real) (C tptp.real) (X tptp.real)) (let ((_let_1 (@ tptp.ord_less_eq_real A))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (= (@ Diff tptp.zero_zero_nat) F) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real A) T6) (@ (@ tptp.ord_less_eq_real T6) B)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (@ _let_1 C) (=> (@ (@ tptp.ord_less_eq_real C) B) (=> (@ _let_1 X) (=> (@ (@ tptp.ord_less_eq_real X) B) (=> (not (= X C)) (exists ((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 ((M3 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff M3) C)) (@ tptp.semiri2265585572941072030t_real M3))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) M3)))) (@ tptp.set_ord_lessThan_nat N))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff N) T6)) (@ tptp.semiri2265585572941072030t_real N))) (@ (@ tptp.power_power_real (@ (@ tptp.minus_minus_real X) C)) N))))))))))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (H2 tptp.real) (Diff (-> tptp.nat tptp.real tptp.real)) (K tptp.nat) (B3 tptp.real)) (=> (forall ((M4 tptp.nat) (T6 tptp.real)) (=> (and (@ (@ tptp.ord_less_nat M4) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T6) (@ (@ tptp.ord_less_eq_real T6) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (@ Diff M4)) (@ (@ Diff (@ tptp.suc M4)) T6)) (@ (@ tptp.topolo2177554685111907308n_real T6) tptp.top_top_set_real)))) (=> (= N (@ tptp.suc K)) (forall ((M2 tptp.nat) (T7 tptp.real)) (let ((_let_1 (@ tptp.suc M2))) (let ((_let_2 (@ (@ tptp.minus_minus_nat N) _let_1))) (=> (and (@ (@ tptp.ord_less_nat M2) N) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) T7) (@ (@ tptp.ord_less_eq_real T7) H2)) (@ (@ (@ tptp.has_fi5821293074295781190e_real (lambda ((U2 tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_nat N) M2))) (@ (@ tptp.minus_minus_real (@ (@ Diff M2) U2)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat M2) P2)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P2))) (@ (@ tptp.power_power_real U2) P2)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.times_times_real B3) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real U2) _let_1)) (@ tptp.semiri2265585572941072030t_real _let_1)))))))) (@ (@ tptp.minus_minus_real (@ (@ Diff _let_1) T7)) (@ (@ tptp.plus_plus_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((P2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real (@ (@ Diff (@ (@ tptp.plus_plus_nat (@ tptp.suc M2)) P2)) tptp.zero_zero_real)) (@ tptp.semiri2265585572941072030t_real P2))) (@ (@ tptp.power_power_real T7) P2)))) (@ tptp.set_ord_lessThan_nat _let_2))) (@ (@ tptp.times_times_real B3) (@ (@ 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))))))))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (X tptp.real)) (let ((_let_1 (@ tptp.root N))) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (=> (@ (@ tptp.ord_less_real 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 N))) (@ (@ tptp.power_power_real (@ _let_1 X)) (@ (@ tptp.minus_minus_nat N) (@ tptp.suc tptp.zero_zero_nat)))))) (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (= (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) (lambda ((Q5 tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat M))) (@ (@ tptp.bit_se2923211474154528505it_int _let_1) (@ (@ tptp.minus_minus_int (@ (@ tptp.power_power_int (@ tptp.numeral_numeral_int (@ tptp.bit0 tptp.one))) _let_1)) (@ tptp.numeral_numeral_int Q5)))))) (@ (@ tptp.bit_take_bit_num _let_1) N))))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_take_bit_num tptp.zero_zero_nat) M) tptp.none_num)))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.68/6.99 (assert (forall ((R tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) tptp.one) (@ tptp.some_num tptp.one))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N) M)))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.suc N)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N) M))))))
% 6.68/6.99 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M)))))
% 6.68/6.99 (assert (forall ((R tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num (@ tptp.numeral_numeral_nat R)) (@ tptp.bit1 M)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num (@ tptp.pred_numeral R)) M))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit0 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num N2) M)))) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (= (@ (@ tptp.bit_take_bit_num N) tptp.one) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num tptp.one))) N))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.num)) (= (@ (@ tptp.bit_take_bit_num N) (@ tptp.bit1 M)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((N2 tptp.nat)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num N2) M))))) N))))
% 6.68/6.99 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M3 tptp.num)) (let ((_let_1 (@ (@ tptp.bit_se2925701944663578781it_nat N2) (@ tptp.numeral_numeral_nat M3)))) (@ (@ (@ tptp.if_option_num (= _let_1 tptp.zero_zero_nat)) tptp.none_num) (@ tptp.some_num (@ tptp.num_of_nat _let_1)))))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit0 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bitM N))))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.68/6.99 (assert (forall ((N tptp.num) (M tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.uminus_uminus_int (@ tptp.numeral_numeral_int (@ tptp.bit1 N)))) (@ tptp.numeral_numeral_int M)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) (@ tptp.bit0 N))))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit1 N)) tptp.none_num)))
% 6.68/6.99 (assert (= (@ (@ tptp.bit_and_not_num tptp.one) tptp.one) tptp.none_num))
% 6.68/6.99 (assert (forall ((M tptp.num)) (let ((_let_1 (@ tptp.bit0 M))) (= (@ (@ tptp.bit_and_not_num _let_1) tptp.one) (@ tptp.some_num _let_1)))))
% 6.68/6.99 (assert (forall ((N tptp.num)) (= (@ (@ tptp.bit_and_not_num tptp.one) (@ tptp.bit0 N)) (@ tptp.some_num tptp.one))))
% 6.68/6.99 (assert (forall ((M tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) tptp.one) (@ tptp.some_num (@ tptp.bit0 M)))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num) (Q2 tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) (@ tptp.some_num Q2)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ tptp.numeral_numeral_int Q2)))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_and_not_num (@ tptp.bit1 M)) (@ tptp.bit0 N)) (@ (@ (@ tptp.case_o6005452278849405969um_num (@ tptp.some_num tptp.one)) (lambda ((N9 tptp.num)) (@ tptp.some_num (@ tptp.bit1 N9)))) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (= (@ (@ tptp.bit_and_not_num M) N) tptp.none_num) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) tptp.zero_zero_int))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int M))) (@ tptp.numeral_numeral_int N)) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num N) M)))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (= (@ (@ tptp.bit_se725231765392027082nd_int (@ tptp.numeral_numeral_int M)) (@ tptp.bit_ri7919022796975470100ot_int (@ tptp.numeral_numeral_int N))) (@ (@ (@ tptp.case_option_int_num tptp.zero_zero_int) tptp.numeral_numeral_int) (@ (@ tptp.bit_and_not_num M) N)))))
% 6.68/6.99 (assert (= tptp.bit_take_bit_num (lambda ((N2 tptp.nat) (M3 tptp.num)) (@ (@ tptp.produc478579273971653890on_num (lambda ((A3 tptp.nat) (X3 tptp.num)) (@ (@ (@ tptp.case_nat_option_num tptp.none_num) (lambda ((O tptp.nat)) (@ (@ (@ (@ tptp.case_num_option_num (@ tptp.some_num tptp.one)) (lambda ((P2 tptp.num)) (@ (@ (@ tptp.case_o6005452278849405969um_num tptp.none_num) (lambda ((Q5 tptp.num)) (@ tptp.some_num (@ tptp.bit0 Q5)))) (@ (@ tptp.bit_take_bit_num O) P2)))) (lambda ((P2 tptp.num)) (@ tptp.some_num (@ (@ (@ tptp.case_option_num_num tptp.one) tptp.bit1) (@ (@ tptp.bit_take_bit_num O) P2))))) X3))) A3))) (@ (@ tptp.product_Pair_nat_num N2) M3)))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (forall ((X6 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X6) (@ (@ tptp.ord_less_eq_real X6) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) F))) (exists ((L6 tptp.real) (M9 tptp.real)) (and (forall ((X4 tptp.real)) (let ((_let_1 (@ F X4))) (=> (and (@ (@ tptp.ord_less_eq_real A) X4) (@ (@ tptp.ord_less_eq_real X4) B)) (and (@ (@ tptp.ord_less_eq_real L6) _let_1) (@ (@ tptp.ord_less_eq_real _let_1) M9))))) (forall ((Y2 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real L6) Y2) (@ (@ tptp.ord_less_eq_real Y2) M9)) (exists ((X6 tptp.real)) (and (@ (@ tptp.ord_less_eq_real A) X6) (@ (@ tptp.ord_less_eq_real X6) B) (= (@ F X6) Y2)))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.sqrt)))
% 6.68/6.99 (assert (forall ((X tptp.real) (N tptp.nat)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) (@ tptp.root N))))
% 6.68/6.99 (assert (forall ((A tptp.real) (X tptp.real) (B tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z5) (=> (@ (@ tptp.ord_less_eq_real Z5) B) (= (@ G (@ F Z5)) Z5)))) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z5) (=> (@ (@ tptp.ord_less_eq_real Z5) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real)) F)))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (not (= X tptp.zero_zero_real)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.ln_ln_real))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcosh_real))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (D4 tptp.real) (G (-> tptp.real tptp.real)) (X tptp.real) (A tptp.real) (B tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (=> (@ (@ (@ tptp.has_fi5821293074295781190e_real F) D4) (@ (@ tptp.topolo2177554685111907308n_real (@ G X)) tptp.top_top_set_real)) (=> (not (= D4 tptp.zero_zero_real)) (=> (@ (@ tptp.ord_less_real A) X) (=> (@ (@ tptp.ord_less_real X) B) (=> (forall ((Y5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Y5) (=> (@ (@ tptp.ord_less_real Y5) B) (= (@ F (@ G Y5)) Y5)))) (=> (@ (@ tptp.topolo4422821103128117721l_real _let_1) G) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ tptp.inverse_inverse_real D4)) _let_1))))))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arccos)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.arcsin)))))
% 6.68/6.99 (assert (forall ((B tptp.real) (X tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real B) X) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) (@ (@ tptp.set_or1633881224788618240n_real B) X)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X6)))) (=> (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) F) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ F X)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.uminus_uminus_real tptp.one_one_real)) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real)) tptp.artanh_real)))))
% 6.68/6.99 (assert (forall ((D tptp.real) (X tptp.real) (G (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) D) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z5) X))) D) (= (@ G (@ F Z5)) Z5))) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real Z5) X))) D) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real)) F))) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real (@ F X)) tptp.top_top_set_real)) G))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z5) (=> (@ (@ tptp.ord_less_eq_real Z5) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real)) F)))) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real A) Z5) (=> (@ (@ tptp.ord_less_eq_real Z5) B) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real)) G)))) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z5) (=> (@ (@ tptp.ord_less_real Z5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 Z5)) (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real))))) (=> (forall ((Z5 tptp.real)) (=> (@ (@ tptp.ord_less_real A) Z5) (=> (@ (@ tptp.ord_less_real Z5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 Z5)) (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real))))) (exists ((C2 tptp.real)) (and (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) (@ G2 C2)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) (@ F5 C2))))))))))))
% 6.68/6.99 (assert (forall ((M5 tptp.set_nat)) (=> (@ tptp.finite_finite_nat M5) (=> (not (= M5 tptp.bot_bot_set_nat)) (=> (not (@ (@ tptp.member_nat tptp.zero_zero_nat) M5)) (= (@ tptp.gcd_Gcd_nat M5) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat (lambda ((M3 tptp.nat)) (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) M3))))) M5)))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (not (= N tptp.zero_zero_nat)) (= (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (@ (@ tptp.dvd_dvd_nat D2) N)))) N))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real L2) tptp.zero_zero_real) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R2)) (@ (@ tptp.ord_less_real (@ F X4)) tptp.zero_zero_real)))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (not (= L2 tptp.zero_zero_real)) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R2)) (not (= (@ F X4) tptp.zero_zero_real))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (L2 tptp.real) (C tptp.real)) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real L2)) (@ (@ tptp.topolo2177554685111907308n_real C) tptp.top_top_set_real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) L2) (exists ((R2 tptp.real)) (and (@ (@ tptp.ord_less_real tptp.zero_zero_real) R2) (forall ((X4 tptp.real)) (=> (and (not (= X4 C)) (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real C) X4))) R2)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) (@ F X4))))))))))
% 6.68/6.99 (assert (forall ((S2 tptp.set_nat)) (=> (@ tptp.finite_finite_nat S2) (@ (@ tptp.ord_less_eq_nat (@ tptp.finite_card_nat S2)) (@ tptp.suc (@ tptp.lattic8265883725875713057ax_nat S2))))))
% 6.68/6.99 (assert (= tptp.complete_Sup_Sup_nat (lambda ((X2 tptp.set_nat)) (@ (@ (@ tptp.if_nat (= X2 tptp.bot_bot_set_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat X2)))))
% 6.68/6.99 (assert (= tptp.divide_divide_nat (lambda ((M3 tptp.nat) (N2 tptp.nat)) (@ (@ (@ tptp.if_nat (= N2 tptp.zero_zero_nat)) tptp.zero_zero_nat) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((K2 tptp.nat)) (@ (@ tptp.ord_less_eq_nat (@ (@ tptp.times_times_nat K2) N2)) M3))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (= (@ (@ tptp.gcd_gcd_nat M) N) (@ tptp.lattic8265883725875713057ax_nat (@ tptp.collect_nat (lambda ((D2 tptp.nat)) (let ((_let_1 (@ tptp.dvd_dvd_nat D2))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.cos_real X3)) (@ tptp.sin_real X3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))) tptp.top_top_set_real)))
% 6.68/6.99 (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 ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat)))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1)))))))))))
% 6.68/6.99 (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 ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.set_or1222579329274155063t_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat _let_1))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat _let_1) tptp.one_one_nat))))))))))))
% 6.68/6.99 (assert (forall ((N tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (@ (@ tptp.dvd_dvd_int D2) N)))) (@ tptp.abs_abs_int N)))))
% 6.68/6.99 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (lambda ((X3 tptp.nat)) (@ (@ tptp.times_times_nat X3) C))) tptp.at_top_nat) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((C tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) C) (@ (@ (@ tptp.filterlim_nat_nat (@ tptp.times_times_nat C)) tptp.at_top_nat) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.topolo6980174941875973593q_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real (@ X8 I4))) B3)) (not (forall ((L6 tptp.real)) (not (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat))))))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))
% 6.68/6.99 (assert (forall ((N tptp.int) (M tptp.int)) (=> (not (= N tptp.zero_zero_int)) (= (@ (@ tptp.gcd_gcd_int M) N) (@ tptp.lattic8263393255366662781ax_int (@ tptp.collect_int (lambda ((D2 tptp.int)) (let ((_let_1 (@ tptp.dvd_dvd_int D2))) (and (@ _let_1 M) (@ _let_1 N))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (G (-> tptp.nat tptp.real))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ G (@ tptp.suc N3))) (@ G N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ G N3))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_real (@ F N2)) (@ G N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (exists ((L4 tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real L4))) (and (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N7)) L4)) (@ (@ (@ tptp.filterlim_nat_real F) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ G N7))) (@ (@ (@ tptp.filterlim_nat_real G) _let_1) tptp.at_top_nat))))))))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.nat tptp.real))) (=> (forall ((R2 tptp.real)) (exists ((N8 tptp.nat)) (forall ((N3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N8) N3) (@ (@ tptp.ord_less_real R2) (@ X8 N3)))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ X8 N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.68/6.99 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) C) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.root N2) C))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))
% 6.68/6.99 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (L2 tptp.real)) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) (@ F (@ tptp.suc N3)))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ F N3)) L2)) (=> (forall ((E2 tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.zero_zero_real) E2) (exists ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L2) (@ (@ tptp.plus_plus_real (@ F N7)) E2))))) (@ (@ (@ tptp.filterlim_nat_real F) (@ tptp.topolo2815343760600316023s_real L2)) tptp.at_top_nat))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_real X) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real X)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.68/6.99 (assert (forall ((X tptp.real) (A tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.divide_divide_real A) (@ (@ tptp.power_power_real X) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((C tptp.real)) (let ((_let_1 (@ tptp.abs_abs_real C))) (=> (@ (@ tptp.ord_less_real _let_1) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real _let_1)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.68/6.99 (assert (forall ((C tptp.real)) (=> (@ (@ tptp.ord_less_real (@ tptp.abs_abs_real C)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (@ tptp.power_power_real C)) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_real tptp.one_one_real) X) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ tptp.inverse_inverse_real (@ (@ tptp.power_power_real X) N2)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.plus_plus_real R) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.power_power_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) (@ tptp.semiri5074537144036343181t_real N2)))) N2))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_nat)))
% 6.68/6.99 (assert (forall ((R tptp.real)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real R) (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ tptp.uminus_uminus_real (@ tptp.inverse_inverse_real (@ tptp.semiri5074537144036343181t_real (@ tptp.suc N2)))))))) (@ tptp.topolo2815343760600316023s_real R)) tptp.at_top_nat)))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2))))))))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ tptp.summable_real (lambda ((N2 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) N2)) (@ A N2)))))))))
% 6.68/6.99 (assert (forall ((Theta (-> tptp.nat tptp.real)) (Theta2 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ (@ tptp.minus_minus_real (@ Theta J3)) Theta2)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (not (forall ((K3 (-> tptp.nat tptp.int))) (not (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real Theta2)) tptp.at_top_nat)))))))
% 6.68/6.99 (assert (forall ((Theta (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ tptp.cos_real (@ Theta J3)))) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_nat) (exists ((K3 (-> tptp.nat tptp.int))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((J3 tptp.nat)) (@ (@ tptp.minus_minus_real (@ Theta J3)) (@ (@ tptp.times_times_real (@ tptp.ring_1_of_int_real (@ K3 J3))) (@ (@ tptp.times_times_real (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))) tptp.pi))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat)))))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real (@ tptp.abs_abs_real X)) tptp.one_one_real) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (let ((_let_1 (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat N2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) tptp.one_one_nat))) (@ (@ tptp.times_times_real (@ (@ tptp.divide_divide_real tptp.one_one_real) (@ tptp.semiri5074537144036343181t_real _let_1))) (@ (@ tptp.power_power_real X) _let_1))))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)))) (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))))))))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.68/6.99 (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 ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)))) L4)) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2))))) _let_1) tptp.at_top_nat) (forall ((N7 tptp.nat)) (@ (@ tptp.ord_less_eq_real L4) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N7)) tptp.one_one_nat))))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) _let_1) tptp.at_top_nat)))))))))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (@ tptp.topolo6980174941875973593q_real A) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat)))))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real)) (N tptp.nat)) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ tptp.ord_less_eq_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5))))) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) tptp.one_one_nat)))))))))
% 6.68/6.99 (assert (forall ((A (-> tptp.nat tptp.real))) (=> (@ (@ (@ tptp.filterlim_nat_real A) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_nat) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) (@ A N3))) (=> (forall ((N3 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ A (@ tptp.suc N3))) (@ A N3))) (@ (@ (@ tptp.filterlim_nat_real (lambda ((N2 tptp.nat)) (@ (@ tptp.groups6591440286371151544t_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))) (@ tptp.set_ord_lessThan_nat (@ (@ tptp.plus_plus_nat (@ (@ tptp.times_times_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N2)) tptp.one_one_nat))))) (@ tptp.topolo2815343760600316023s_real (@ tptp.suminf_real (lambda ((I5 tptp.nat)) (@ (@ tptp.times_times_real (@ (@ tptp.power_power_real (@ tptp.uminus_uminus_real tptp.one_one_real)) I5)) (@ A I5)))))) tptp.at_top_nat))))))
% 6.68/6.99 (assert (= tptp.real_V5970128139526366754l_real (lambda ((F6 (-> tptp.real tptp.real))) (exists ((C3 tptp.real)) (= F6 (lambda ((X3 tptp.real)) (@ (@ tptp.times_times_real X3) C3)))))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y3 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.times_times_real X) Y3))) (@ (@ tptp.divide_divide_real tptp.one_one_real) Y3)))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= tptp.real_V975177566351809787t_real (lambda ((X3 tptp.real) (Y3 tptp.real)) (@ tptp.abs_abs_real (@ (@ tptp.minus_minus_real X3) Y3)))))
% 6.68/6.99 (assert (= tptp.real_V3694042436643373181omplex (lambda ((X3 tptp.complex) (Y3 tptp.complex)) (@ tptp.real_V1022390504157884413omplex (@ (@ tptp.minus_minus_complex X3) Y3)))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arcosh_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5849166863359141190n_real tptp.one_one_real))))
% 6.68/6.99 (assert (= (@ tptp.set_or1210151606488870762an_nat tptp.zero_zero_nat) (@ (@ tptp.image_nat_nat tptp.suc) tptp.top_top_set_nat)))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (let ((_let_1 (@ tptp.suc K))) (= (@ tptp.set_or1210151606488870762an_nat _let_1) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_or1210151606488870762an_nat K)) (@ (@ tptp.insert_nat _let_1) tptp.bot_bot_set_nat))))))
% 6.68/6.99 (assert (= (@ tptp.comple7806235888213564991et_nat (@ (@ tptp.image_nat_set_nat tptp.set_or1210151606488870762an_nat) tptp.top_top_set_nat)) tptp.bot_bot_set_nat))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.68/6.99 (assert (= (@ tptp.set_ord_atLeast_nat tptp.zero_zero_nat) tptp.top_top_set_nat))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ tptp.set_or1210151606488870762an_nat K))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.exp_real) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_bot_real))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5984915006950818249n_real tptp.zero_zero_real))))
% 6.68/6.99 (assert (= (@ tptp.comple7399068483239264473et_nat (@ (@ tptp.image_nat_set_nat tptp.set_ord_atLeast_nat) tptp.top_top_set_nat)) tptp.top_top_set_nat))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (= (@ tptp.set_ord_atLeast_nat (@ tptp.suc K)) (@ (@ tptp.minus_minus_set_nat (@ tptp.set_ord_atLeast_nat K)) (@ (@ tptp.insert_nat K) tptp.bot_bot_set_nat)))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real tptp.one_one_real))) tptp.at_bot_real))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.ln_ln_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 6.68/6.99 (assert (let ((_let_1 (@ tptp.uminus_uminus_real tptp.one_one_real))) (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_bot_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1)))))
% 6.68/6.99 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real X6) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_bot_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (not (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_bot_real) F3))))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ tptp.uminus_uminus_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one)))))) tptp.at_bot_real))
% 6.68/6.99 (assert (forall ((N tptp.nat) (F (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (=> (@ (@ (@ tptp.filterlim_real_real F) tptp.at_bot_real) F3) (=> (@ (@ tptp.dvd_dvd_nat (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one))) N) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.power_power_real (@ F X3)) N))) tptp.at_top_real) F3))))))
% 6.68/6.99 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_bot_real) tptp.at_infinity_real))
% 6.68/6.99 (assert (@ (@ tptp.ord_le4104064031414453916r_real tptp.at_top_real) tptp.at_infinity_real))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.sqrt) tptp.at_top_real) tptp.at_top_real))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.tanh_real) (@ tptp.topolo2815343760600316023s_real tptp.one_one_real)) tptp.at_top_real))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.artanh_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.one_one_real) (@ tptp.set_or5984915006950818249n_real tptp.one_one_real))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ tptp.ln_ln_real X3)) X3))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.inverse_inverse_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) tptp.at_top_real))
% 6.68/6.99 (assert (forall ((K tptp.nat)) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ (@ tptp.power_power_real X3) K)) (@ tptp.exp_real X3)))) (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real)) tptp.at_top_real)))
% 6.68/6.99 (assert (forall ((X tptp.real)) (@ (@ (@ tptp.filterlim_real_real (lambda ((Y3 tptp.real)) (@ (@ tptp.powr_real (@ (@ tptp.plus_plus_real tptp.one_one_real) (@ (@ tptp.divide_divide_real X) Y3))) Y3))) (@ tptp.topolo2815343760600316023s_real (@ tptp.exp_real X))) tptp.at_top_real)))
% 6.68/6.99 (assert (let ((_let_1 (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) (@ (@ (@ tptp.filterlim_real_real tptp.tan_real) tptp.at_top_real) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5984915006950818249n_real _let_1)))))
% 6.68/6.99 (assert (forall ((B tptp.real) (F (-> tptp.real tptp.real)) (Flim tptp.real)) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_eq_real B) X6) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real))))) (=> (@ (@ (@ tptp.filterlim_real_real F) (@ tptp.topolo2815343760600316023s_real Flim)) tptp.at_top_real) (@ (@ tptp.ord_less_real Flim) (@ F B))))))
% 6.68/6.99 (assert (@ (@ (@ tptp.filterlim_real_real tptp.arctan) (@ tptp.topolo2815343760600316023s_real (@ (@ tptp.divide_divide_real tptp.pi) (@ tptp.numeral_numeral_real (@ tptp.bit0 tptp.one))))) tptp.at_top_real))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (= (@ (@ tptp.eventually_nat (lambda ((N2 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat N2) K)))) tptp.at_top_nat) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((C tptp.nat) (P (-> tptp.nat Bool))) (=> (forall ((X6 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat C) X6) (@ P X6))) (@ (@ tptp.eventually_nat P) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((P (-> tptp.nat Bool))) (= (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (exists ((N6 tptp.nat)) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P N2)))))))
% 6.68/6.99 (assert (forall ((F3 tptp.filter_nat)) (= (@ (@ tptp.ord_le2510731241096832064er_nat F3) tptp.at_top_nat) (forall ((N6 tptp.nat)) (@ (@ tptp.eventually_nat (@ tptp.ord_less_eq_nat N6)) F3)))))
% 6.68/6.99 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat)) (=> (@ (@ tptp.eventually_nat P) tptp.at_top_nat) (@ (@ tptp.eventually_nat (lambda ((I5 tptp.nat)) (@ P (@ (@ tptp.plus_plus_nat I5) K)))) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((P (-> tptp.real Bool)) (A tptp.real)) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ (@ tptp.plus_plus_real X3) A)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) tptp.at_top_real) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ tptp.inverse_inverse_real X3)))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.real Bool))) (= (@ (@ tptp.eventually_real P) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ P (@ tptp.inverse_inverse_real X3)))) tptp.at_top_real))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F3) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) tptp.top_top_set_real))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) tptp.at_top_real) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_1) tptp.at_top_real) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_1) tptp.at_top_real)))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F3) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((F0 (-> tptp.real tptp.real)) (G0 (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F0) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G0) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G0 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F0) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G0) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F0 X3)) (@ G0 X3)))) F3) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.real tptp.real)) (X tptp.real) (G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (F3 tptp.filter_real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5984915006950818249n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real tptp.zero_zero_real))) (=> (@ (@ (@ tptp.filterlim_real_real F) _let_2) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real G) _let_2) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) F3) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) F3) _let_1))))))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (X tptp.real) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (Y tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real X) (@ tptp.set_or5849166863359141190n_real X)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real Y))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 6.68/6.99 (assert (forall ((G (-> tptp.real tptp.real)) (G2 (-> tptp.real tptp.real)) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real)) (X tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))) (let ((_let_2 (@ tptp.topolo2815343760600316023s_real X))) (=> (@ (@ (@ tptp.filterlim_real_real G) tptp.at_top_real) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (not (= (@ G2 X3) tptp.zero_zero_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) (@ F5 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ tptp.eventually_real (lambda ((X3 tptp.real)) (@ (@ (@ tptp.has_fi5821293074295781190e_real G) (@ G2 X3)) (@ (@ tptp.topolo2177554685111907308n_real X3) tptp.top_top_set_real)))) _let_1) (=> (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F5 X3)) (@ G2 X3)))) _let_2) _let_1) (@ (@ (@ tptp.filterlim_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.divide_divide_real (@ F X3)) (@ G X3)))) _let_2) _let_1))))))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.nat Bool)) (K tptp.nat) (B tptp.nat)) (=> (@ P K) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ (@ tptp.ord_less_eq_nat K) (@ tptp.order_Greatest_nat P))))))
% 6.68/6.99 (assert (forall ((P (-> tptp.nat Bool)) (B tptp.nat)) (=> (exists ((X_12 tptp.nat)) (@ P X_12)) (=> (forall ((Y5 tptp.nat)) (=> (@ P Y5) (@ (@ tptp.ord_less_eq_nat Y5) B))) (@ P (@ tptp.order_Greatest_nat P))))))
% 6.68/6.99 (assert (forall ((F (-> tptp.nat tptp.real)) (A tptp.real) (B tptp.real)) (=> (@ (@ tptp.ord_less_eq_set_real (@ (@ tptp.image_nat_real F) tptp.top_top_set_nat)) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.bfun_nat_real F) tptp.at_top_nat))))
% 6.68/6.99 (assert (forall ((X tptp.real)) (=> (@ (@ tptp.ord_less_eq_real tptp.zero_zero_real) X) (=> (@ (@ tptp.ord_less_eq_real X) tptp.one_one_real) (@ (@ tptp.bfun_nat_real (@ tptp.power_power_real X)) tptp.at_top_nat)))))
% 6.68/6.99 (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 ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X6) (@ (@ 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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I4))) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_9091379641038594480t_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real B3) (@ X8 I4))) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real L6) (@ X8 I2)))))))))))
% 6.68/6.99 (assert (forall ((Mima2 tptp.option4927543243414619207at_nat) (Deg tptp.nat) (TreeList2 tptp.list_VEBT_VEBT) (Summary tptp.vEBT_VEBT) (Deg4 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (@ (@ tptp.vEBT_VEBT_valid (@ (@ (@ (@ tptp.vEBT_Node Mima2) Deg) TreeList2) Summary)) Deg4) (and (= Deg Deg4) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ 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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg) (@ (@ tptp.divide_divide_nat Deg) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList2) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary) I5))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList2)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg) _let_1)) TreeList2) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima2)))))))
% 6.68/6.99 (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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_2) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_1) _let_2)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))))
% 6.68/6.99 (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 ((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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))))))))))))
% 6.68/6.99 (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 ((X6 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X6) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X6) (@ (@ 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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))))))))))))))
% 6.68/6.99 (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 ((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 ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima)))))))))))))))
% 6.68/6.99 (assert (= tptp.complete_Sup_Sup_int (lambda ((X2 tptp.set_int)) (@ tptp.the_int (lambda ((X3 tptp.int)) (and (@ (@ tptp.member_int X3) X2) (forall ((Y3 tptp.int)) (=> (@ (@ tptp.member_int Y3) X2) (@ (@ tptp.ord_less_eq_int Y3) X3)))))))))
% 6.68/6.99 (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 ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (@ (@ tptp.vEBT_VEBT_valid X3) (@ (@ tptp.divide_divide_nat Deg2) (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))))) (@ (@ tptp.vEBT_VEBT_valid Summary2) _let_3) (= (@ tptp.size_s6755466524823107622T_VEBT TreeList3) (@ (@ tptp.power_power_nat _let_2) _let_3)) (@ (@ (@ tptp.case_o184042715313410164at_nat (and (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) X2))) (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2))))))) (@ tptp.produc6081775807080527818_nat_o (lambda ((Mi3 tptp.nat) (Ma3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (let ((_let_2 (= Mi3 Ma3))) (and (@ (@ tptp.ord_less_eq_nat Mi3) Ma3) (@ (@ tptp.ord_less_nat Ma3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (forall ((I5 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat I5) (@ (@ tptp.power_power_nat _let_1) (@ (@ tptp.minus_minus_nat Deg2) (@ (@ tptp.divide_divide_nat Deg2) _let_1)))) (= (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions (@ (@ tptp.nth_VEBT_VEBT TreeList3) I5)) X2)) (@ (@ tptp.vEBT_V8194947554948674370ptions Summary2) I5))))) (=> _let_2 (forall ((X3 tptp.vEBT_VEBT)) (=> (@ (@ tptp.member_VEBT_VEBT X3) (@ tptp.set_VEBT_VEBT2 TreeList3)) (not (exists ((X2 tptp.nat)) (@ (@ tptp.vEBT_V8194947554948674370ptions X3) X2)))))) (=> (not _let_2) (and (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) Ma3) (forall ((X3 tptp.nat)) (let ((_let_1 (@ tptp.numeral_numeral_nat (@ tptp.bit0 tptp.one)))) (=> (@ (@ tptp.ord_less_nat X3) (@ (@ tptp.power_power_nat _let_1) Deg2)) (=> (@ (@ (@ tptp.vEBT_V5917875025757280293ildren (@ (@ tptp.divide_divide_nat Deg2) _let_1)) TreeList3) X3) (and (@ (@ tptp.ord_less_nat Mi3) X3) (@ (@ tptp.ord_less_eq_nat X3) Ma3)))))))))))))) Mima))) (not (@ (@ tptp.accp_P2887432264394892906BT_nat tptp.vEBT_VEBT_valid_rel) (@ (@ tptp.produc738532404422230701BT_nat _let_1) Xa2)))))))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (G (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X6 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X6) (@ (@ tptp.ord_less_eq_real X6) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) F))) (=> (forall ((X6 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X6) (@ (@ tptp.ord_less_real X6) B)) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)))) (=> (forall ((X6 tptp.real)) (=> (and (@ (@ tptp.ord_less_eq_real A) X6) (@ (@ tptp.ord_less_eq_real X6) B)) (@ (@ tptp.topolo4422821103128117721l_real (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) G))) (=> (forall ((X6 tptp.real)) (=> (and (@ (@ tptp.ord_less_real A) X6) (@ (@ tptp.ord_less_real X6) B)) (@ (@ tptp.differ6690327859849518006l_real G) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)))) (exists ((G_c tptp.real) (F_c tptp.real) (C2 tptp.real)) (let ((_let_1 (@ (@ tptp.topolo2177554685111907308n_real C2) tptp.top_top_set_real))) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real G) G_c) _let_1) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) F_c) _let_1) (@ (@ tptp.ord_less_real A) C2) (@ (@ tptp.ord_less_real C2) B) (= (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ F B)) (@ F A))) G_c) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real (@ G B)) (@ G A))) F_c))))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))))) (exists ((L4 tptp.real) (Z5 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z5) (@ (@ tptp.ord_less_real Z5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) L4) (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real)) (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ tptp.times_times_real (@ (@ tptp.minus_minus_real B) A)) L4)))))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.ord_less_eq_real tptp.one_one_real) (@ F X6)))) (@ _let_1 (lambda ((X3 tptp.real)) (@ tptp.arcosh_real (@ F X3)))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_eq_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (exists ((C2 tptp.real) (D3 tptp.real)) (and (= (@ (@ tptp.image_real_real F) (@ (@ tptp.set_or1222579329274155063t_real A) B)) (@ (@ tptp.set_or1222579329274155063t_real C2) D3)) (@ (@ tptp.ord_less_eq_real C2) D3)))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ tptp.set_ord_atLeast_real tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.arcosh_real))))
% 6.68/6.99 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arccos))
% 6.68/6.99 (assert (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) tptp.arcsin))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real) (F (-> tptp.real tptp.real))) (let ((_let_1 (@ tptp.topolo5044208981011980120l_real A2))) (=> (@ _let_1 F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.member_real X6) A2) (@ (@ tptp.member_real (@ F X6)) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)))) (@ _let_1 (lambda ((X3 tptp.real)) (@ tptp.artanh_real (@ F X3)))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F5 X6)) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))))) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z5) (@ (@ tptp.ord_less_real Z5) B) (= (@ F5 Z5) (lambda ((V4 tptp.real)) tptp.zero_zero_real))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (F5 (-> tptp.real tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (@ (@ (@ tptp.has_de1759254742604945161l_real F) (@ F5 X6)) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))))) (not (forall ((Xi tptp.real)) (=> (@ (@ tptp.ord_less_real A) Xi) (=> (@ (@ tptp.ord_less_real Xi) B) (not (= (@ (@ tptp.minus_minus_real (@ F B)) (@ F A)) (@ (@ F5 Xi) (@ (@ tptp.minus_minus_real B) A)))))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))))) (= (@ F B) (@ F A)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real Y2) tptp.zero_zero_real)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F B)) (@ F A)))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (exists ((Y2 tptp.real)) (and (@ (@ (@ tptp.has_fi5821293074295781190e_real F) Y2) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real)) (@ (@ tptp.ord_less_real tptp.zero_zero_real) Y2)))))) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (@ (@ tptp.ord_less_real (@ F A)) (@ F B)))))))
% 6.68/6.99 (assert (forall ((A2 tptp.set_real)) (=> (@ (@ tptp.ord_less_eq_set_real A2) (@ (@ tptp.set_or1633881224788618240n_real (@ tptp.uminus_uminus_real tptp.one_one_real)) tptp.one_one_real)) (@ (@ tptp.topolo5044208981011980120l_real A2) tptp.artanh_real))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real)) (X tptp.real)) (=> (@ (@ tptp.ord_less_real A) B) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))))) (=> (@ (@ tptp.ord_less_eq_real A) X) (=> (@ (@ tptp.ord_less_eq_real X) B) (= (@ F X) (@ F A)))))))))
% 6.68/6.99 (assert (forall ((A tptp.real) (B tptp.real) (F (-> tptp.real tptp.real))) (=> (@ (@ tptp.ord_less_real A) B) (=> (= (@ F A) (@ F B)) (=> (@ (@ tptp.topolo5044208981011980120l_real (@ (@ tptp.set_or1222579329274155063t_real A) B)) F) (=> (forall ((X6 tptp.real)) (=> (@ (@ tptp.ord_less_real A) X6) (=> (@ (@ tptp.ord_less_real X6) B) (@ (@ tptp.differ6690327859849518006l_real F) (@ (@ tptp.topolo2177554685111907308n_real X6) tptp.top_top_set_real))))) (exists ((Z5 tptp.real)) (and (@ (@ tptp.ord_less_real A) Z5) (@ (@ tptp.ord_less_real Z5) B) (@ (@ (@ tptp.has_fi5821293074295781190e_real F) tptp.zero_zero_real) (@ (@ tptp.topolo2177554685111907308n_real Z5) tptp.top_top_set_real))))))))))
% 6.68/6.99 (assert (= tptp.topolo1511823702728130853y_real (@ tptp.comple2936214249959783750l_real (@ (@ tptp.image_2178119161166701260l_real (lambda ((E3 tptp.real)) (@ tptp.princi6114159922880469582l_real (@ tptp.collec3799799289383736868l_real (@ tptp.produc5414030515140494994real_o (lambda ((X3 tptp.real) (Y3 tptp.real)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V975177566351809787t_real X3) Y3)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= tptp.topolo896644834953643431omplex (@ tptp.comple8358262395181532106omplex (@ (@ tptp.image_5971271580939081552omplex (lambda ((E3 tptp.real)) (@ tptp.princi3496590319149328850omplex (@ tptp.collec8663557070575231912omplex (@ tptp.produc6771430404735790350plex_o (lambda ((X3 tptp.complex) (Y3 tptp.complex)) (@ (@ tptp.ord_less_real (@ (@ tptp.real_V3694042436643373181omplex X3) Y3)) E3))))))) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.68/6.99 (assert (forall ((P (-> tptp.product_prod_nat_nat Bool))) (= (@ (@ tptp.eventu1038000079068216329at_nat P) (@ (@ tptp.prod_filter_nat_nat tptp.at_top_nat) tptp.at_top_nat)) (exists ((N6 tptp.nat)) (forall ((M3 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) M3) (forall ((N2 tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat N6) N2) (@ P (@ (@ tptp.product_Pair_nat_nat N2) M3))))))))))
% 6.68/6.99 (assert (forall ((N tptp.nat)) (=> (@ (@ tptp.ord_less_nat tptp.zero_zero_nat) N) (@ tptp.order_mono_nat_nat (@ tptp.times_times_nat N)))))
% 6.68/6.99 (assert (@ tptp.order_mono_nat_nat tptp.suc))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B3)) (@ (@ tptp.bfun_nat_real X8) tptp.at_top_nat)))))
% 6.68/6.99 (assert (forall ((D tptp.real) (A tptp.real)) (let ((_let_1 (@ (@ tptp.minus_minus_real A) D))) (= (@ (@ tptp.filtermap_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.minus_minus_real X3) D))) (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A))) (@ (@ tptp.topolo2177554685111907308n_real _let_1) (@ tptp.set_or5849166863359141190n_real _let_1))))))
% 6.68/6.99 (assert (forall ((X8 (-> tptp.nat tptp.real)) (B3 tptp.real)) (=> (@ tptp.order_mono_nat_real X8) (=> (forall ((I4 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I4)) B3)) (not (forall ((L6 tptp.real)) (=> (@ (@ (@ tptp.filterlim_nat_real X8) (@ tptp.topolo2815343760600316023s_real L6)) tptp.at_top_nat) (not (forall ((I2 tptp.nat)) (@ (@ tptp.ord_less_eq_real (@ X8 I2)) L6))))))))))
% 6.68/6.99 (assert (forall ((A tptp.real)) (= (@ (@ tptp.topolo2177554685111907308n_real A) (@ tptp.set_or5849166863359141190n_real A)) (@ (@ tptp.filtermap_real_real (lambda ((X3 tptp.real)) (@ (@ tptp.plus_plus_real X3) A))) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))))))
% 6.68/6.99 (assert (= (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)) (@ (@ tptp.filtermap_real_real tptp.inverse_inverse_real) tptp.at_top_real)))
% 6.68/6.99 (assert (= tptp.at_top_real (@ (@ tptp.filtermap_real_real tptp.inverse_inverse_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real)))))
% 6.68/6.99 (assert (= (@ (@ tptp.filtermap_real_real tptp.ln_ln_real) (@ (@ tptp.topolo2177554685111907308n_real tptp.zero_zero_real) (@ tptp.set_or5849166863359141190n_real tptp.zero_zero_real))) tptp.at_bot_real))
% 6.68/6.99 (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 ((M3 tptp.nat)) (@ (@ tptp.minus_minus_nat (@ (@ tptp.power_power_nat K) M3)) M3))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (let ((_let_1 (@ (@ tptp.upt M) N))) (= (@ tptp.remdups_nat _let_1) _let_1))))
% 6.68/6.99 (assert (forall ((I tptp.nat) (J tptp.nat)) (= (@ tptp.size_size_list_nat (@ (@ tptp.upt I) J)) (@ (@ tptp.minus_minus_nat J) I))))
% 6.68/6.99 (assert (forall ((J tptp.nat) (I tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat J) I) (= (@ (@ tptp.upt I) J) tptp.nil_nat))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ tptp.linord2614967742042102400et_nat (@ (@ tptp.set_or4665077453230672383an_nat M) N)) (@ (@ tptp.upt M) N))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (forall ((M tptp.num) (N tptp.num)) (let ((_let_1 (@ tptp.numeral_numeral_nat N))) (let ((_let_2 (@ tptp.numeral_numeral_nat M))) (let ((_let_3 (@ (@ tptp.upt _let_2) _let_1))) (let ((_let_4 (@ (@ tptp.ord_less_nat _let_2) _let_1))) (and (=> _let_4 (= _let_3 (@ (@ tptp.cons_nat _let_2) (@ (@ tptp.upt (@ tptp.suc _let_2)) _let_1)))) (=> (not _let_4) (= _let_3 tptp.nil_nat)))))))))
% 6.68/6.99 (assert (= tptp.set_ord_lessThan_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) N2)))))
% 6.68/6.99 (assert (= tptp.set_ord_atMost_nat (lambda ((N2 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt tptp.zero_zero_nat) (@ tptp.suc N2))))))
% 6.68/6.99 (assert (= tptp.set_or1269000886237332187st_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt N2) (@ tptp.suc M3))))))
% 6.68/6.99 (assert (= tptp.set_or5834768355832116004an_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) M3)))))
% 6.68/6.99 (assert (= tptp.set_or6659071591806873216st_nat (lambda ((N2 tptp.nat) (M3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt (@ tptp.suc N2)) (@ tptp.suc M3))))))
% 6.68/6.99 (assert (= tptp.set_or4665077453230672383an_nat (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ tptp.set_nat2 (@ (@ tptp.upt I5) J3)))))
% 6.68/6.99 (assert (forall ((I tptp.nat)) (= (@ (@ tptp.upt I) tptp.zero_zero_nat) tptp.nil_nat)))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat) (Ns tptp.list_nat) (Q2 tptp.nat)) (let ((_let_1 (@ (@ tptp.cons_nat N) Ns))) (= (= (@ (@ tptp.cons_nat M) _let_1) (@ (@ tptp.upt M) Q2)) (= _let_1 (@ (@ tptp.upt (@ tptp.suc M)) Q2))))))
% 6.68/6.99 (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))))))
% 6.68/6.99 (assert (forall ((I tptp.nat) (J tptp.nat)) (@ tptp.distinct_nat (@ (@ tptp.upt I) J))))
% 6.68/6.99 (assert (forall ((N tptp.nat) (M tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((I5 tptp.nat)) (@ (@ tptp.plus_plus_nat I5) N))) (@ (@ tptp.upt tptp.zero_zero_nat) M)) (@ (@ tptp.upt N) (@ (@ tptp.plus_plus_nat M) N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat tptp.suc) (@ (@ tptp.upt M) N)) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N)))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (= (@ (@ tptp.map_nat_nat (lambda ((N2 tptp.nat)) (@ (@ tptp.minus_minus_nat N2) (@ tptp.suc tptp.zero_zero_nat)))) (@ (@ tptp.upt (@ tptp.suc M)) (@ tptp.suc N))) (@ (@ tptp.upt M) N))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (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)))))
% 6.68/6.99 (assert (= tptp.upt (lambda ((I5 tptp.nat) (J3 tptp.nat)) (@ (@ (@ tptp.if_list_nat (@ (@ tptp.ord_less_nat I5) J3)) (@ (@ tptp.cons_nat I5) (@ (@ tptp.upt (@ tptp.suc I5)) J3))) tptp.nil_nat))))
% 6.68/6.99 (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)))))))
% 6.68/6.99 (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))))))))
% 6.68/6.99 (assert (forall ((M tptp.nat) (N tptp.nat)) (=> (@ (@ tptp.ord_less_eq_nat M) N) (= (@ tptp.groups4561878855575611511st_nat (@ (@ tptp.upt M) N)) (@ (@ tptp.groups3542108847815614940at_nat (lambda ((X3 tptp.nat)) X3)) (@ (@ tptp.set_or4665077453230672383an_nat M) N))))))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.int) (Y tptp.int)) (= (@ (@ (@ tptp.if_int true) X) Y) X)))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.nat) (Y tptp.nat)) (= (@ (@ (@ tptp.if_nat true) X) Y) X)))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.num) (Y tptp.num)) (= (@ (@ (@ tptp.if_num true) X) Y) X)))
% 6.68/6.99 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.rat) (Y tptp.rat)) (= (@ (@ (@ tptp.if_rat true) X) Y) X)))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.real) (Y tptp.real)) (= (@ (@ (@ tptp.if_real true) X) Y) X)))
% 6.68/6.99 (assert (forall ((P (-> tptp.real Bool))) (= (@ P (@ tptp.fChoice_real P)) (exists ((X2 tptp.real)) (@ P X2)))))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.complex) (Y tptp.complex)) (= (@ (@ (@ tptp.if_complex true) X) Y) X)))
% 6.68/6.99 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.extended_enat) (Y tptp.extended_enat)) (= (@ (@ (@ tptp.if_Extended_enat true) X) Y) X)))
% 6.68/6.99 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer false) X) Y) Y)))
% 6.68/6.99 (assert (forall ((X tptp.code_integer) (Y tptp.code_integer)) (= (@ (@ (@ tptp.if_Code_integer true) X) Y) X)))
% 6.68/6.99 (assert (forall ((X tptp.set_int) (Y tptp.se/export/starexec/sandbox2/solver/bin/do_THM_THF: line 35: 18097 Alarm clock ( read result; case "$result" in
% 299.91/300.23 unsat)
% 299.91/300.23 echo "% SZS status $unsatResult for $tptpfilename"; echo "% SZS output start Proof for $tptpfilename"; cat; echo "% SZS output end Proof for $tptpfilename"; exit 0
% 299.91/300.23 ;;
% 299.91/300.23 sat)
% 299.91/300.23 echo "% SZS status $satResult for $tptpfilename"; cat; exit 0
% 299.91/300.23 ;;
% 299.91/300.23 esac; exit 1 )
% 299.91/300.24 Alarm clock
% 299.91/300.24 % cvc5---1.0.5 exiting
% 299.91/300.24 % cvc5---1.0.5 exiting
%------------------------------------------------------------------------------